Monday, July 16, 2007

Feynman to me in 1968 at Cal Tech in his office: "Jack, always try to prove yourself wrong."

Hal missed his chance to cite The Son of God to me: "Let He who is without Sin cast the first stone." ;-)
A possible problem with my theory dawned on me at the gym just now, undoubtedly from increased blood circulation to my brain?

Note below 2nd draft in which I correct the 10^-22 error that should be 10^+22 and also some spacing errors in the excerpt from Ng's paper done in the Acrobat transformation from pdf to editable text. It's easier to read now.

I have to watch out that I also do not get numbers for the ZPE density that are much too large in ordinary space just like Hal does.

The induced gravity effect of this ZPE from Einstein's GR is approximately from

Guv + /\zpfguv = 0

d^2U/dr^2 ~ c^2/\zpf

U = ZPE induced gravity potential energy per unit test mass.

Note if /\zpf ~ constant

U ~ (1/2)c^2/\zpfr^2

3D harmonic oscillator.

for 1 cm scale

U ~ 10^21 r^2 ergs/gram

"g-acceleration" ~ - dU/dr ~ 10^21 r cm/sec^2

Much too big.

Yet on cosmic scale the formula does work.

i.e. 10^28/10^-33 ~ 10^61 whose square is 10^122

Note that hc/Lp4 ~ 10^-17 10^132 ~ 10^115 ergs/cc

10^-122 10^115 ~ 10^-7 ergs/cc

Note for comparison that the energy density of water in these units is 10^21 ergs/cc.

Note that on the scale of 1 cm if we use the general hologram formula

zero point energy density ~ hc/Lp^2(Area of surrounding surface of Volume-without-volume)^-1

we still get big numbers. For example if Area ~ 1 cm^2

ZPE density (1 cm scale) ~ 10^-17 10^66 ~ 10^49 ergs/cc ~ 10^28 density of water

Ng's hologram argument seems perfectly general for any scale. Yet Bekenstein's thermodynamics only applied to the event horizons of black holes where the light cones tipped over so much to form a trapped surface. The future causal horizon of dark energy de Sitter space may also qualify.

Hence, we seem to arrive at the rule

You can only use the hologram formula to compute ZPE density when there is a natural horizon in the problem.

The electron is like a tiny Kerr black hole but the effective gravity is much stronger.

You can still use the hologram generally for purposes of packing information into the fabric of spacetime, but you need the extra physics of a horizon to compute the zero point energy?

So it's not as simple as I thought. Never is.

On Jul 16, 2007, at 5:52 PM, Jack Sarfatti wrote:

What's wrong is that Hal has not identified all of the relevant parameters of the problem of the structure of the electron. There is no gravity in his model. In fact gravity gets stronger as the scale decreases. This last statement comes from a Wignerian analysis of quantum gravity measurement as shown by Ng & Van Dam below.

Let me make it as simple as possible, but not, like Hal's model, simpler than is possible.

You have a shell of electric charge. How do you prevent it from exploding under its self-repulsion?

You have two options:

1. Press in radially on the thin shell of charge from outside the shell.

2. Suck in from the inside of the shell.

Hal chooses 1. The correct answer is 2.

The problem with 1 is that it requires too much zero point energy ZPE density on the outside of the shell. So much that the universe could not exist. Hal needs ~(hc/Lp^2)(mc/h)^2 ZPE energy density outside the shell of charge to contain the charge. The virtual photon density outside the charge has w = -1 and is positive. Therefore, the pressure is negative. Hal cannot use w = +1/3 DeWitt outside the charged shell. DeWitt's solution is inside the charged shell.

Pressure acts in two different ways, mechanically and gravitationally. Usually the gravitation of pressure is much weaker than its mechanical action. Note that this mechanical action is basically electrical in origin. The Casimir effect is mechanical.

Hal models his electric shell as empty inside with mechanical pressure from virtual photons on the outside pushing radially inward on the charge. This is his picture. It's wrong for several reasons.

