“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
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
Emergent Gravity and Torsion: String Theory Without String Theory, Why the Cosmic Dark Energy Is So Small
(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: email@example.com
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.
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, thatspacetime ﬂuctuations scale as the cube root of distances or time durations.Then we argue thatthis 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 distancel. The question now is: how accurately can we measure this distance?Let us denote by dl the accuracy with which we can measurel. We will also refer to dl as the uncertainty or ﬂuctuation of the distancelfor 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 tto 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 estimatedlby 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 counterintuitive, 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 thandl. 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.
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); inProc.of Fundamental Problems inQuantum Theory, eds. D.M. Greenberger and A. Zeilinger, Ann. New York Acad. Sci.755, 579 (1995). Also see F. Karolyhazy,NuovoCimentoA42, 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, inSalamfestschrift, 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 inProc.ofOCPA2000, 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:
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.
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.
Get a sneak peak of the all-new AOL.com.