Question for Hal - where is the PV in Hal's PV?
Is there any "there" there?
In QED to leading order, the Vacuum Polarization tensor in momentum space is
Puv(q) = (quqv - guvq^2)P(q^2)
Where using Pauli-Villars regularization
Puv(q^2) to leading order in perturbation series is
Puv(0) ~ 1 + (1/137)log(M^2/m^2)
where m is the rest mass of the electron and
h/Mc is the short wave cutoff. If the cutoff is at h/mc as Hal wants in his Type II Casimir force model then
Puv(0) = 1
In general
P(q^2) ~ Integral x = 0 to 1 of dxx(1 - x)log[M^2(m^2 - x(1 - x)q^2)^-1]
In space-time X
P(X) = 4D Fourier transform of P(q^2) for isotropic vacuum approximation.
OK then
c^2 = co^2[1 + P(X)]^-1
Using Hal's PV Notation
c^2 = co^2/K
Where in Hal's simple SSS model
K = e^2G(Source Mass)/c^2r
Is that c or co in K?
How does Hal justify such a connection between his PV phenomenology and QED?
It seems totally adhoc with no deep plausibility?
How can Hal use "PV" without at least attempting to connect his model to QED?
Monday, September 27, 2004
expanded typo-corrected 2nd draft from earlier message
Casimir Force: The irrelevant explanation of EVOs for the wrong reasons
On Sep 25, 2004, at 12:04 PM, Jack Sarfatti wrote:
Remember, macro-quantum vacuum coherence hides random micro-quantum zero point vacuum energy under the rug. Any random zero point energy that leaks out is exotic vacuum that contributes to the cosmological constant either as dark energy or dark matter depending on the sign of the pressure negative or positive respectively. Dark energy at a distance is a universal repulsive antigravity field. Dark matter at a distance is a universal attractive gravity field. Both fields can be stronger than what is expected from Newton’s constant. That is the effective Planck energy is smaller than 1019Gev. However, as possibly in the case of Ken Shoulders “charge clusters” the effective forces inside an extended exotic vacuum region can change sign! Indeed, that is why the EVO is stable and that is also why the single electron is stable.
Alexander Burinskii in Moscow has rightly raised the issue of the distinction between renormalization and regularization of interacting field Feynman diagrams in special relativistic quantum field perturbation theory expansions in relation to the zero point energy problem. We need to see how all these ideas survive in quantum field theory in a c-number curved space dynamical background like in Birrell and Davies text book "Quantum Fields in Curved Space". The issue of the reality of quantum gravity foam of Einstein metric field Heisenberg uncertainty fluctuations is problematical in the soft condensed matter physics approach to gravity as a bottom-up emergent ODLRO macro-quantum phenomenon. That is gravity is a low energy effective c-number ODLRO macro-quantum coherent field theory that in principle is not to be quantized in the usual way the way QED is done. This feature is now being tested in gamma ray astronomy.
Why do Milonni's two naive free virtual photon field models of the Casimir force ~ hcA/d4 as virtual photon effects give, like Ptolemy’s epicycles, closed to the correct empirical answer for the wrong reasons?
In the simple boundary condition model using only free virtual photons Milonni computes
E(d) - E(infinity)
and he gets the cutoff-independent correct answer.
However, what he should compute is
E(d) + E(L - d)
Letting L >> d at the end.
The virtual photon ZPF force is then the negative gradient of this sum. This vanishes in 1 + 1 space-time.
The cosmological constant problem is that E(d) + E(L - d) is directly observable in general relativity. This is why Hal's "Type II Casimir Force" model is unacceptable because it requires a huge cosmological constant vacuum energy filling all space outside Ken Shoulders EVOs which have zero ZPE inside their charged shells at least below h/mc short wave cutoff. This contradicts general relativity that is the covering theory here. Any result from unstable globally flat quantum field theory that contradicts general relativity must be rejected. That is the basic problem with what Hal Puthoff is suggesting for metric engineering of warp, wormhole and weapon. Puthoff’s PV version of gravity is not consistent with Einstein’s general relativity as shown by his own assistant Michael Ibison. Lest, there be any confusion, I am not suggesting that the direct warping of space-time by zero point energy density is the explanation of the Casimir force. Indeed, the Casimir force as a direct electrostatic force of mutually induced dipoles in the uncharged conductors is observable only in the absenceof such strong zero point warping of space-time. I am suggesting that Ken Shoulders EVOs have such strong warping and have nothing to do with the Casimir force at all in the dominating approximation. Therefore, as Ian Peterson says, the Casimir force is not a way to tap the zero point vacuum energy of the virtual photons as the popular literature suggests. The only energy you can recover from the Casimir force is the weak mutually induced dipole electrostatic energies. Using the Casimir force as a pedagogical tool for zero point energy physics is profoundly misleading.
Casimir Force: The irrelevant explanation of EVOs for the wrong reasons
On Sep 25, 2004, at 12:04 PM, Jack Sarfatti wrote:
Remember, macro-quantum vacuum coherence hides random micro-quantum zero point vacuum energy under the rug. Any random zero point energy that leaks out is exotic vacuum that contributes to the cosmological constant either as dark energy or dark matter depending on the sign of the pressure negative or positive respectively. Dark energy at a distance is a universal repulsive antigravity field. Dark matter at a distance is a universal attractive gravity field. Both fields can be stronger than what is expected from Newton’s constant. That is the effective Planck energy is smaller than 1019Gev. However, as possibly in the case of Ken Shoulders “charge clusters” the effective forces inside an extended exotic vacuum region can change sign! Indeed, that is why the EVO is stable and that is also why the single electron is stable.
Alexander Burinskii in Moscow has rightly raised the issue of the distinction between renormalization and regularization of interacting field Feynman diagrams in special relativistic quantum field perturbation theory expansions in relation to the zero point energy problem. We need to see how all these ideas survive in quantum field theory in a c-number curved space dynamical background like in Birrell and Davies text book "Quantum Fields in Curved Space". The issue of the reality of quantum gravity foam of Einstein metric field Heisenberg uncertainty fluctuations is problematical in the soft condensed matter physics approach to gravity as a bottom-up emergent ODLRO macro-quantum phenomenon. That is gravity is a low energy effective c-number ODLRO macro-quantum coherent field theory that in principle is not to be quantized in the usual way the way QED is done. This feature is now being tested in gamma ray astronomy.
Why do Milonni's two naive free virtual photon field models of the Casimir force ~ hcA/d4 as virtual photon effects give, like Ptolemy’s epicycles, closed to the correct empirical answer for the wrong reasons?
In the simple boundary condition model using only free virtual photons Milonni computes
E(d) - E(infinity)
and he gets the cutoff-independent correct answer.
However, what he should compute is
E(d) + E(L - d)
Letting L >> d at the end.
The virtual photon ZPF force is then the negative gradient of this sum. This vanishes in 1 + 1 space-time.
The cosmological constant problem is that E(d) + E(L - d) is directly observable in general relativity. This is why Hal's "Type II Casimir Force" model is unacceptable because it requires a huge cosmological constant vacuum energy filling all space outside Ken Shoulders EVOs which have zero ZPE inside their charged shells at least below h/mc short wave cutoff. This contradicts general relativity that is the covering theory here. Any result from unstable globally flat quantum field theory that contradicts general relativity must be rejected. That is the basic problem with what Hal Puthoff is suggesting for metric engineering of warp, wormhole and weapon. Puthoff’s PV version of gravity is not consistent with Einstein’s general relativity as shown by his own assistant Michael Ibison. Lest, there be any confusion, I am not suggesting that the direct warping of space-time by zero point energy density is the explanation of the Casimir force. Indeed, the Casimir force as a direct electrostatic force of mutually induced dipoles in the uncharged conductors is observable only in the absenceof such strong zero point warping of space-time. I am suggesting that Ken Shoulders EVOs have such strong warping and have nothing to do with the Casimir force at all in the dominating approximation. Therefore, as Ian Peterson says, the Casimir force is not a way to tap the zero point vacuum energy of the virtual photons as the popular literature suggests. The only energy you can recover from the Casimir force is the weak mutually induced dipole electrostatic energies. Using the Casimir force as a pedagogical tool for zero point energy physics is profoundly misleading.
On Sep 25, 2004, at 12:04 PM, Jack Sarfatti wrote:
Remember, macro-quantum vacuum coherence hides random micro-quantum zero point vacuum energy under the rug. Any random zero point energy that leaks out is exotic vacuum that contributes to the cosmological constant either as dark energy or dark matter depending on the sign of the pressure negative or positive respectively. Dark energy at a distance is a universal repulsive antigravity field. Dark matter at a distance is a universal attractive gravity field. Both fields can be stronger than what is expected from Newton’s constant. That is the effective Planck energy is smaller than 10^19Gev. However, as possibly in the case of Ken Shoulders “charge clusters” the effective forces inside an extended exotic vacuum region can change sign! Indeed, that is why the EVO is stable and that is also why the single electron is stable.
Alexander Burinskii in Moscow has rightly raised the issue of the the distinction between renormalization and regularization of interacting field Feynman diagrams in special relativistic quantum field theory in relation to the zero point energy problem. We need to see how all these ideas survive in quantum field theory in a c-number curved space background like in Birrill and Davies text book. The issue of the reality of quantum foam is problematical in the soft condensed matter physics approach to gravity as an emergent ODLRO macro-quantum phenomenon. That is gravity is a low energy effective c-number ODLRO macro-quantum coherent field theory that in principle is not to be quantized in the usual way the way QED is done. This feature is now being tested in gamma ray astronomy.
Why do Milonni's two naive free photon field models of the Casimir force ~ hcA/d^4 as virtual photon effects give the correct empirical answer for the wrong reasons?
In the simple boundary condition model using only free virtual photons Milonni computes
E(d) - E(infinity)
and he gets the cutoff independent correct answer.
However, what he should compute is
E(d) + E(L - d)
Letting L >> d at the end.
The virtual photon ZPF force is then the negative gradient of this sum. This vanishes in 1 + 1 space-time.
The cosmological constant problem is that E(d) + E(L - d) is directly observable in general relativity. This is why Hal's "Type II Casimir Force" model is unacceptable because it requires a huge cosmological constant vacuum energy filling all space outside Ken Shoulders EVOs which have zero ZPE inside their charged shells at least below h/mc short wave cutoff. This contradicts general relativity that is the covering theory here. Any result from globally flat quantum field theory that contradicts general relativity must be rejected. That is the basic problem with what Hal Puthoff is suggesting for metric engineering of warp, wormhole and weapon.
Remember, macro-quantum vacuum coherence hides random micro-quantum zero point vacuum energy under the rug. Any random zero point energy that leaks out is exotic vacuum that contributes to the cosmological constant either as dark energy or dark matter depending on the sign of the pressure negative or positive respectively. Dark energy at a distance is a universal repulsive antigravity field. Dark matter at a distance is a universal attractive gravity field. Both fields can be stronger than what is expected from Newton’s constant. That is the effective Planck energy is smaller than 10^19Gev. However, as possibly in the case of Ken Shoulders “charge clusters” the effective forces inside an extended exotic vacuum region can change sign! Indeed, that is why the EVO is stable and that is also why the single electron is stable.
Alexander Burinskii in Moscow has rightly raised the issue of the the distinction between renormalization and regularization of interacting field Feynman diagrams in special relativistic quantum field theory in relation to the zero point energy problem. We need to see how all these ideas survive in quantum field theory in a c-number curved space background like in Birrill and Davies text book. The issue of the reality of quantum foam is problematical in the soft condensed matter physics approach to gravity as an emergent ODLRO macro-quantum phenomenon. That is gravity is a low energy effective c-number ODLRO macro-quantum coherent field theory that in principle is not to be quantized in the usual way the way QED is done. This feature is now being tested in gamma ray astronomy.
Why do Milonni's two naive free photon field models of the Casimir force ~ hcA/d^4 as virtual photon effects give the correct empirical answer for the wrong reasons?
In the simple boundary condition model using only free virtual photons Milonni computes
E(d) - E(infinity)
and he gets the cutoff independent correct answer.
However, what he should compute is
E(d) + E(L - d)
Letting L >> d at the end.
The virtual photon ZPF force is then the negative gradient of this sum. This vanishes in 1 + 1 space-time.
The cosmological constant problem is that E(d) + E(L - d) is directly observable in general relativity. This is why Hal's "Type II Casimir Force" model is unacceptable because it requires a huge cosmological constant vacuum energy filling all space outside Ken Shoulders EVOs which have zero ZPE inside their charged shells at least below h/mc short wave cutoff. This contradicts general relativity that is the covering theory here. Any result from globally flat quantum field theory that contradicts general relativity must be rejected. That is the basic problem with what Hal Puthoff is suggesting for metric engineering of warp, wormhole and weapon.
Sunday, September 26, 2004
Benjamin Franklin, American Genius
This is the basic physics discovery of Ben Franklin’s oil calming the turbulent waters presented in this book for the first time. Here is how I also smooth Hal Puthoff's choppy electromagnetic zero point waves into emergent gravity.
A Letter from Benjamin Franklin to William Brownrigg, 1773
"Dear Sir: I thank you for the remarks of your learned friend at Carlisle. I had, when a youth, read and smiled at Pliny's account of a practice among the seamen of his time, to still the waves in a storm by pouring oil into the sea; which he mentions as well as the use made of oil by the divers; but the stilling a tempest by throwing vinegar into the air had escaped me. I think with your friend that it has been of late too much the mode to slight the learning of the ancients. The learned, too, are apt to slight too much the knowledge of the vulgar. The cooling by evaporation was long an instance of the latter. The art of smoothing the waves by oil is an instance of both.
Perhaps you may not dislike to have an account of all I have heard, and learnt, and done in this way. Take it if you please as follows:"
http://jcbmac.chem.brown.edu/baird/Chem22I/Avogadro/BenFranklin.html
On Sep 26, 2004, at 11:47 AM, Jack Sarfatti wrote:
Furthermore, the issue of the “flow of time”, i.e. “Arrow of Time” is not found directly in the formalism of space-time that is a “block universe”. One must look elsewhere to the boundary conditions at the Big Bang to explain why the irreversibility of the Second Law of Thermodynamics points the same way as the expanding 3D space of our local Hubble horizoned universe. Roger Penrose deals with this problem extensively, e.g. his online lecture “Fashion, Faith and Fantasy” http://www.princeton.edu/WebMedia/lectures/
In my theory, the low initial entropy of the early post-inflationary universe is explained by the collapse of the volume of phase space of the pre-inflationary unstable globally flat false vacuum in the formation of the vacuum condensate of primarily bound virtual electron-positron pairs glued together by virtual photon exchange in the battle-tested non-perturbative background-independent BCS manner. The false vacuum prior to inflation may itself emerge from a spin foam, but one without emergent gravity that only comes after the formation of the vacuum condensate whose phase variations give Einstein’s metric field. There is no inertia without gravity and that is why the pre-inflationary globally flat false vacuum has only off-mass-shell massless charges. When the vacuum coherence vanishes inside a vortex core, for example, you do not get a “nonlinear graviton” (Roger Penrose) quantum gravity foam in my model. Therefore, you should not see any quantum gravity foam fluctuations in high energy gamma rays from way back in time if my model is correct. Einstein’s metric field is a smooth c-number ODLRO field from the vacuum coherence. Trying to quantize the metric field top-down is redundant as it is an emergent bottom-up “More is different” macro-quantum phenomenon. There is no such thing as “classical space-time”. What we have is “macro-quantum space-time.” However, just as a superfluid has “normal fluid” you can do perturbation theory with a spin 2 quantum field on the smooth curved space-time background ODLRO metric field. When the vacuum coherence vanishes you then get the “linear graviton” spin 2 quantum tensor field on the flat Minkowski background.
This is the basic physics discovery of Ben Franklin’s oil calming the turbulent waters presented in this book for the first time. Here is how I also smooth Hal Puthoff's choppy electromagnetic zero point waves into emergent gravity.
A Letter from Benjamin Franklin to William Brownrigg, 1773
"Dear Sir: I thank you for the remarks of your learned friend at Carlisle. I had, when a youth, read and smiled at Pliny's account of a practice among the seamen of his time, to still the waves in a storm by pouring oil into the sea; which he mentions as well as the use made of oil by the divers; but the stilling a tempest by throwing vinegar into the air had escaped me. I think with your friend that it has been of late too much the mode to slight the learning of the ancients. The learned, too, are apt to slight too much the knowledge of the vulgar. The cooling by evaporation was long an instance of the latter. The art of smoothing the waves by oil is an instance of both.
Perhaps you may not dislike to have an account of all I have heard, and learnt, and done in this way. Take it if you please as follows:"
http://jcbmac.chem.brown.edu/baird/Chem22I/Avogadro/BenFranklin.html
On Sep 26, 2004, at 11:47 AM, Jack Sarfatti wrote:
Furthermore, the issue of the “flow of time”, i.e. “Arrow of Time” is not found directly in the formalism of space-time that is a “block universe”. One must look elsewhere to the boundary conditions at the Big Bang to explain why the irreversibility of the Second Law of Thermodynamics points the same way as the expanding 3D space of our local Hubble horizoned universe. Roger Penrose deals with this problem extensively, e.g. his online lecture “Fashion, Faith and Fantasy” http://www.princeton.edu/WebMedia/lectures/
In my theory, the low initial entropy of the early post-inflationary universe is explained by the collapse of the volume of phase space of the pre-inflationary unstable globally flat false vacuum in the formation of the vacuum condensate of primarily bound virtual electron-positron pairs glued together by virtual photon exchange in the battle-tested non-perturbative background-independent BCS manner. The false vacuum prior to inflation may itself emerge from a spin foam, but one without emergent gravity that only comes after the formation of the vacuum condensate whose phase variations give Einstein’s metric field. There is no inertia without gravity and that is why the pre-inflationary globally flat false vacuum has only off-mass-shell massless charges. When the vacuum coherence vanishes inside a vortex core, for example, you do not get a “nonlinear graviton” (Roger Penrose) quantum gravity foam in my model. Therefore, you should not see any quantum gravity foam fluctuations in high energy gamma rays from way back in time if my model is correct. Einstein’s metric field is a smooth c-number ODLRO field from the vacuum coherence. Trying to quantize the metric field top-down is redundant as it is an emergent bottom-up “More is different” macro-quantum phenomenon. There is no such thing as “classical space-time”. What we have is “macro-quantum space-time.” However, just as a superfluid has “normal fluid” you can do perturbation theory with a spin 2 quantum field on the smooth curved space-time background ODLRO metric field. When the vacuum coherence vanishes you then get the “linear graviton” spin 2 quantum tensor field on the flat Minkowski background.
Saturday, September 25, 2004
Correction - that paper by Modanese was already given in 2004. I am amazed that no one corrected that obvious error! It's minor of course.
Note that what really matters for the metric engineering of warp, wormhole and weapon that we see in the UFOs Out There is not real graviton beams. That is folly. What matters are the the c-number guv curved space-time dynamical fields coming from the rigid Goldstone phase of the vacuum condensate that forms weak Josephson links to the real superconductors, or other macro-quantum coherent order parameters like in the quantum Hall effect of 2D electron sheets forming anyons at high Tc. Modanese does not understand the role of the vacuum condensate generating the emergent guv field. Modanese only has a fragment of the problem showing that given a real superconductor order parameter it will influence the /\ contribution to Einstein's guv field. That is good, but does not go deep enough. Modanese does not have my metric engineering equation
Induced /\ = (Short-Wave Cut-Off)^-2(Vacuum Condensate Density)^1/2(Control Condensate Density)^1/2(Common Overlap Volume)Cosine of the relative phase between the vacuum and control coherent order parameters.
On Sep 25, 2004, at 2:04 PM, Jack Sarfatti wrote:
On Sep 25, 2004, at 12:04 PM, Jack Sarfatti wrote:
Remember, macro-quantum vacuum coherence hides random micro-quantum zero point vacuum energy under the rug. Any random zero point energy that leaks out is exotic vacuum that contributes to the cosmological constant either as dark energy or dark matter depending on the sign of the pressure negative or positive respectively. Dark energy at a distance is a universal repulsive antigravity field. Dark matter at a distance is a universal attractive gravity field. Both fields can be stronger than what is expected from Newton’s constant. That is the effective Planck energy is smaller than 10^19Gev. However, as possibly in the case of Ken Shoulders “charge clusters” the effective forces inside an extended exotic vacuum region can change sign! Indeed, that is why the EVO is stable and that is also why the single electron is stable.
Modanese's paper below is of interest of course. There is an error in his eq. 6 that may be a problem in the broken English of the Italian authors. What they call "phase velocity" there should really be "group velocity."
Phase velocity is E/p = hf/hk. Modanese writes it upside down as p/E.
Note that when
E^2 = (pc)^2 + (mc^2)^2
group velocity is
vg = dE/dp
i.e.
2EdE = 2pc^2dp
Therefore,
vg = dE/dp = c^2(p/E)
That is
(vgroup)(vphase) = c^2
for both m^2 > 0 and m^2 < 0
However, this error is not fatal and the paper has some interesting ideas that overlap my own independent research.
The emphasis at STAIF on real gravitons I think is a mistake. They will only produce small effects not directly relevant to the real metric engineering we see Out There in the UFO phenomenon. That empirical purely descriptive part is nicely presented in the recent NIDS paper by Jacques Vallee and Eric Davis.
On Sep 25, 2004, at 9:42 AM, Gary S. Bekkum wrote:
http://www.arxiv.org/abs/physics/0409098
Effect of the Vacuum Energy Density on Graviton Propagation
Authors: Giovanni Modanese, Giorgio Fontana
Comments: CP699, Space Technology and Applications International Forum-STAIF 2004, proceedings published by AIP and edited by M.S. El-Genk
Subj-class: General Physics
"It is known that the value L of the vacuum energy density affects the propagation equation for gravitons: A mass term appears in the propagation equation, such that m^2=-L. As a consequence, the polarization states of gravitons also change. This effect of the L-term has been confirmed by recent calculations in a curved background, which is the only proper setting, since solutions of the classical Einstein equations in the presence of a L-term represent a space with constant curvature. A real value for the mass (when L<0) will show up as a slight exponential damping in the gravitational potential, which is however strongly constrained by astronomical data. The consequences of an imaginary mass (for L>0) are still unclear; on general grounds, one can expect the onset of instabilities in this case. This is also confirmed by numerical simulations of quantum gravity which became recently available. These properties gain a special interest in consideration of the following. (1) The most recent cosmological data indicate that L is positive and of the order of 0.1 J/m^3. Is this value compatible with a stable propagation of gravitons? (2) The answer to the previous question lies perhaps in the scale dependence of the effective value of L. L may be negative at the small distance/large energy scale at which the quantum behavior of gravitational fields and waves becomes relevant. Furthermore, local contributions to the vacuum energy density (in superconductors in certain states, and in very strong static electromagnetic fields) can change locally the sign of L, and so affect locally the propagation and the properties of gravitons. The graviton wavefunction, for different values of the parameters, may be characterized by superluminal phase velocity or by unitarity only in imaginary valued time."