1) the virtual photon pressure on the outside is negative not positive because w = -1 on the outside.

2) there are virtual photons on the inside and from Dw Witt w = +1/3 on the inside.

Therefore, mechanically the positive pressure on the inside pushes the charge outward, and the negative pressure on the outside also sucks the charge radially outward. Therefore, there is no mechanical (electrical) containment of the shell of charge at all!

Remember pressure is the component of force along the normal unit vector of a surface per unit area of that surface.

That's the mechanical action. The gravity action of pressure is opposite to the mechanical action, although usually it is too small to notice compared to the mechanical action in every case except for this one of zero point energy!

Positive pressure gravitates attractively. Therefore, a positive pressure inside the shell of charge will suck the charge radially inward. The issue is how strong is it? Also negative pressure outside the shell of charge anti-gravitates pushing the charge radially inward.

Now it turns out that the zero point energy density inside the shell of charge is

(hc/Lp^2)(mc/h)^2 ~ 10^-27 10^10 10^66 10^+22 ergs/cc ~ 10^71 ergs/cc

The induced gravity effect of this ZPE from Einstein's GR is approximately from

Guv + /\zpfguv = 0

d^2U/dr^2 ~ c^2/\zpf ~ c^2(mc/h)^2

U = ZPE induced gravity potential energy per unit test mass.

Note if /\zpf ~ constant

U ~ (1/2)c^2(mc/h)^2r^2

3D harmonic oscillator.

In fact, the ZPE density outside the charge, if there are no further boundaries is very small

PS the above formula and also

(hc/Lp^2)(mc/h)^2

are both consistent with the world hologram hypothesis - see below.

On Jul 15, 2007, at 3:30 PM, Jack Sarfatti wrote:

PS There is no mention of ZPE induced gravity in Hal's paper. Therefore the paper is wrong. Hal has not asked the correct question to solve the problem - neither did Casimir of course.

On Jul 15, 2007, at 1:30 PM, Puthoff@aol.com wrote:

Hi Paul, attached is my latest use of the ZPE formalism, just came out in Int. Jour. Theor. Phys.  Shows how the formalism leads naturally to a point electron without infinite mass generated by the coulomb fields.

Cheers,
Hal

http://arxiv.org/abs/gr-qc/0403057 v1 13 Mar 2004

“In essence, the holographic principle says that although the world around us appears to have three spatial dimensions, its contents can actually be encoded on a two-dimensional surface, like a hologram … According to the holographic principle, the number of degrees of freedom that this cubic region can contain is bounded by the surface area of the region in Planck units, i.e., l^2/LP^2instead of by the volume l^3/LP^3 of the region as one may naively expect. This principle is counter-intuitive, but is supported by black hole physics in conjunction with the laws of thermodynamics, and it is embraced by both string theory and loop quantum gravity … the “strange” holographic principle has its origin in quantum ﬂuctuations of spacetime.”

I. And also by my theory where the emergent coherent macro-quantum vacuum condensate tetrad 1-forms are

e^a = I^a + (LP^2/l^2)^1/3A^a

A^a= M^a^a

is the renormalizable spin 1 Yang-Mills tetrad field "square root" of Einstein's non-renormalizable spin 2 tensor theory. The Mystery Matrix of Goldstone phase 0-forms of the coherent post-inflationary vacuum is

M^a^a= Theta^a/\dPhi^a- dTheta^a/\Phi^a

Where Einstein's 1916 GR is recovered in the bilinear forms of the spin 1 tetrad fields

ds^2 = guvdx^udx^v = e^aea

That in a nutshell is my new and completely original theory in my

http://arxiv.org/abs/gr-qc/0602022

Emergent Gravity and Torsion: String Theory Without String Theory, Why the Cosmic Dark Energy Is So Small

