Metric Engineering Flying Saucer Engines
The key quantity in Puthoff's PV model, a wrong model falsified by experiment, better than not-even-wrong models (W. Pauli) is g00. What is goo really? What it is, is
g00(LNIF) = (I0^a + LpB0^aPa(Goldstone Phase)/ih)(LIF)ab(I0^b + LpB0^bPb(Goldstone Phase)/ih)
Where (LIF)ab is the Minkowski metric i.e +1, -1,-1,-1 all off-diagonals = 0, and I is the Kronecker delta, i = 1,2,3
g00 = 1 + 2LpB0^0P0(GP)/ih - 2LpB0^iPi(GP)/ih - Lp^2(B0^0P0(GP)/ih)^2 - Lp^2(B0^iPi(GP)/ih)^2
if I did not make a mistake in algebra.
What is really interesting are the LINEAR terms in Lp that are much larger than the quadratic terms!
In particular, when there is a gravimagnetic field goi from a rotating high Tc superconducting part of the saucer fuselage maybe, we get something like
g0i(LNIF) = (I0^a + LpB0^aPa(Goldstone Phase)/ih)(LIF)ab(Ii^b + LpBi^bPb(Goldstone Phase)/ih)
Again there will be relatively large Lp terms in the gravimagnetic field to couple to the EM 3-vector potential Ai in the Ray Chiao "gravity radio transducer" idea.
This is a BRUTE FORCE method. Mine is more subtle like Tai Chi i.e. imagine a the control macro-quantum phase is something like
Theta = (e/hc)Integral A.dl
With Pa operating on the Josephson phase difference
Goldstone Phase (GP) - Theta
The local zero point energy density is ~ cos[GP - Theta].
When this zero point energy density is negative we have equal opposite positive pressure causing an attractive contractive warp. On the other hand, when this zero point energy density is positive we have a negative pressure repulsive expansive warp. This is exactly what the Alcubierre "G-Engine" weightless timelike geodesic glider globally faster-than-light (locally standing still) time travel machine needs! The objections of Matt Visser and Stephen Hawking et-al are obviously not fatal barriers since we see the damn things over our nuclear missile bases according to Peter Jennings ABC TV Special on Feb 24, 2005. The Cat is Alive and Out of the Box. You want Disclosure? Now you got it. What's up Pussy Cat? We got a Tiger Tiger Eyes Shining Bright in The Dark Energy of The Knight! :-)
On Mar 12, 2005, at 3:08 PM, Jack Sarfatti wrote:
On Mar 12, 2005, at 2:05 PM, firstname.lastname@example.org wrote:
Coming from someone who has now completely caved in to my position re: Einstein equivalence, this is hilarious.
Paul you continue in your delusion that somehow I renounce EEP? In fact, the opposite is true. EEP in math form is simply
g(LNIF) = (I + B)(Minkowski)(I + B)
e = (I + B) is Einstein-Cartan tetrad
B is the "gauge force" picture i.e. T4 -> Diff(4)
B is the compensating field that RESTORES conservation of Pu currents including the new dynamical degrees of freedom of the B connection field.
The B connection is not the same as the (LC) connection in the geometrodynamic picture.
The EEP is the BRIDGE between the Gauge Force picture and the Geometrodynamic picture!
I do not in any sense "renounce equivalence"!
Given a metric without gravimagnetism i.e. goi = 0 (no rotating sources)
ds^2 = goo(cdt)^2 - gijdx^idx^j
i,j = 1,2,3
dT = (goo)^1/2dt
dL = (gijdx^idx^j)^1/2
For a light ray
ds^2 = c^2dT^2 - dL^2 in the LNIF
ds = 0 (null geodesic)
Therefore, the PHYSICALLY MEASURED SPEED OF LIGHT for that LNIF observer who sees the above metric will be c the same as in special relativity, i.e.
dL/dT = c in the LNIF as well as the COINCIDENT LIFs.
The COINCIDENT LIFs and LNIFs are connected together by the Einstein-Cartan tetrad (I + B) where B is the compensating gauge potential connection field from locally gauging global T4 to Diff(4).
Z: Excuse me -- my contention was that *in 1916 Einstein GR* the locally measured speed of light is always c *only in free-fall frames*.
J: Well you are wrong!
Z: The above is not 1916 GR.
J: It certainly is. You do not know enough of the math to see GR when it is staring you in the face as it is.
dT = goo^1/2dt
dL = (gijdx^idx^j)^1/2
i,j = 1,2,3
in LNIFs is in GR text books.
You get rotational Sagnac interferometer shifts in SPEED of light only when there is a gravimagnetic field H = (goi) as defined by Ray Chiao in his "gravity radio" papers.
His superconducting high-efficiency transducer posits a H.A gravity-EM coupling where A is the 3-vector potential of EM in the NR Galilean relativity limit.
Z: It's really very simple. Suppose you have a plane wave in gravity-free spacetime, propagating at every point at the invariant speed c as measured in an inertial frame K. Now go to an accelerating frame K' that is accelerating in a direction perpendicular to the direction of propagation of the wave. The normals to the wave fronts of the formerly plane wave now appear to change continuously in time, tracing *curved* spatial trajectories.
J: Show the math Paul! This is essentially gravity lensing. It does not imply that magnitude is changing only refraction change of direction.