Note that what really matters for the metric engineering of warp, wormhole and weapon that we see in the UFOs Out There is not real graviton beams. That is folly. What matters are the the c-number guv curved space-time dynamical fields coming from the rigid Goldstone phase of the vacuum condensate that forms weak Josephson links to the real superconductors, or other macro-quantum coherent order parameters like in the quantum Hall effect of 2D electron sheets forming anyons at high Tc. Modanese does not understand the role of the vacuum condensate generating the emergent guv field. Modanese only has a fragment of the problem showing that given a real superconductor order parameter it will influence the /\ contribution to Einstein's guv field. That is good, but does not go deep enough. Modanese does not have my metric engineering equation
Induced /\ = (Short-Wave Cut-Off)^-2(Vacuum Condensate Density)^1/2(Control Condensate Density)^1/2(Common Overlap Volume)Cosine of the relative phase between the vacuum and control coherent order parameters.
On Sep 25, 2004, at 2:04 PM, Jack Sarfatti wrote:
On Sep 25, 2004, at 12:04 PM, Jack Sarfatti wrote:
Remember, macro-quantum vacuum coherence hides random micro-quantum zero point vacuum energy under the rug. Any random zero point energy that leaks out is exotic vacuum that contributes to the cosmological constant either as dark energy or dark matter depending on the sign of the pressure negative or positive respectively. Dark energy at a distance is a universal repulsive antigravity field. Dark matter at a distance is a universal attractive gravity field. Both fields can be stronger than what is expected from Newton’s constant. That is the effective Planck energy is smaller than 10^19Gev. However, as possibly in the case of Ken Shoulders “charge clusters” the effective forces inside an extended exotic vacuum region can change sign! Indeed, that is why the EVO is stable and that is also why the single electron is stable.
Modanese's paper below is of interest of course. There is an error in his eq. 6 that may be a problem in the broken English of the Italian authors. What they call "phase velocity" there should really be "group velocity."
Phase velocity is E/p = hf/hk. Modanese writes it upside down as p/E.
Note that when
E^2 = (pc)^2 + (mc^2)^2
group velocity is
vg = dE/dp
i.e.
2EdE = 2pc^2dp
Therefore,
vg = dE/dp = c^2(p/E)
That is
(vgroup)(vphase) = c^2
for both m^2 > 0 and m^2 < 0
However, this error is not fatal and the paper has some interesting ideas that overlap my own independent research.
The emphasis at STAIF on real gravitons I think is a mistake. They will only produce small effects not directly relevant to the real metric engineering we see Out There in the UFO phenomenon. That empirical purely descriptive part is nicely presented in the recent NIDS paper by Jacques Vallee and Eric Davis.
On Sep 25, 2004, at 9:42 AM, Gary S. Bekkum wrote:
http://www.arxiv.org/abs/physics/0409098
Effect of the Vacuum Energy Density on Graviton Propagation
Authors: Giovanni Modanese, Giorgio Fontana
Comments: CP699, Space Technology and Applications International Forum-STAIF 2004, proceedings published by AIP and edited by M.S. El-Genk
Subj-class: General Physics
"It is known that the value L of the vacuum energy density affects the propagation equation for gravitons: A mass term appears in the propagation equation, such that m^2=-L. As a consequence, the polarization states of gravitons also change. This effect of the L-term has been confirmed by recent calculations in a curved background, which is the only proper setting, since solutions of the classical Einstein equations in the presence of a L-term represent a space with constant curvature. A real value for the mass (when L<0) will show up as a slight exponential damping in the gravitational potential, which is however strongly constrained by astronomical data. The consequences of an imaginary mass (for L>0) are still unclear; on general grounds, one can expect the onset of instabilities in this case. This is also confirmed by numerical simulations of quantum gravity which became recently available. These properties gain a special interest in consideration of the following. (1) The most recent cosmological data indicate that L is positive and of the order of 0.1 J/m^3. Is this value compatible with a stable propagation of gravitons? (2) The answer to the previous question lies perhaps in the scale dependence of the effective value of L. L may be negative at the small distance/large energy scale at which the quantum behavior of gravitational fields and waves becomes relevant. Furthermore, local contributions to the vacuum energy density (in superconductors in certain states, and in very strong static electromagnetic fields) can change locally the sign of L, and so affect locally the propagation and the properties of gravitons. The graviton wavefunction, for different values of the parameters, may be characterized by superluminal phase velocity or by unitarity only in imaginary valued time."
On Sep 25, 2004, at 12:04 PM, Jack Sarfatti wrote:
Remember, macro-quantum vacuum coherence hides random micro-quantum zero point vacuum energy under the rug. Any random zero point energy that leaks out is exotic vacuum that contributes to the cosmological constant either as dark energy or dark matter depending on the sign of the pressure negative or positive respectively. Dark energy at a distance is a universal repulsive antigravity field. Dark matter at a distance is a universal attractive gravity field. Both fields can be stronger than what is expected from Newton’s constant. That is the effective Planck energy is smaller than 10^19Gev. However, as possibly in the case of Ken Shoulders “charge clusters” the effective forces inside an extended exotic vacuum region can change sign! Indeed, that is why the EVO is stable and that is also why the single electron is stable.
Modanese's paper below is of interest of course. There is an error in his eq. 6 that may be a problem in the broken English of the Italian authors. What they call "phase velocity" there should really be "group velocity."
Phase velocity is E/p = hf/hk. Modanese writes it upside down as p/E.
Note that when
E^2 = (pc)^2 + (mc^2)^2
group velocity is
vg = dE/dp
i.e.
2EdE = 2pc^2dp
Therefore,
vg = dE/dp = c^2(p/E)
That is
(vgroup)(vphase) = c^2
for both m^2 > 0 and m^2 < 0
However, this error is not fatal and the paper has some interesting ideas that overlap my own independent research.
The emphasis at STAIF on real gravitons I think is a mistake. They will only produce small effects not directly relevant to the real metric engineering we see Out There in the UFO phenomenon. That empirical purely descriptive part is nicely presented in the recent NIDS paper by Jacques Vallee and Eric Davis.
On Sep 25, 2004, at 9:42 AM, Gary S. Bekkum wrote:
http://www.arxiv.org/abs/physics/0409098
Effect of the Vacuum Energy Density on Graviton Propagation
Authors: Giovanni Modanese, Giorgio Fontana
Comments: CP699, Space Technology and Applications International Forum-STAIF 2004, proceedings published by AIP and edited by M.S. El-Genk
Subj-class: General Physics
"It is known that the value L of the vacuum energy density affects the propagation equation for gravitons: A mass term appears in the propagation equation, such that m^2=-L. As a consequence, the polarization states of gravitons also change. This effect of the L-term has been confirmed by recent calculations in a curved background, which is the only proper setting, since solutions of the classical Einstein equations in the presence of a L-term represent a space with constant curvature. A real value for the mass (when L<0) will show up as a slight exponential damping in the gravitational potential, which is however strongly constrained by astronomical data. The consequences of an imaginary mass (for L>0) are still unclear; on general grounds, one can expect the onset of instabilities in this case. This is also confirmed by numerical simulations of quantum gravity which became recently available. These properties gain a special interest in consideration of the following. (1) The most recent cosmological data indicate that L is positive and of the order of 0.1 J/m^3. Is this value compatible with a stable propagation of gravitons? (2) The answer to the previous question lies perhaps in the scale dependence of the effective value of L. L may be negative at the small distance/large energy scale at which the quantum behavior of gravitational fields and waves becomes relevant. Furthermore, local contributions to the vacuum energy density (in superconductors in certain states, and in very strong static electromagnetic fields) can change locally the sign of L, and so affect locally the propagation and the properties of gravitons. The graviton wavefunction, for different values of the parameters, may be characterized by superluminal phase velocity or by unitarity only in imaginary valued time."
Remember, macro-quantum vacuum coherence hides random micro-quantum zero point vacuum energy under the rug. Any random zero point energy that leaks out is exotic vacuum that contributes to the cosmological constant either as dark energy or dark matter depending on the sign of the pressure negative or positive respectively. Dark energy at a distance is a universal repulsive antigravity field. Dark matter at a distance is a universal attractive gravity field. Both fields can be stronger than what is expected from Newton’s constant. That is the effective Planck energy is smaller than 10^19Gev. However, as possibly in the case of Ken Shoulders “charge clusters” the effective forces inside an extended exotic vacuum region can change sign! Indeed, that is why the EVO is stable and that is also why the single electron is stable.
Modanese's paper below is of interest of course. There is an error in his eq. 6 that may be a problem in the broken English of the Italian authors. What they call "phase velocity" there should really be "group velocity."
Phase velocity is E/p = hf/hk. Modanese writes it upside down as p/E.
Note that when
E^2 = (pc)^2 + (mc^2)^2
group velocity is
vg = dE/dp
i.e.
2EdE = 2pc^2dp
Therefore,
vg = dE/dp = c^2(p/E)
That is
(vgroup)(vphase) = c^2
for both m^2 > 0 and m^2 < 0
However, this error is not fatal and the paper has some interesting ideas that overlap my own independent research.
The emphasis at STAIF on real gravitons I think is a mistake. They will only produce small effects not directly relevant to the real metric engineering we see Out There in the UFO phenomenon. That empirical purely descriptive part is nicely presented in the recent NIDS paper by Jacques Vallee and Eric Davis.
On Sep 25, 2004, at 9:42 AM, Gary S. Bekkum wrote:
http://www.arxiv.org/abs/physics/0409098
Effect of the Vacuum Energy Density on Graviton Propagation
Authors: Giovanni Modanese, Giorgio Fontana
Comments: CP699, Space Technology and Applications International Forum-STAIF 2004, proceedings published by AIP and edited by M.S. El-Genk
Subj-class: General Physics
"It is known that the value L of the vacuum energy density affects the propagation equation for gravitons: A mass term appears in the propagation equation, such that m^2=-L. As a consequence, the polarization states of gravitons also change. This effect of the L-term has been confirmed by recent calculations in a curved background, which is the only proper setting, since solutions of the classical Einstein equations in the presence of a L-term represent a space with constant curvature. A real value for the mass (when L<0) will show up as a slight exponential damping in the gravitational potential, which is however strongly constrained by astronomical data. The consequences of an imaginary mass (for L>0) are still unclear; on general grounds, one can expect the onset of instabilities in this case. This is also confirmed by numerical simulations of quantum gravity which became recently available. These properties gain a special interest in consideration of the following. (1) The most recent cosmological data indicate that L is positive and of the order of 0.1 J/m^3. Is this value compatible with a stable propagation of gravitons? (2) The answer to the previous question lies perhaps in the scale dependence of the effective value of L. L may be negative at the small distance/large energy scale at which the quantum behavior of gravitational fields and waves becomes relevant. Furthermore, local contributions to the vacuum energy density (in superconductors in certain states, and in very strong static electromagnetic fields) can change locally the sign of L, and so affect locally the propagation and the properties of gravitons. The graviton wavefunction, for different values of the parameters, may be characterized by superluminal phase velocity or by unitarity only in imaginary valued time."
Remember, macro-quantum vacuum coherence hides random micro-quantum zero point vacuum energy under the rug. Any random zero point energy that leaks out is exotic vacuum that contributes to the cosmological constant either as dark energy or dark matter depending on the sign of the pressure negative or positive respectively. Dark energy at a distance is a universal repulsive antigravity field. Dark matter at a distance is a universal attractive gravity field. Both fields can be stronger than what is expected from Newton’s constant. That is the effective Planck energy is smaller than 1019Gev. However, as possibly in the case of Ken Shoulders “charge clusters” the effective forces inside an extended exotic vacuum region can change sign! Indeed, that is why the EVO is stable and that is alsowhy the single electron is stable.
On Sep 24, 2004, at 10:28 AM, Jack Sarfatti wrote:
Puthoff on Casimir Force
Strange that Puthoff wrote today
“I'm not trying to scale up the Casimir force effect, never have, never even thought about it. Discussion of the Casimir effect in ZPE discussions are purely pedagogical, not application oriented, and this is clear to everyone else on your list who emails me privately. The devices that have not scaled up are Ken's charge cluster devices, not Casimir devices. My thoughts for ZPE extraction are based on totally different other approaches. I understand Petersen's work and the implications long before I ever even heard of Petersen. Where in my work have I ever talked about scaling up Casimir effect for engineering energy extraction devices, where?!”
However, in the interview he said:
(Puthoff) For example, Casimir plates in the vacuum can be considered coupled to an open system, and when driven together by vacuum forces, the vacuum has decayed to a lower energy state and heat has been generated by the collision of the plates, pretty standard stuff. For a more detailed discussion of the thermodynamic aspects of zero-point energy extraction, see D.C. Cole and H.E. Puthoff, "Extracting energy and heat from the vacuum”Phys. Rev. E, vol. 48, p. 1562, 1993."
Rebutted by Ian Peterson who wrote:
"The complexity of the Casimir analysis has led to some untenable assertions. It
has been claimed that the parallel-mirror configuration provides access to an infinite
source of energy [18,***19]. However the maximum energy that can be extracted by
allowing the separation of the mirrors to drop to zero cannot exceed the surface energy
of their constituent metals, which is typically of the order of 1 J.m-2 [20]. There have
also been claims that energy can be extracted by cycling a machine 21].
...
16. J Schwinger, L L De Raad, K A Milton Ann. Phys. 115, 1 (1978).
17. S K Lamoreaux Phys. Rev. A 59, R3149-R3153 (1999).
18. R Forward Phys. Rev. B 30, 1700 (1984).
***19. D C Cole, H E Puthoff Phys. Rev. E 48, 1562-1565 (1993).
20. CRC Handbook of Chemistry, Physics, 80th Edn., (Ed D R Lide) (CRC Press, Boca
Raton, FL 1999) pp4-120, 6-144.
21. G J Maclay Phys. Rev. A 61, 052110 (2000).
22. T H Boyer Phys. Rev. A 9, 2078-2084 (1974).”
Note that Peterson from University of Coventry UK also rebuts Maclay another one of the NASA BPP "usual suspects"! ;-)
Then on August 31, 2004, Hal tried to explain Ken Shoulders charge clusters as a Casimir force which contradicts his above remark:
“The devices that have not scaled up are Ken's charge cluster devices, not Casimir devices.”
I had written to Hal: Even if that is what you mean, I do not see how anything gets "balanced" here? You have a "classical" electrostatic energy density and a micro-quantum ZPF virtual photon density. Both are positive. In what sense do they balance?
Hal replied: “Force balance. The ZPE pressure (as in Milonni et al.'s paper "Radiation pressure from the vacuum: Physical interpretation of the Casimir force", Phys. Rev. A, Vol. 38, No. 3, pp. 1621-1623, 1988) outside the sphere presses inward, and there being no pressure from within the ZPE-depleted sphere - - at least from below the Compton freq - - pressing outward, so the net ZPE pressure is inward. This is what balances (with stability) the outward Coulomb pressure. This is specifically displayed in http://arxiv.org/abs/physics/0408114 .”
What is wrong here is that virtual photons have negative pressure since w = -1 for them and their energy density is positive. It is wrong to use the positive pressure of real photons here. Real photons have w = +1/3 and Milonni’s paper is wrong for that reason. Note also that I do not claim that the strong direct gravity warping of space-time by unbalanced zero point energy pressures have anything to do with the Casimir force. They don’t. These are two qualitatively different physical effects. Hal misunderstood what I actually am claiming when he wrongly said that my effect predicts repulsion between the Casimir plates from the virtual photon negative pressure. In fact, I predict nothing of the kind. Under conditions of the Casimir force, the virtual photon pressure should be zero compensated by the vacuum coherence. The Casimir force is then explained as Ian Peterson does as an induced electric dipole-dipole electrostatic force. The naïve photon pressure models give the right answer for the wrong reasons. It is an interesting fluke like Ptolemy’s epicycles.
Puthoff on Casimir Force
Strange that Puthoff wrote today
“I'm not trying to scale up the Casimir force effect, never have, never even thought about it. Discussion of the Casimir effect in ZPE discussions are purely pedagogical, not application oriented, and this is clear to everyone else on your list who emails me privately. The devices that have not scaled up are Ken's charge cluster devices, not Casimir devices. My thoughts for ZPE extraction are based on totally different other approaches. I understand Petersen's work and the implications long before I ever even heard of Petersen. Where in my work have I ever talked about scaling up Casimir effect for engineering energy extraction devices, where?!”
However, in the interview he said:
(Puthoff) For example, Casimir plates in the vacuum can be considered coupled to an open system, and when driven together by vacuum forces, the vacuum has decayed to a lower energy state and heat has been generated by the collision of the plates, pretty standard stuff. For a more detailed discussion of the thermodynamic aspects of zero-point energy extraction, see D.C. Cole and H.E. Puthoff, "Extracting energy and heat from the vacuum”Phys. Rev. E, vol. 48, p. 1562, 1993."
Rebutted by Ian Peterson who wrote:
"The complexity of the Casimir analysis has led to some untenable assertions. It
has been claimed that the parallel-mirror configuration provides access to an infinite
source of energy [18,***19]. However the maximum energy that can be extracted by
allowing the separation of the mirrors to drop to zero cannot exceed the surface energy
of their constituent metals, which is typically of the order of 1 J.m-2 [20]. There have
also been claims that energy can be extracted by cycling a machine 21].
...
16. J Schwinger, L L De Raad, K A Milton Ann. Phys. 115, 1 (1978).
17. S K Lamoreaux Phys. Rev. A 59, R3149-R3153 (1999).
18. R Forward Phys. Rev. B 30, 1700 (1984).
***19. D C Cole, H E Puthoff Phys. Rev. E 48, 1562-1565 (1993).
20. CRC Handbook of Chemistry, Physics, 80th Edn., (Ed D R Lide) (CRC Press, Boca
Raton, FL 1999) pp4-120, 6-144.
21. G J Maclay Phys. Rev. A 61, 052110 (2000).
22. T H Boyer Phys. Rev. A 9, 2078-2084 (1974).”
Note that Peterson from University of Coventry UK also rebuts Maclay another one of the NASA BPP "usual suspects"! ;-)
Then on August 31, 2004, Hal tried to explain Ken Shoulders charge clusters as a Casimir force which contradicts his above remark:
“The devices that have not scaled up are Ken's charge cluster devices, not Casimir devices.”
I had written to Hal: Even if that is what you mean, I do not see how anything gets "balanced" here? You have a "classical" electrostatic energy density and a micro-quantum ZPF virtual photon density. Both are positive. In what sense do they balance?
Hal replied: “Force balance. The ZPE pressure (as in Milonni et al.'s paper "Radiation pressure from the vacuum: Physical interpretation of the Casimir force", Phys. Rev. A, Vol. 38, No. 3, pp. 1621-1623, 1988) outside the sphere presses inward, and there being no pressure from within the ZPE-depleted sphere - - at least from below the Compton freq - - pressing outward, so the net ZPE pressure is inward. This is what balances (with stability) the outward Coulomb pressure. This is specifically displayed in http://arxiv.org/abs/physics/0408114 .”
What is wrong here is that virtual photons have negative pressure since w = -1 for them and their energy density is positive. It is wrong to use the positive pressure of real photons here. Real photons have w = +1/3 and Milonni’s paper is wrong for that reason. Note also that I do not claim that the strong direct gravity warping of space-time by unbalanced zero point energy pressures have anything to do with the Casimir force. They don’t. These are two qualitatively different physical effects. Hal misunderstood what I actually am claiming when he wrongly said that my effect predicts repulsion between the Casimir plates from the virtual photon negative pressure. In fact, I predict nothing of the kind. Under conditions of the Casimir force, the virtual photon pressure should be zero compensated by the vacuum coherence. The Casimir force is then explained as Ian Peterson does as an induced electric dipole-dipole electrostatic force. The naïve photon pressure models give the right answer for the wrong reasons. It is an interesting fluke like Ptolemy’s epicycles.
Sunday, September 19, 2004
Suppose one knew almost no physics. One could easily compute the functional form of the Casimir force as
Casimir force ~ hcA/d^4
Where A = area of plates
d = separation of plates
from the idea that the force must decrease as separation of plates increases and that it must increase as area of plates increases all in the simplest way i.e. linearly as the area A.
Also it must depend on h and c.
But also note that hc has same dimensions as e^2, i.e. a classical electrostatic VdW effect that does not require infinite virtual photon energy densities and pressures that form INFINITE CURVATURE SINGULARITIES everywhere in space!
Therefore, attributing the Casimir force to FREE virtual photon pressure differences across the plates is far from compelling.
On Sep 19, 2004, at 10:03 PM, Jack Sarfatti wrote:
PS
Milonni assume zero length cutoff a -> 0, therefore INFINITE virtual photon zero point energies. He subtracts two infinite energies E(d) and E(infinity) to get a finite energy that appears to agree with an experimental result.
1. This violates Einstein's general theory of relativity where these virtual energies strongly warp space-time. This is essentially the cosmological constant problem that greatly worries Princeton's IAS Genius Ed Witten but does not seem to bother Hal Puthoff at his same name "IAS" in Austin. Well I suppose it is no surprise that another fellow from Austin now in The White House thinks things are going well in Iraq! Both seem out of touch with reality. :-)
2. In contrast, I do not look at E(d) - E(infinity) I keep a finite cutoff a, but I calculate FINITE E on both sides of each plate in the parallel plate experiment using only the relevant virtual photons from the relevant longitudinal modes along the normal to the planes of the plates and I take the total force
-(d/dx)[E(inside) + E(outside)] to get
Introducing vacuum coherence gives for the free virtual photon ZPF force
- (1/2)(hc/d^2)(A/a^2)[1 - a^3|Vacuum Coherence|^2]
d = separation of plates
A = area of plates
a = short-wave cutoff
This whole thing vanishes in ordinary vacuum because of the vacuum coherence that solves the cosmological constant problem as well.
The observed Casimir force ~ 1/d^4 must be calculated from summing over all molecules in both plates the retarded r^-7 VdW potential between two mutually induced electric dipoles one in each of the two plates.
Casimir force ~ hcA/d^4
Where A = area of plates
d = separation of plates
from the idea that the force must decrease as separation of plates increases and that it must increase as area of plates increases all in the simplest way i.e. linearly as the area A.
Also it must depend on h and c.
But also note that hc has same dimensions as e^2, i.e. a classical electrostatic VdW effect that does not require infinite virtual photon energy densities and pressures that form INFINITE CURVATURE SINGULARITIES everywhere in space!
Therefore, attributing the Casimir force to FREE virtual photon pressure differences across the plates is far from compelling.