Jack Sarfatti
(Submitted on 7 Feb 2006 (v1), last revised 11 Jul 2007 (this version, v21))
A surprisingly simple holographic explanation for the low dark energy density is suggested. I derive the Einstein-Cartan disclination curvature tetrads and the physically independent dislocation torsion gap spin connections from an "M-Matrix" of non-closed Cartan 1-forms made from 8 Goldstone phase 0-forms of the vacuum ODLRO condensate inflation field in which the non-compact 10-parameter Poincare symmetry group is locally gauged for all invariant matter field actions. Quantum gravity zero point vacuum fluctuations should be renormalizable at the spin 1 tetrad level where there is a natural scale-dependent holographic dimensionless coupling (hG/\zpf/c^3)^1/3 ~ (Bekenstein BITS)^-1/3. The spacetime tetrad rotation coefficients play the same role as do the Lie algebra structure constants in internal symmetry spin 1 Yang-Mills local gauge theories. This suggests an intuitively pleasing natural "organizing idea" now missing in superstring theory. It is then clear why supersymmetry must break in order for our pocket universe to come into being with a small w = -1 negative pressure zero point exotic vacuum dark energy density. Just as the Michelson-Morley experiment gave a null result, this model predicts that the Large Hadron Collider will never find any viable on-mass-shell dark matter exotic particles able to explain Omega(DM) ~ 0.23 as a matter of fundamental principle, neither will any other conceivable dark matter detector because dark matter forming galactic halos et-al is entirely virtual exotic vacuum w = - 1 with positive irreducibly random quantum zero point pressure that mimics w = 0 CDM in its gravity lensing and all effects that we can observe from afar.

Comments: This version is the second major revision addressing several unresolved fundamental empirical problems
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:gr-qc/0602022v21

II. Next to Ng & Van Dam

"SPACETIME FOAM, HOLOGRAPHIC PRINCIPLE, AND BLACKHOLE QUANTUM COMPUTERS

Y. JACK NG AND H. VAN DAM

Institute of Field Physics, Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC27599-3255,USA E-mail: yjng@physics.unc.edu

Spacetime foam, also known as quantum foam, has its origin in quantum ﬂuctuations of spacetime. Arguably it is the source of the holographic principle, which severely limits how densely information can be packed in space. Its physics is also intimately linked to that of black holes and computation. In particular, the same underlying physics is shown to govern the computational power of black hole quantum computers.

1. Introduction

Early last century, Einstein’s general relativity promoted spacetime from a passive and static arena to an active and dynamical entity. Nowadays many physicists also believe that spacetime, like all matter and energy, undergoes quantum ﬂuctuations. These quantum ﬂuctuations make spacetime foamy on small spacetime scales. (For a discussion of the relevant phenomenology and for a more complete list of references, see Ref. 1.)

But how large are the ﬂuctuations? How foamy is spacetime? Is there any theoretical evidence of quantum foam? In what follows, we address these questions. By analysing a gedanken experiment for spacetime measurement, we show, in section 2, that spacetime ﬂuctuations scale as the cube root of distances or time durations.Then we argue that this cube root dependence is consistent with the holographic principle. In section 3, we discuss how quantum foam affects the physics of clocks (accuracy and lifetime) and computers (computational rate and memory space). We also show that the physics of spacetime foam is intimately connected to that of black holes, giving a poor man’s derivation of the Hawking black hole lifetime and the area law of black hole entropy. Lastly a black hole computer is shown to compute at a rate linearly proportionalto its mass.

2. Quantum Fluctuations of Spacetime

If spacetime indeed undergoes quantum ﬂuctuations, the ﬂuctuations will show up when we measure a distance (or a time duration), in the form of uncertainties in the measurement. Conversely, if in any distance (or time duration) measurement, we cannot measure the distance (or time duration) precisely, we interpret this intrinsic limitation to spacetime measurements as resulting from ﬂuctuations of spacetime.

