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Home Jack Sarfatti's Blog Blog (Full Text Display) Ted Jacobson's paper on gravity, entropy, holography - 2nd draft

Dec
17

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We have a chicken - egg problem - a horizon is part of a solution to Einstein's Guv + kTuv = 0. So we need a self-creating back-from-the-future post-selection effect for the whole thing to make sense on the cosmological scale. Note that Jacobson has a local argument based on the EEP/Rindler Horizon - very very clever. It shows to my mind that Zielinski's attempt to try to chuck the EEP is not correct. Similarly with the other philosophers, mathematicians, and theorists that Zielinski cites.

What happens when we replace Jacobson's thermal equilibrium by a Prigogine dissipative structure - a pump preventing thermal equilibrium like a laser, also sub-quantal non-equilibrium's signal nonlocality? Indeed, Jacobson is aware of such a possibility.

"Our thermodynamic derivation of the Einstein equation of state presumed

the existence of local equilibrium conditions in that the relation

dQ = TdS only applies to variations between nearby states of local thermodynamic

equilibrium. For instance, in free expansion of a gas, entropy

increase is not associated with any heat flow, and this relation is not valid.

Moreover, local temperature and entropy are not even well defined away

from equilibrium. In the case of gravity, we chose our systems to be defined

by local Rindler horizons, which are instantaneously stationary, in order to

have systems in local equilibrium. At a deeper level, we also assumed the

usual form of short distance vacuum fluctuations in quantum fields when we

motivated the proportionality of entropy and horizon area and the use of the

Unruh acceleration temperature. Viewing the usual vacuum as a zero temperature

thermal state[11], this also amounts to a sort of local equilibrium

assumption. This deeper assumption is probably valid only in some extremely

good approximation. We speculate that out of equilibrium vacuum

fluctuations would entail an ill-defined spacetime metric.

Given local equilibrium conditions, we have in the Einstein equation a

system of local partial differential equations that is time reversal invariant

and whose solutions include propagating waves. One might think of these as

analogous to sound in a gas propagating as an adiabatic compression wave.

Such a wave is a travelling disturbance of local density, which propagates via

a myriad of incoherent collisions. Since the sound field is only a statistically

defined observable on the fundamental phase space of the multiparticle system,

it should not be canonically quantized as if it were a fundamental field,

even though there is no question that the individual molecules are quantum

mechanical. By analogy, the viewpoint developed here suggests that it may

not be correct to canonically quantize the Einstein equations, even if they

describe a phenomenon that is ultimately quantum mechanical.

For sufficiently high sound frequency or intensity one knows that the

local equilibrium condition breaks down, entropy increases, and sound no

longer propagates in a time reversal invariant manner. Similarly, one might

expect that sufficiently high frequency or large amplitude disturbances of the

gravitational field would no longer be described by the Einstein equation,

not because some quantum operator nature of the metric would become

relevant, but because the local equilibrium condition would fail. It is my

hope that, by following this line of inquiry, we shall eventually reach an

understanding of the nature of “non-equilibrium spacetime”.

tying up a loose end

Physics as quantum information processing1

Giacomo Mauro D’Ariano

QUIT Group, Dipartimento di Fisica “A. Volta”, 27100 Pavia, Italy, http://www.qubit.it

Istituto Nazionale di Fisica Nucleare, Gruppo IV, Sezione di Pavia

On closer reading the paper did not make any sense to me really - too much informal language - no "there" there in my opinion.

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On Dec 16, 2010, at 6:55 PM, JACK SARFATTI wrote:

The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation δQ = TdS connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with δQ and T interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime in just such a way that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.

i.e., Rindler horizon points to local equivalence of accelerating LNIF to Newton's gravity force.

Newton's gravity force is zero on a timelike geodesic - real forces are always measured from non-geodesics.

What we think of as Newton's gravity force is always, in reality an electrical reaction force sustaining the LNIF.

"The four laws of black hole mechanics, which are analogous to those of thermodynamics, were originally derived from the classical Einstein equation[1]. With the discovery of the quantum Hawking radiation[2], it became clear that the analogy is in fact an identity. How did classical General Relativity know that horizon area would turn out to be a form of entropy, and that surface gravity is a temperature? In this letter I will answer that question by turning the logic around and deriving the Einstein equation from the proportionality of entropy and horizon area together with the fundamental relation δQ = TdS connecting heat Q, entropy S, and temperature T. Viewed in this way, the Einstein equation is an equation of state. It is born in the thermodynamic limit as a relation between thermodynamic variables, and its validity is seen to depend on the existence of local equilibrium conditions. This perspective suggests that it may be no more appropriate to quantize the Einstein equation than it would be to quantize the wave equation for sound in air.