On Sep 19, 2004, at 10:03 PM, Jack Sarfatti wrote:
PS
Milonni assume zero length cutoff a -> 0, therefore INFINITE virtual photon zero point energies. He subtracts two infinite energies E(d) and E(infinity) to get a finite energy that appears to agree with an experimental result.
1. This violates Einstein's general theory of relativity where these virtual energies strongly warp space-time. This is essentially the cosmological constant problem that greatly worries Princeton's IAS Genius Ed Witten but does not seem to bother Hal Puthoff at his same name "IAS" in Austin. Well I suppose it is no surprise that another fellow from Austin now in The White House thinks things are going well in Iraq! Both seem out of touch with reality. :-)
2. In contrast, I do not look at E(d) - E(infinity) I keep a finite cutoff a, but I calculate FINITE E on both sides of each plate in the parallel plate experiment using only the relevant virtual photons from the relevant longitudinal modes along the normal to the planes of the plates and I take the total force
-(d/dx)[E(inside) + E(outside)] to get
Introducing vacuum coherence gives for the free virtual photon ZPF force
- (1/2)(hc/d^2)(A/a^2)[1 - a^3|Vacuum Coherence|^2]
d = separation of plates
A = area of plates
a = short-wave cutoff
This whole thing vanishes in ordinary vacuum because of the vacuum coherence that solves the cosmological constant problem as well.
The observed Casimir force ~ 1/d^4 must be calculated from summing over all molecules in both plates the retarded r^-7 VdW potential between two mutually induced electric dipoles one in each of the two plates.
Ref. The Quantum Vacuum by Peter Milonni, Acad Press, 1994
2.7 The Casimir Effect pp 54 - 58
This calculation was plausible until the 1999 discovery of dark energy as most of the stuff of our mostly "virtual" (i.e. off mass shell) universe. The problem is that the virtual photon zero point energy density as well as all the other contributions like virtual electron-positron pairs are directly observable in principle because of the laws of gravity! This is precisely the cosmological constant paradox, which is to physics today, what the black body radiation paradox was 100 years ago.
Even if we take Milonni's calculation as is, it fails because it posits an infinite virtual photon zero point energy background. The universe cannot exist in that case. It is no longer a valid rule in The Game to pretend that this infinite energy can be simply "subtracted". Indeed one must put in a short-wave cutoff, but one can do it in a generally covariant way.
You need vacuum coherence to absorb the large but finite incoherent zero point fluctuation energy in the ordinary vacuum, which when disturbed, results in anomalous "dark energy" exotic vacuum of negative pressure or anomalous "dark matter" exotic vacuum of positive pressure. Both forms of exotic vacuum have w = (pressure/energy density) = -1. w = -1 because of the generally covariant laws of Einstein's gravity theory AKA "GR".
For example, look at Milonni's E(infinity) i.e. eq. (2.100) p.57
What you really have there is E(a) where a is the short-wave cutoff, but E(a) has the vacuum coherence factor
(1 - a^3|Vacuum Coherence|^2) = 0 under "normal conditions".
Look at Milonni's "spectral density" of quantum harmonic field oscillators (2.73) p.49 that comes from the more fundamental quantity
Mode Density ~ 4pip^2dp/h^3 = phase space factor per unit volume = = number of quantum harmonic field oscillators per unit volume
Because of spherical symmetry, take pc/2 as the common virtual photon energy of that spherical shell in momentum space to get
ZPE density per unit volume = (2pi)cp^3dp/h^3
In general, with finite asymmetric boundary conditions you need to use
ZPE Mode Density ~ dpxdpydpz/h^3 = number of quantum harmonic field oscillators per unit volume
i.e. as I showed yesterday, without the vacuum coherence factor that can be put in at end of the calculation.
Given the asymmetric boundary conditions of parallel plates, we need to
be careful about how to do the integration in momentum space. We cannot
use spherical coordinates in momentum space. We must use Cartesian
rectangular coordinates, i.e. for the spectral density
dpxdpydpz not 4pip^2dp
Let the parallel plates be separated by x along the x-axis.
Between the plates, the limits are from px(min) = h/2x to px(max) = h/a.
However, in the plane of the plates the limits are from 0 to p(max) =
h/a.
How do we do the virtual photon ZPE integral?
That integral must split into longitudinal and transverse parts.
The longitudinal FREE VIRTUAL PHOTON ZPE integral BETWEEN THE PLATES is
ZPE(x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)xYZ/h^3
= (1/2)c[(h/a)^2 - (h/x)^2](h/a)^2xYZ/h^3
= (1/2)(h/a)^2(h/a)^2xYZ/h^3 - (1/2)c(h/x)^2(h/a)^2xYZ/h^3
= (1/2)(hc/a)(xYZ/a^3) - (1/2)(hc/x)(YZ/a^2)
The ZPF force from this term is
-(d/dx)ZPE(x) = -(1/2)(hc/a^2)(YZ/a^2) - (1/2)(hc/x^2)(YZ/a^2)
= -(1/2)(hc/a^4)YZ - (1/2)(hc/x^2)(YZ/a^2)
The longitudinal FREE VIRTUAL PHOTON ZPE integral OUTSIDE THE PLATES is
ZPE(X-x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)(X-x)YZ/h^3
= (1/2)c[(h/a)^2 - (h/(X-x))^2](h/a)^2(X-x)xYZ/h^3
= (1/2)(hc/a)((X-x)YZ/a^3) - (1/2)(hc/(X-x))(YZ/a^2)
The ZPF force from this term is from -(d/dx)ZPE(X-x) =
+(1/2)(hc/a^2)(YZ/a^2) + (hc/2)(YZ/a^2)(d/dx)(1/(X-x))
(d/dx)(1/(X-x)) = +(X - x)^-2
Next look at the transverse free virtual photon integral ZPE(xYZ).
ZPE(xYZ) = (c/2)xYZ[(px(max) - px(min)](Integral of 2pip^2dp from 0 to
p(max))/h^3
= (hc/2)[(1/a) - (1/x)]xYZ(Integral of 2pip^2dp from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/x)]xYZ(2pi/3)(1/a)^3
This term gives a net attractive force along x of -(hc/2a^4)YZ.
ZPE((X-x)YZ) = (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(Integral of 2pip^2dp
from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(2pi/3)(1/a)^3
This term gives a net repulsive force along x of +(hc/2a^4)YZ.
Therefore, as expected, we need only look at the longitudinal integral
for these non-spherically symmetric parallel plate boundary conditions.
Area of plates A = YZ.
Thus the NET ZPF force along x at the plate located at x is
-(1/2)(hc/a^4)A - (1/2)(hc/x^2)(A/a^2) +(1/2)(hc/a^2)(A/a^2) +
(hc/2)(A/a^2)(d/dx)(1/(X-x))
- (1/2)(hc/x^2)(A/a^2) + (hc/2)(A/a^2)(1/(X-x)^2)
Assume x << X. As X --> infinity we can ignore the second term from
outside the plates.
This is a net attractive force ~ -1/x^2 not - 1/x^4, but it is too weak
to contain unbalanced charges in the EVO.
This FINITE WAY of mode counting does not agree with Milonni's Rube Goldberg sleight-of-hand shell game giving the observed Casimir force potential (2.108) p. 58
U(d) = -(pi^2hc/720d^3)A
from subtracting two infinities to get this finite difference.
It's the right empirical answer for the wrong reasons!
Milonni's 3.10 is also spurious because virtual photons do not propagate energy and momentum the way real photons do! Milonni here assumes w = +1/3, which is true for real photons, but not for virtual photons where w = -1. The only acceptable explanation for the Casimir force is indicated in Milonni's 3.11 on the Van der Waals forces. Of course the virtual photons play a vital role there but not as directly as they do in the first two models that are misleading because they are not consistent with the laws of Einstein's general relativity that reach down even to the microscale. It's not enough to get the right empirical answer. One must get it for the right reasons. Again up until the discovery of dark energy the choices between the three ways Milonni presents of looking at the orgin of the Casimir force was moot or degenerate. The discovery of dark energy "lifts the degeneracy" and only the retarded Casimir-Polder VdW potential eq. (3.91) p.105 ~ r^-7, which when integrated over many induced dipoles in both parallel plates allegedly gives the result close to (2.108) p. 58 is physically acceptable. See Ian Peterson's papers on this that the only energy you can get from the Casimir force is the small electrostatic induced dipole energy not the large virtual photon ZPE energy!
That is, zero point energy densities and their equal-in-magnitude but opposite-in-sign pressures STRONGLY WARP space-time geometry if not absorbed into the vacuum condensate! Upsetting that equilibrium is the key to the practical metric engineering of warp, wormhole and weapon that we see in the flying saucer evidence on the NIDS website.
That is,
Guv + /\zpfguv = 0
/\zpf = a^-2[1 - a^3|Vacuum Coherence|^2]
a = short-wave invariant cutoff (proper spacelike interval)
/\zpf is a "scalar"
ZPE density = t00(vac) = (c^4/8piG*)/\zpfgoo = (String Tension)(Micro-Quantum ZPE Curvature of Vacuum)goo
For example, in the Schwarzschild vacuum solution
goo = (1 - 2r*/r) when r* < r
But /\zpf is a function of r as well.
2.7 The Casimir Effect pp 54 - 58
This calculation was plausible until the 1999 discovery of dark energy as most of the stuff of our mostly "virtual" (i.e. off mass shell) universe. The problem is that the virtual photon zero point energy density as well as all the other contributions like virtual electron-positron pairs are directly observable in principle because of the laws of gravity! This is precisely the cosmological constant paradox, which is to physics today, what the black body radiation paradox was 100 years ago.
Even if we take Milonni's calculation as is, it fails because it posits an infinite virtual photon zero point energy background. The universe cannot exist in that case. It is no longer a valid rule in The Game to pretend that this infinite energy can be simply "subtracted". Indeed one must put in a short-wave cutoff, but one can do it in a generally covariant way.
You need vacuum coherence to absorb the large but finite incoherent zero point fluctuation energy in the ordinary vacuum, which when disturbed, results in anomalous "dark energy" exotic vacuum of negative pressure or anomalous "dark matter" exotic vacuum of positive pressure. Both forms of exotic vacuum have w = (pressure/energy density) = -1. w = -1 because of the generally covariant laws of Einstein's gravity theory AKA "GR".
For example, look at Milonni's E(infinity) i.e. eq. (2.100) p.57
What you really have there is E(a) where a is the short-wave cutoff, but E(a) has the vacuum coherence factor
(1 - a^3|Vacuum Coherence|^2) = 0 under "normal conditions".
Look at Milonni's "spectral density" of quantum harmonic field oscillators (2.73) p.49 that comes from the more fundamental quantity
Mode Density ~ 4pip^2dp/h^3 = phase space factor per unit volume = = number of quantum harmonic field oscillators per unit volume
Because of spherical symmetry, take pc/2 as the common virtual photon energy of that spherical shell in momentum space to get
ZPE density per unit volume = (2pi)cp^3dp/h^3
In general, with finite asymmetric boundary conditions you need to use
ZPE Mode Density ~ dpxdpydpz/h^3 = number of quantum harmonic field oscillators per unit volume
i.e. as I showed yesterday, without the vacuum coherence factor that can be put in at end of the calculation.
Given the asymmetric boundary conditions of parallel plates, we need to
be careful about how to do the integration in momentum space. We cannot
use spherical coordinates in momentum space. We must use Cartesian
rectangular coordinates, i.e. for the spectral density
dpxdpydpz not 4pip^2dp
Let the parallel plates be separated by x along the x-axis.
Between the plates, the limits are from px(min) = h/2x to px(max) = h/a.
However, in the plane of the plates the limits are from 0 to p(max) =
h/a.
How do we do the virtual photon ZPE integral?
That integral must split into longitudinal and transverse parts.
The longitudinal FREE VIRTUAL PHOTON ZPE integral BETWEEN THE PLATES is
ZPE(x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)xYZ/h^3
= (1/2)c[(h/a)^2 - (h/x)^2](h/a)^2xYZ/h^3
= (1/2)(h/a)^2(h/a)^2xYZ/h^3 - (1/2)c(h/x)^2(h/a)^2xYZ/h^3
= (1/2)(hc/a)(xYZ/a^3) - (1/2)(hc/x)(YZ/a^2)
The ZPF force from this term is
-(d/dx)ZPE(x) = -(1/2)(hc/a^2)(YZ/a^2) - (1/2)(hc/x^2)(YZ/a^2)
= -(1/2)(hc/a^4)YZ - (1/2)(hc/x^2)(YZ/a^2)
The longitudinal FREE VIRTUAL PHOTON ZPE integral OUTSIDE THE PLATES is
ZPE(X-x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)(X-x)YZ/h^3
= (1/2)c[(h/a)^2 - (h/(X-x))^2](h/a)^2(X-x)xYZ/h^3
= (1/2)(hc/a)((X-x)YZ/a^3) - (1/2)(hc/(X-x))(YZ/a^2)
The ZPF force from this term is from -(d/dx)ZPE(X-x) =
+(1/2)(hc/a^2)(YZ/a^2) + (hc/2)(YZ/a^2)(d/dx)(1/(X-x))
(d/dx)(1/(X-x)) = +(X - x)^-2
Next look at the transverse free virtual photon integral ZPE(xYZ).
ZPE(xYZ) = (c/2)xYZ[(px(max) - px(min)](Integral of 2pip^2dp from 0 to
p(max))/h^3
= (hc/2)[(1/a) - (1/x)]xYZ(Integral of 2pip^2dp from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/x)]xYZ(2pi/3)(1/a)^3
This term gives a net attractive force along x of -(hc/2a^4)YZ.
ZPE((X-x)YZ) = (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(Integral of 2pip^2dp
from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(2pi/3)(1/a)^3
This term gives a net repulsive force along x of +(hc/2a^4)YZ.
Therefore, as expected, we need only look at the longitudinal integral
for these non-spherically symmetric parallel plate boundary conditions.
Area of plates A = YZ.
Thus the NET ZPF force along x at the plate located at x is
-(1/2)(hc/a^4)A - (1/2)(hc/x^2)(A/a^2) +(1/2)(hc/a^2)(A/a^2) +
(hc/2)(A/a^2)(d/dx)(1/(X-x))
- (1/2)(hc/x^2)(A/a^2) + (hc/2)(A/a^2)(1/(X-x)^2)
Assume x << X. As X --> infinity we can ignore the second term from
outside the plates.
This is a net attractive force ~ -1/x^2 not - 1/x^4, but it is too weak
to contain unbalanced charges in the EVO.
This FINITE WAY of mode counting does not agree with Milonni's Rube Goldberg sleight-of-hand shell game giving the observed Casimir force potential (2.108) p. 58
U(d) = -(pi^2hc/720d^3)A
from subtracting two infinities to get this finite difference.
It's the right empirical answer for the wrong reasons!
Milonni's 3.10 is also spurious because virtual photons do not propagate energy and momentum the way real photons do! Milonni here assumes w = +1/3, which is true for real photons, but not for virtual photons where w = -1. The only acceptable explanation for the Casimir force is indicated in Milonni's 3.11 on the Van der Waals forces. Of course the virtual photons play a vital role there but not as directly as they do in the first two models that are misleading because they are not consistent with the laws of Einstein's general relativity that reach down even to the microscale. It's not enough to get the right empirical answer. One must get it for the right reasons. Again up until the discovery of dark energy the choices between the three ways Milonni presents of looking at the orgin of the Casimir force was moot or degenerate. The discovery of dark energy "lifts the degeneracy" and only the retarded Casimir-Polder VdW potential eq. (3.91) p.105 ~ r^-7, which when integrated over many induced dipoles in both parallel plates allegedly gives the result close to (2.108) p. 58 is physically acceptable. See Ian Peterson's papers on this that the only energy you can get from the Casimir force is the small electrostatic induced dipole energy not the large virtual photon ZPE energy!
That is, zero point energy densities and their equal-in-magnitude but opposite-in-sign pressures STRONGLY WARP space-time geometry if not absorbed into the vacuum condensate! Upsetting that equilibrium is the key to the practical metric engineering of warp, wormhole and weapon that we see in the flying saucer evidence on the NIDS website.
That is,
Guv + /\zpfguv = 0
/\zpf = a^-2[1 - a^3|Vacuum Coherence|^2]
a = short-wave invariant cutoff (proper spacelike interval)
/\zpf is a "scalar"
ZPE density = t00(vac) = (c^4/8piG*)/\zpfgoo = (String Tension)(Micro-Quantum ZPE Curvature of Vacuum)goo
For example, in the Schwarzschild vacuum solution
goo = (1 - 2r*/r) when r* < r
But /\zpf is a function of r as well.
Saturday, September 18, 2004
Let d be the separation between the flat uncharged plates.
The observed Casimir VdW force is ~ A/d^4 ~ 0.016/d^4 dynes per square cm. Do a Google search.
I have calculated the FREE VIRTUAL PHOTON ZPF attractive force in this same situation to be
- (1/2)(hc/d^2)(A/a^2)
A is area of the plates and a is the short-wave cutoff.
Therefore, unless Hal & Co can point out a specific error in the precise detailed phase space calculation below, all the articles and text books that attribute the Casimir force to a pressure differential of purely free virtual photons between the inside and the outside of the plates are simply wrong.
In fact the free virtual photon ZPF force must be exactly ZERO in the non-exotic vacuum limit where the real formula is
ZPF Free Virtual Photon Force (parallel plates) = - (1/2)(hc/d^2)(A/a^2)[1 - a^3|Vacuum Coherence|^2] = 0
=/= Casimir VdW Force ~ 0.016/d^4 dynes per square cm
The precise calculation of the ZPF Free Virtual Photon Force is short-wave cutoff dependent from simple phase space calculations. The error Milonni and other Pundits make in their text books is to do the phase space integrations incorrectly to get the spurious result ~ 1/d^4 for the virtual photons. That is they use the spherically symmetric phase space integral in an inappropriate situation that does not match the non-spherically symmetric boundary conditions!
On Sep 18, 2004, at 6:50 AM, Jack Sarfatti wrote:
On Sep 18, 2004, at 2:57 AM, RKiehn2352@aol.com wrote:
Dear Jack
I find it miraculous that you admit to a mistake (re ZPF). (grin)
Milonni and Hal Puthoff appear to have made even bigger ones!
My today's correction to my yesterday's correction now agrees in form, i.e. -x^-2 attraction (mod dimensionless coefficient that one must use QED with j.A to get) with A. Zee's calculation in "Quantum Field Theory in a Nutshell" and as I recall disagrees with Milonni's in "The Quantum Vacuum". I have former book with me but not the latter here in Southern California. See below
*
There may be another way to interpret Ken Shoulders EVO's.
**
Ken put together a meeting (financed by Church's Fried Chicken) a long time ago in the SAF bay area. Attendants: Shoulders, Aharonov, Puthoff, Kiehn.
*
Since then,I have always been interested in Ken's experiments.
**
Last week I attended euromech448 conference on Vortex Dynamics and Field interactions.
Crowdy from Imperial college gave an interesting talk on exact COMPACT vortex solutions to the Euler equations in terms of complex variable theory. The key idea here is COMPACT structures of reasonable lifetimes.
The numerical people had been experimenting with "Patch Distributions" of vorticity (curl V) combined with vortex line "1-D singularities" or strings. The key result is they got numeric results that seemed to mimic compact vortex structures (like hurricanes). Now Crowdy comes along and finds exact families of analytic solutions. Neat.
*
That evening I woke up with the idea of how to generalize Crowdy's ideas beyond 2 dimensions, and express the ideas in terms of exterior differential forms. The technique combines "2-D singularities" or branes with patches of charge-current densities to form COMPACT charge structures. The combination of the singularities and the patches can be used to define a deformable boundary of a COMPACT topological cohererent structure (blobs) -- the higher dimensional analogue of the COMPACT vortex topologically coherent structures in fluids. This of course does not require metric.
*
I immediately thought of Ken's experiments.
*
You might find interest in
http://www22.pair.com/csdc/download/kiehneuromech448.pdf
and
http://www.cartan.pair.com/ebooks.htm
regards,
RMK
More corrections. Puthoff's argument is still not correct. It's easy to
make a mistake of a - sign. Appealing to text books is not good enough.
They may all be wrong about these ZPE calculations because the rules of
QED conflict with the rules of GR and one cannot really use tricks like
normal ordering of the photon creation and destruction operators.
Milonni's book, for example, completely ignores GR. The discovery of
dark energy shows one cannot ignore GR even at small scales.
On waking next morning at 5AM I realized we better take another look.
Given the asymmetric boundary conditions of parallel plates, we need to
be careful about how to do the integration in momentum space. We cannot
use spherical coordinates in momentum space. We must use Cartesian
rectangular coordinates, i.e. for the spectral density
dpxdpydpz not 4pip^2dp
Let the parallel plates be separated by x along the x-axis.
Between the plates, the limits are from px(min) = h/2x to px(max) = h/a.
However, in the plane of the plates the limits are from 0 to p(max) =
h/a.
How do we do the virtual photon ZPE integral?
That integral must split into longitudinal and transverse parts.
The longitudinal FREE VIRTUAL PHOTON ZPE integral BETWEEN THE PLATES is
ZPE(x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)xYZ/h^3
= (1/2)c[(h/a)^2 - (h/x)^2](h/a)^2xYZ/h^3
= (1/2)(h/a)^2(h/a)^2xYZ/h^3 - (1/2)c(h/x)^2(h/a)^2xYZ/h^3
= (1/2)(hc/a)(xYZ/a^3) - (1/2)(hc/x)(YZ/a^2)
The ZPF force from this term is
-(d/dx)ZPE(x) = -(1/2)(hc/a^2)(YZ/a^2) - (1/2)(hc/x^2)(YZ/a^2)
= -(1/2)(hc/a^4)YZ - (1/2)(hc/x^2)(YZ/a^2)
The longitudinal FREE VIRTUAL PHOTON ZPE integral OUTSIDE THE PLATES is
ZPE(X-x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)(X-x)YZ/h^3
= (1/2)c[(h/a)^2 - (h/(X-x))^2](h/a)^2(X-x)xYZ/h^3
= (1/2)(hc/a)((X-x)YZ/a^3) - (1/2)(hc/(X-x))(YZ/a^2)
The ZPF force from this term is from -(d/dx)ZPE(X-x) =
+(1/2)(hc/a^2)(YZ/a^2) + (hc/2)(YZ/a^2)(d/dx)(1/(X-x))
(d/dx)(1/(X-x)) = +(X - x)^-2
Next look at the transverse free virtual photon integral ZPE(xYZ).
ZPE(xYZ) = (c/2)xYZ[(px(max) - px(min)](Integral of 2pip^2dp from 0 to
p(max))/h^3
= (hc/2)[(1/a) - (1/x)]xYZ(Integral of 2pip^2dp from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/x)]xYZ(2pi/3)(1/a)^3
This term gives a net attractive force along x of -(hc/2a^4)YZ.
