Entropy, microscopic quantum theory of space-time, lorentz invariance

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The existence of entropy in gravity implies that there are microscopic degrees of freedom in space that carries the entropy. This implies space is discrete. Discrete space breaks lorentz invariance, which has been strongly constrained by both FERMI and thought experiments.

String theory preserves lorentz invariance as an exact symmetry in nature. Can its description of space as continuous carry entropy?

Searching for spacetime granularity: analyzing a concrete experimental setup
Yuri Bonder, Daniel Sudarsky
9 pages. For the proceedings of the VIII School of the Gravitation and Mathematical Physics Division of the Mexican Physical Society 'Speakable and unspeakable in gravitational physics: testing gravity from submillimeter to cosmic scale'.

"In this work we show that the spin pendulum techniques developed by the Eöt-Wash group could be used to put very stringent bounds on the free parameters of a Lorentz invariant phenomenological model of quantum gravity. The model is briefly described as well as the experimental setup that we have in mind."

Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity
T. Padmanabhan
20 pages
(Submitted on 29 Mar 2010)
"I show that the principle of equipartition, applied to area elements of a surface which are in equilibrium at the local Davies-Unruh temperature, allows one to determine the surface number density of the microscopic spacetime degrees of freedom in any diffeomorphism invariant theory of gravity. The entropy associated with these degrees of freedom matches with the Wald entropy for the theory. This result also allows one to attribute an entropy density to the spacetime in a natural manner. The field equations of the theory can then be obtained by extremising this entropy. Moreover, when the microscopic degrees of freedom are in local thermal equilibrium, the spacetime entropy of a bulk region resides on its boundary."

Go with the Flow, Average Holographic Universe
George F. Smoot
14 pages
(Submitted on 31 Mar 2010)
"Gravity is a macroscopic manifestation of a microscopic quantum theory of space-time, just as the theories of elasticity and hydrodynamics are the macroscopic manifestation of the underlying quantum theory of atoms. The connection of gravitation and thermodynamics is long and deep. The observation that space-time has a temperature for accelerating observers and horizons is direct evidence that there are underlying microscopic degrees of freedom. The equipartition of energy, meaning of temperature, in these modes leads one to anticipate that there is also an entropy associated. When this entropy is maximized on a volume of space-time, then one retrieves the metric of space-time (i.e. the equations of gravity, e.g. GR). Since the metric satisfies the extremum in entropy on the volume, then the volume integral of the entropy can readily be converted to surface integral, via Gauss's Theorem. This surface integral is simply an integral of the macroscopic entropy flow producing the mean entropy holographic principle. This approach also has the added value that it naturally dispenses with the cosmological constant/vacuum energy problem in gravity except perhaps for second order quantum effects on the mean surface entropy."

[The abstract is sober and straightforward---tending to allay suspicion that might be raised by the exuberant title. But if you look into the article itself, you may find it a bit over-the-top. Given that it's early April, I'm not entirely certain how to take this article.
Readers can decide for themselves.]

On the consistency of the Horava Theory
Jorge Bellorin, Alvaro Restuccia
(Submitted on 1 Apr 2010)
The new proposal of Horava for a renormalizable theory of gravity has received a considerable amount of criticisms. It particular, it has been argued that the propagating physical degrees of freedom do not match with those of General Relativity. Moreover, it has been proposed that the only possibility for the lapse function is no other than to be zero everywhere, which would be catastrophic for the theory. With the goal of giving a test for the theoretical admissibility of the Horava Theory, we perform the Hamiltonian analysis of its effective action for large distances. This effective action has the same potential term of General Relativity, but the kinetic term is modified by the inclusion of an arbitrary coupling constant $\lambda$. Since this constant breaks the general space-time diffeomorphisms symmetry, it is believed that the model with arbitrary $\lambda$ deviates from General Relativity. Indeed, part of the computations done in previous papers to support the arguments against the Horava theory were performed using not the complete theory but precisely the effective model. In this paper we shown that this model is not a deviation at all, instead it is completely equivalent to General Relativity in a particular partial gauge fixing for it. In particular the physical degrees of freedom of both theories are identical. To show this, we identify a second class constraint of the model that was erroneously interpreted as a condition for the lapse function in previous papers. The lapse function is determined by another conservation equation following the Dirac approach, an equation that was already known from General Relativity and that has solutions with the correct asymptotic physical properties.

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  • #2
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The existence of entropy in gravity implies that there are microscopic degrees of freedom in space that carries the entropy. This implies space is discrete. Discrete space breaks lorentz invariance,...

Faulty logic. It is geometry which has thermodynamic properties.

We do not know that space itself is discrete, in the simple-minded sense of being broken up into little bitty pieces.

Geometry can have microscopic degrees of freedom (as e.g. in LQG) without in any sense breaking Lorentz invariance. We've been over that ground numerous times :smile:

What you have is a chain of non sequiturs, 'Sabah.
  • #3
Science Advisor
... This implies space is discrete. Discrete space breaks lorentz invariance ...
I don't see this conclusion. In any quantum mechanical theory a symmetry (in this case local Lorentz invariance) is manifest if a certain operator algebra is non-anomalous on the physical Hilbert space. This does not automatically rule out discreteness.

If you look at angular momentum it somehow becomes descrete; even states and energy may become discrete as in the harmonic oscillator case; nevertheless rotational symmetry is manifest as the angular momentum algebra closes w/o anomalous terms.

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