CHR&R answer 20year Jacobson question (GR foundations+Thermo)

[marcus]

The authors Chirco, Haggard, Riello, and Rovelli (CHR&R) have just posted what I think is a major paper proposing to resolve a question raised by Jacobson almost 20 years ago, in 1995.
https://www.physicsforums.com/showthread.php?p=4637856#post4637856
Jacobson (as many posting here are aware) managed to DERIVE the Einstein GR equation from Thermodynamic assumptions, as if (to put it fancifully) the GR equation were simply the equation of state of something like a "gas of little molecules of geometry" jittering wiggling dividing recombining etc.

So one way of posing the outstanding question raised by J's paper would be "what after all are the underlying degrees of freedom, from which the Einstein Field Equation arises as the EoS?"
And does it even make sense to quantize the GR equation?
Well, do we quantize the pressure wave equation by which sound propagates in air? No. It describes a bulk large scale process quite different from the behavior of individual air molecules. QM applies at the level of individual air molecules, not to the equation for sound in air.

To get Jacobson's landmark 1995 paper, google "Einstein equation of state"
or "Jacobson Einstein equation" or any of several other choices of words from the title
http://arxiv.org/abs/gr-qc/9504004

Chirco et al present an answer to the question of what underlies the Einstein Field Equation.

To get the CHR&R paper, which coming after nearly 20 years is also itself something of a landmark, google "haggard riello spacetime" or "haggard riello thermodynamics". Either one will get you http://arxiv.org/abs/1401.5262 as the first hit.

 

[marcus]

I'd be interested to hear other's comments on the CHRR paper. To me it seems remarkable that it seems to confirm the spinfoam quantization of spacetime geometry because this quantum version of the gravitational field has the properties that let you derive the Einstein equation.

We should explain the importance of the phrase in the title: without hidden degrees of freedom.

The thermodynamic properties of light and radiant heat (like the Planck black body curve) do NOT arise from hidden degrees of freedom, as far as we know, but simply arise from (the quantum nature of) the electromagnetic field itself.

Likewise, Chirco Haggard Riello Rovelli are showing that you don't need to imagine underlying hidden degrees of freedom to understand the thermo character of gravity/geometry. It arises directly from the quantum properties of the gravitational field itself.

The spinfoam quantum version of the gravitational field has what is required (without inventing any so far unrevealed variables) to supply the desired thermodynamics. The field itself, in quantum version, is sufficient---just as it was in the case of electrodynamics.

In any case that is the message of 1401.5262, the CHRR paper. I'm urging you to check it out and see how convincing you find their argument.

 

[atyy]

In his original paper http://arxiv.org/abs/gr-qc/9504004, Jacobson wrote "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."

But he later recanted http://arxiv.org/abs/gr-qc/0308048: "This led me at first to suggest that the metric shouldn’t be quantized at all. However I think this is wrong. Condensed matter physics abounds with examples of collective modes that become meaningless at short length scales, and which are nevertheless accurately treated as quantum fields within the appropriate domain." He went on to indicate the usefulness of perturbative quantum gravity, and indicated it left non-perturbative problems open. It remains to be seen if the nonperturbative problems can be solved by approaches like asymptotic safety or LQG which don't introduce new degrees of freedom.

I am very interested in how CHRR http://arxiv.org/abs/1401.5262 is related to the gauge/gravity papers which also link the derivation of the Einstein equations, but only at linear level, to Jacobson's work via entanglement thermodynamics: http://arxiv.org/abs/1308.3716, http://arxiv.org/abs/1312.7856.

That Bianchi and Myers wrote one paper on this subject http://arxiv.org/abs/1212.5183, suggests they thought there might be a link. Bianchi's http://arxiv.org/abs/1211.0522 was an important precursor to CCHR on the LQG side, while Myers, with Blanco, Casini and Huang, formulated the entanglement thermodynamics http://arxiv.org/abs/1305.3182 that was essential for the most recent developments on the gauge/gravity side.

 

[Chronos]

It's a fascinating paper, perhaps among the most important in years. A little above my pay grade, so I need to read it again ... slowly. There is much to conceptualize.