ZPE((X-x)YZ) = (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(Integral of 2pip^2dp
from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(2pi/3)(1/a)^3
This term gives a net repulsive force along x of +(hc/2a^4)YZ.
Therefore, as expected, we need only look at the longitudinal integral
for these non-spherically symmetric parallel plate boundary conditions.
Area of plates A = YZ.
Thus the NET ZPF force along x at the plate located at x is
-(1/2)(hc/a^4)A - (1/2)(hc/x^2)(A/a^2) +(1/2)(hc/a^2)(A/a^2) +
(hc/2)(A/a^2)(d/dx)(1/(X-x))
- (1/2)(hc/x^2)(A/a^2) + (hc/2)(A/a^2)(1/(X-x)^2)
Assume x << X. As X --> infinity we can ignore the second term from
outside the plates.
This is a net attractive force ~ -1/x^2 not - 1/x^4, but it is too weak
to contain unbalanced charges in the EVO.
The observed Casimir VdW force is ~ A/d^4 ~ 0.016/d^4 dynes per square cm. Do a Google search.
I have calculated the FREE VIRTUAL PHOTON ZPF attractive force in this same situation to be
- (1/2)(hc/d^2)(A/a^2)
A is area of the plates and a is the short-wave cutoff.
Therefore, unless Hal & Co can point out a specific error in the precise detailed phase space calculation below, all the articles and text books that attribute the Casimir force to a pressure differential of purely free virtual photons between the inside and the outside of the plates are simply wrong.
In fact the free virtual photon ZPF force must be exactly ZERO in the non-exotic vacuum limit where the real formula is
ZPF Free Virtual Photon Force (parallel plates) = - (1/2)(hc/d^2)(A/a^2)[1 - a^3|Vacuum Coherence|^2] = 0
=/= Casimir VdW Force ~ 0.016/d^4 dynes per square cm
The precise calculation of the ZPF Free Virtual Photon Force is short-wave cutoff dependent from simple phase space calculations. The error Milonni and other Pundits make in their text books is to do the phase space integrations incorrectly to get the spurious result ~ 1/d^4 for the virtual photons. That is they use the spherically symmetric phase space integral in an inappropriate situation that does not match the non-spherically symmetric boundary conditions!
On Sep 18, 2004, at 6:50 AM, Jack Sarfatti wrote:
On Sep 18, 2004, at 2:57 AM, RKiehn2352@aol.com wrote:
Dear Jack
I find it miraculous that you admit to a mistake (re ZPF). (grin)
Milonni and Hal Puthoff appear to have made even bigger ones!
My today's correction to my yesterday's correction now agrees in form, i.e. -x^-2 attraction (mod dimensionless coefficient that one must use QED with j.A to get) with A. Zee's calculation in "Quantum Field Theory in a Nutshell" and as I recall disagrees with Milonni's in "The Quantum Vacuum". I have former book with me but not the latter here in Southern California. See below
*
There may be another way to interpret Ken Shoulders EVO's.
**
Ken put together a meeting (financed by Church's Fried Chicken) a long time ago in the SAF bay area. Attendants: Shoulders, Aharonov, Puthoff, Kiehn.
*
Since then,I have always been interested in Ken's experiments.
**
Last week I attended euromech448 conference on Vortex Dynamics and Field interactions.
Crowdy from Imperial college gave an interesting talk on exact COMPACT vortex solutions to the Euler equations in terms of complex variable theory. The key idea here is COMPACT structures of reasonable lifetimes.
The numerical people had been experimenting with "Patch Distributions" of vorticity (curl V) combined with vortex line "1-D singularities" or strings. The key result is they got numeric results that seemed to mimic compact vortex structures (like hurricanes). Now Crowdy comes along and finds exact families of analytic solutions. Neat.
*
That evening I woke up with the idea of how to generalize Crowdy's ideas beyond 2 dimensions, and express the ideas in terms of exterior differential forms. The technique combines "2-D singularities" or branes with patches of charge-current densities to form COMPACT charge structures. The combination of the singularities and the patches can be used to define a deformable boundary of a COMPACT topological cohererent structure (blobs) -- the higher dimensional analogue of the COMPACT vortex topologically coherent structures in fluids. This of course does not require metric.
*
I immediately thought of Ken's experiments.
*
You might find interest in
http://www22.pair.com/csdc/download/kiehneuromech448.pdf
and
http://www.cartan.pair.com/ebooks.htm
regards,
RMK
More corrections. Puthoff's argument is still not correct. It's easy to
make a mistake of a - sign. Appealing to text books is not good enough.
They may all be wrong about these ZPE calculations because the rules of
QED conflict with the rules of GR and one cannot really use tricks like
normal ordering of the photon creation and destruction operators.
Milonni's book, for example, completely ignores GR. The discovery of
dark energy shows one cannot ignore GR even at small scales.
On waking next morning at 5AM I realized we better take another look.
Given the asymmetric boundary conditions of parallel plates, we need to
be careful about how to do the integration in momentum space. We cannot
use spherical coordinates in momentum space. We must use Cartesian
rectangular coordinates, i.e. for the spectral density
dpxdpydpz not 4pip^2dp
Let the parallel plates be separated by x along the x-axis.
Between the plates, the limits are from px(min) = h/2x to px(max) = h/a.
However, in the plane of the plates the limits are from 0 to p(max) =
h/a.
How do we do the virtual photon ZPE integral?
That integral must split into longitudinal and transverse parts.
The longitudinal FREE VIRTUAL PHOTON ZPE integral BETWEEN THE PLATES is
ZPE(x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)xYZ/h^3
= (1/2)c[(h/a)^2 - (h/x)^2](h/a)^2xYZ/h^3
= (1/2)(h/a)^2(h/a)^2xYZ/h^3 - (1/2)c(h/x)^2(h/a)^2xYZ/h^3
= (1/2)(hc/a)(xYZ/a^3) - (1/2)(hc/x)(YZ/a^2)
The ZPF force from this term is
-(d/dx)ZPE(x) = -(1/2)(hc/a^2)(YZ/a^2) - (1/2)(hc/x^2)(YZ/a^2)
= -(1/2)(hc/a^4)YZ - (1/2)(hc/x^2)(YZ/a^2)
The longitudinal FREE VIRTUAL PHOTON ZPE integral OUTSIDE THE PLATES is
ZPE(X-x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)(X-x)YZ/h^3
= (1/2)c[(h/a)^2 - (h/(X-x))^2](h/a)^2(X-x)xYZ/h^3
= (1/2)(hc/a)((X-x)YZ/a^3) - (1/2)(hc/(X-x))(YZ/a^2)
The ZPF force from this term is from -(d/dx)ZPE(X-x) =
+(1/2)(hc/a^2)(YZ/a^2) + (hc/2)(YZ/a^2)(d/dx)(1/(X-x))
(d/dx)(1/(X-x)) = +(X - x)^-2
Next look at the transverse free virtual photon integral ZPE(xYZ).
ZPE(xYZ) = (c/2)xYZ[(px(max) - px(min)](Integral of 2pip^2dp from 0 to
p(max))/h^3
= (hc/2)[(1/a) - (1/x)]xYZ(Integral of 2pip^2dp from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/x)]xYZ(2pi/3)(1/a)^3
This term gives a net attractive force along x of -(hc/2a^4)YZ.
ZPE((X-x)YZ) = (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(Integral of 2pip^2dp
from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(2pi/3)(1/a)^3
This term gives a net repulsive force along x of +(hc/2a^4)YZ.
Therefore, as expected, we need only look at the longitudinal integral
for these non-spherically symmetric parallel plate boundary conditions.
Area of plates A = YZ.
Thus the NET ZPF force along x at the plate located at x is
-(1/2)(hc/a^4)A - (1/2)(hc/x^2)(A/a^2) +(1/2)(hc/a^2)(A/a^2) +
(hc/2)(A/a^2)(d/dx)(1/(X-x))
- (1/2)(hc/x^2)(A/a^2) + (hc/2)(A/a^2)(1/(X-x)^2)
Assume x << X. As X --> infinity we can ignore the second term from
outside the plates.
This is a net attractive force ~ -1/x^2 not - 1/x^4, but it is too weak
to contain unbalanced charges in the EVO.
More corrections. Puthoff's argument is still not correct. It's easy to make a mistake of a - sign. Appealing to text books is not good enough. They may all be wrong about these ZPE calculations because the rules of QED conflict with the rules of GR and one cannot really use tricks like normal ordering of the photon creation and destruction operators. Milonni's book, for example, completely ignores GR. The discovery of dark energy shows one cannot ignore GR even at small scales.
On waking next morning at 5AM I realized we better take another look.
Given the asymmetric boundary conditions of parallel plates, we need to be careful about how to do the integration in momentum space. We cannot use spherical coordinates in momentum space. We must use Cartesian rectangular coordinates, i.e. for the spectral density
dpxdpydpz not 4pip^2dp
Let the parallel plates be separated by x along the x-axis.
Between the plates, the limits are from px(min) = h/2x to px(max) = h/a.
However, in the plane of the plates the limits are from 0 to p(max) = h/a.
How do we do the virtual photon ZPE integral?
That integral must split into longitudinal and transverse parts.
The longitudinal FREE VIRTUAL PHOTON ZPE integral BETWEEN THE PLATES is
ZPE(x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)xYZ/h^3
= (1/2)c[(h/a)^2 - (h/x)^2](h/a)^2xYZ/h^3
= (1/2)(h/a)^2(h/a)^2xYZ/h^3 - (1/2)c(h/x)^2(h/a)^2xYZ/h^3
= (1/2)(hc/a)(xYZ/a^3) - (1/2)(hc/x)(YZ/a^2)
The ZPF force from this term is
-(d/dx)ZPE(x) = -(1/2)(hc/a^2)(YZ/a^2) - (1/2)(hc/x^2)(YZ/a^2)
= -(1/2)(hc/a^4)YZ - (1/2)(hc/x^2)(YZ/a^2)
The longitudinal FREE VIRTUAL PHOTON ZPE integral OUTSIDE THE PLATES is
ZPE(X-x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)(X-x)YZ/h^3
= (1/2)c[(h/a)^2 - (h/(X-x))^2](h/a)^2(X-x)xYZ/h^3
= (1/2)(hc/a)((X-x)YZ/a^3) - (1/2)(hc/(X-x))(YZ/a^2)
The ZPF force from this term is from -(d/dx)ZPE(X-x) =
+(1/2)(hc/a^2)(YZ/a^2) + (hc/2)(YZ/a^2)(d/dx)(1/(X-x))
(d/dx)(1/(X-x)) = +(X - x)^-2
Next look at the transverse free virtual photon integral ZPE(xYZ).
ZPE(xYZ) = (c/2)xYZ[(px(max) - px(min)](Integral of 2pip^2dp from 0 to p(max))/h^3
= (hc/2)[(1/a) - (1/x)]xYZ(Integral of 2pip^2dp from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/x)]xYZ(2pi/3)(1/a)^3
This term gives a net attractive force along x of -(hc/2a^4)YZ.
ZPE((X-x)YZ) = (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(Integral of 2pip^2dp from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(2pi/3)(1/a)^3
This term gives a net repulsive force along x of +(hc/2a^4)YZ.
Therefore, as expected, we need only look at the longitudinal integral for these non-spherically symmetric parallel plate boundary conditions.
Area of plates A = YZ.
Thus the NET ZPF force along x at the plate located at x is
-(1/2)(hc/a^4)A - (1/2)(hc/x^2)(A/a^2) +(1/2)(hc/a^2)(A/a^2) + (hc/2)(A/a^2)(d/dx)(1/(X-x))
- (1/2)(hc/x^2)(A/a^2) + (hc/2)(A/a^2)(1/(X-x)^2)
Assume x << X. As X --> infinity we can ignore the second term from outside the plates.
This is a net attractive force ~ -1/x^2 not - 1/x^4, but it is too weak to contain unbalanced charges in the EVO.
Therefore, this calculation corrects the wrong calculation below.
On Sep 17, 2004, at 6:18 AM, Jack Sarfatti wrote:
On waking this morning, I realized that I ignored the lower infrared limit pmin in the calculations below integrating from 0 to pmax. The boundary conditions determine the nature of this term. For parallel plates perpendicular to x reaching to the end of the BIG BOX we need to integrate from pmin = h/2x to pmax = h/a for the little box.
This gives the additional total ZPE term in 3D case for the small box
-(pi/32)(hc/x)(V/x^3) = -(pi/32)(hc/x^3)yz
for the little box.
Similarly for the BIG BOX pmin = h/2(X - x)
-(pi/32)(hc/(X - x))(V/(X - x)^3) = -(pi/32)(hc/(X - x))((X - x)(Y - Y)(Z - Z)/(X - x)^3) = 0
So this asymmetric boundary condition does give a net ZPF force ~ - 1/x^4.
This is wrong.
Spherical shells will give a different answer.
*Therefore, I retract my previous remark that there is no net free virtual photon ZPF force under any conditions.
Corrected 3rd draft below.
On Sep 16, 2004, at 6:24 PM, Jack Sarfatti wrote:
Review of standard phase space calculations of zero point energy.
Spectral density in 3D space is from a spherical shell in momentum space.
4pip^2dp/h^3 = 3D Spectral Density
Where for the zero point virtual photon the energy is pc/2.
Therefore, integrate from p = 0 to p(max) to get
Total virtual photon zero point energy is in volume V
ZPE(3D) = Integral of (pc/2)4pip^2dp/h^3V = (4pic/8)p^4(max)V/h^3 = (pi/2)(hc/a)(V/a^3)
where p(max) = h/a
a = short-wave cutoff
This assumes Euclidean geometry continuum in 3D momentum space with basically ignoring oddly shaped cavities.
Same kind of calculation in 2D with an annulus in 2D momentum space gives (ignoring factors of 2, pi etc)
2pipdp/h^2 = 2D Spectral Density
ZPE(2D) ~ (hc/a)(A/a^2)
And in 1D along a line
dp/h = 1D Spectral Density
ZPE(1D) ~ (hc/a)(L/a)
In 1D one can do an exact calculation using finite series Sum of n from 1 to N = (1/2)N(N+1), but when L/a >> 1 you get essentially the same result as using the continuum integration.
Next go back to 3D with ZERO VACUUM COHERENCE.
3D Pressure = -d(Internal Energy)/dV
In this case
3D ZPF Pressure = -(pi/2)(hc/a^4) Independent of V! Also the pressure is negative!
w = Pressure/(Energy Density) = -1 not Hal Puthoff's "w = + 1/3" which is true only for real photons not virtual ZPF photons.
If you have a little box of volume v = xyz inside a large BOX of volume V = XYZ, then the total ZPE inside the little box is in 3D
ZPE(v) ~ (hc/a^4)v
The total ZPE inside the BIG outer BOX is
ZPE(V - v) ~ (hc/a^4)(V - v)
Note the LINEAR additive rule
ZPE(v) + ZPE(V - v) = ZPE(V)
Similarly in 2D for ZPE(A) and in 1D for ZPE(L).
Back to 3D what is the total ZPF force perpendicular to the wall x of the little box?
It is obviously
Fx(ZPF) = -dZPE(v)/dx - dZPE(V - v)/dx = -yz(hc/a^4)(1 - 1) = 0
Similarly in 2D and 1D. The number of effective space dimensions in conditions of different symmetries on the boundary conditionns makes no essential difference to this general conclusion.
Typo-corrected 2nd Draft
On Sep 16, 2004, at 7:26 AM, Jack Sarfatti wrote:
My previous calculations below for the free photon field without any j.A coupling to electric charges assumes zero vacuum coherence. Putting in the virtual electron-positron pairs is equivalent to one virtual quantum of negative energy per transverse polarized mode. This is because of the Pauli exclusion principle's anti-commutation rules for the Dirac electron field. The electron has spin 1/2, the photon spin 1, neglecting supersymmetry is OK since there is no evidence for it at all, therefore, the longitudinally polarized virtual photon mode is not compensated for by the virtual electron-positron pairs.
In general with the macro-quantum vacuum coherence, the net virtual photon + virtual electron positron, zero point energy density is positive ~ (hc/2a^4)(1 - a^3|Vacuum Coherence|^2), which is adjusted to ZERO in the non-exotic vacuum without any dark energy and any dark matter. The latter two are simply exotic vacuum phases where
a^3|Vacuum Coherence|^2 < 1
a^3|Vacuum Coherence|^2 > 1
respectively.
Ken Shoulders EVOs are stabilized by DARK ENERGY core that holds the unbalanced charge -Ne together via
V(r) = +(Ne)^2/mr + c^2/\zpfr^2
Note that the gradients of these two terms are of opposite sign allowing dynamical stability. This also explains the stability of a single spatially-extended electron as a Bohm hidden variable possibly allowing Vigier's tight atomic states as a new form of atomic energy investigated by Maric and Dragic in Beograd. We need to add the rotation term of course.
Where
/\zpf = (8piG*/c^4)(ZPE Density) > 0
[/\zpf] = 1/Area, i.e. curvature
[8piG*/c^4] = [String Tension]^-1 = [Energy/Length]^-1 = Length/Energy
[ZPE Density] = Energy/Volume
G* is the effective gravity constant at the small scale ~ 10^-5 - 10^-3 cm of the EVO, which may, or may not be, Newton's G. That is an empirical question.
Furthermore
N(h/mc)^2 = (Space-Warp Factor)4pi(Observed EVO Radius)^2
Where Space-Warp Factor << 1, i.e. non-Euclidean 3D space geometry for the mesoscopic EVO is my prediction.
On Sep 16, 2004, at 3:31 AM, Jack Sarfatti wrote:
In 3D case for a little box of volume xyz inside a big box of VOLUME XYX
The total free virtual photon ZPE in the little box is, with short-wave cutoff a:
~ (hc/2a)(xyx/a^3)
The total free virtual photon ZPE in the BIG BOX outside the little box is
~ (hc/2a)((X-x)(Y-y)(X-x)/a^3)
Note that in both cases the total 3D free virtual photon positive ZPE density is the same, i.e. ~ hc/2a^4, on both inside and outside of the little box inside the BIG BOX and is - the NEGATIIVE pressure, i.e. w = -1 not Puthoff's wrong value w = +1/3 that he uses in his most recent paper about Ken Shoulders EVO data.
On Sep 15, 2004, at 7:09 PM, Jack Sarfatti wrote:
typo-corrected 2nd draft
If you posit that momentum space is a CONTINUUM metric space and assume FLAT Euclidean geometry with the Pythagorean theorem, then
1. Virtual photon ZPE on a 1D line of length L with short wave cutoff "a", L >> a, with standing wave modes ~ (L)^-1/2sin(kx)
Total ZPE per polarization ~ pi(hc/4a)(L/a) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
1D ZPE PRESSURE = STRING TENSION = -(d/dL)(Total ZPE) = pi(hc/4a^2) = constant = -ZPE LINE DENSITY, i.e. w = -1
2. Virtual photon ZPE on a 2D lattice of area A with short wave cutoff "a", A >> a^2, with standing wave modes ~(L)^-1sin(kx)sin(k'y)
Total ZPE per polarization ~ pi(hc/4a)(A/a^2) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
2D ZPE PRESSURE = Membrane Tension = -(d/dA)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE Membrane DENSITY, i.e. w = -1
3. Virtual photon ZPE on a 3D volume V with short wave cutoff "a", V >> a^3, with standing wave modes ~ (L)^-3/2sin(kx)sin(k'y)sin(k"z)
Total ZPE per polarization ~ pi(hc/4a)(V/a^3) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
3D ZPE PRESSURE = -(d/dV)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE DENSITY, i.e. w = -1
In all three cases, no contribution of virtual photons to any vacuum pressure difference that can be attributed to a VdW "Casimir force".
The effect of EFFECTIVE dimension is in how the "pressure" scales with short-wave cutoff. One could also imagine FRACTALS with a non-integer power of the short-wave cutoff.
On waking next morning at 5AM I realized we better take another look.
Given the asymmetric boundary conditions of parallel plates, we need to be careful about how to do the integration in momentum space. We cannot use spherical coordinates in momentum space. We must use Cartesian rectangular coordinates, i.e. for the spectral density
dpxdpydpz not 4pip^2dp
Let the parallel plates be separated by x along the x-axis.
Between the plates, the limits are from px(min) = h/2x to px(max) = h/a.
However, in the plane of the plates the limits are from 0 to p(max) = h/a.
How do we do the virtual photon ZPE integral?
That integral must split into longitudinal and transverse parts.
The longitudinal FREE VIRTUAL PHOTON ZPE integral BETWEEN THE PLATES is
ZPE(x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)xYZ/h^3
= (1/2)c[(h/a)^2 - (h/x)^2](h/a)^2xYZ/h^3
= (1/2)(h/a)^2(h/a)^2xYZ/h^3 - (1/2)c(h/x)^2(h/a)^2xYZ/h^3
= (1/2)(hc/a)(xYZ/a^3) - (1/2)(hc/x)(YZ/a^2)
The ZPF force from this term is
-(d/dx)ZPE(x) = -(1/2)(hc/a^2)(YZ/a^2) - (1/2)(hc/x^2)(YZ/a^2)
= -(1/2)(hc/a^4)YZ - (1/2)(hc/x^2)(YZ/a^2)
The longitudinal FREE VIRTUAL PHOTON ZPE integral OUTSIDE THE PLATES is
ZPE(X-x) = (1/2)c[px(max)^2 - px(min)^2]py(max)pz(max)(X-x)YZ/h^3
= (1/2)c[(h/a)^2 - (h/(X-x))^2](h/a)^2(X-x)xYZ/h^3
= (1/2)(hc/a)((X-x)YZ/a^3) - (1/2)(hc/(X-x))(YZ/a^2)
The ZPF force from this term is from -(d/dx)ZPE(X-x) =
+(1/2)(hc/a^2)(YZ/a^2) + (hc/2)(YZ/a^2)(d/dx)(1/(X-x))
(d/dx)(1/(X-x)) = +(X - x)^-2
Next look at the transverse free virtual photon integral ZPE(xYZ).
ZPE(xYZ) = (c/2)xYZ[(px(max) - px(min)](Integral of 2pip^2dp from 0 to p(max))/h^3
= (hc/2)[(1/a) - (1/x)]xYZ(Integral of 2pip^2dp from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/x)]xYZ(2pi/3)(1/a)^3
This term gives a net attractive force along x of -(hc/2a^4)YZ.
ZPE((X-x)YZ) = (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(Integral of 2pip^2dp from 0 to p(max))/h^2
= (hc/2)[(1/a) - (1/(X-x))](X-x)YZ(2pi/3)(1/a)^3
This term gives a net repulsive force along x of +(hc/2a^4)YZ.