The question is: does spacetime undergo quantum ﬂuctuations? And if so, how large are the ﬂuctuations? To quantify the problem, let us consider measuring a distance l. The question now is: how accurately can we measure this distance? Let us denote by dl the accuracy with which we can measure l. We will also refer to dl as the uncertainty or ﬂuctuation of the distance l for reasons that will become obvious shortly. We will show that dl has a lower bound and will use two ways to calculate it. Neither method is rigorous, but the fact that the two very different methods yield the same result bodes well for the robustness of the conclusion. (Furthermore, the result is also consistent with well-known semi-classical black hole physics. See section 3.)

3. Gedanken Experiment. In the ﬁrst method, we conduct a thought experiment to measure l. The importance of carrying out spacetime measurements to ﬁnd the quantum ﬂuctuations in the fabric of spacetime cannot be over-emphasized. According to general relativity, coordinates do not have any intrinsic meaning independent of observations; a coordinate system is deﬁned only by explicitly carrying out spacetime distance measurements. Let us measure the distance between two points. Following Wigner 2, we put a clock at one point and a mirror at the other. Then the distance l that we want to measure is given by the distance between the clock and the mirror. By sending a light signal from the clock to the mirror in a timing experiment, we can determine the distance l. However, quantum uncertainties in the positions of the clock and the mirror introduce an inaccuracy dl in the distance measurement. We expect the clock and the mirror to contribute comparable uncertainties to the measurement. Let us concentrate on the clock and denote its mass by m. Wigner argued that if it has a linear spread dl when the light signal leaves the clock, then its position spread grows to dl+hl(mcdl)^-1 when the light signal returns to the clock, with the minimum at dl =(hl/mc)^1/2."

[Note by JS: this is the geometric mean of the shortest Compton quantum length and the “longest” length we are measuring. No gravity as yet.]

"Hence one concludes that

dl^2 > hl/mc  (1)

General relativity provides a complementary bound.To see this, let the clock be a light-clock consisting of a spherical cavity of diameter D, surrounded by a mirror wall of mass m, between which bounces a beam of light. For the uncertainty in distance measurement not to be greater than D, the clock must tick off time fast enough that
D/c < dl/c. But D, the size of the clock, must be larger than the Schwarzschild radius rS = 2Gm/c^2 of the mirror, for otherwise one cannot read the time registered on the clock. From these two requirements, it follows that

dl > Gm/c2  (2)

The product of Eq. (2) with Eq. (1) yields Eq. (3)

dl > [(hl/mc)(Gm/c2)] 1/3 = (LP2l)1/3  (3)

where LP = (hG/c3)^1/2 is the Planck length. (Note that the result is independent of the mass m of the clock and, hence, one would hope, of the properties of the speciﬁc clock used in the measurement.) The end result is as simple as it is strange and appears to be universal: the uncertainty dl in the measurement of the distance l cannot be smaller than the cube root of LP^2l.

Obviously the accuracy of the distance measurement is intrinsically limited by this amount of uncertainty or quantum ﬂuctuation. We conclude that there is a limit to the accuracy with which one can measure a distance; in other words, we can never know the distance l to a better accuracy than the cube root of LP^2l .

Similarly one can show that we can never know a time duration t to a better accuracy than the cube root of LP^2t/c2 = tP^2t where tP= LP/c is the Planck time. Because the Planck length is so inconceivably short, the uncertainty or intrinsic limitation to the accuracy in the measurement of any distance, though much larger than the Planck length, is still very small. For example, in the measurement of a distance of one kilometer, the uncertainty in the distance is to an atom as an atom is to a human being.

4. The Holographic Principle. Alternatively we can estimate dl by applying the holographic principle. 4,5 In essence, the holographic principle 6 says that although the world around us appears to have three spatial dimensions, its contents can actually be encoded on a two-dimensional surface, like a hologram. To be more precise, let us consider a spatial region measuring l by l by l. According to the holographic principle, the number of degrees of freedom that this cubic region can contain is bounded by the surface area of the region in Planck units, i.e.,l^2/LP^2 instead of by the volume l^3/LP^3 of the region as one may naively expect. This principle is counter-intuitive, but is supported by black hole physics in conjunction with the laws of thermodynamics, and it is embraced by both string theory and loop quantum gravity. So strange as it may be, let us now apply the holographic principle to deduce the accuracy with which one can measure a distance.