 

[Berlin]

I emailed prof. Rovelli a few months ago asking his opinion on the '95 Jacobson paper. He replied by saying that he did not believe Einsteins GR is an equation of state. Excellent to see the CHRR paper so shortly afterwards! The paper (more than little above my pay grade!), gives me the impression that all of Jacobsons starting points (like the Unruh temperature etc, equation 1-3 in the paper) are explained from the bottom up. However, these assumptions are replaced by other ones which "follows only from the quantum properties of gravity". Later in the paper it is stated that the framework is built on the foundations of LQG with its spin networks. Are these foundations somehow more 'fundamental' (the paper calls this a "simpler and tighter scenario", which does not seem like a scientific remark) than Jacobsons? Are these spin networks not the same as the underlying degrees of freedom Jacobson mentions, or are these fundamantally different? May be semantics, but important to judge progress.

berlin

 

[atyy]

Later in the paper it is stated that the framework is built on the foundations of LQG with its spin networks. Are these foundations somehow more 'fundamental' (the paper calls this a "simpler and tighter scenario", which does not seem like a scientific remark) than Jacobsons? Are these spin networks not the same as the underlying degrees of freedom Jacobson mentions, or are these fundamantally different? May be semantics, but important to judge progress.

The common elements in the gauge/gravity and CCHR links to Jacobson seem to be some form of (1) entanglement thermodynamics and (2) a relationship between entropy and area. In CCHR, both seem to arise from the postulate of Hadamard states. In gauge gravity, the entanglement thermodyanics is a property of the CFT, and the Ryu-Takayanagi formula gives the relationship between entanglement entropy and an area of the bulk.

Swingle has argued that the gauge/gravity duality has a tensor network/spin network picture http://arxiv.org/abs/0905.1317, http://arxiv.org/abs/1209.3304, so I would be interested to know what CCHR's Hadamard states look like. In particular, are they an example of the quantum expanders mentioned by Swingle?

 

[Chronos]

Upon further review, I have some issues. Chirco has apparently been championing this cause at least since 2009: http://arxiv.org/abs/0909.4194. I can't quite wrap my head around how it can now be viewed as 'revelatory', when it failed to draw significant earlier interest. That gives me pause to suspect it has leaks.

 

[marcus]

It's a fascinating paper, perhaps among the most important in years. ...

I agree, it could be. In any case fascinating. We should go over the basic intuition of Jacobson's proof.

Upon further review, I have some issues. Chirco has apparently been championing this cause at least since 2009: http://arxiv.org/abs/0909.4194. I can't quite wrap my head around how it can now be viewed as 'revelatory', when it failed to draw significant earlier interest. That gives me pause to suspect it has leaks.

Chirco is a recent PhD. (I think 2011 or 2012) Now postdoc at Marseille. Stefano Liberati at Trieste was the senior author of that paper, probably was also Chirco's PhD advisor. I don't know that the approach is actually the same. It certainly has been a natural problem to work on any time since 1995---trying to understand Jacobson's 1995 result. Probably Liberati is one of several who have tried to make headway in the meantime.

One thing that distinguishes the recent CHRR paper, and means that its approach is substantially different from earlier attempts, is that it is based on 2012 work by Bianchi and by Bianchi Myers. Obviously Liberati's work could not be using the 2012 results. CHRR is essentially quite new, IMO.

I think I will not worry about whether the CHRR paper could have leaks or not, at the moment (any new research paper can have, I'll just wait and see what happens on that score.) I think I will focus a little on intuitively understanding Jacobson's result. CHRR give some intuition in the first paragraph of page 1.

 

[strangerep]

[...] We should go over the basic intuition of Jacobson's proof.

I was feeling quite dejected about the other thread, but this CHRR paper perked up my interest.

Here's installment #1 of my attempt to make the intuition clearer...