Therefore, as expected, we need only look at the longitudinal integral for these non-spherically symmetric parallel plate boundary conditions.
Area of plates A = YZ.
Thus the NET ZPF force along x at the plate located at x is
-(1/2)(hc/a^4)A - (1/2)(hc/x^2)(A/a^2) +(1/2)(hc/a^2)(A/a^2) + (hc/2)(A/a^2)(d/dx)(1/(X-x))
- (1/2)(hc/x^2)(A/a^2) + (hc/2)(A/a^2)(1/(X-x)^2)
Assume x << X. As X --> infinity we can ignore the second term from outside the plates.
This is a net attractive force ~ -1/x^2 not - 1/x^4, but it is too weak to contain unbalanced charges in the EVO.
Therefore, this calculation corrects the wrong calculation below.
On Sep 17, 2004, at 6:18 AM, Jack Sarfatti wrote:
On waking this morning, I realized that I ignored the lower infrared limit pmin in the calculations below integrating from 0 to pmax. The boundary conditions determine the nature of this term. For parallel plates perpendicular to x reaching to the end of the BIG BOX we need to integrate from pmin = h/2x to pmax = h/a for the little box.
This gives the additional total ZPE term in 3D case for the small box
-(pi/32)(hc/x)(V/x^3) = -(pi/32)(hc/x^3)yz
for the little box.
Similarly for the BIG BOX pmin = h/2(X - x)
-(pi/32)(hc/(X - x))(V/(X - x)^3) = -(pi/32)(hc/(X - x))((X - x)(Y - Y)(Z - Z)/(X - x)^3) = 0
So this asymmetric boundary condition does give a net ZPF force ~ - 1/x^4.
This is wrong.
Spherical shells will give a different answer.
*Therefore, I retract my previous remark that there is no net free virtual photon ZPF force under any conditions.
Corrected 3rd draft below.
On Sep 16, 2004, at 6:24 PM, Jack Sarfatti wrote:
Review of standard phase space calculations of zero point energy.
Spectral density in 3D space is from a spherical shell in momentum space.
4pip^2dp/h^3 = 3D Spectral Density
Where for the zero point virtual photon the energy is pc/2.
Therefore, integrate from p = 0 to p(max) to get
Total virtual photon zero point energy is in volume V
ZPE(3D) = Integral of (pc/2)4pip^2dp/h^3V = (4pic/8)p^4(max)V/h^3 = (pi/2)(hc/a)(V/a^3)
where p(max) = h/a
a = short-wave cutoff
This assumes Euclidean geometry continuum in 3D momentum space with basically ignoring oddly shaped cavities.
Same kind of calculation in 2D with an annulus in 2D momentum space gives (ignoring factors of 2, pi etc)
2pipdp/h^2 = 2D Spectral Density
ZPE(2D) ~ (hc/a)(A/a^2)
And in 1D along a line
dp/h = 1D Spectral Density
ZPE(1D) ~ (hc/a)(L/a)
In 1D one can do an exact calculation using finite series Sum of n from 1 to N = (1/2)N(N+1), but when L/a >> 1 you get essentially the same result as using the continuum integration.
Next go back to 3D with ZERO VACUUM COHERENCE.
3D Pressure = -d(Internal Energy)/dV
In this case
3D ZPF Pressure = -(pi/2)(hc/a^4) Independent of V! Also the pressure is negative!
w = Pressure/(Energy Density) = -1 not Hal Puthoff's "w = + 1/3" which is true only for real photons not virtual ZPF photons.
If you have a little box of volume v = xyz inside a large BOX of volume V = XYZ, then the total ZPE inside the little box is in 3D
ZPE(v) ~ (hc/a^4)v
The total ZPE inside the BIG outer BOX is
ZPE(V - v) ~ (hc/a^4)(V - v)
Note the LINEAR additive rule
ZPE(v) + ZPE(V - v) = ZPE(V)
Similarly in 2D for ZPE(A) and in 1D for ZPE(L).
Back to 3D what is the total ZPF force perpendicular to the wall x of the little box?
It is obviously
Fx(ZPF) = -dZPE(v)/dx - dZPE(V - v)/dx = -yz(hc/a^4)(1 - 1) = 0
Similarly in 2D and 1D. The number of effective space dimensions in conditions of different symmetries on the boundary conditionns makes no essential difference to this general conclusion.
Typo-corrected 2nd Draft
On Sep 16, 2004, at 7:26 AM, Jack Sarfatti wrote:
My previous calculations below for the free photon field without any j.A coupling to electric charges assumes zero vacuum coherence. Putting in the virtual electron-positron pairs is equivalent to one virtual quantum of negative energy per transverse polarized mode. This is because of the Pauli exclusion principle's anti-commutation rules for the Dirac electron field. The electron has spin 1/2, the photon spin 1, neglecting supersymmetry is OK since there is no evidence for it at all, therefore, the longitudinally polarized virtual photon mode is not compensated for by the virtual electron-positron pairs.
In general with the macro-quantum vacuum coherence, the net virtual photon + virtual electron positron, zero point energy density is positive ~ (hc/2a^4)(1 - a^3|Vacuum Coherence|^2), which is adjusted to ZERO in the non-exotic vacuum without any dark energy and any dark matter. The latter two are simply exotic vacuum phases where
a^3|Vacuum Coherence|^2 < 1
a^3|Vacuum Coherence|^2 > 1
respectively.
Ken Shoulders EVOs are stabilized by DARK ENERGY core that holds the unbalanced charge -Ne together via
V(r) = +(Ne)^2/mr + c^2/\zpfr^2
Note that the gradients of these two terms are of opposite sign allowing dynamical stability. This also explains the stability of a single spatially-extended electron as a Bohm hidden variable possibly allowing Vigier's tight atomic states as a new form of atomic energy investigated by Maric and Dragic in Beograd. We need to add the rotation term of course.
Where
/\zpf = (8piG*/c^4)(ZPE Density) > 0
[/\zpf] = 1/Area, i.e. curvature
[8piG*/c^4] = [String Tension]^-1 = [Energy/Length]^-1 = Length/Energy
[ZPE Density] = Energy/Volume
G* is the effective gravity constant at the small scale ~ 10^-5 - 10^-3 cm of the EVO, which may, or may not be, Newton's G. That is an empirical question.
Furthermore
N(h/mc)^2 = (Space-Warp Factor)4pi(Observed EVO Radius)^2
Where Space-Warp Factor << 1, i.e. non-Euclidean 3D space geometry for the mesoscopic EVO is my prediction.
On Sep 16, 2004, at 3:31 AM, Jack Sarfatti wrote:
In 3D case for a little box of volume xyz inside a big box of VOLUME XYX
The total free virtual photon ZPE in the little box is, with short-wave cutoff a:
~ (hc/2a)(xyx/a^3)
The total free virtual photon ZPE in the BIG BOX outside the little box is
~ (hc/2a)((X-x)(Y-y)(X-x)/a^3)
Note that in both cases the total 3D free virtual photon positive ZPE density is the same, i.e. ~ hc/2a^4, on both inside and outside of the little box inside the BIG BOX and is - the NEGATIIVE pressure, i.e. w = -1 not Puthoff's wrong value w = +1/3 that he uses in his most recent paper about Ken Shoulders EVO data.
On Sep 15, 2004, at 7:09 PM, Jack Sarfatti wrote:
typo-corrected 2nd draft
If you posit that momentum space is a CONTINUUM metric space and assume FLAT Euclidean geometry with the Pythagorean theorem, then
1. Virtual photon ZPE on a 1D line of length L with short wave cutoff "a", L >> a, with standing wave modes ~ (L)^-1/2sin(kx)
Total ZPE per polarization ~ pi(hc/4a)(L/a) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
1D ZPE PRESSURE = STRING TENSION = -(d/dL)(Total ZPE) = pi(hc/4a^2) = constant = -ZPE LINE DENSITY, i.e. w = -1
2. Virtual photon ZPE on a 2D lattice of area A with short wave cutoff "a", A >> a^2, with standing wave modes ~(L)^-1sin(kx)sin(k'y)
Total ZPE per polarization ~ pi(hc/4a)(A/a^2) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
2D ZPE PRESSURE = Membrane Tension = -(d/dA)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE Membrane DENSITY, i.e. w = -1
3. Virtual photon ZPE on a 3D volume V with short wave cutoff "a", V >> a^3, with standing wave modes ~ (L)^-3/2sin(kx)sin(k'y)sin(k"z)
Total ZPE per polarization ~ pi(hc/4a)(V/a^3) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
3D ZPE PRESSURE = -(d/dV)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE DENSITY, i.e. w = -1
In all three cases, no contribution of virtual photons to any vacuum pressure difference that can be attributed to a VdW "Casimir force".
The effect of EFFECTIVE dimension is in how the "pressure" scales with short-wave cutoff. One could also imagine FRACTALS with a non-integer power of the short-wave cutoff.
Friday, September 17, 2004
There is still a problem here on the SIGN of the ZPF force for parallel plates! It is repulsive NOT ATTRACTIVE!
Therefore Hal Puthoff is still wrong to explain the observed attractive Casimir force as simply due to free virtual photon pressure differences. You still need the j.A coupling to real charges inside the neutral plates to explain the Casimir force! Saying that the virtual photon energy between the plates is negative is a false argument!
On Sep 17, 2004, at 6:18 AM, Jack Sarfatti wrote:
On waking this morning, I realized that I ignored the lower infrared limit pmin in the calculations below integrating from 0 to pmax. The boundary conditions determine the nature of this term. For parallel plates perpendicular to x reaching to the end of the BIG BOX we need to integrate from pmin = h/2x to pmax = h/a for the little box.
This gives the additional total POSITIVE ZPE term in 3D case for the small box
~(pi/32)(hc/x)(V/x^3) = +(pi/32)(hc/x^3)yz
for the little box.
Similarly for the BIG BOX pmin = h/2(X - x)
-(pi/32)(hc/(X - x))(V/(X - x)^3) = -(pi/32)(hc/(X - x))((X - x)(Y - Y)(Z - Z)/(X - x)^3) = 0
You get ZERO because y = Y and z = Z in this case.
So this asymmetric boundary condition does give a net ZPF REPULSIVE force ~ +1/x^4.
Therefore Hal Puthoff is still wrong to explain the observed attractive Casimir force as simply due to free virtual photon pressure differences. You still need the j.A coupling to real charges inside the neutral plates to explain the Casimir force! Saying that the virtual photon energy between the plates is negative is a false argument!
On Sep 17, 2004, at 6:18 AM, Jack Sarfatti wrote:
On waking this morning, I realized that I ignored the lower infrared limit pmin in the calculations below integrating from 0 to pmax. The boundary conditions determine the nature of this term. For parallel plates perpendicular to x reaching to the end of the BIG BOX we need to integrate from pmin = h/2x to pmax = h/a for the little box.
This gives the additional total POSITIVE ZPE term in 3D case for the small box
~(pi/32)(hc/x)(V/x^3) = +(pi/32)(hc/x^3)yz
for the little box.
Similarly for the BIG BOX pmin = h/2(X - x)
-(pi/32)(hc/(X - x))(V/(X - x)^3) = -(pi/32)(hc/(X - x))((X - x)(Y - Y)(Z - Z)/(X - x)^3) = 0
You get ZERO because y = Y and z = Z in this case.
So this asymmetric boundary condition does give a net ZPF REPULSIVE force ~ +1/x^4.
My remarks about Hal Puthoff using wrong w = +1/3 factor in his EVO model still apply of course.
Let us look at the 3D spherical boundary case.
pmin = h/2r
where r is radius of the inner spherical conducting shell enclosed in a larger shell of radius R.
Therefore, there will be the infrared ZPE term ~ +(hc/r))(V/r)^3
But in this case V ~ r^3 so the net infrared ZPF boundary force term from the little sphere in this case is only ~ hc/r^2 and is repulsive. What about the big sphere?
pmin = h/2(R - r) giving outer ZPE term ~ [hc/(R - r)^4](R^3 - r^3)
However, when R -> infinity this term -> 0 as 1/R and can be ignored.
Note, that this problem is instructive because we now easily see how sensitive the net infrared ZPF force is to the precise nature of the mesoscopic boundary conditions!
Ken Shoulders EVO is to first approximation a spherical shell of N electrons. The free virtual ZPF force will be repulsive here and cannot stabilize it! This is distinct from the direct gravity warping induced by the same net ZPF pressure that requires a different set of equations from Einstein's GR - done elsewhere.
On Sep 17, 2004, at 6:18 AM, Jack Sarfatti wrote:
Further corrected.
On waking this morning, I realized that I ignored the lower infrared limit pmin in the calculations below integrating from 0 to pmax. The boundary conditions determine the nature of this term. For parallel plates perpendicular to x reaching to the end of the BIG BOX we need to integrate from pmin = h/2x to pmax = h/a for the little box.
This gives the additional total ZPE term in 3D case for the small box
-(pi/32)(hc/x)(V/x^3) = -(pi/32)(hc/x^3)yz
for the little box.
Similarly for the BIG BOX pmin = h/2(X - x)
-(pi/32)(hc/(X - x))(V/(X - x)^3) = -(pi/32)(hc/(X - x))((X - x)(Y - Y)(Z - Z)/(X - x)^3) = 0
So this asymmetric boundary condition does give a net ZPF force ~ - 1/x^4.
Spherical shells will give a different answer.
*Therefore, I retract my previous remark that there is no net free virtual photon ZPF force under any conditions.
Corrected 3rd draft below.
On Sep 16, 2004, at 6:24 PM, Jack Sarfatti wrote:
Review of standard phase space calculations of zero point energy.
Spectral density in 3D space is from a spherical shell in momentum space.
4pip^2dp/h^3 = 3D Spectral Density
Where for the zero point virtual photon the energy is pc/2.
Therefore, integrate from p = 0 to p(max) to get
Total virtual photon zero point energy is in volume V
ZPE(3D) = Integral of (pc/2)4pip^2dp/h^3V = (4pic/8)p^4(max)V/h^3 = (pi/2)(hc/a)(V/a^3)
where p(max) = h/a
a = short-wave cutoff
This assumes Euclidean geometry continuum in 3D momentum space with basically ignoring oddly shaped cavities.
Same kind of calculation in 2D with an annulus in 2D momentum space gives (ignoring factors of 2, pi etc)
2pipdp/h^2 = 2D Spectral Density
ZPE(2D) ~ (hc/a)(A/a^2)
And in 1D along a line
dp/h = 1D Spectral Density
ZPE(1D) ~ (hc/a)(L/a)
In 1D one can do an exact calculation using finite series Sum of n from 1 to N = (1/2)N(N+1), but when L/a >> 1 you get essentially the same result as using the continuum integration.
Next go back to 3D with ZERO VACUUM COHERENCE.
3D Pressure = -d(Internal Energy)/dV
In this case
3D ZPF Pressure = -(pi/2)(hc/a^4) Independent of V! Also the pressure is negative!
w = Pressure/(Energy Density) = -1 not Hal Puthoff's "w = + 1/3" which is true only for real photons not virtual ZPF photons.
If you have a little box of volume v = xyz inside a large BOX of volume V = XYZ, then the total ZPE inside the little box is in 3D
ZPE(v) ~ (hc/a^4)v
The total ZPE inside the BIG outer BOX is
ZPE(V - v) ~ (hc/a^4)(V - v)
Note the LINEAR additive rule
ZPE(v) + ZPE(V - v) = ZPE(V)
Similarly in 2D for ZPE(A) and in 1D for ZPE(L).
Back to 3D what is the total ZPF force perpendicular to the wall x of the little box?
It is obviously
Fx(ZPF) = -dZPE(v)/dx - dZPE(V - v)/dx = -yz(hc/a^4)(1 - 1) = 0
Similarly in 2D and 1D. The number of effective space dimensions in conditions of different symmetries on the boundary conditionns makes no essential difference to this general conclusion.
Typo-corrected 2nd Draft
On Sep 16, 2004, at 7:26 AM, Jack Sarfatti wrote:
My previous calculations below for the free photon field without any j.A coupling to electric charges assumes zero vacuum coherence. Putting in the virtual electron-positron pairs is equivalent to one virtual quantum of negative energy per transverse polarized mode. This is because of the Pauli exclusion principle's anti-commutation rules for the Dirac electron field. The electron has spin 1/2, the photon spin 1, neglecting supersymmetry is OK since there is no evidence for it at all, therefore, the longitudinally polarized virtual photon mode is not compensated for by the virtual electron-positron pairs.
In general with the macro-quantum vacuum coherence, the net virtual photon + virtual electron positron, zero point energy density is positive ~ (hc/2a^4)(1 - a^3|Vacuum Coherence|^2), which is adjusted to ZERO in the non-exotic vacuum without any dark energy and any dark matter. The latter two are simply exotic vacuum phases where
a^3|Vacuum Coherence|^2 < 1
a^3|Vacuum Coherence|^2 > 1
respectively.
Ken Shoulders EVOs are stabilized by DARK ENERGY core that holds the unbalanced charge -Ne together via
V(r) = +(Ne)^2/mr + c^2/\zpfr^2
Note that the gradients of these two terms are of opposite sign allowing dynamical stability. This also explains the stability of a single spatially-extended electron as a Bohm hidden variable possibly allowing Vigier's tight atomic states as a new form of atomic energy investigated by Maric and Dragic in Beograd. We need to add the rotation term of course.
Where
/\zpf = (8piG*/c^4)(ZPE Density) > 0
[/\zpf] = 1/Area, i.e. curvature
[8piG*/c^4] = [String Tension]^-1 = [Energy/Length]^-1 = Length/Energy
[ZPE Density] = Energy/Volume
G* is the effective gravity constant at the small scale ~ 10^-5 - 10^-3 cm of the EVO, which may, or may not be, Newton's G. That is an empirical question.
Furthermore
N(h/mc)^2 = (Space-Warp Factor)4pi(Observed EVO Radius)^2
Where Space-Warp Factor << 1, i.e. non-Euclidean 3D space geometry for the mesoscopic EVO is my prediction.
On Sep 16, 2004, at 3:31 AM, Jack Sarfatti wrote:
In 3D case for a little box of volume xyz inside a big box of VOLUME XYX
The total free virtual photon ZPE in the little box is, with short-wave cutoff a:
~ (hc/2a)(xyx/a^3)
The total free virtual photon ZPE in the BIG BOX outside the little box is
~ (hc/2a)((X-x)(Y-y)(X-x)/a^3)
Note that in both cases the total 3D free virtual photon positive ZPE density is the same, i.e. ~ hc/2a^4, on both inside and outside of the little box inside the BIG BOX and is - the NEGATIIVE pressure, i.e. w = -1 not Puthoff's wrong value w = +1/3 that he uses in his most recent paper about Ken Shoulders EVO data.
On Sep 15, 2004, at 7:09 PM, Jack Sarfatti wrote:
typo-corrected 2nd draft
If you posit that momentum space is a CONTINUUM metric space and assume FLAT Euclidean geometry with the Pythagorean theorem, then
1. Virtual photon ZPE on a 1D line of length L with short wave cutoff "a", L >> a, with standing wave modes ~ (L)^-1/2sin(kx)
Total ZPE per polarization ~ pi(hc/4a)(L/a) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
1D ZPE PRESSURE = STRING TENSION = -(d/dL)(Total ZPE) = pi(hc/4a^2) = constant = -ZPE LINE DENSITY, i.e. w = -1
2. Virtual photon ZPE on a 2D lattice of area A with short wave cutoff "a", A >> a^2, with standing wave modes ~(L)^-1sin(kx)sin(k'y)
Total ZPE per polarization ~ pi(hc/4a)(A/a^2) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
2D ZPE PRESSURE = Membrane Tension = -(d/dA)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE Membrane DENSITY, i.e. w = -1
3. Virtual photon ZPE on a 3D volume V with short wave cutoff "a", V >> a^3, with standing wave modes ~ (L)^-3/2sin(kx)sin(k'y)sin(k"z)
Total ZPE per polarization ~ pi(hc/4a)(V/a^3) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
3D ZPE PRESSURE = -(d/dV)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE DENSITY, i.e. w = -1
The effect of EFFECTIVE dimension is in how the "pressure" scales with short-wave cutoff. One could also imagine FRACTALS with a non-integer power of the short-wave cutoff.
Let us look at the 3D spherical boundary case.
pmin = h/2r
where r is radius of the inner spherical conducting shell enclosed in a larger shell of radius R.
Therefore, there will be the infrared ZPE term ~ +(hc/r))(V/r)^3
But in this case V ~ r^3 so the net infrared ZPF boundary force term from the little sphere in this case is only ~ hc/r^2 and is repulsive. What about the big sphere?
pmin = h/2(R - r) giving outer ZPE term ~ [hc/(R - r)^4](R^3 - r^3)
However, when R -> infinity this term -> 0 as 1/R and can be ignored.
Note, that this problem is instructive because we now easily see how sensitive the net infrared ZPF force is to the precise nature of the mesoscopic boundary conditions!
Ken Shoulders EVO is to first approximation a spherical shell of N electrons. The free virtual ZPF force will be repulsive here and cannot stabilize it! This is distinct from the direct gravity warping induced by the same net ZPF pressure that requires a different set of equations from Einstein's GR - done elsewhere.
On Sep 17, 2004, at 6:18 AM, Jack Sarfatti wrote:
Further corrected.
On waking this morning, I realized that I ignored the lower infrared limit pmin in the calculations below integrating from 0 to pmax. The boundary conditions determine the nature of this term. For parallel plates perpendicular to x reaching to the end of the BIG BOX we need to integrate from pmin = h/2x to pmax = h/a for the little box.
This gives the additional total ZPE term in 3D case for the small box
-(pi/32)(hc/x)(V/x^3) = -(pi/32)(hc/x^3)yz
for the little box.
Similarly for the BIG BOX pmin = h/2(X - x)
-(pi/32)(hc/(X - x))(V/(X - x)^3) = -(pi/32)(hc/(X - x))((X - x)(Y - Y)(Z - Z)/(X - x)^3) = 0
So this asymmetric boundary condition does give a net ZPF force ~ - 1/x^4.
Spherical shells will give a different answer.
*Therefore, I retract my previous remark that there is no net free virtual photon ZPF force under any conditions.
Corrected 3rd draft below.
On Sep 16, 2004, at 6:24 PM, Jack Sarfatti wrote:
Review of standard phase space calculations of zero point energy.
Spectral density in 3D space is from a spherical shell in momentum space.
4pip^2dp/h^3 = 3D Spectral Density
Where for the zero point virtual photon the energy is pc/2.
Therefore, integrate from p = 0 to p(max) to get
Total virtual photon zero point energy is in volume V
ZPE(3D) = Integral of (pc/2)4pip^2dp/h^3V = (4pic/8)p^4(max)V/h^3 = (pi/2)(hc/a)(V/a^3)
where p(max) = h/a
a = short-wave cutoff
This assumes Euclidean geometry continuum in 3D momentum space with basically ignoring oddly shaped cavities.