First, imagine partitioning the big cube into small cubes. The small cubes so constructed should be as small as physical laws allow so that we can associate one degree of freedom with each small cube. In other words, the number of degrees of freedom that the region can hold is given by the number of small cubes that can be put inside that region. But how small can such cubes be? A moment’s thought tells us that each side of a small cube cannot be smaller than the accuracy dl with which we can measure each side l of the big cube. This can be easily shown by applying the method of contradiction: assume that we can construct small cubes each of which has sides less than dl. Then by lining up a row of such small cubes along a side of the big cube from end to end, and by counting the number of such small cubes, we would be able to measure that side (of length l) of the big cube to a better accuracy than dl. But, by deﬁnition, dl is the best accuracy with which we can measure l. The ensuing contradiction is evaded by the realization that each of the smallest cubes (that can be put inside the big cube) measures dl by dl by dl. Thus, the number of degrees of freedom in the region (measuring l by l by l) is given by l^3/dl^3, which, according to the holographic principle, is no more than l^2/LP^2. It follows that

l^3/dl^3 < l^2/LP^2"

JS: Note the algebra

l^3 < l^2dl^3/LP^2

l < dl^3/LP^2

lLP^2 < dl^3

"dl is bounded (from below) by the cube root of lLP^2 the same result as found above in the gedanken experiment argument. Thus, to the extent that the holographic principle is correct, spacetime indeed ﬂuctuates, forming foams of size dl on the scale of l. Actually, considering the fundamental nature of spacetime and the ubiquity of quantum ﬂuctuations, we should reverse the argument and then we will come to the conclusion that the 'strange' holographic principle has its origin in quantum ﬂuctuations of spacetime."

Rest of paper is deleted from this excerpt as it is peripheral to my purpose at the moment. BTW I knew Saleckar at UCSD La Jolla in the 60’s.

"One of us (YJN) thanks the organizers of the Coral Gables Conference for inviting him to present the materials contained in this paper. We dedicate this article to our colleague Paul Frampton on the occasion of his sixtieth birthday. This work was supported in part bythe US Department of Energy and the Bahnson Fund of the University of North Carolina. We thank L. L. Ng and T. Takahashi for their help in the preparation of this manuscript.

References

1. Y. J. Ng, Mod.Phys.Lett.A18, 1073 (2003). See also Y.J. Ng, gr-qc/0401015.

2. E.P. Wigner, Rev.Mod.Phys.29, 255 (1957); H. Salecker and E.P. Wigner, Phys.Rev.109, 571 (1958).

3. Y.J. Ngand H. van Dam, Mod.Phys.Lett.A9, 335 (1994);A10, 2801 (1995); in Proc.of Fundamental Problems in Quantum Theory, eds. D.M. Greenberger and A. Zeilinger, Ann. New York Acad. Sci.755, 579 (1995). Also see F. Karolyhazy, Nuovo CimentoA42, 390 (1966);T. Padmanabhan,Class.Quan.Grav.4, L107 (1987); D.V. Ahluwalia, Phys.Lett.B339, 301 (1994); and N. Sasakura,Prog.Theor.Phys.102, 169 (1999).

4. Y. J. Ng and H. van Dam, Found.Phys.30, 795 (2000);Phys.Lett. B477, 429 (2000).

5. Y. J. Ng, Int.J.Mod.Phys.D11, 1585 (2002).

6. G. ’t Hooft, in Salamfestschrift, edited by A. Ali et al. (World Scientiﬁc, Singapore, 1993), p. 284; L. Susskind, J.Math.Phys.(N.Y.)36, 6377 (1995). Also see J.A. Wheeler, Int.J.Theor.Phys.21, 557 (1982); J.D. Bekenstein, Phys.Rev.D7, 2333 (1973); S. Hawking, Comm.Math.Phys.43, 199 (1975).