The key seems to lie in eqns (16),(28),(20), i.e.,
$$\delta S ~=~ \delta E / T ~~~~~~~~~ \text{(16)}$$$$\delta S ~=~ \alpha \, \delta A ~~~~~~~~ \text{(29)}$$$$\Rightarrow \delta E ~=~ T\alpha \, \delta A ~~~~~~~~ \text{(29)}$$
The $R_{\mu\nu}$ part comes by the change in area in terms of Riemannian geometry and null congruences. That's done in appendix C: a change in area associated with expansion of a congruence of null geodesics can be expressed in terms of the $R_{\mu\nu}$ -- that's just textbook Riemannian geometry -- to get:
$$\delta S ~=~ \alpha \delta A
~=~ -\alpha \int_H \tilde\epsilon \lambda (R_{\mu\nu} \ell^\mu \ell^\nu)_p d\lambda
~~~~~~~~~~ (C4) ~.$$
The corresponding change in energy can be expressed in terms of $T_{\mu\nu}$ on a surface related in a particular way to the Rindler horizon.

Equating the two, and demanding it hold for arbitrary null congruences $\ell^\mu$ gives
$$\frac{2\pi}{\hbar\alpha} \, T_{\mu\nu} \ell^\mu \ell^\nu
~=~ R_{\mu\nu} \ell^\mu \ell^\nu ~. ~~~~~~~~~ \text{(C7)}$$ Insisting this hold in any frame gives
$$\frac{2\pi}{\hbar\alpha} \, T_{\mu\nu}
~=~ R_{\mu\nu} + \Phi g_{\mu\nu} ~,~~~~~~~~\text{(C8)}$$where $\Phi$ is an arbitrary scalar. Demanding conservation of energy forces $\Phi = -\frac{1}{2} R - \Lambda$, where $\Lambda$ is another arbitrary scalar. So,
$$\frac{2\pi}{\hbar\alpha} \, T_{\mu\nu}
~=~ R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} - \Lambda g_{\mu\nu} ~.
~~~~~~~~\text{(C9)}$$and identifying $\alpha = 1/4\hbar G$ finally gives the EFE.

Earlier, in section II, CHRR related the statistical entropy (ignorance of the microstate) and entanglement entropy (system in a nonpure quantum state). Then, in section III, they note that statistical entropy and entanglement entropy are different, but also how they share some properties and -- in the case of Rindler space -- entanglement entropy does indeed indicate a thermal situation, as can be seen by detailed analysis of the actual (Rindler) quantum field modes, being suitable Bogoliubov transforms of the free modes, and show that the B-transformed vacuum has a spectrum matching that of thermal black-body radiation.

So it's all about connecting the geometrical concept $\delta A$ with the mechanical concept $\delta E$ via an intermediary of entanglement entropy. IOW, demonstrating that the notions of entropy on both sides of this fence really do match up physically, and are not just a piece of highly sophisticated algebraic numerology. That's the bit I'm still not comfortable with. Maybe that will become clearer after I understand how the spin foam framework provides these necessary features.

It's also noteworthy (imho) how a cosmological scalar $\Lambda$ pops up as an arbitrary scalar in the above -- though remaining a mystery so far.

(To be continued.)

 

[atyy]

Upon further review, I have some issues. Chirco has apparently been championing this cause at least since 2009: http://arxiv.org/abs/0909.4194. I can't quite wrap my head around how it can now be viewed as 'revelatory', when it failed to draw significant earlier interest. That gives me pause to suspect it has leaks.

Perhaps it has leaks, but thinking about it in a different way from the earlier Chirco paper may suggest that it is interesting, and on the right track.

First, there is definite progress from the gauge/gravity conjecture of how Einstein's equations can emerge from entanglement thermodynamics, at least at linear level http://arxiv.org/abs/1312.7856.

Second, Bianchi (LQG guy) and Myers (one of the authors of http://arxiv.org/abs/1312.7856) did write a paper together http://arxiv.org/abs/1212.5183. They have a section (p5) on how this may play out in LQG, and this CHRR paper is really trying to build on the picture in Bianchi-Myers.