Same kind of calculation in 2D with an annulus in 2D momentum space gives (ignoring factors of 2, pi etc)
2pipdp/h^2 = 2D Spectral Density
ZPE(2D) ~ (hc/a)(A/a^2)
And in 1D along a line
dp/h = 1D Spectral Density
ZPE(1D) ~ (hc/a)(L/a)
In 1D one can do an exact calculation using finite series Sum of n from 1 to N = (1/2)N(N+1), but when L/a >> 1 you get essentially the same result as using the continuum integration.
Next go back to 3D with ZERO VACUUM COHERENCE.
3D Pressure = -d(Internal Energy)/dV
In this case
3D ZPF Pressure = -(pi/2)(hc/a^4) Independent of V! Also the pressure is negative!
w = Pressure/(Energy Density) = -1 not Hal Puthoff's "w = + 1/3" which is true only for real photons not virtual ZPF photons.
If you have a little box of volume v = xyz inside a large BOX of volume V = XYZ, then the total ZPE inside the little box is in 3D
ZPE(v) ~ (hc/a^4)v
The total ZPE inside the BIG outer BOX is
ZPE(V - v) ~ (hc/a^4)(V - v)
Note the LINEAR additive rule
ZPE(v) + ZPE(V - v) = ZPE(V)
Similarly in 2D for ZPE(A) and in 1D for ZPE(L).
Back to 3D what is the total ZPF force perpendicular to the wall x of the little box?
It is obviously
Fx(ZPF) = -dZPE(v)/dx - dZPE(V - v)/dx = -yz(hc/a^4)(1 - 1) = 0
Similarly in 2D and 1D. The number of effective space dimensions in conditions of different symmetries on the boundary conditionns makes no essential difference to this general conclusion.
Typo-corrected 2nd Draft
On Sep 16, 2004, at 7:26 AM, Jack Sarfatti wrote:
My previous calculations below for the free photon field without any j.A coupling to electric charges assumes zero vacuum coherence. Putting in the virtual electron-positron pairs is equivalent to one virtual quantum of negative energy per transverse polarized mode. This is because of the Pauli exclusion principle's anti-commutation rules for the Dirac electron field. The electron has spin 1/2, the photon spin 1, neglecting supersymmetry is OK since there is no evidence for it at all, therefore, the longitudinally polarized virtual photon mode is not compensated for by the virtual electron-positron pairs.
In general with the macro-quantum vacuum coherence, the net virtual photon + virtual electron positron, zero point energy density is positive ~ (hc/2a^4)(1 - a^3|Vacuum Coherence|^2), which is adjusted to ZERO in the non-exotic vacuum without any dark energy and any dark matter. The latter two are simply exotic vacuum phases where
a^3|Vacuum Coherence|^2 < 1
a^3|Vacuum Coherence|^2 > 1
respectively.
Ken Shoulders EVOs are stabilized by DARK ENERGY core that holds the unbalanced charge -Ne together via
V(r) = +(Ne)^2/mr + c^2/\zpfr^2
Note that the gradients of these two terms are of opposite sign allowing dynamical stability. This also explains the stability of a single spatially-extended electron as a Bohm hidden variable possibly allowing Vigier's tight atomic states as a new form of atomic energy investigated by Maric and Dragic in Beograd. We need to add the rotation term of course.
Where
/\zpf = (8piG*/c^4)(ZPE Density) > 0
[/\zpf] = 1/Area, i.e. curvature
[8piG*/c^4] = [String Tension]^-1 = [Energy/Length]^-1 = Length/Energy
[ZPE Density] = Energy/Volume
G* is the effective gravity constant at the small scale ~ 10^-5 - 10^-3 cm of the EVO, which may, or may not be, Newton's G. That is an empirical question.
Furthermore
N(h/mc)^2 = (Space-Warp Factor)4pi(Observed EVO Radius)^2
Where Space-Warp Factor << 1, i.e. non-Euclidean 3D space geometry for the mesoscopic EVO is my prediction.
On Sep 16, 2004, at 3:31 AM, Jack Sarfatti wrote:
In 3D case for a little box of volume xyz inside a big box of VOLUME XYX
The total free virtual photon ZPE in the little box is, with short-wave cutoff a:
~ (hc/2a)(xyx/a^3)
The total free virtual photon ZPE in the BIG BOX outside the little box is
~ (hc/2a)((X-x)(Y-y)(X-x)/a^3)
Note that in both cases the total 3D free virtual photon positive ZPE density is the same, i.e. ~ hc/2a^4, on both inside and outside of the little box inside the BIG BOX and is - the NEGATIIVE pressure, i.e. w = -1 not Puthoff's wrong value w = +1/3 that he uses in his most recent paper about Ken Shoulders EVO data.
On Sep 15, 2004, at 7:09 PM, Jack Sarfatti wrote:
typo-corrected 2nd draft
If you posit that momentum space is a CONTINUUM metric space and assume FLAT Euclidean geometry with the Pythagorean theorem, then
1. Virtual photon ZPE on a 1D line of length L with short wave cutoff "a", L >> a, with standing wave modes ~ (L)^-1/2sin(kx)
Total ZPE per polarization ~ pi(hc/4a)(L/a) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
1D ZPE PRESSURE = STRING TENSION = -(d/dL)(Total ZPE) = pi(hc/4a^2) = constant = -ZPE LINE DENSITY, i.e. w = -1
2. Virtual photon ZPE on a 2D lattice of area A with short wave cutoff "a", A >> a^2, with standing wave modes ~(L)^-1sin(kx)sin(k'y)
Total ZPE per polarization ~ pi(hc/4a)(A/a^2) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
2D ZPE PRESSURE = Membrane Tension = -(d/dA)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE Membrane DENSITY, i.e. w = -1
3. Virtual photon ZPE on a 3D volume V with short wave cutoff "a", V >> a^3, with standing wave modes ~ (L)^-3/2sin(kx)sin(k'y)sin(k"z)
Total ZPE per polarization ~ pi(hc/4a)(V/a^3) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
3D ZPE PRESSURE = -(d/dV)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE DENSITY, i.e. w = -1
The effect of EFFECTIVE dimension is in how the "pressure" scales with short-wave cutoff. One could also imagine FRACTALS with a non-integer power of the short-wave cutoff.
Thursday, September 16, 2004
Review of standard phase space calculations of zero point energy.
Spectral density in 3D space is from a spherical shell in momentum space.
4pip^2dp/h^3 = 3D Spectral Density
Where for the zero point virtual photon the energy is pc/2.
Therefore, integrate from p = 0 to p(max) to get
Total virtual photon zero point energy is in volume V
ZPE(3D) = Integral of (pc/2)4pip^2dp/h^3V = (4pic/8)p^4(max)V/h^3 = (pi/2)(hc/a)(V/a^3)
where p(max) = h/a
a = short-wave cutoff
This assumes Euclidean geometry continuum in 3D momentum space with basically ignoring oddly shaped cavities.
Same kind of calculation in 2D with an annulus in 2D momentum space gives (ignoring factors of 2, pi etc)
2pipdp/h^2 = 2D Spectral Density
ZPE(2D) ~ (hc/a)(A/a^2)
And in 1D along a line
dp/h = 1D Spectral Density
ZPE(1D) ~ (hc/a)(L/a)
In 1D one can do an exact calculation using finite series Sum of n from 1 to N = (1/2)N(N+1), but when L/a >> 1 you get essentially the same result as using the continuum integration.
Next go back to 3D with ZERO VACUUM COHERENCE.
3D Pressure = -d(Internal Energy)/dV
In this case
3D ZPF Pressure = -(pi/2)(hc/a^4) Independent of V! Also the pressure is negative!
w = Pressure/(Energy Density) = -1 not Hal Puthoff's "w = + 1/3" which is true only for real photons not virtual ZPF photons.
If you have a little box of volume v = xyz inside a large BOX of volume V = XYZ, then the total ZPE inside the little box is in 3D
ZPE(v) ~ (hc/a^4)v
The total ZPE inside the BIG outer BOX is
ZPE(V - v) ~ (hc/a^4)(V - v)
Note the LINEAR additive rule
ZPE(v) + ZPE(V - v) = ZPE(V)
Similarly in 2D for ZPE(A) and in 1D for ZPE(L).
Back to 3D what is the total ZPF force perpendicular to the wall x of the little box?
It is obviously
Fx(ZPF) = -dZPE(v)/dx - dZPE(V - v)/dx = -yz(hc/a^4)(1 - 1) = 0
That is, with ZERO VACUUM COHERENCE there is NEVER any NET purely FREE virtual photon force on any wall. Therefore, you can never explain the actual Casimir force as some kind of free virtual photon ZPF pressure differential on a pair of electrically UNCHARGED conducting parallel plates as Hal Puthoff, and others, have repeatedly done in popular physics articles. The Casimir force is a Van der Waals electrostatic force and in no way can ever tap the completely random free virtual ZPF photons neglecting the actual QED coupling j.A.
Similarly in 2D and 1D. The number of effective space dimensions in conditions of different symmetries on the boundary conditionns makes no essential difference to this general conclusion.
Spectral density in 3D space is from a spherical shell in momentum space.
4pip^2dp/h^3 = 3D Spectral Density
Where for the zero point virtual photon the energy is pc/2.
Therefore, integrate from p = 0 to p(max) to get
Total virtual photon zero point energy is in volume V
ZPE(3D) = Integral of (pc/2)4pip^2dp/h^3V = (4pic/8)p^4(max)V/h^3 = (pi/2)(hc/a)(V/a^3)
where p(max) = h/a
a = short-wave cutoff
This assumes Euclidean geometry continuum in 3D momentum space with basically ignoring oddly shaped cavities.
Same kind of calculation in 2D with an annulus in 2D momentum space gives (ignoring factors of 2, pi etc)
2pipdp/h^2 = 2D Spectral Density
ZPE(2D) ~ (hc/a)(A/a^2)
And in 1D along a line
dp/h = 1D Spectral Density
ZPE(1D) ~ (hc/a)(L/a)
In 1D one can do an exact calculation using finite series Sum of n from 1 to N = (1/2)N(N+1), but when L/a >> 1 you get essentially the same result as using the continuum integration.
Next go back to 3D with ZERO VACUUM COHERENCE.
3D Pressure = -d(Internal Energy)/dV
In this case
3D ZPF Pressure = -(pi/2)(hc/a^4) Independent of V! Also the pressure is negative!
w = Pressure/(Energy Density) = -1 not Hal Puthoff's "w = + 1/3" which is true only for real photons not virtual ZPF photons.
If you have a little box of volume v = xyz inside a large BOX of volume V = XYZ, then the total ZPE inside the little box is in 3D
ZPE(v) ~ (hc/a^4)v
The total ZPE inside the BIG outer BOX is
ZPE(V - v) ~ (hc/a^4)(V - v)
Note the LINEAR additive rule
ZPE(v) + ZPE(V - v) = ZPE(V)
Similarly in 2D for ZPE(A) and in 1D for ZPE(L).
Back to 3D what is the total ZPF force perpendicular to the wall x of the little box?
It is obviously
Fx(ZPF) = -dZPE(v)/dx - dZPE(V - v)/dx = -yz(hc/a^4)(1 - 1) = 0
That is, with ZERO VACUUM COHERENCE there is NEVER any NET purely FREE virtual photon force on any wall. Therefore, you can never explain the actual Casimir force as some kind of free virtual photon ZPF pressure differential on a pair of electrically UNCHARGED conducting parallel plates as Hal Puthoff, and others, have repeatedly done in popular physics articles. The Casimir force is a Van der Waals electrostatic force and in no way can ever tap the completely random free virtual ZPF photons neglecting the actual QED coupling j.A.
Similarly in 2D and 1D. The number of effective space dimensions in conditions of different symmetries on the boundary conditionns makes no essential difference to this general conclusion.
My previous calculations below for the free photon field without any j.A coupling to electric charges assumes zero vacuum coherence. Putting in the virtual electron-positron pairs is equivalent to one virtual quantum of negative energy per transverse polarized mode. This is because of the Pauli exclusion principle's anti-commutation rules for the Dirac electron field. The electron has spin 1/2, the photon spin 1, neglecting supersymmetry is OK since there is no evidence for it at all, therefore, the longitudinally polarized virtual photon mode is not compensated for by the virtual electron-positron pairs.
In general with the macro-quantum vacuum coherence, the net virtual photon + virtual electron positron, zero point energy density is positive ~ (hc/2a^4)(1 - a^3|Vacuum Coherence|^2), which is adjusted to ZERO in the non-exotic vacuum without any dark energy and any dark matter. The latter two are simply exotic vacuum phases where
a^3|Vacuum Coherence|^2 < 1
a^3|Vacuum Coherence|^2 > 1
respectively.
Ken Shoulders EVOs are stabilized by DARK ENERGY core that holds the unbalanced charge -Ne together via
V(r) = +(Ne)^2/mr + c^2/\zpfr^2
Note that the gradients of these two terms are of opposite sign allowing dynamical stability. This also explains the stability of a single spatially-extended electron as a Bohm hidden variable possibly allowing Vigier's tight atomic states as a new form of atomic energy investigated by Maric and Dragic in Beograd. We need to add the rotation term of course.
Where
/\zpf = (8piG*/c^4)(ZPE Density) > 0
G* is the effective gravity constant at the small scale ~ 10^-5 - 10^-3 cm of the EVO, which may, or may not be, Newton's G. That is an empirical question.
Furthermore
N(h/mc)^2 = (Space-Warp Factor)4pi(Observed EVO Radius)^2
Where Space-Warp Factor << 1, i.e. non-Euclidean 3D space geometry for the mesoscopic EVO is my prediction.
On Sep 16, 2004, at 3:31 AM, Jack Sarfatti wrote:
In 3D case for a little box of volume xyz inside a big box of VOLUME XYX
The total free virtual photon ZPE in the little box is, with short-wave cutoff a:
~ (hc/2a)(xyx/a^3)
The total free virtual photon ZPE in the BIG BOX outside the little box is
~ (hc/2a)((X-x)(Y-y)(X-x)/a^3)
Note that in both cases the total 3D free virtual photon positive ZPE density is the same, i.e. ~ hc/2a^4, on both inside and outside of the little box inside the BIG BOX and is - the NEGATIIVE pressure, i.e. w = -1 not Puthoff's wrong value w = +1/3 that he uses in his most recent paper about Ken Shoulders EVO data.
What is the total ZPF force at the walls of the little box?
It is obviously ZERO!
For example, the total ZPF force perpendicular to the wall x cancels from both sides.
Take -(d/dx) of total ZPE inside + outside wall x. The -x term outside the wall in BIG BOX cancels the x term inside the box when you take the gradient!
This works same in any number of dimensions, also if you use spherical shell method with Pythagorean theorem, same final answer, i.e. r^3 and R^3 - r^3 terms, the radial gradients also cancel.
On Sep 15, 2004, at 7:09 PM, Jack Sarfatti wrote:
typo-corrected 2nd draft
If you posit that momentum space is a CONTINUUM metric space and assume FLAT Euclidean geometry with the Pythagorean theorem, then
1. Virtual photon ZPE on a 1D line of length L with short wave cutoff "a", L >> a, with standing wave modes ~ (L)^-1/2sin(kx)
Total ZPE per polarization ~ pi(hc/4a)(L/a) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
1D ZPE PRESSURE = STRING TENSION = -(d/dL)(Total ZPE) = pi(hc/4a^2) = constant = -ZPE LINE DENSITY, i.e. w = -1
2. Virtual photon ZPE on a 2D lattice of area A with short wave cutoff "a", A >> a^2, with standing wave modes ~(L)^-1sin(kx)sin(k'y)
Total ZPE per polarization ~ pi(hc/4a)(A/a^2) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
2D ZPE PRESSURE = Membrane Tension = -(d/dA)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE Membrane DENSITY, i.e. w = -1
3. Virtual photon ZPE on a 3D volume V with short wave cutoff "a", V >> a^3, with standing wave modes ~ (L)^-3/2sin(kx)sin(k'y)sin(k"z)
Total ZPE per polarization ~ pi(hc/4a)(V/a^3) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
3D ZPE PRESSURE = -(d/dV)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE DENSITY, i.e. w = -1
In all three cases, no contribution of virtual photons to any vacuum pressure difference that can be attributed to a VdW "Casimir force".
The effect of EFFECTIVE dimension is in how the "pressure" scales with short-wave cutoff. One could also imagine FRACTALS with a non-integer power of the short-wave cutoff.
In general with the macro-quantum vacuum coherence, the net virtual photon + virtual electron positron, zero point energy density is positive ~ (hc/2a^4)(1 - a^3|Vacuum Coherence|^2), which is adjusted to ZERO in the non-exotic vacuum without any dark energy and any dark matter. The latter two are simply exotic vacuum phases where
a^3|Vacuum Coherence|^2 < 1
a^3|Vacuum Coherence|^2 > 1
respectively.
Ken Shoulders EVOs are stabilized by DARK ENERGY core that holds the unbalanced charge -Ne together via
V(r) = +(Ne)^2/mr + c^2/\zpfr^2
Note that the gradients of these two terms are of opposite sign allowing dynamical stability. This also explains the stability of a single spatially-extended electron as a Bohm hidden variable possibly allowing Vigier's tight atomic states as a new form of atomic energy investigated by Maric and Dragic in Beograd. We need to add the rotation term of course.
Where
/\zpf = (8piG*/c^4)(ZPE Density) > 0
G* is the effective gravity constant at the small scale ~ 10^-5 - 10^-3 cm of the EVO, which may, or may not be, Newton's G. That is an empirical question.
Furthermore
N(h/mc)^2 = (Space-Warp Factor)4pi(Observed EVO Radius)^2
Where Space-Warp Factor << 1, i.e. non-Euclidean 3D space geometry for the mesoscopic EVO is my prediction.
On Sep 16, 2004, at 3:31 AM, Jack Sarfatti wrote:
In 3D case for a little box of volume xyz inside a big box of VOLUME XYX
The total free virtual photon ZPE in the little box is, with short-wave cutoff a:
~ (hc/2a)(xyx/a^3)
The total free virtual photon ZPE in the BIG BOX outside the little box is
~ (hc/2a)((X-x)(Y-y)(X-x)/a^3)
Note that in both cases the total 3D free virtual photon positive ZPE density is the same, i.e. ~ hc/2a^4, on both inside and outside of the little box inside the BIG BOX and is - the NEGATIIVE pressure, i.e. w = -1 not Puthoff's wrong value w = +1/3 that he uses in his most recent paper about Ken Shoulders EVO data.
What is the total ZPF force at the walls of the little box?
It is obviously ZERO!
For example, the total ZPF force perpendicular to the wall x cancels from both sides.
Take -(d/dx) of total ZPE inside + outside wall x. The -x term outside the wall in BIG BOX cancels the x term inside the box when you take the gradient!
This works same in any number of dimensions, also if you use spherical shell method with Pythagorean theorem, same final answer, i.e. r^3 and R^3 - r^3 terms, the radial gradients also cancel.
On Sep 15, 2004, at 7:09 PM, Jack Sarfatti wrote:
typo-corrected 2nd draft
If you posit that momentum space is a CONTINUUM metric space and assume FLAT Euclidean geometry with the Pythagorean theorem, then
1. Virtual photon ZPE on a 1D line of length L with short wave cutoff "a", L >> a, with standing wave modes ~ (L)^-1/2sin(kx)
Total ZPE per polarization ~ pi(hc/4a)(L/a) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
1D ZPE PRESSURE = STRING TENSION = -(d/dL)(Total ZPE) = pi(hc/4a^2) = constant = -ZPE LINE DENSITY, i.e. w = -1
2. Virtual photon ZPE on a 2D lattice of area A with short wave cutoff "a", A >> a^2, with standing wave modes ~(L)^-1sin(kx)sin(k'y)
Total ZPE per polarization ~ pi(hc/4a)(A/a^2) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
2D ZPE PRESSURE = Membrane Tension = -(d/dA)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE Membrane DENSITY, i.e. w = -1
3. Virtual photon ZPE on a 3D volume V with short wave cutoff "a", V >> a^3, with standing wave modes ~ (L)^-3/2sin(kx)sin(k'y)sin(k"z)
Total ZPE per polarization ~ pi(hc/4a)(V/a^3) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
3D ZPE PRESSURE = -(d/dV)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE DENSITY, i.e. w = -1
In all three cases, no contribution of virtual photons to any vacuum pressure difference that can be attributed to a VdW "Casimir force".
The effect of EFFECTIVE dimension is in how the "pressure" scales with short-wave cutoff. One could also imagine FRACTALS with a non-integer power of the short-wave cutoff.
Wednesday, September 15, 2004
If you posit that momentum space is a CONTINUUM metric space and assume FLAT Euclidean geometry with the Pythagorean theorem, then
1. Virtual photon ZPE on a 1D line of length L with short wave cutoff "a", L >> a, with standing wave modes (L)^-1/2sin(kx)
Total ZPE per polarization ~ pi(hc/4a)(L/a) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
1D ZPE PRESSURE = STRING TENSION = -(d/dL)(Total ZPE) = pi(hc/4a^2) = constant = -ZPE LINE DENSITY, i.e. w = -1
2. Virtual photon ZPE on a 2D lattice of area A with short wave cutoff "a", L >> a, with standing wave modes (L)^-1sin(kx)sin(k'y)
Total ZPE per polarization ~ pi(hc/4a)(A/a^2) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
2D ZPE PRESSURE = Membrane Tension = -(d/dA)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE Membrane DENSITY, i.e. w = -1
3. Virtual photon ZPE on a 3D volume V with short wave cutoff "a", V >> a^3, with standing wave modes (L)^-3/2sin(kx)sin(k'y)sin(k"z)
Total ZPE per polarization ~ pi(hc/4a)(V/a^3) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
3D ZPE PRESSURE = -(d/dV)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE LINE DENSITY, i.e. w = -1
In all three cases, no contribution of virtual photons to any vacuum pressure difference that can be attributed to a "Casimir force".
The effect of EFFECTIVE dimension is in how the "pressure" scales with short-wave cutoff. One could also imagine FRACTALS with a non-integer power of the short-wave cutoff.