On Dec 16, 2010, at 6:55 PM, JACK SARFATTI cited Ted Jacobson:*"The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation δQ = TdS connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with δQ and T interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime in just such a way that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air."*

i.e., Rindler horizon points to local equivalence of accelerating LNIF to Newton's gravity force.

Newton's gravity force is zero on a timelike geodesic - real forces are always measured from non-geodesics.

What we think of as Newton's gravity force is always, in reality an electrical reaction force sustaining the LNIF.*"The four laws of black hole mechanics, which are analogous to those of thermodynamics, were originally derived from the classical Einstein equation[1]. With the discovery of the quantum Hawking radiation[2], it became clear that the analogy is in fact an identity. How did classical General Relativity know that horizon area would turn out to be a form of entropy, and that surface gravity is a temperature? In this letter I will answer that question by turning the logic around and deriving the Einstein equation from the proportionality of entropy and horizon area together with the fundamental relation δQ = TdS connecting heat Q, entropy S, and temperature T. Viewed in this way, the Einstein equation is an equation of state. It is born in the thermodynamic limit as a relation between thermodynamic variables, and its validity is seen to depend on the existence of local equilibrium conditions. This perspective suggests that it may be no more appropriate to quantize the Einstein equation than it would be to quantize the wave equation for sound in air.*"*"In thermodynamics, heat is energy that flows between degrees of freedom that are not macroscopically observable. In spacetime dynamics, we shall define heat as energy that flows across a causal horizon. It can be felt via the gravitational field it generates, but its particular form or nature is unobservable from outside the horizon. For the purposes of this definition it is not necessary that the horizon be a black hole event horizon. It can be simply the boundary of the past of any set O (for “observer”). This sort of horizon is a null hypersurface (not necessarily smooth) and, assuming cosmic censorship, it is composed of generators which are null geodesic segments emanating backwards in time from the set O. We can consider a kind of local gravitational thermodynamics associated with such causal horizons, where the “system” is the degrees of freedom beyond the horizon. The outside world is separated from the system not by a diathermic wall, but by a causality barrier."*

the observation that they hide information[3]. In fact, the overwhelming

majority of the information that is hidden resides in correlations between

vacuum fluctuations just inside and outside of the horizon[4]. Because of

the infinite number of short wavelength field degrees of freedom near the

horizon, the associated “entanglement entropy” is divergent in continuum

quantum field theory. If, on the other hand, there is a fundamental cutoff

length lc, then the entanglement entropy is finite and proportional to the

horizon area in units of lc^2 as long as the radius of curvature of spacetime is

much longer than lc.

So far we have argued that energy flux across a causal horizon is a kind

of heat flow, and that entropy of the system beyond is proportional to the

area of that horizon. It remains to identify the temperature of the system

into which the heat is flowing. Recall that the origin of the large entropy is

the vacuum fluctuations of quantum fields. According to the Unruh effect[8],

those same vacuum fluctuations have a thermal character when seen from

the perspective of a uniformly accelerated observer. We shall thus take the

temperature of the system to be the Unruh temperature associated with

such an observer hovering just inside the horizon. For consistency, the same

observer should be used to measure the energy flux that defines the heat

flow. Different accelerated observers will obtain different results. In the

limit that the accelerated worldline approaches the horizon the acceleration

diverges, so the Unruh temperature and energy flux diverge, however

their ratio approaches a finite limit. It is in this limit that we analyse the

thermodynamics, in order to make the arguments as local as possible.

Up to this point we have been thinking of the system as defined by any

causal horizon. However, in general, such a system is not in “equilibrium”

because the horizon is expanding, contracting, or shearing. Since we wish to

apply equilibrium thermodynamics, the system is further specified as follows.

The equivalence principle is invoked to view a small neighborhood of each

spacetime point p as a piece of flat spacetime.

Through p we consider a small

spacelike 2-surface element P whose past directed null normal congruence to

one side (which we call the “inside”) has vanishing expansion and shear at p.

It is always possible to choose P through p so that the expansion and shear

vanish in a first order neighborhood of p. We call the past horizon of such a

P the “local Rindler horizon of P”, and we think of it as defining a system—

the part of spacetime beyond the Rindler horizon—that is instantaneously

stationary (in “local equilibrium”) at p. Through any spacetime point there

are local Rindler horizons in all null directions.

The fundamental principle at play in our analysis is this: The equilibrium

thermodynamic relation Q = TdS, as interpreted here in terms of

energy flux and area of local Rindler horizons, can only be satisfied if gravitational

lensing by matter energy distorts the causal structure of spacetime

in just such a way that the Einstein equation holds. We turn now to a

demonstration of this claim."

to be continued

Note how clever and elegant Jacobson's argument is. He uses Einstein LOCAL EEP (in sense of Pauli 1921 Encyclopedia article) to get the local

Guv + kTuv = 0