Third, the Hilbert space of LQG http://arxiv.org/abs/1102.3660 is "essentially nothing else" than that of SU(2) lattice gauge theory, so LQG is also a gauge/gravity correspondence http://arxiv.org/abs/0802.0880 http://arxiv.org/abs/1109.0036

 

[marcus]

Here's a paraphrase of CHRR page 1 paragraph 1. Oversimplified sketch of how Jacobson derived einstein field eqn from:
1. acceleration temperature (keywords Rindler Unruh)
2. entropy-area (keywords Hawk Beck Rind Unrh)
3. entropy-energy changes (keywords Clausius, ∂S=∂E/T)

You want to know how much the local matter curves the local geometry. You know stuff about horizons. How do you create horizons? By accelerating little observer probes outwards in every direction from a given point.

Consider an observer accelerating in some direction. Behind him is a causal (rindler) horizon. He measures a temp T. All this mass-energy is flowing back disappearing across the horizon, never again to affect him. That is ∂E across a given patch of horizon area. We know T so we know ∂E/T.

BTW this flow is affected by the curvature, whatever it is (we want to determine the curvature, given the matter). The curvature can either focus or defocus to flow of energy back across the
horizon in his wake.

So the upshot is that probed by accelerating in any given direction, the curvature seen from that direction is determined. There is only one value curvature can have that will make the area of the horizon patch and the ∂E/T flow across that patch match up.

Hi Strangerep and Atyy! I didn't see your recent posts as I was writing this. I'll leave it extant however---it's an attempt at a very basic account of how GR eqn could derive from some thermodynamic relations (Unruh, Clausius etc)

 

[atyy]

IOW, demonstrating that the notions of entropy on both sides of this fence really do match up physically, and are not just a piece of highly sophisticated algebraic numerology. That's the bit I'm still not comfortable with. Maybe that will become clearer after I understand how the spin foam framework provides these necessary features.

This part of CHRR's argument (their Eq 52-56) is very unclear to me also. The corresponding step of getting dS=dE in the gauge/gravity side given in http://arxiv.org/abs/1305.3182 seems quite different.

Edit 1: I guess eq 52-56 are not so crucial. The more important steps in CHRR are Eq 44-48. What is the status of the area operator? I thought it was not gauge-invariant, which is why Dittrich and Thiemann have challenged their meaning http://arxiv.org/abs/0708.1721. Rovelli replied in http://arxiv.org/abs/0708.2481. The review by Girelli, Hinterleitner and Major http://arxiv.org/abs/1210.1485 says: "Using examples, Dittrich and Thiemann [87] argue that the discreteness of the geometric operators, being gauge non-invariant, may not survive implementation in the full dynamics of LQG. Ceding the point in general, Rovelli [225] argues in favor of the reasonableness of physical geometric discreteness, showing in one case that the preservation of discreteness in the generally covariant context is immediate. In phenomenology this discreteness has been a source of inspiration for models. Nonetheless as the discussion of these operators makes clear, there are subtleties that wait to be resolved, either through further completion of the theory or, perhaps, through observational constraints on phenomenological models."

Edit 2: I am happy to take the area definition in Eq 44-45 provisionally. In Swingle's http://arxiv.org/abs/0905.1317, he also defines a new concept of length, and says his picture only provides an inequality. If the tensor network/spin network picture is correct presumably we get an equality only in gauge theories with a classical spacetime dual.

 

[atyy]

In LQG the existence of a classical spacetime is still unknown. Even if we accept Eq 44-45, wouldn't CHRR need to assume that a Hadamard state evolves into another Hadamard state? But is this guaranteed by spinfoam dynamics?

 

[MTd2]

Even if we accept Eq 44-45, wouldn't CHRR need to assume that a Hadamard state evolves into another Hadamard state

Sure it will. Hadmart is one of the authors!

But it's odd to think that space time is quantized, but not gravity.

 

[marcus]

Hi Strangerep, this post #9 of yours is a really helpful summary of how Jacobson's derivation of Einstein Field Equation works.
https://www.physicsforums.com/showthread.php?p=4639484#post4639484 Thanks! I corrected some trivial typos in the equation numbering in your post, which matches the numbering in the CHRR paper. It's convenient to be able to refer to the CHRR paper for additional context of the equations.