Z: According to the equivalence principle, the effect of some homogeneous gravitational field on the same wave, as observed from the original inertia frame K, must be identical to the effect of going to the accelerating frame K' Clearly, if the light path is now curved, then the speed of propagation of the waves must vary from point to point on any given wavefront,
J: NONSENSE PAUL! When the metric is of the form:
ds^2 = goo(cdt)^2 - gijdx^idx^j = (cdT)^2 - dL^2
i,j = 1,2,3
the LNIF measured speed of light when ds = 0 is still
dL/dT = c same as in the COINCIDENT LIF.
, either in a gravity-free accelerating frame, or in a gravitational field viewed from an inertial frame -- as consistently affirmed by Einstein himself:
". . . according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position."
- A. Einstein, "The Meaning of Relativity"
J: Hey Professor! Einstein uses "velocity" not "speed" there! Clean your glasses.
"A curvature of rays of light can only take place when the VELOCITY of propagation of light varies with position."
IS GENERALLY TRUE FOR ALL WARPED METRICS
"A curvature of rays of light can only take place when the SPEED of propagation of light varies with position."
IS FALSE and that is not what Einstein wrote! Paul, you garbled the difference between 'velocity" and "speed"!
A gravimagnetic field (Lense-Thirring frame drag) will IN ADDITION change the SPEED of light in vacuum, e.g. Sagnac effect, which even happens in special relativity and even in the Galilean limiting case since the fringe shifts are seen in lab experiments.
Now, if there is gravimagnetic Lense-Thirring "frame drag", then, in the LNIF
ds^2 = c^2dT^2 - dL^2 - Hcdt.dr
H is the gravimagnetic 3-vector with components (g0i) and dr is the 3-vector with components (dx^i)
Again ds = 0
(dL/dT)^2 = c^2 - cH(dt/dT).(dr/dT)
The speed of light in a gravimagnetic field is then
dL/dt = c[1 - (dt/dT)H.(dr/cdT)]^1/2
Note the effective sign inside the square root flips when you change the rotation sense. Of course, Paul you never formulated this mathematically, nor did he make any specific remarks of any utility on this problem.
Z: You are not addressing my actual statement, which is that *in 1916 Einstein GR* the locally measured speed of light is always c only in free-fall frames:
". . . according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [. . .] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position."
- A. Einstein, "The Meaning of Relativity"
J: Answered above. Your sloppy thinking again mistaking "velocity" a vector for "speed" the magnitude of the vector.
Puthoff also makes a similar mistake thinking that goo is a "dielectric", i.e. Puthoff-Davis-Yilmaz use:
ds^2 = goo(cdt)^2 - goo^-1(dx^2 + dy^2 + dz^2)
dl^2 = dx^2 + dy^2 + dz^2
Therefore, when ds = 0
dL/dT = c
dl/dt = c/goo = c/K
goo = n = index of refraction in PV picture
goo = e^-2GM/c^2r is further assumed.
But of course this is wrong since dl/dt is never measured. Hal Puthoff does an ultra-heretical meta-theoretical song and dance Dog and Pony show here that makes Matt Visser and Cliff Will red in the face, that, no doubt, you will think is brilliant. "No possible doubt whatever!"(Gondoliers);-)
*The Sagnac effect for rotating interferometers is an example. This formula applies even in GLOBAL SR without tidal curvature in the rotating GNIF.
Z: That's another can of worms.
J: Not at all. It's simply until you mistify and mystify it with your ultra-heretical meta-theoretics
On Mar 12, 2005, at 10:25 AM, Jack Sarfatti wrote:
On Mar 11, 2005, at 10:12 PM, email@example.com wrote:
Jack Sarfatti wrote:
"Replace light signals with sound to define time" - a genius idea from Zielinski! ;-)
Z: Well, the sophistication of this dialectical maneuver evidently went right over your head.
J: Oh yeah? Tell us how to do cosmology with sound waves? The point Paul is that the invariant light cone structure is essential to all practical applications in precision cosmology. Indeed, tidal curvature, as shown by Penrose, is a relative tilt between neighboring invariant light cones.
Z: Once you adopt 1905 Einstein kinematics, then of course it becomes fundamental to cosmology.
J: How else would YOU do cosmology? Also you cannot use Lorentz theory to get gravity!
Z: Except that GR, which is in fact the actual chronogeometric basis for modern cosmology, supersedes SR and only preserves the empirical predictions of SR locally, by way of correspondence -- and it even does away with invariant light speed as to local observations made in *non-inertial* frames!
J: Of course, so what? You characteristically state well-known facts of relativity AS IF somehow they are defects in it when just the opposite is true! You have no understanding of local gauge invariance, which, in this case is the local gauging of T4 to Diff(4) whose compensating field Bu^a is precisely the non-trivial part of the Einstein-Cartan tetrad responsible for "intrinsic warpage" distinguishing the REAL gravity from the ARTIFICIAL gravity in Minkowski space-time. A problem you were interested in, that you never formulated properly, much less solve. I solved it. In Minkowski space-time Bu^a = 0, the Einstein-Cartan tetrad is the trivial identity Iu^a, the tangent bundle and the base space are degenerate and any GCT made on (Minkowski)uv is simply ARTIFICIAL gravity like in a rotating GNIF since the tidal curvature tensor vanishes in (Minkowski)uv it will vanish in any GCT made on it. You need the B field to get real gravity.