Monday, September 05, 2005

Leonard Susskind's book on Black Holes & Strings

6. "The Questions are: What are [Lenny's] Questions?"

"It was assumed that all observers would agree on the usual invariant relationships between events. This view persisted even in classical general relativity. But the paradigm is gradually shifting. It was never adequate to deal with the combination of quantum mechanics and general relativity."

Actually Lenny is raising a Red Herring here, although it does not affect some of his conclusions.

The agreement of observers is strictly for LOCAL COINCIDENT observers all in the same local neighborhood. It does not at all apply to widely separated observers in the "black hole complementarity" gedanken experiment.

The issue however is to avoid contradictions when LIF Alice or coincident LNIF hovering Bob communicates with distant LNIF Eve in the asymptotic flat region before Alice plunges into the horizon like Tit Willow into the billowy wave.

Consider a proton passing through the horizon, the time for the virtual transitions is stretched out for the distant observer Eve by the red shift. Eve sees a "short-lived virtual fluctuation stretched out into a real process" p. 92. Essentially all contradictions are avoided by the implications of this insight. The proper temperature T of the Hawking radiation is ~ hovering "g-force" acceleration by the Unruh effect so that it is also going to infinity as (1 - 2GM/c^2r)^-3/2 as r approaches 2GM/c^2 from the outside.

"In order to make an observation while the proton" [LIF Alice] is in a region of temperature" [greater than that needed for baryon number violation for example] "the" [coincident LNIF observer Bob] must do so very quickly. In the proton's" [LIF] "frame the time spent in the hot region before crossing the horizon" [is very short] "1/Mx. Thus, to obtain a single bit of information" [Bob] "must probe it with at least one quantum of energy of order Mx. But such an interaction ... can cause a baryon violation even from the perspective of the proton" [Alice] "Thus the observer" [Bob] cannot measure and report" [to Eve] "the absence of a baryon-violating interaction without himself causing it."

The situation here is akin to the Einstein-Bohr Box gedankenexperiment.

"an unprecedented mix of short distance and long distance. Radical changes ..."

As Above, So Below

"Black Hole Complementarity ... a new kind of relativity in which the location of phenomena depends upon the resolution time available to the experimenter who probes the system ... Alice" [Through The Looking Glass, Down the Wabbit Hole]", falling into an enormous black hole with Schwarzschild radius of a billion years. According to the low frequency observer, namely Alice herself ... nothing special is felt at the horizon ... In apparent complete contradiction, the high frequency observer who stays outside the black hole finds that his description involves Alice falling into a hellish region of extreme temperature, being thermalized, and eventually re-emitted as Hawking radiation. All of this takes place just outside the mathematical horizon ... the key to black hole complementarity is the extreme red shift of the quantum fluctuations as seen by the external observer."

Note that to a hovering rest LNIF observer Bob outside, but near to, the horizon Alice's LIF 21 cm signal, in her rest frame, to Bob sent from when she was far away from the horizon in the asymptotic flat region coincident with Eve is, is blue shifted to a much shorter wavelength, That same 21 cm signal sent by Alice when coincident with Bob near, but outside the horizon will be red shifted to a much longer wavelength received by Eve also hovering but at a huge distance from the horizon. Both Bob and Eve are non-geodesic feeling g-force from firing a rocket in space. Eve is practically weightless compared to Bob. Bob's g-force approaches infinity as he gets closer HOVERING a small distance above the horizon, i.e., (g-force)^i ~ mc^2(LC)^i00 ~ [(1 - 2GM/c^2r)^-3/2](GMm/r^2) (check this formula I did it quick & dirty).

"The second new idea is the Infrared/Ultraviolet connection ... If one wished to study ... smaller and smaller objects one had to use higher and higher energy probes ...But once gravity is involved that trend is reversed ... At energies above the Planck scale any possible short scale physics is shrouded behind an event horizon."

Note that Hal Puthoff's PV SSS metric without an event horizon is inconsistent with this IR/UV duality. It has other things wrong with it as well of course.

"Third is the holographic principle, the non-redundant degrees of freedom that describe a region of space are on its boundary."

Remember the generalized Stoke's theorem

(p+1|d|p) = (&(p+1)|p)

d = exterior derivative

& = boundary operator

|p) = p-form

(p+1| is a p+1 co-form manifold on which to integrate p+1 forms (bra-ket inner product).

When the manifold co-form is multiply-connected with cohomology group larger than the identity, there are cycles that are not boundaries.

Let p = 2 in 4D space-time, then

(3|d|2) = (&3|2)

In 3D-space this would be the static divergence theorem, but now we are in 4D space-time. The World Hologram seems to be connected with this theorem?

In general relativity both curvature and torsion are |2> forms.

The curvature 2-form is

R = DW = dW + W/\W

W = the spin connection 1-form

The torsion is

T = De = de + W/\e = 0 in 1915 GR so W determined by e

e = Einstein-Cartan tetrad "square root" of the metric tensor.