You mention that this is "installment #1" to be continued. As a reminder to any newcomers who might be reading this thread, equation (16) here is called the CLAUSIUS RELATION--a famous classical 19th Century thermodynamics equation by the guy who first defined Entropy.
So it's kind of like an AXIOM on which the derivation is based.

Also axiomatic is the area-entropy relation first discovered by BEKENSTEIN-HAWKING for black holes, but here assumed to be universal for any causal horizon. That's equation (28) here. Then a simple algebraic manipulation gives equation (29).
===quote Strangerep's post ===
The key seems to lie in eqns (16),(28),(29), i.e.,
$$\delta S ~=~ \delta E / T ~~~~~~~~~ \text{(16)}$$$$\delta S ~=~ \alpha \, \delta A ~~~~~~~~ \text{(28)}$$$$\Rightarrow \delta E ~=~ T\alpha \, \delta A ~~~~~~~~ \text{(29)}$$
==endquote==
The next thing CHRR do is to take (29) and substitute in the UNRUH ACCELERATION TEMPERATURE for T. This gives their equation (30) which they refer to as "the fundamental relation".
The Unruh temperature $$T = \frac {a\hbar}{2\pi}$$ is that measured by an accelerating observer, whose acceleration creates a causal horizon behind him analogous to a black hole event horizon.
$$\delta E ~=~\frac {a\hbar}{2\pi}\alpha \, \delta A ~~~~~~~~ \text{(30)}$$
==continuing with Strangerep's post, quote==
The $R_{\mu\nu}$ part comes by the change in area in terms of Riemannian geometry and null congruences. That's done in appendix C: a change in area associated with expansion of a congruence of null geodesics can be expressed in terms of the $R_{\mu\nu}$ -- that's just textbook Riemannian geometry -- to get:
$$\delta S ~=~ \alpha \delta A
~=~ -\alpha \int_H \tilde\epsilon \lambda (R_{\mu\nu} \ell^\mu \ell^\nu)_p d\lambda
~~~~~~~~~~ (C4) ~.$$
The corresponding change in energy can be expressed in terms of $T_{\mu\nu}$ on a surface related in a particular way to the Rindler horizon.

Equating the two, and demanding it hold for arbitrary null congruences $\ell^\mu$ gives
$$\frac{2\pi}{\hbar\alpha} \, T_{\mu\nu} \ell^\mu \ell^\nu
~=~ R_{\mu\nu} \ell^\mu \ell^\nu ~. ~~~~~~~~~ \text{(C7)}$$ Insisting this hold in any frame gives
$$\frac{2\pi}{\hbar\alpha} \, T_{\mu\nu}
~=~ R_{\mu\nu} + \Phi g_{\mu\nu} ~,~~~~~~~~\text{(C8)}$$where $\Phi$ is an arbitrary scalar. Demanding conservation of energy forces $\Phi = -\frac{1}{2} R - \Lambda$, where $\Lambda$ is another arbitrary scalar. So,
$$\frac{2\pi}{\hbar\alpha} \, T_{\mu\nu}
~=~ R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} - \Lambda g_{\mu\nu} ~.
~~~~~~~~\text{(C9)}$$and identifying $\alpha = 1/4\hbar G$ finally gives the EFE.

Earlier, in section II, CHRR related the statistical entropy (ignorance of the microstate) and entanglement entropy (system in a nonpure quantum state). Then, in section III, they note that statistical entropy and entanglement entropy are different, but also how they share some properties and -- in the case of Rindler space -- entanglement entropy does indeed indicate a thermal situation, as can be seen by detailed analysis of the actual (Rindler) quantum field modes, being suitable Bogoliubov transforms of the free modes, and show that the B-transformed vacuum has a spectrum matching that of thermal black-body radiation.

So it's all about connecting the geometrical concept $\delta A$ with the mechanical concept $\delta E$ via an intermediary of entanglement entropy. IOW, demonstrating that the notions of entropy on both sides of this fence really do match up physically, and are not just a piece of highly sophisticated algebraic numerology. That's the bit I'm still not comfortable with. Maybe that will become clearer after I understand how the spin foam framework provides these necessary features.