1. Virtual photon ZPE on a 1D line of length L with short wave cutoff "a", L >> a, with standing wave modes (L)^-1/2sin(kx)
Total ZPE per polarization ~ pi(hc/4a)(L/a) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
1D ZPE PRESSURE = STRING TENSION = -(d/dL)(Total ZPE) = pi(hc/4a^2) = constant = -ZPE LINE DENSITY, i.e. w = -1
2. Virtual photon ZPE on a 2D lattice of area A with short wave cutoff "a", L >> a, with standing wave modes (L)^-1sin(kx)sin(k'y)
Total ZPE per polarization ~ pi(hc/4a)(A/a^2) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
2D ZPE PRESSURE = Membrane Tension = -(d/dA)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE Membrane DENSITY, i.e. w = -1
3. Virtual photon ZPE on a 3D volume V with short wave cutoff "a", V >> a^3, with standing wave modes (L)^-3/2sin(kx)sin(k'y)sin(k"z)
Total ZPE per polarization ~ pi(hc/4a)(V/a^3) = (pi/2)(ZPE of shortest wave virtual photon)(Number of cells of phase space)
3D ZPE PRESSURE = -(d/dV)(Total ZPE) = pi(hc/4a^3) = constant = -ZPE LINE DENSITY, i.e. w = -1
In all three cases, no contribution of virtual photons to any vacuum pressure difference that can be attributed to a "Casimir force".
The effect of EFFECTIVE dimension is in how the "pressure" scales with short-wave cutoff. One could also imagine FRACTALS with a non-integer power of the short-wave cutoff.
On Sep 15, 2004, at 12:38 PM, main_engineering wrote:
I understand your math and the physics perfectly well. I don't understand
why you are using the wrong math in this example and limiting yourself to a
1 dimensional problem when in fact 3 are required to model reality.
Because, my model is true any dimension. Also the piston in the cylinder is the simplest situation and it is effectively 1D by symmetry since the important parameter is the movement of the piston in the cylinder.
The same calculation works in all dimensions because the space-dimensions are LINEARLY INDEPENDENT.
The key conclusion that, contrary to Hal Puthoff's frequent claims to science journalists, FREE virtual zero point photons without any j.A coupling to electrons and protons make exactly ZERO contribution to the measured Casimir force, which is not at all a direct zero point force, but is, rather, an electrostatic Van Der Waals force between real charges placed outside the vacuum in spatially separated charge neutral configurations. The free virtual photon pressure is CONSTANT in the case of zero vacuum coherence and it obeys w = -1 with a positive ZPE density and an equal in magnitude but opposite in sign NEGATIVE PRESSURE. I prove this explicitly below using the standard continuum spherically symmetric Lorentz-invariant spectral density of field oscillators, which is an APPROXIMATION to the more exact discrete sum in a finite cavity problem. Contrary to QED, in GR you cannot subtract off even these constant free virtual photon ZPE densities, which have STRONG direct space-time warping power when not suppressed by MACRO-QUANTUM VACUUM COHERENCE out of which Einstein's gravity and the inertia of ordinary matter emerges. Note Hal Puthoff's category confusion here. I am NOT claiming that the Casimir force is in anyway related to the origin of gravity and inertia as Hal has suggested in numerous pop interviews with the media.
Look the idea is very simple.
Suppose you have a finite 3D box cavity, independent x,y,z axes with a little box of variable size X, Y, Z inside a big box of fixed size Lx, Ly, Lz. The counting of the LINEARLY INDEPENDENT standing wave modes along each direction works the same way.
Count the number of independent modes along each space direction exactly as I did. Assume a common short-wave cutoff a for simplicity. The EXACT total number of modes is then inside the little box
N = NxNyNz = (1/8((X/a)(X/a + 1)(Y/a)(Y/a + 1)(Z/a)(Z/a + 1)
But there is only 1 virtual photon per independent mode, and their virtual zero point energies add linearly even though the modes in different independent directions multiply.
That is the Hamiltonian for a sum of independent field oscillators is
H = Sum over all independent modes of hck(a*kak + 1/2)
where we sandwich the LINEAR ENERGY OPERATOR between the VACUUM STATE
|0> that is a product of the vacuum states |0>k one for each independent mode. Standing wave cavity modes in different directions are independent as well as those along the same direction with different nx, ny, nz and
k<0|a*kak|0>k = 0
using 2nd quantization in Fock occupation number space in the traditional textbook way.
a* creates a real photon, a destroys a real photon.
The wave number for each independent standing wave cavity mode field oscillator, that in the vacuum has NO real photons is
knx = nxpi/X
where nx = 1 to X/a, similarly for y, z
DO NOT CONFUSE THESE MODE INTEGERS WITH THE EIGENVALUES OF a*kak for the number of REAL PHOTONS in each independent cavity mode field oscillator k that is a standing wave obeying the cavity boundary conditions.
Note that
Nx = SUM of ALL the MODE INTEGERS nx from 1 to X/a (in sense of nearest least integer to X/a).
Similarly for ny & nz.
Each independent mode of wave number knx = nxpi/X contributes a zero point energy hckni/2 with a fixed coefficient hcpi/2X, so that the key quantity is sum of nx from 1 to (X/a) which is (1/2)(X/a)(X/a + 1). Similarly for y and z and you simply ADD the separate linearly independent zero point virtual photon energies for EACH independent oscillator! So my EXACT calculation obviously works in 1D, 2D, 3D ... ND.
This is simple and obvious.
Now
you're not just saying that Hal is wrong, you're trying to tell me that
Planck, Casimir, Milonni and everything else QED has to say about the ZPF is
wrong without any justification other than your desire to prove you're right
and everyone else is wrong. I know better than to believe such nonsense.
I never said Planck was wrong. Show me where Planck did such a calculation?
Show what is wrong with the above simple exact DISCRETE counting?
The standard CONTINUUM SPHERICALLY SYMMETRIC argument is:
Density of oscillator states in 3D is 4pik^2dk per polarization.
k^2 = kx^2 + ky^2 + kz^2
= (nxpi/X)^2 + (nypi/Y)^2 + (nzpi/Z)^2
FOR GLOBALLY FLAT MOMENTUM SPACE WITH EUCLIDEAN CONTINUUM GEOMETRY USING PYTHAGOREAN THEOREM.
But this discrete sum is approximated by a continuous integral below and spherical symmetry is assumed. These two approximations introduce mathematical artifacts LIKE LORENTZ INVARIANCE!
The total zero point energy density is then
Integral (hc/2)4pik^3dk = 4pi(hc/8)k(MAX)^4
k(MAX) = 2pi/a
a = short wave cut off
Total zero point energy ZPE is then
ZPE = 4pi(hc/8)(2pi/a)^4V > 0 in a spatial volume V.
Note LINEAR DEPENDENCE OF TOTAL VIRTUAL PHOTON ZPE ON VOLUME V.
Note that even in this calculation, the PRESSURE is - d(ZPE)/dV = - 4pi(hc/8)(2pi/a)^4 is CONSTANT independent of changes in volume V. AND IT IS NEGATIVE and it is - the ZPE DENSITY! That is w = -1!
Therefore even in this continuum spherical symmetric model one gets the same effective result I get with my more exact purely discretum model with NO SPHERICAL SYMMETRY IMPOSED ADHOC! There is NO net ZPE pressure differential on any wall. You have exactly the same negative free virtual photon pressures on each side of the wall NO MATTER HOW YOU CALCULATE IT!
If the formula used to derive the ZPF mode pressure presented by Milonni is
wrong, then so is the spectral energy density of the ZPF and the Lorentz
invariance of that density.
No it's not as I just showed. To the extent that V --> infinity and a --> 0 which is what you need for globally flat continuum of special relativity with EFFECTIVE SPATIAL SPHERICAL SYMMETRY (no finite cavity walls of arbitrary shape), you get same essential result! That same essential result is that there is NO contribution to the Casimir force from purely free virtual zero point photons! The Casimir force requires the j.A coupling to properly compute as a Van Der Waals force between real charges. This is NOT a pure vacuum problem!
That cannot be so. It has been verified by more
than 1 kind of experiment. QED is the best tested theory there ever was.
IMO, test after test it has proven itself correct. It is even more battle
tested and proven in day to day life than GR ever was.
Not true! The domain of validity of QED is much more limited than anyone realized even though the accuracy of the QED measurements is very high and even though renormalization methods work very well - too well, although not even Richard Feynman understood why! Feynman told me that directly BTW!
main_engineering
-----Original Message-----
From: Jack:
completely.
I count the number of modes exactly. There is one FREE virtual photon
per mode (AKA field oscillator). Therefore, the calculation is exact
and simple.
I understand your math and the physics perfectly well. I don't understand
why you are using the wrong math in this example and limiting yourself to a
1 dimensional problem when in fact 3 are required to model reality.
Because, my model is true any dimension. Also the piston in the cylinder is the simplest situation and it is effectively 1D by symmetry since the important parameter is the movement of the piston in the cylinder.
The same calculation works in all dimensions because the space-dimensions are LINEARLY INDEPENDENT.
The key conclusion that, contrary to Hal Puthoff's frequent claims to science journalists, FREE virtual zero point photons without any j.A coupling to electrons and protons make exactly ZERO contribution to the measured Casimir force, which is not at all a direct zero point force, but is, rather, an electrostatic Van Der Waals force between real charges placed outside the vacuum in spatially separated charge neutral configurations. The free virtual photon pressure is CONSTANT in the case of zero vacuum coherence and it obeys w = -1 with a positive ZPE density and an equal in magnitude but opposite in sign NEGATIVE PRESSURE. I prove this explicitly below using the standard continuum spherically symmetric Lorentz-invariant spectral density of field oscillators, which is an APPROXIMATION to the more exact discrete sum in a finite cavity problem. Contrary to QED, in GR you cannot subtract off even these constant free virtual photon ZPE densities, which have STRONG direct space-time warping power when not suppressed by MACRO-QUANTUM VACUUM COHERENCE out of which Einstein's gravity and the inertia of ordinary matter emerges. Note Hal Puthoff's category confusion here. I am NOT claiming that the Casimir force is in anyway related to the origin of gravity and inertia as Hal has suggested in numerous pop interviews with the media.
Look the idea is very simple.
Suppose you have a finite 3D box cavity, independent x,y,z axes with a little box of variable size X, Y, Z inside a big box of fixed size Lx, Ly, Lz. The counting of the LINEARLY INDEPENDENT standing wave modes along each direction works the same way.
Count the number of independent modes along each space direction exactly as I did. Assume a common short-wave cutoff a for simplicity. The EXACT total number of modes is then inside the little box
N = NxNyNz = (1/8((X/a)(X/a + 1)(Y/a)(Y/a + 1)(Z/a)(Z/a + 1)
But there is only 1 virtual photon per independent mode, and their virtual zero point energies add linearly even though the modes in different independent directions multiply.
That is the Hamiltonian for a sum of independent field oscillators is
H = Sum over all independent modes of hck(a*kak + 1/2)
where we sandwich the LINEAR ENERGY OPERATOR between the VACUUM STATE
|0> that is a product of the vacuum states |0>k one for each independent mode. Standing wave cavity modes in different directions are independent as well as those along the same direction with different nx, ny, nz and
k<0|a*kak|0>k = 0
using 2nd quantization in Fock occupation number space in the traditional textbook way.
a* creates a real photon, a destroys a real photon.
The wave number for each independent standing wave cavity mode field oscillator, that in the vacuum has NO real photons is
knx = nxpi/X
where nx = 1 to X/a, similarly for y, z
DO NOT CONFUSE THESE MODE INTEGERS WITH THE EIGENVALUES OF a*kak for the number of REAL PHOTONS in each independent cavity mode field oscillator k that is a standing wave obeying the cavity boundary conditions.
Note that
Nx = SUM of ALL the MODE INTEGERS nx from 1 to X/a (in sense of nearest least integer to X/a).
Similarly for ny & nz.
Each independent mode of wave number knx = nxpi/X contributes a zero point energy hckni/2 with a fixed coefficient hcpi/2X, so that the key quantity is sum of nx from 1 to (X/a) which is (1/2)(X/a)(X/a + 1). Similarly for y and z and you simply ADD the separate linearly independent zero point virtual photon energies for EACH independent oscillator! So my EXACT calculation obviously works in 1D, 2D, 3D ... ND.
This is simple and obvious.
Now
you're not just saying that Hal is wrong, you're trying to tell me that
Planck, Casimir, Milonni and everything else QED has to say about the ZPF is
wrong without any justification other than your desire to prove you're right
and everyone else is wrong. I know better than to believe such nonsense.
I never said Planck was wrong. Show me where Planck did such a calculation?
Show what is wrong with the above simple exact DISCRETE counting?
The standard CONTINUUM SPHERICALLY SYMMETRIC argument is:
Density of oscillator states in 3D is 4pik^2dk per polarization.
k^2 = kx^2 + ky^2 + kz^2
= (nxpi/X)^2 + (nypi/Y)^2 + (nzpi/Z)^2
FOR GLOBALLY FLAT MOMENTUM SPACE WITH EUCLIDEAN CONTINUUM GEOMETRY USING PYTHAGOREAN THEOREM.
But this discrete sum is approximated by a continuous integral below and spherical symmetry is assumed. These two approximations introduce mathematical artifacts LIKE LORENTZ INVARIANCE!
The total zero point energy density is then
Integral (hc/2)4pik^3dk = 4pi(hc/8)k(MAX)^4
k(MAX) = 2pi/a
a = short wave cut off
Total zero point energy ZPE is then
ZPE = 4pi(hc/8)(2pi/a)^4V > 0 in a spatial volume V.
Note LINEAR DEPENDENCE OF TOTAL VIRTUAL PHOTON ZPE ON VOLUME V.
Note that even in this calculation, the PRESSURE is - d(ZPE)/dV = - 4pi(hc/8)(2pi/a)^4 is CONSTANT independent of changes in volume V. AND IT IS NEGATIVE and it is - the ZPE DENSITY! That is w = -1!
Therefore even in this continuum spherical symmetric model one gets the same effective result I get with my more exact purely discretum model with NO SPHERICAL SYMMETRY IMPOSED ADHOC! There is NO net ZPE pressure differential on any wall. You have exactly the same negative free virtual photon pressures on each side of the wall NO MATTER HOW YOU CALCULATE IT!
If the formula used to derive the ZPF mode pressure presented by Milonni is
wrong, then so is the spectral energy density of the ZPF and the Lorentz
invariance of that density.
No it's not as I just showed. To the extent that V --> infinity and a --> 0 which is what you need for globally flat continuum of special relativity with EFFECTIVE SPATIAL SPHERICAL SYMMETRY (no finite cavity walls of arbitrary shape), you get same essential result! That same essential result is that there is NO contribution to the Casimir force from purely free virtual zero point photons! The Casimir force requires the j.A coupling to properly compute as a Van Der Waals force between real charges. This is NOT a pure vacuum problem!
That cannot be so. It has been verified by more
than 1 kind of experiment. QED is the best tested theory there ever was.
IMO, test after test it has proven itself correct. It is even more battle
tested and proven in day to day life than GR ever was.
Not true! The domain of validity of QED is much more limited than anyone realized even though the accuracy of the QED measurements is very high and even though renormalization methods work very well - too well, although not even Richard Feynman understood why! Feynman told me that directly BTW!
main_engineering
-----Original Message-----
From: Jack:
completely.
I count the number of modes exactly. There is one FREE virtual photon
per mode (AKA field oscillator). Therefore, the calculation is exact
and simple.
On Sep 15, 2004, at 8:01 AM, Jack Sarfatti wrote:
PS I had not read the thread that came with Dan's stuff below. Indeed,
I do also agree with Scott that I do not take the theological mish mash
seriously. I suspect neither does Puthoff.
On Sep 15, 2004, at 7:56 AM, Jack Sarfatti wrote:
I have not read the piece by Scott Dan is responding to. However,
Dan's description of post-quantum physics with metric engineering is
accurate. Precision cosmology shows we live in the virtual universe
that is effectively a cosmic video game of IT (material) from BIT
(mind) in a two-way loop including BIT from IT to generate the streams
of consciousness attached to globs of IT. I have shown explicitly how
IT in the form of Einstein's guv field emerges from the coherent phase
of MACRO-BIT, which in turn emerges from an instability in the
micro-qubit vacuum with the local gauge fields and lepto-quark fields
already there. So they need to emerge from a BIT like spin-foam in a 2
step process. Something like loop quantum gravity to get to unstable
globally flat pre-inflationary false vacuum prior to second step
emergence of gravity and inertia.
On the material plane:
1. Hal Puthoff and I have the same strategic objectives. I am saying
his physics to achieve them is seriously wrong. Because of Hal's black
ops connections from way back to National Security Agency his wrong
ideas are leading to USG intelligence threat assessment blunders, that
in the long run, will be worse than the Leo Strauss Utopian Cult Neo
Con blunders on Iraq WMD in Doug Feith's OSP prior to the
ill-conceived attack on Iraq. As Seymour Hersh and Pat Buchanan et-al
put it "Eight or nine Neo Cons" essentially pulled the wool over
Bushie's eyes in the panic of 911 where we have jumped from the frying
pan into the fire. Kerry has no solution either. "What a revolting
development this is." William Bendix. There is no "End Game". Easy to
see now in hindsight, but not 2 years ago.
2.
On Sep 15, 2004, at 6:59 AM, Ken Shoulders wrote:
ELECTRON CONDENSER
by
Ken Shoulders
Abstract
An apparatus is proposed for the condensation of electrons to a
containable fluid state. This miniature apparatus consists of an ion
pumped vacuum system, a split anode magnetron and a quadrupole
electron trap fitted with suitable electron injectors, in the form of
EVO generators, and numerous ways for analyzing the effluent captured
in the trap. The apparatus design emphasizes simplicity and uses only
minimal hand tools for construction. The cost of the easily found
construction materials required is in the range of a few hundred
dollars.
This recent paper can be downloaded from: http://www.svn.net/krscfs/
3. As to zero point energy. It's easy to do the free virtual photon
cavity mode problem exactly. There is no net free virtual photon zero
point force on any wall.
Think of a piston in a cylinder to total length L. The piston is at
distance z from the left wall. There is cylindrical symmetry. All we
need do is think of the virtual photon waves that can fit between 0
and z and between z and L. Each wave that fits has virtual photon
energy hck/2 per polarization mode.
The largest mode that fits in z has wave number k = pi/z.
Each mode has wave number npi/z.
The total number of such modes is simply (z/a)(z/a + 1)/2 where a is
the short-wave cut off and we mean smallest closest integer to z/a.
The total zero point free virtual photon energy for the left partition
between 0 and z is obviously, where z/a >> 1
Sum n = 1 to d/a of (hc/2)(pi/z)n ~ (hc/4)(pi/z)(z/a)^2 = (hc/4a^2)z
linear in z.
Similarly for the right partition between z and L - z
Total free virtual photon ZPE is (hc/4a^2)(L - z)
The total ZPE at the piston is the sum. Whose force total negative
gradient -d/dz is exactly zero independent of cutoff a.
Now this is not what is usually calculated for the Casimir force that
is really a weak Van der Waals force between the neutral molecules
making up the uncharged walls of the cylinder and piston. The weak
Casimir force does not tap the free random totally incoherent virtual
photon ZPF. Calculations that make such a claim are wrong.
On Sep 14, 2004, at 7:28 PM, Dan Smith wrote:
Scott,
Oh, you, of little imagination. For once in your life, see if you
can remove your blinders for but a few seconds.
You cling to your 'rock solid' reality for dear life. Why would
cling so tightly unless you were afraid that it might finally elude
your grasp?
Now you see reality dimly as through a darkened glass, but then you
shall see it face to face.
The visitors are here simply to awaken us from our slumber of
materialism.
Any ufologist worth her salt knows that they can bend our reality to
their will. They see through our thoughts, they walk through our
walls. This is not technology, Scott, this is mind over matter.
This is the unobstructable power of Spirit.
We all know that the visitors do not come here in rocket ships. They
come here by warping our space and our time. Our space and our time,
they bend to their will.
They can transit between universes they way we can transit between
the rooms of a building.
Your attempt to apply 19th century physics to the visitors and their
hyper dimensional reality is really nothing short of grotesque.
Have you never played an arcade game? The younger generation is
being fed on virtual reality, the way you were fed on oatmeal. They
are no longer going to be stuck in the mud of your materialism. They
are being prepared for the other dimensions, the power of the
imagination and spirit that lies just beyond the Green Door in Area
51. They don't call it Dreamland for nothing.
You rail against the larger cosmos. You demand that reality must fit
your Procrustean bed. The visitors make a mockery of your
metaphysical prudery.
Look around you, Scott. Where are your fellow scientists? They are
sufficiently prudent not to pick a fight with the paranormal Tar
Baby. They know they will not win this battle. Nay, they will not
win this war. They continue to fiddle with their formulas while Rome
continues to burn.
Jack and Hal attempt to carve out little pieces of the paranormal.
Their strategy is to divide and conquer. My hat is off to their
perseverance. They stand at the edge of their reality and grasp at
straws. They might as well reap the whirl wind.
We inhabit but a cocoon in the cosmic Matrix. There is a crack in
that cosmic egg. We are trying to peck our way out of the shell.
The visitors are here to show us how.
But first we must marshal our spirit. Perhaps that is where I come
into the picture. There are some mental calisthenics that will help
us to limber up our spirits.
Can you stretch your mind, Scott? Has it become sclerotic?
Dan
-----Original Message-----
From: Scott Littleton [mailto:yokatta@oxy.edu]
Sent: Tuesday, September 14, 2004 5:01 PM
To: Dan Smith; caryn anscomb; Jack Sarfatti; Nick Cook
Subject: RE: Smelling a rat....
Hi Caryn, et al.
Let me respond to you and your excellent (and extremely kind)
message, as well as to our resident “prophet” (soi dissant) re his
attempt to put a Christian eschatological spin on the agenda of the
“Alien Raj.” First of all, Saint Daniel’s concept of an “eschaton”
is utterly absurd, no matter who endorses it. Indeed, I seriously
doubt whether either Jack Sarfatti or Hal Puthoff, no matter how at
odds they may be over the arcana of post-quantum physics, or any
other credible physical scientists, for that matter, take this
bizarre theological mishmash seriously. Indeed, the whole notion of
eschatology, Christian and otherwise, reflects an archaic stage in
the evolution of human thought, one that took shape long before our
ancestors had any accurate knowledge whatsoever of how the universe
works. Yes, I’m convinced that all traditional human belief systems,
from animism to Zoroastrianism—which, BTW, is chock full of
eschatological concepts that were already ancient by the time Yeshua
ben Yosuf (aka in Latin Jesus) was “magically” conceived aboard a
hovering UFO, if in fact there’s any glimmer of truth behind the
“virgin birth” legend—are, as the late Mircea Eliade pointed out some
years ago, essentially anthropocentric attempts to turn “Chaos” into
“Cosmos,” to impose an imagined order on what was, given the meager
objective knowledge base available to all pre-modern societies, an
otherwise utterly chaotic existence. Or, as the well-known
Anglo-Polish anthropologist Bronislaw Malinowski, whose researches
into the nature of religion were generally isomorphic with Eliade’s,
phased it: If human beings don’t have rational explanations and/or
empirically-based mechanisms that will allow them a modicum of
control over their environment, they will invent them. (Indeed,
Voltaire probably summed up this line of reasoning as succinctly as
anyone who came after him: If there were no God, it would be
necessary to invent one.)