7. Y. J. Ng, Phys.Rev.Lett.86, 2946 (2001), and (erratum)88, 139902-1 (2002);

Y. J.Ng in Proc.of OCPA2000, eds. N. P. Chang et al. (World Scientiﬁc, Singapore, 2002), p.235.

J.D. Barrow, Phys.Rev.D54, 6563 (1996).

N. Margolus and L. B. Levitin,Physica D120, 188 (1998).

S. Lloyd, Nature(London)406, 1047 (2000)."
---------------------------------------------------
On Jul 15, 2007, at 3:14 PM, Jack Sarfatti wrote:

<52458_bPU113005_2sm.jpg>
http://www.innovations-report.de/html/berichte/physik_astronomie/bericht-52458.html

The close-packed little (figuratively speaking of course) "green balls" of "Volume-without-volume" are of size

&l ~ N^1/6 Lp

There is a point gravity monopole inside each "green ball" where the vacuum ODLRO order parameter drops to zero leaving the two effective 3D + 1 Goldstone phases undefined corresponding to this S^2 "vacuum manifold" of minima for coherently ordered holgraphic ground states of virtual quanta.

the surrounding surface area is A

N ~ A/Lp^2

In the case of a single electron

A ~ 10^-22 cm^2 corresponding to the shell of electric charge

N ~ 10^-2210^66 ~ 10^44

&l ~ 10^7Lp ~ 10^-27 cm

This is very much like Ken Wilson's "renormalization group" in lattice gauge theory.

http://nobelprize.org/nobel_prizes/physics/laureates/1982/wilson-lecture.pdf

Note also on meaning of holography

"Euclidean quantum field theory in d-dimensional spacetime ~ classical statistical mechanics in d-dimensional space." A. Zee p. 262 "Quantum Field Theory in a Nutshell"

Therefore Euclidean quantum field theory on the ANYONIC fractional QM statistics 3-dimensional spacetime of the surrounding surface ~ classical statistical mechanics in 3-dimensional space, i.e. volume without volume.

On Jul 15, 2007, at 2:30 PM, Jack Sarfatti wrote:

For the record I think Hal's paper is wrong. He has it inside out. Indeed the de Witt calculation show that the interior ZPF has w = +1/3 therefore positive ZPF pressure with positive ZPE density /\zpe ~ (mc/h)^2 ~ 10+22 cm^-2 is INSIDE and induces strong enough micro-gravity to glue the surface electric charge together. The outside ZPE density has w = -1 and is very small. Hal's picture is qualitatively wrong IMHO.

Note in the world hologram picture of t'Hooft as further clarified by Jack Ng's very readable papers (Univ. Maryland):

ZPE density is hc/NLp^4 = (hc/Lp^2)/\zpf

/\zpf ~ 1/NLp^2 ~ (10^66/N)cm^-2

N ~ 10^-2210^66 ~ 10^44

/\zpf ~ 10^22 cm^-2

Very very pretty picture!

It works. It really works semi-quantitatively.

Also the electron is not a point. It is a spatially extended Bohm hidden variable, but its gravity is so strong that it looks like a point by the time the scattering momentum transfers are ~ 2mc ~ 1 Mev

Hal's picture only works if you assume that uniform ZPE does not gravitate. This is wrong and squarely contradicts Einstein's GR as does his PV model.

Hal's paper shows what not to do.

On Jul 15, 2007, at 1:30 PM, Puthoff@aol.com wrote:

Hi Paul, attached is my latest use of the ZPE formalism, just came out in Int. Jour. Theor. Phys.  Shows how the formalism leads naturally to a point electron without infinite mass generated by the coulomb fields.

Cheers,
Hal