It's also noteworthy (imho) how a cosmological scalar $\Lambda$ pops up as an arbitrary scalar in the above -- though remaining a mystery so far.

(To be continued.)
==endquote==

 

[strangerep]

Hi Strangerep, this post #9 of yours is a really helpful summary of how Jacobson's derivation of Einstein Field Equation works.

You have a unique skill for stopping people suffering a slight case of ADD from wandering away from a thread.

I corrected some trivial typos in the equation numbering in your post, which matches the numbering in the CHRR paper. It's convenient to be able to refer to the CHRR paper for additional context of the equations.

Indeed. Dunno why I made all those typos. I guess that's what comes from composing a post while simultaneously trying to follow and understand a journal article.

You mention that this is "installment #1" to be continued.

It should have been "installment #2", with the 1st installment covering instead the Frodden+Gosh+Perez derivation of the energy--area equation from the EFE. Jacobson's result is just the reverse direction, iiuc.

But there's a LOT more I need to understand better before attempting an "installment #3". E.g., the gory details about spin networks, and how/why area therein is related to the rotation operator, and why the rotation operator is proportional to the boost operator (which is an essential part of the thermodynamical Hamiltonian on an accelerated worldline), and so on.

 

[marcus]

As best as I can tell the CHRR argument works, but as Strangerep indicates, it is complicated: depending on prior work by Eugenio Bianchi in turn resting on work by Frodden Ghosh Perez. Eventually we'll learn if it all checks out. If so, then it looks to me that Einstein GR equation has been derived from the covariant LQG quantum field model.
Here is a hand wave sketch of the Jacobson 1995 argument which served CHRR as a guide. Essentially they had to show that Jacobson's assumptions could be granted to the LQG quantum gravitational field.

Here's a paraphrase of CHRR page 1 paragraph 1. Oversimplified sketch of how Jacobson derived einstein field eqn from:
1. acceleration temperature (keywords Rindler Unruh)
2. entropy-area (keywords Hawk Beck Rind Unrh)
3. entropy-energy changes (keywords Clausius, ∂S=∂E/T)

You want to know how much the local matter curves the local geometry. You know stuff about horizons. How do you create horizons? By accelerating little observer probes outwards in every direction from a given point.

Consider an observer accelerating in some direction. Behind him is a causal (rindler) horizon. He measures a temp T. All this mass-energy is flowing back disappearing across the horizon, never again to affect him. That is ∂E across a given patch of horizon area. We know T so we know ∂E/T.

BTW this flow is affected by the curvature, whatever it is (we want to determine the curvature, given the matter). The curvature can either focus or defocus to flow of energy back across the
horizon in his wake.

So the upshot is that probed by accelerating in any given direction, the curvature seen from that direction is determined. There is only one value curvature can have that will make the area of the horizon patch and the ∂E/T flow across that patch match up...

So it looks like CHRR could be quite an important paper. What other papers that appeared this month have a comparable level of interest? And why?

As a reminder, here is the CHRR abstract:
http://arxiv.org/abs/1401.5262
Spacetime thermodynamics without hidden degrees of freedom
Goffredo Chirco, Hal M. Haggard, Aldo Riello, Carlo Rovelli
(Submitted on 21 Jan 2014)
A celebrated result by Jacobson is the derivation of Einstein's equations from Unruh's temperature, the Bekenstein-Hawking entropy and the Clausius relation. This has been repeatedly taken as evidence for an interpretation of Einstein's equations as equations of state for unknown degrees of freedom underlying the metric. We show that a different interpretation of Jacobson result is possible, which does not imply the existence of additional degrees of freedom, and follows only from the quantum properties of gravity. We introduce the notion of quantum gravitational Hadamard states, which give rise to the full local thermodynamics of gravity.
12 pages, 1 figure