That most, if not traditional human belief systems deeply reflect the
presence of the “Alien Raj” is undoubted. But that presence itself
was an integral part of the pre-modern chaos that, according to
Eliade, et al., engendered religion in the first place. That is,
the aliens came to be conceived of as divine beings, fairly folk,
etc.
The trap that Dan and his fellow “eschaton” mavens have fallen into,
aside from the absurdity of drawing specifically on the dogma of a
single, extremely derivative and highly syncretic religious belief
system that began as what amounted to a Judean “cargo cult” preached
by a figure who was most probably a heavily conditioned an alien
“subject,” is to take seriously the patently mythological concepts
our ancestors used to make sense out of the world. Indeed, the
inherently irrational concept of “faith” is part and parcel of this
archaic Weltanschauung, and it is faith rather than reason that
drives Smith and his fellow eschatologists.
A much more efficient model here, one that owes more to Marx than to
the Bible, is that the “Alien Raj” is an imperialist, exploitative
oppressor, rather than a supernatural phenomenon, as Dan and his
buddies appear to conceive it, despite their rhetoric, that has
managed to impose its will on this planet. To be sure, at present,
this authority is for the most part exercised clandestinely, but ask
any woman whose fetus has been forcibly removed whether this
authority actually exists. Dan dismisses the “Raj’s” DNA harvesting
as trivial, but I think he’s dead wrong here. Whatever else they may
be exploiting, human DNA appears to be the prime target, just as gold
was to the Conquistadors in Mexico and Peru half a millennium ago.
Indeed, the process of hybridization seems to be a central aspect of
their agenda, and, while I don’t take quite as pessimistic a position
David Jacobs does in THE THREAT, as I’m not convinced that they’re
out to totally replace us, it seems abundantly clear that their
agenda is NOT framed in terms of an altruistic effort to “uplift” us
to a “:higher spiritual level,” that is, to realize Dan’s
eschatological fantasies. Rather, like its terrestrial prototype,
the British Raj, its primary purpose is to administer the affairs of
this planet in such a way as to facilitate its imperialist agenda.
Thus, I while I don’t think they’re out to annihilate us—they could
have done so long since—I do think that we’re the “natives” and will
remain such until we manage to overthrow our planetary oppressors,
either through the efforts of a Gandhi-like moral force that appeals
to their “:better” nature (assuming they have one), or, more
probably, by someday getting our hands on enough of their technology
so we can effectively rise up against them. In other words, by
instigating a war of “planetary liberation,” I would, however,
caution against any rash actions here, as the technology we’re up
against makes the gap between Cortes and Moteczuma look
infinitesimal.
Complicating this “liberation” scenario is the high probability that
there exists a cadre of sell-outs, vendidos, as my Latino friends
would call them, who have sold out human autonomy for the
technological “trinkets” I mentioned in my previous post. These
would include the “insiders” Dan mentioned, as well as MJ-12 (or
whatever they call it at the moment), assuming they’re not one and
the same, as well as their counterparts in other highly developed
human societies, such as the U.K., Russia, Japan, and yes Israel,
etc.). I suspect this began with an unratified “treaty” negotiated
by Eisenhower at Edwards AFB in 1954, which, although periodically
modified, has continued in force up to the present. Again, there
are a many analogs in the history of terrestrial colonialism: the
Anglo-Indians, the Vietnamese Catholics, and other subsets of
conquered populations that accommodate to their oppressors in return
for some crumbs from the latters’ table. Indeed, the old
African-American label “Uncle Tom”—perhaps recast as “Uncle Homo
sapiens”—would seem apt here.
Finally, Caryn, as I’ve said before in our correspondence, to the
best of my conscious knowledge, I’ve never had the “pleasure” of
meeting the little buggers up close & personal. But I can certainly
sympathize with what you say here. The fact that you were unable to
perceive whether your captors were here “to save us or eat us!” fits
nicely with the hypothesis I’ve suggested, that is, that they, like
your fellow countrymen in India back in the 19th century, they are
here neither to destroy us nor to “redeem” us (although the British
Raj did have its share of pious missionaries who, when they weren’t
exploiting them, did their best to convert the Hindu and Moslem
“Wogs” to Christianity), but rather simply to exploit us (i.e., our
DNA) and other terrestrial resources they may need or desire.
Cheers,
Scotty
-----Original Message-----
From: Dan Smith [mailto:dantsmith@comcast.net]
Sent: Tuesday, September 14, 2004 10:49 AM
To: caryn anscomb; Scott Littleton; Jack Sarfatti; Nick Cook
Cc: Joel Isaacson; Colin Bennett; S-P Sirag; john dering; Warren
Hinckle; Tim Jerome; nancyWerd@aol.com; Randall Stickrod;
Amara@Kurzweilai. Net; RAY HUDSON; John Brandenburg; Dick Farley;
mitc1615@bellsouth.net; RICK DOTY; james norwood pratt; Jagdish Mann;
Constantin Ivanenko; David Gladstone; Gary S. Bekkum
Subject: Smelling a rat....
bcc.
Caryn,
We have insiders and outsiders. If the insiders wish to communicate
with the outsiders, they would naturally use intermediaries. It
appears that I'm being used as an intermediary.
The insiders and the visitors will come out of the closet at the
appropriate time. I am helping them to test the waters. That is
what the EFG is for.
Why don't your entities inform you about their agenda? It is simply
a matter of the Prime Directive, minimal interference.
The main point, however, is that the Eschaton is not their agenda.
It is OUR agenda. The Eschaton is of us, by us and for us. The
visitors are here as helpers. They are here to facilitate our
awakening to our own destiny.
You want to hear all this from the 'horse's mouth'. My purpose here
is to help demonstrate that we are the ultimate source for what has
happened and what is about to. You have come to the 'horse's mouth'
and it is us. Temporarily I am being the spokesperson, the
intermediary in helping us to realize that fundamentally we are the
co-creators of this reality, and we are its redeemers.
I do interpret this role in Christian terms. That is how it was
presented to me by Sophia. This is simply the completion of the
christ event. This is that unfinished business. Sophia is my
'horse's mouth'.
I am facilitating her communication. I'm playing the role of a
prophet. This role is traditionally reserved for mortals, rather
like you and me, not for ETs/UTs/Visitors.
Whatever role I am playing is apparently being overseen by the
insiders, the visitors and Sophia.
Now, Caryn, you are welcome to object to the prophetic tradition and
to my role as a putative prophet, but then you are under some
obligation to come up with a better plan. I'm certainly open to
discuss that, but I think you will end up reinventing this
same wheel.
The sooner that I can obtain a fair hearing from my peers, the sooner
will I be able to ride off into the sunset. So why don't we get onto
the business of discussing the why's and wherefores of all this?
Dan
P.S. I have just received a note from Gary Bekkum pointing to Steve
Greer's Aug. 8/9 interview on the Art Bell show. Here is an
excerpt:
SG: [chuckles] Look, this is - part of this isn't a rational
discussion and
here's why. You have people in this policy group, and there are two
or three
hundred people in it (some people call it the MJ-12 group, it's not
called
that anymore) and I know a number of these people in it.
AB: Do you think it really was once called that?
SG: Yes.
AB: Okay.
SG: What's interesting is that there is a hardcore center of it that
are
eschatologists. Okay? These are people who fantasize about how the
world is
going to end.
---------------------------------
Some folks have been trying to get this same message to Steve, but,
evidently, it is not quite fitting into his paradigm.
PS I had not read the thread that came with Dan's stuff below. Indeed,
I do also agree with Scott that I do not take the theological mish mash
seriously. I suspect neither does Puthoff.
On Sep 15, 2004, at 7:56 AM, Jack Sarfatti wrote:
I have not read the piece by Scott Dan is responding to. However,
Dan's description of post-quantum physics with metric engineering is
accurate. Precision cosmology shows we live in the virtual universe
that is effectively a cosmic video game of IT (material) from BIT
(mind) in a two-way loop including BIT from IT to generate the streams
of consciousness attached to globs of IT. I have shown explicitly how
IT in the form of Einstein's guv field emerges from the coherent phase
of MACRO-BIT, which in turn emerges from an instability in the
micro-qubit vacuum with the local gauge fields and lepto-quark fields
already there. So they need to emerge from a BIT like spin-foam in a 2
step process. Something like loop quantum gravity to get to unstable
globally flat pre-inflationary false vacuum prior to second step
emergence of gravity and inertia.
On the material plane:
1. Hal Puthoff and I have the same strategic objectives. I am saying
his physics to achieve them is seriously wrong. Because of Hal's black
ops connections from way back to National Security Agency his wrong
ideas are leading to USG intelligence threat assessment blunders, that
in the long run, will be worse than the Leo Strauss Utopian Cult Neo
Con blunders on Iraq WMD in Doug Feith's OSP prior to the
ill-conceived attack on Iraq. As Seymour Hersh and Pat Buchanan et-al
put it "Eight or nine Neo Cons" essentially pulled the wool over
Bushie's eyes in the panic of 911 where we have jumped from the frying
pan into the fire. Kerry has no solution either. "What a revolting
development this is." William Bendix. There is no "End Game". Easy to
see now in hindsight, but not 2 years ago.
2.
On Sep 15, 2004, at 6:59 AM, Ken Shoulders wrote:
ELECTRON CONDENSER
by
Ken Shoulders
Abstract
An apparatus is proposed for the condensation of electrons to a
containable fluid state. This miniature apparatus consists of an ion
pumped vacuum system, a split anode magnetron and a quadrupole
electron trap fitted with suitable electron injectors, in the form of
EVO generators, and numerous ways for analyzing the effluent captured
in the trap. The apparatus design emphasizes simplicity and uses only
minimal hand tools for construction. The cost of the easily found
construction materials required is in the range of a few hundred
dollars.
This recent paper can be downloaded from: http://www.svn.net/krscfs/
3. As to zero point energy. It's easy to do the free virtual photon
cavity mode problem exactly. There is no net free virtual photon zero
point force on any wall.
Think of a piston in a cylinder to total length L. The piston is at
distance z from the left wall. There is cylindrical symmetry. All we
need do is think of the virtual photon waves that can fit between 0
and z and between z and L. Each wave that fits has virtual photon
energy hck/2 per polarization mode.
The largest mode that fits in z has wave number k = pi/z.
Each mode has wave number npi/z.
The total number of such modes is simply (z/a)(z/a + 1)/2 where a is
the short-wave cut off and we mean smallest closest integer to z/a.
The total zero point free virtual photon energy for the left partition
between 0 and z is obviously, where z/a >> 1
Sum n = 1 to d/a of (hc/2)(pi/z)n ~ (hc/4)(pi/z)(z/a)^2 = (hc/4a^2)z
linear in z.
Similarly for the right partition between z and L - z
Total free virtual photon ZPE is (hc/4a^2)(L - z)
The total ZPE at the piston is the sum. Whose force total negative
gradient -d/dz is exactly zero independent of cutoff a.
Now this is not what is usually calculated for the Casimir force that
is really a weak Van der Waals force between the neutral molecules
making up the uncharged walls of the cylinder and piston. The weak
Casimir force does not tap the free random totally incoherent virtual
photon ZPF. Calculations that make such a claim are wrong.
On Sep 14, 2004, at 7:28 PM, Dan Smith wrote:
Scott,
Oh, you, of little imagination. For once in your life, see if you
can remove your blinders for but a few seconds.
You cling to your 'rock solid' reality for dear life. Why would
cling so tightly unless you were afraid that it might finally elude
your grasp?
Now you see reality dimly as through a darkened glass, but then you
shall see it face to face.
The visitors are here simply to awaken us from our slumber of
materialism.
Any ufologist worth her salt knows that they can bend our reality to
their will. They see through our thoughts, they walk through our
walls. This is not technology, Scott, this is mind over matter.
This is the unobstructable power of Spirit.
We all know that the visitors do not come here in rocket ships. They
come here by warping our space and our time. Our space and our time,
they bend to their will.
They can transit between universes they way we can transit between
the rooms of a building.
Your attempt to apply 19th century physics to the visitors and their
hyper dimensional reality is really nothing short of grotesque.
Have you never played an arcade game? The younger generation is
being fed on virtual reality, the way you were fed on oatmeal. They
are no longer going to be stuck in the mud of your materialism. They
are being prepared for the other dimensions, the power of the
imagination and spirit that lies just beyond the Green Door in Area
51. They don't call it Dreamland for nothing.
You rail against the larger cosmos. You demand that reality must fit
your Procrustean bed. The visitors make a mockery of your
metaphysical prudery.
Look around you, Scott. Where are your fellow scientists? They are
sufficiently prudent not to pick a fight with the paranormal Tar
Baby. They know they will not win this battle. Nay, they will not
win this war. They continue to fiddle with their formulas while Rome
continues to burn.
Jack and Hal attempt to carve out little pieces of the paranormal.
Their strategy is to divide and conquer. My hat is off to their
perseverance. They stand at the edge of their reality and grasp at
straws. They might as well reap the whirl wind.
We inhabit but a cocoon in the cosmic Matrix. There is a crack in
that cosmic egg. We are trying to peck our way out of the shell.
The visitors are here to show us how.
But first we must marshal our spirit. Perhaps that is where I come
into the picture. There are some mental calisthenics that will help
us to limber up our spirits.
Can you stretch your mind, Scott? Has it become sclerotic?
Dan
-----Original Message-----
From: Scott Littleton [mailto:yokatta@oxy.edu]
Sent: Tuesday, September 14, 2004 5:01 PM
To: Dan Smith; caryn anscomb; Jack Sarfatti; Nick Cook
Subject: RE: Smelling a rat....
Hi Caryn, et al.
Let me respond to you and your excellent (and extremely kind)
message, as well as to our resident “prophet” (soi dissant) re his
attempt to put a Christian eschatological spin on the agenda of the
“Alien Raj.” First of all, Saint Daniel’s concept of an “eschaton”
is utterly absurd, no matter who endorses it. Indeed, I seriously
doubt whether either Jack Sarfatti or Hal Puthoff, no matter how at
odds they may be over the arcana of post-quantum physics, or any
other credible physical scientists, for that matter, take this
bizarre theological mishmash seriously. Indeed, the whole notion of
eschatology, Christian and otherwise, reflects an archaic stage in
the evolution of human thought, one that took shape long before our
ancestors had any accurate knowledge whatsoever of how the universe
works. Yes, I’m convinced that all traditional human belief systems,
from animism to Zoroastrianism—which, BTW, is chock full of
eschatological concepts that were already ancient by the time Yeshua
ben Yosuf (aka in Latin Jesus) was “magically” conceived aboard a
hovering UFO, if in fact there’s any glimmer of truth behind the
“virgin birth” legend—are, as the late Mircea Eliade pointed out some
years ago, essentially anthropocentric attempts to turn “Chaos” into
“Cosmos,” to impose an imagined order on what was, given the meager
objective knowledge base available to all pre-modern societies, an
otherwise utterly chaotic existence. Or, as the well-known
Anglo-Polish anthropologist Bronislaw Malinowski, whose researches
into the nature of religion were generally isomorphic with Eliade’s,
phased it: If human beings don’t have rational explanations and/or
empirically-based mechanisms that will allow them a modicum of
control over their environment, they will invent them. (Indeed,
Voltaire probably summed up this line of reasoning as succinctly as
anyone who came after him: If there were no God, it would be
necessary to invent one.)
That most, if not traditional human belief systems deeply reflect the
presence of the “Alien Raj” is undoubted. But that presence itself
was an integral part of the pre-modern chaos that, according to
Eliade, et al., engendered religion in the first place. That is,
the aliens came to be conceived of as divine beings, fairly folk,
etc.
The trap that Dan and his fellow “eschaton” mavens have fallen into,
aside from the absurdity of drawing specifically on the dogma of a
single, extremely derivative and highly syncretic religious belief
system that began as what amounted to a Judean “cargo cult” preached
by a figure who was most probably a heavily conditioned an alien
“subject,” is to take seriously the patently mythological concepts
our ancestors used to make sense out of the world. Indeed, the
inherently irrational concept of “faith” is part and parcel of this
archaic Weltanschauung, and it is faith rather than reason that
drives Smith and his fellow eschatologists.
A much more efficient model here, one that owes more to Marx than to
the Bible, is that the “Alien Raj” is an imperialist, exploitative
oppressor, rather than a supernatural phenomenon, as Dan and his
buddies appear to conceive it, despite their rhetoric, that has
managed to impose its will on this planet. To be sure, at present,
this authority is for the most part exercised clandestinely, but ask
any woman whose fetus has been forcibly removed whether this
authority actually exists. Dan dismisses the “Raj’s” DNA harvesting
as trivial, but I think he’s dead wrong here. Whatever else they may
be exploiting, human DNA appears to be the prime target, just as gold
was to the Conquistadors in Mexico and Peru half a millennium ago.
Indeed, the process of hybridization seems to be a central aspect of
their agenda, and, while I don’t take quite as pessimistic a position
David Jacobs does in THE THREAT, as I’m not convinced that they’re
out to totally replace us, it seems abundantly clear that their
agenda is NOT framed in terms of an altruistic effort to “uplift” us
to a “:higher spiritual level,” that is, to realize Dan’s
eschatological fantasies. Rather, like its terrestrial prototype,
the British Raj, its primary purpose is to administer the affairs of
this planet in such a way as to facilitate its imperialist agenda.
Thus, I while I don’t think they’re out to annihilate us—they could
have done so long since—I do think that we’re the “natives” and will
remain such until we manage to overthrow our planetary oppressors,
either through the efforts of a Gandhi-like moral force that appeals
to their “:better” nature (assuming they have one), or, more
probably, by someday getting our hands on enough of their technology
so we can effectively rise up against them. In other words, by
instigating a war of “planetary liberation,” I would, however,
caution against any rash actions here, as the technology we’re up
against makes the gap between Cortes and Moteczuma look
infinitesimal.
Complicating this “liberation” scenario is the high probability that
there exists a cadre of sell-outs, vendidos, as my Latino friends
would call them, who have sold out human autonomy for the
technological “trinkets” I mentioned in my previous post. These
would include the “insiders” Dan mentioned, as well as MJ-12 (or
whatever they call it at the moment), assuming they’re not one and
the same, as well as their counterparts in other highly developed
human societies, such as the U.K., Russia, Japan, and yes Israel,
etc.). I suspect this began with an unratified “treaty” negotiated
by Eisenhower at Edwards AFB in 1954, which, although periodically
modified, has continued in force up to the present. Again, there
are a many analogs in the history of terrestrial colonialism: the
Anglo-Indians, the Vietnamese Catholics, and other subsets of
conquered populations that accommodate to their oppressors in return
for some crumbs from the latters’ table. Indeed, the old
African-American label “Uncle Tom”—perhaps recast as “Uncle Homo
sapiens”—would seem apt here.
Finally, Caryn, as I’ve said before in our correspondence, to the
best of my conscious knowledge, I’ve never had the “pleasure” of
meeting the little buggers up close & personal. But I can certainly
sympathize with what you say here. The fact that you were unable to
perceive whether your captors were here “to save us or eat us!” fits
nicely with the hypothesis I’ve suggested, that is, that they, like
your fellow countrymen in India back in the 19th century, they are
here neither to destroy us nor to “redeem” us (although the British
Raj did have its share of pious missionaries who, when they weren’t
exploiting them, did their best to convert the Hindu and Moslem
“Wogs” to Christianity), but rather simply to exploit us (i.e., our
DNA) and other terrestrial resources they may need or desire.
Cheers,
Scotty
-----Original Message-----
From: Dan Smith [mailto:dantsmith@comcast.net]
Sent: Tuesday, September 14, 2004 10:49 AM
To: caryn anscomb; Scott Littleton; Jack Sarfatti; Nick Cook
Cc: Joel Isaacson; Colin Bennett; S-P Sirag; john dering; Warren
Hinckle; Tim Jerome; nancyWerd@aol.com; Randall Stickrod;
Amara@Kurzweilai. Net; RAY HUDSON; John Brandenburg; Dick Farley;
mitc1615@bellsouth.net; RICK DOTY; james norwood pratt; Jagdish Mann;
Constantin Ivanenko; David Gladstone; Gary S. Bekkum
Subject: Smelling a rat....
bcc.
Caryn,
We have insiders and outsiders. If the insiders wish to communicate
with the outsiders, they would naturally use intermediaries. It
appears that I'm being used as an intermediary.
The insiders and the visitors will come out of the closet at the
appropriate time. I am helping them to test the waters. That is
what the EFG is for.
Why don't your entities inform you about their agenda? It is simply
a matter of the Prime Directive, minimal interference.
The main point, however, is that the Eschaton is not their agenda.
It is OUR agenda. The Eschaton is of us, by us and for us. The
visitors are here as helpers. They are here to facilitate our
awakening to our own destiny.
You want to hear all this from the 'horse's mouth'. My purpose here
is to help demonstrate that we are the ultimate source for what has
happened and what is about to. You have come to the 'horse's mouth'
and it is us. Temporarily I am being the spokesperson, the
intermediary in helping us to realize that fundamentally we are the
co-creators of this reality, and we are its redeemers.
I do interpret this role in Christian terms. That is how it was
presented to me by Sophia. This is simply the completion of the
christ event. This is that unfinished business. Sophia is my
'horse's mouth'.
I am facilitating her communication. I'm playing the role of a
prophet. This role is traditionally reserved for mortals, rather
like you and me, not for ETs/UTs/Visitors.
Whatever role I am playing is apparently being overseen by the
insiders, the visitors and Sophia.
Now, Caryn, you are welcome to object to the prophetic tradition and
to my role as a putative prophet, but then you are under some
obligation to come up with a better plan. I'm certainly open to
discuss that, but I think you will end up reinventing this
same wheel.
The sooner that I can obtain a fair hearing from my peers, the sooner
will I be able to ride off into the sunset. So why don't we get onto
the business of discussing the why's and wherefores of all this?
Dan
P.S. I have just received a note from Gary Bekkum pointing to Steve
Greer's Aug. 8/9 interview on the Art Bell show. Here is an
excerpt:
SG: [chuckles] Look, this is - part of this isn't a rational
discussion and
here's why. You have people in this policy group, and there are two
or three
hundred people in it (some people call it the MJ-12 group, it's not
called
that anymore) and I know a number of these people in it.
AB: Do you think it really was once called that?
SG: Yes.
AB: Okay.
SG: What's interesting is that there is a hardcore center of it that
are
eschatologists. Okay? These are people who fantasize about how the
world is
going to end.
---------------------------------
Some folks have been trying to get this same message to Steve, but,
evidently, it is not quite fitting into his paradigm.
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