In my emergent vacuum ODLRO c-number theory

e = 1 + B

this is all local frame-invariant

B = (hG/c^3)^1/2d(Mean Goldstone Phase of SU(2)hypercharge SSB)

Therefore, from topological

(3|d|2) = (&3|2)

(3|(D - W/\|R) = (&3|R)

Which is kind of interesting to ponder before going on to black hole as string idea.

to be continued

On Sep 5, 2005, at 10:37 AM, Jack Sarfatti wrote:


"It was assumed that all observers would agree on the usual invariant relationships between events. This view persisted even in classical general relativity. But the paradigm is gradually shifting. It was never adequate to deal with the combination of quantum mechanics and general relativity."

Actually Lenny is raising a Red Herring here, although it does not affect some of his conclusions.

The agreement of observers is strictly for LOCAL COINCIDENT observers all in the same local neighborhood. It does not at all apply to widely separated observers in the "black hole complementarity" gedanken experiment. That is consider three observers, Alice, Bob and Eve.

Alice is LIF ("FREDO") and Bob is LNIF ("FIDO") but instantly coincident with Alice. Eve is the asymptotic LNIF (FIDO) observer far away from the black hole horizon in the asymptotic flat region receiving redshifted signals from outside the horizon. Black Hole complementarity is the relation between Alice and Eve. The usual invariant relation of ds^2 = guvdx^udx^v still obtains between Alice and Bob even when they are inside the event horizon.

Typo-corrected "micro-geon" below:
On Sep 5, 2005, at 9:28 AM, Jack Sarfatti wrote:

Lenny's densely mathematical book is not a popular book. It is incomprehensible to the general reader and it is not easy going for the professional theoretical physicist not in the sub-field. However, it has moments of great clarity and if it is wrong, as George Chapline thinks, it is brilliantly wrong. Certainly pieces of Lenny's thesis will survive. So, to really see what the book is about, it's best to read the end of the book first and then go back to the beginning. Lenny emphasizes the key role on nonlocality (e.g. nonlocality of gravity energy?) in black hole complementarity.

"In order to reconcile the equivalence principle with the rules of quantum mechanics the rules of locality must be massively modified."

I like the idea of the blackhole as a string since I already published in 1974 the explanation of the Regge slope alpha' (for strings)

J ~ alpha'E^2

alpha' ~ (1Gev)^-2

as rotating Kerr black hole Wheeler "micro-geon" with effective strong gravity G* ~ 10^40G in Herbert Frohlich's "Collective Phenomena". Indeed, that's why Abdus Salam invited me to ICTP Trieste, Italy 1973-74 (e.g. contact Jagdish Mehra).

What will survive is the IR/UV duality. What about LIF/LNIF complementarity? Intriguing. What is completely missing in Lenny's theory is Vacuum ODLRO. For example, Lenny never considers a Bose-Einstein condensate in the vacuum in which there is a macroscopic eigenvalue of the first reduced density matrix. All eigenvalues must be less than 1 in Lenny's theory. Second, Lenny used a positive energy density to derive some of his key results when in fact negative zero point energy density would describe dark matter. Third, Lenny's ADS model has the wrong sign of the actually observed small post-inflation cosmological constant. How fatal this is I do not know yet. Perhaps he analytically continues to the DS model? That is ADS is "dark matter" with negative zero point energy density and positive pressure. DS is "dark energy" with positive zero point energy density and negative pressure. Furthermore, Lenny's equation for p the power of t in the FRW scale factor a(t) ~ t^p breaks down in the most important case, i.e. p -> infinity when w -> -1, which is the case for zero point energy. One nice idea is that the D3 brane of M-theory is the kind of 3+1 space-time we live in with the 6 extra space-time dimensions as "scalar fields". This fits well with Gennady Shipov's torsion field theory extension of 1915 GR. Indeed, if we interpret these scalar fields as vacuum ODLRO Higgs-Goldstone fields associated with the local gauging of the Lorentz group O(1,3) then the vacuum order parameter space is SU(2)xSU(2) consistent with the Hedgehog anomaly centered at Sun seen in the TWO NASA Pioneer Space Probes where a_g = - cH(t). All stars may have this property, i.e. part of stellar formation? Maybe even galaxies have it? That is vacuum ODLRO topological defects as seeds for early galaxy formation explaining galactic halos as well?