For me, the other two January 2014 papers roughly on par with CHRR are:
http://arxiv.org/abs/1401.6441
A new vacuum for Loop Quantum Gravity
Bianca Dittrich, Marc Geiller
(Submitted on 24 Jan 2014)
We construct a new vacuum for loop quantum gravity, which is dual to the Ashtekar-Lewandowski vacuum. Because it is based on BF theory, this new vacuum is physical for (2+1)-dimensional gravity, and much closer to the spirit of spin foam quantization in general. To construct this new vacuum and the associated representation of quantum observables, we introduce a modified holonomy-flux algebra which is cylindrically consistent with respect to the notion of refinement by time evolution suggested in [1]. This supports the proposal for a construction of a physical vacuum made in [1,2], also for (3+1)-dimensional gravity. We expect that the vacuum introduced here will facilitate the extraction of large scale physics and cosmological predictions from loop quantum gravity.
10 pages, 5 figures

http://arxiv.org/abs/1401.6562
Planck stars
Carlo Rovelli, Francesca Vidotto
(Submitted on 25 Jan 2014)
A star that collapses gravitationally can reach a further stage of its life, where quantum-gravitational pressure counteracts weight. The duration of this stage is very short in the star proper time, yielding a bounce, but extremely long seen from the outside, because of the huge gravitational time dilation. Since the onset of quantum-gravitational effects is governed by energy density --not by size-- the star can be much larger than Planckian in this phase. The object emerging at the end of the Hawking evaporation of a black hole can then be larger than Planckian by a factor (m/m_P)ⁿ, where m is the mass fallen into the hole, m_P is the Planck mass, and n is positive. The existence of these objects alleviates the black-hole information paradox. More interestingly, these objects could have astrophysical and cosmological interest: they produce a detectable signal, of quantum gravitational origin, around the 10⁻¹⁴cm wavelength.
5 pages, 3 figures.

It looks to me as if Bianca Dittrich is bidding to replace spin networks and spin foams with
TRIANGULATIONS, which will then perhaps represent quantum states of geometry and histories thereof. If this gains support it would bring LQG closer to dynamical triangulations and to simplicial QG generally. The move may offer the chance to overcome some of the obstacles that have held these other approaches back, and to carry over some of the good Lqg results. I can only wait and see how this turns out.

The PLANCK STARS paper offers a way of looking at LQG BH collapse that finally seems to me to make sense. It always seemed as if the LQG BH picture should involve a bounce. (After all the cosmic Big B turns out in LQG to be a bounce.) But where was that bounce supposed to GO? If it bounced back at us, then we wouldn't see any BHs because they'd all have bounced. So it must rebound into a separate tract of space, making a new "baby universe". Attempts to picture that didn't seem entirely satisfactory for various reasons. Then the Planck Stars authors cut through that puzzle by point out that the bounce could be happening here in OUR space because it would be subject to EXTREME TIME-DILATION. Geometry and matter are comparatively sluggish when they are deep in a gravity well. The bounce in a BH could be happening veeerrrrry slowly and the BH could be GOING to explode. It just hasn't yet.

It seems obvious once you're told: what's inside a black hole event horizon is a slo-mo bounce.
This resolves a long-standing conceptual tension about what could actually be down in there, instead of an unphysical "singularity". So that is a major January 2014 development.

Those three seem to me to be the QG pick for this month. Any comments or other nominations?

 

[marcus]

Stefano Liberati gave a talk at Perimeter this week where he mentioned the Chirco et al paper in the conclusions. I'll get the PIRSA link. It's highly relevant to the overall topic of the talk which is his investigation of the emergence of GR from thermodynamics. Jacobson pointed out that GR *looks like* it arises from thermodynamics of some deeper hidden degrees of freedom. Liberati has been investigating this possibility and finds that postulating hidden degrees of freedom (from which gravity arises) is fraught with Lorentz breakage problems. He partially addresses these, but notes that CHRR have GR equation arise from thermodynamics of *gravitational* degrees of freedom (already in a sense there). They dispense with the need to assume additional hidden ones.

 

[marcus]

Stefano's talk at Perimeter Institute on this topic was 19 June (just a few days ago).

