Dear Dr. Medved,

Regarding your recent comment on black hole entropy [Ref. 1], I wonder if you would agree that the (yet-to-be-clarified) set of microscopic states that can account for this entropy might be *undenumerable*, with the following important clarification.

For example, the counting procedure/algorithm for the set of "points" from the circumference of a circle is unknown,

http://God-does-not-play-dice.net/Kiefer.html

We can obtain some indecisive value of circumference of a circle, which we can calculate with precision suitable for our engineering purposes, but the "real" value "out there" is unknown.

The same puzzle persists in the holographic conjecture: if we imagine partitioning an *arbitrary large* cube into small cubes, the size of the "ultimate smallest cube" that would build the large cube without any gaps of "empty space" is unknown; see the Thompson's lamp paradox,

http://God-does-not-play-dice.net/Jack.html

The puzzle becomes even more acute if we try to enlarge the cube to the "dimensions" of the whole universe, since we would need to address the issue of some absolute time, as implied in the temperature of the Cosmic Background Radiation [Ref. 2].

Hence the clarification that I promised to deliver is the following: in order to count the set of microscopic states, we would need to position ourselves in some absolute reference frame and have access to some absolute cosmological time, which is forbidden by the theory of relativity. Therefore we obtain some indecisive value in some local reference frame, and the whole task of clarifying the black hole entropy cannot be achieved *in principle*.

I wonder if you or some of your colleagues would agree to comment.

Regards,

Dimi Chakalov
--
http://God-does-not-play-dice.net
 

Reference

[Ref. 1] A.J.M. Medved, A comment on black hole entropy, gr-qc/0406044 v2, 11 June 2004

"Although the black hole area law initially followed from thermodynamic considerations (e.g., protecting the second law of thermodynamics in the presence of a black hole [1]), it is often presumed to have a statistical meaning as well [3]. Which is to say, one would naturally expect there to be a (yet-to-be-clarified) set of microscopic states that can account for this entropy by way of state-counting procedures. At this point, it is reasonable to suggest that such a statistical framework will ultimately be traced to some fundamental theory that is able to unify gravitational physics with quantum mechanics."
 

[Ref. 2] C.S. Unnikrishnan, Existence of absolute time and implications to relativity, TIFR preprint, unpublished (1995).
 

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Subject: Re: A (yet-to-be-clarified) set of microscopic states
Date: Mon, 14 Jun 2004 22:48:05 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Joey Medved <Joey.Medved@mcs.vuw.ac.nz>
CC: visser@mcs.vuw.ac.nz, yjng@physics.unc.edu, unni@tifr.res.in, thomas.waters2@mail.dcu.ie, vishnu@vt.edu, dminic@vt.edu, kahong@vt.edu

Dear Joey,

Thank you for your reply of Tue, 15 Jun 2004 05:50:16 +1200 (NZST). If you wish to address the specific issue raised in my preceding email, may I ask you to reply to me only.

> it is possible that the "yet-to-be clarified set of microstates"
> may not be accessible. that is, there is no a priori reason
> to believe that quantum gravity can be described
> mathematically by observers of the universe (even if  the
> effective/coarse grained manifestations of Q.G.  can be).

I think it depends on what you imply by effective/coarse grained manifestations of quantum gravity.

For example, a physical observer confined *inside* the universe will certainly observe some "blueprint" from the cosmological time arrow, which perhaps can be described mathematically by her/him. But the direct observation of this arrow driven by the so-called dark energy is impossible in principle,

http://God-does-not-play-dice.net/Hongsheng.html

I suppose you've discussed this possibility with Mat Visser,

http://God-does-not-play-dice.net/Visser.html#note

> Nevertheless, i think most physicists (myself included)
> overlook this possibility while doing research;
> otherwise progress would be impossible and
> such meta-physical questions are best left to
> the philosophers (after all, they gotta eat too).

Let's not leave anything to the philosophers, even if they are good in math. See how they managed to ignore the fundamental problems of classical GR known since 1917, fifty years prior to the discovery of Wheeler-DeWitt equation,

http://God-does-not-play-dice.net/Dolby.html

They will always ignore what doesn't suit their beliefs. That's why they do philosophy, not science.

Kindest regards,

Dimi
 

Note: To understand the fundamental problems of classical GR known since 1917, see (i) the generalized d'Alembert’s principle by T. Levi-Civita [Ref. 3], and (ii) the complete cancellation of the two fluxes, due to the dynamical nature of the background metric, by M. Montesinos here.

Hence we need the global mode of spacetime. It shows up also as 'empty space' in the examination of the dark energy and cosmological constant problems by L. Krauss here.

Some philosophers, such as Clifford Will and John Stachel, do not like "empty space", and keep trying to explain the nature of spacetime exclusively as a "structural quality of the gravitational field". Their argument was best explained by another philosopher, Lee Smilon, here: "If we take out all the words we are not left with an empty sentence, we are left with with nothing." True, but this does not imply that if we keep all the words in a sentence, there would be nothing 'outside' this sentence. This 'outside' is exactly the global mode of spacetime. It sets the 'context' for fixing the spacetime "curvature" dynamically, by a bi-directional "talk" (J. Wheeler) between matter and geometry, which too "takes place" in the global mode of spacetime.

No, we should never leave this to philosophers. They will always ignore it, since they play with science as a hobby. Try to convince some philatelist to switch to collecting bottle labels, and you will get nothing but a dark silence. There is no way they would consider changing their hobby. They live in total socialism.

The future belongs to our kids.

D. Chakalov
June 14, 2004
 
 

[Ref. 3] T. Levi-Civita, On the analytic expression that must be given to the gravitational tensor in Einstein's theory, Rendiconti della Reale Accademia dei Lincei, vol. 26, 381 (1917),

http://lanl.arxiv.org/abs/physics/9906004

"The nature of ds² is always such as to balance all mechanical actions; in fact the sum of the energy tensor and of the inertial one identically vanishes.

"One is naturally led to associate this proposition with d’Alembert’s principle "the lost forces (i.e. directly applied forces and inertial ones) balance each other". The equilibrium expressed by (10’) is just the most complete occurrence that can be conceived from the mechanical standpoint. In fact, not only the total force applied to each single element comes to vanish, but also stresses, energy flow and energy density (by taking inertia into account through A_ik) behave in this way.

"It is clear that this total lack of mechanical entities pertains to isolated systems.
...

"In fact, by virtue of (10’) or, if one likes, of the generalised d’Alembert’s principle, when the energy tensor T_ik vanishes, the same occurrence must happen to the gravitational tensor A_ik. This fact entails total lack of stresses, of energy flow, and also of a simple localisation of energy."