On Sep 1, 2005, at 1:53 PM, Jack Sarfatti wrote:

Comment 3
Lenny's book will not be comprehensible to the math-illiterate New Age reader. He opens up with the math of black holes in different coordinate representations nicely presented in a way that implicitly clearly shows why Hal Puthoff's PV alternative to the black hole is not a good theory. But you need to remember (or look up) your high school logarithms and the trigonometry formula for the tangent of the half-angle to show from eqs (1.1.2) to (1.1.4) that a signal from the black hole surface horizon never reaches the distant observers. The Penrose diagram makes that instantly obvious of course. Hal uses isotropic coordinates inside the event horizon where they are not appropriate. He says he can do that because his exponential metric does not have an event horizon. But in that case his solution does not obey Einstein's vacuum GR equation Ruv = 0. Therefore, PV theory conflicts with GR. Indeed, PV theory is not consistent with Diff(4) tensors and therefore, it violates the equivalence principle. In spite of that Hal Puthoff claims he is not offering a theory different from GR but only an "engineer's" way to do it. This, of course, is self-contradictory. Note that in George Chapline's "dark star" theory there is dark energy behind the event horizon, i.e. not Ruv = 0, but the same equation I use

Guv + /\zpfguv = 0

We do seem to need Gennady Shipov's torsion field beyond 1915 GR to allow

/\zpf^,v =/= 0 at the event horizon boundary because the Bianchi identities without torsion demand /\zpf^,v = 0.

On Aug 31, 2005, at 10:15 PM, Jack Sarfatti wrote:

Comment 2

Lenny: "Eventually the black hole must completely evaporate. Hawking then raised the question of what becomes of the quantum correlations between matter outside the black hole and matter that disappears behind the horizon. ... Hawking then made arguments that there is no way, consistent with causality, for the correlations to be carried by the outgoing evaporation products."

Jack: So much the worse for causality, which here means no space-like influences outside the local light cones. Bell's theorem shows that such space-like influences are needed and they are locally random in micro-quantum theory consistent with the blackbody radiation.

Lenny: "Thus, according to Hawking, the existence of black holes inevitably causes a loss of quantum coherence and breakdown of one of the basic principles of quantum mechanics - the evolution of pure states into pure states."

Jack: So much the worse for micro-quantum mechanics. It's time to slaughter that Sacred Cow. Global special relativity of 1905 is violated by the necessity of gravity and inertia in local general relativity of 1915 where it is relegated to a purely local tangent space by the equivalence principle. In the same way micro-quantum mechanics is not complete, but merely corresponds to nonlocally entangled small fluctuations about the stiff macro-quantum vacuum ODLRO coherent order parameter that provides the local fabric of space-time via

B = (hG/c^3)^1/2d(argVacuum ODLRO).

Lenny: "Hawking further argued that once the loss of quantum coherence is permitted in black hole evaporation, it becomes compulsory in all processes involving the Planck scale. The world would behave as if it were in a noisy environment which continuously leads to a loss of coherence. The trouble with this is that there is no known way to destroy coherence without at the same time violating energy conservation by heating the world."

Jack: I need to see the math of the above argument. Why does not the expansion of the universe cool down this alleged heating effect? Also total energy is not necessarily conserved in curved space-time because of the breakdown of time translation symmetry. Presumably the book will explain this argument in more detail. Lenny wants to hold on to micro-quantum unitarity at all costs and I think this is the basic error in his thesis, but I could be wrong. The macro-quantum vacuum ODLRO order parameter does not obey a unitary time evolution. You cannot think of |psi|^2 as a Born quantum probability density like you can for micro-quantum wave functions.

Indeed the space integral of |psi(x)|^2 need not be a constant of the motion at all. For example, you have a pot of superfluid helium at almost T = 0 at t = 0 and then you slowly heat it. As you heat the superfluid it turns to normal fluid completely disappearing at the lambda point. In the case of vacuum ODLRO the "normal fluid" is the dark energy!

On Aug 31, 2005, at 9:07 PM, Jack Sarfatti wrote:

"Black Holes, Information and the String Theory Revolution: The Holographic Universe"

Comment 1

Lenny: "The paradox was discovered by Jacob Bekenstein and turned into a serious crisis by Stephen Hawking. ... Bekenstein realized that if the second law of thermodynamics was not to be violated in the presence of a black hole, the black hole must possess an intrinsic entropy. ... How and why a classical solution of field equations should be endowed with thermodynamical attributes has remained obscure."

Jack: The black hole is a property of Einstein's vacuum equation

Ruv = 0

However, this equation is a c-number emergent field theory from vacuum ODLRO. George Chapline, Jr and I have both arrived at this general idea quite independently. Let the vacuum ODLRO order parameter be

psi = |psi|e^iargpsi

suppress internal symmetry indices, but think of SU(2)hypercharge that has a neutral VEV in the standard model (evidence from NASA Pioneer anomaly a_g = -cH(t) as a hedgehog topological defect centered at Sun).

Let the Einstein-Cartan 1-form be

e = 1 + B

My ansatz is

B = (hG/c^3)^1/2d(argtheta)

with "string" branch cuts in argtheta

Therefore, there is no gravity and inertia when h -> 0 and c -> infinity even when G =/= 0. There is still some residual "normal fluid" fluctuations around the stiff vacuum order parameter psi that obeys the rules of micro-quantum theory as given by Lenny. The ratio of normal to superfluid obviously has a temperature parameter T. Therefore, Lenny's question is answered.

to be continued

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