Stefano Liberati gave a talk at Perimeter this week where he mentioned the Chirco et al paper in the conclusions. I'll get the PIRSA link. It's highly relevant to the overall topic of the talk which is his investigation of the emergence of GR from thermodynamics. Jacobson pointed out that GR *looks like* it arises from thermodynamics of some deeper hidden degrees of freedom. Liberati has been investigating this possibility and finds that postulating hidden degrees of freedom (from which gravity arises) is fraught with Lorentz breakage problems. He partially addresses these, but notes that CHRR have GR equation arise from thermodynamics of *gravitational* degrees of freedom (already in a sense there). They dispense with the need to assume additional hidden ones.

As a reminder, here is the CHRR abstract:
http://arxiv.org/abs/1401.5262
Spacetime thermodynamics without hidden degrees of freedom
Goffredo Chirco, Hal M. Haggard, Aldo Riello, Carlo Rovelli
(Submitted on 21 Jan 2014)
A celebrated result by Jacobson is the derivation of Einstein's equations from Unruh's temperature, the Bekenstein-Hawking entropy and the Clausius relation. This has been repeatedly taken as evidence for an interpretation of Einstein's equations as equations of state for unknown [hidden] degrees of freedom underlying the metric. We show that a different interpretation of Jacobson result is possible, which does not imply the existence of additional degrees of freedom, and follows only from the quantum properties of gravity. We introduce the notion of quantum gravitational Hadamard states, which give rise to the full local thermodynamics of gravity.
12 pages, 1 figure

As a reminder here is the CHRR basic argument.

Here's a paraphrase of CHRR page 1 paragraph 1. Oversimplified sketch of how Jacobson derived einstein field eqn from:
1. acceleration temperature (keywords Rindler Unruh)
2. entropy-area (keywords Hawk Beck Rind Unrh)
3. entropy-energy changes (keywords Clausius, ∂S=∂E/T)

You want to know how much the local matter curves the local geometry. You know stuff about horizons. How do you create horizons? By accelerating little observer probes outwards in every direction from a given point.

Consider an observer accelerating in some direction. Behind him is a causal (rindler) horizon. He measures a temp T. All this mass-energy is flowing back disappearing across the horizon, never again to affect him. That is ∂E across a given patch of horizon area. We know T so we know ∂E/T.

BTW this flow is affected by the curvature, whatever it is (we want to determine the curvature, given the matter). The curvature can either focus or defocus to flow of energy back across the
horizon in his wake.

So the upshot is that probed by accelerating in any given direction, the curvature seen from that direction is determined. There is only one value curvature can have that will make the area of the horizon patch and the ∂E/T flow across that patch match up.

Hi Strangerep and Atyy! I didn't see your recent posts as I was writing this. I'll leave it extant however---it's an attempt at a very basic account of how GR eqn could derive from some thermodynamic relations (Unruh, Clausius etc)

To recap, the reason Stefano Liberati mentioned CHRR prominently in his talk last week at Perimeter (see slide #37/39 in conclusions) is apparently because he has devoted considerable time to investigating ALTERNATIVES to it and encountered problems with Lorentz Invariance Violation (LIV). Liberati's alternative approach was to assume there actually are unknown additional hidden degrees of freedom whose thermodynamics underlies the GR equation. The CHRR paper argues these are unnecessary.

Here is the PIRSA link to his 19 June talk:
http://pirsa.org/14060002/
Gravity, an unexpected journey: from thermodynamics to emergent gravity, Lorentz breaking and back...
Stefano Liberati
Abstract: Thermodynamical aspects of gravity have been a tantalising puzzle for more than forty years now and are still at the center of much activity in semiclassical and quantum gravity. We shall explore the possibility that they might hint toward an emergent nature of gravity exploring the possible implications of such hypothesis. Among these we shall focus on the possibility that Lorentz invariance might be only a low energy/emergent feature by discussing viable theoretical frameworks, present constraints and open issues which make this path problematic. In the end we shall focus on black hole thermodynamics in Lorentz breaking gravity by presenting some recent results that seems to hint towards a surprising resilience of thermodynamics aspect of gravity even in these scenarios.
Date: 19/06/2014