# GR/StatMech/QM foundations, epistemic views only please

1. Jan 12, 2014

### marcus

If you have seen interesting recent research papers on foundations/interpretation of these branches of physics, please share your links and thoughts. Argument along ontic versus epistemic lines is not approved--it is frequently a waste of time. So if you please use a separate thread if your views are ontic.

For a simple explanation of the difference, google "Mermin pirsa". You get a 45 minute video lecture "Confusing Ontic and Epistemic Causes Trouble in Classical Physics Too"
And the summary which you can read immediately without watching the talk says:
" A central issue is whether quantum states describe reality (the ontic view) or an agent's knowledge of reality (the epistemic view)."

The title of that video talk is a reminder that "QM interpretation" is only part of a tangle of foundational puzzles involving GR, Statistical Mechanics, Thermodynamics as well. In other words foundational confusion can cause trouble in CLASSICAL branches as well as quantum. I would like to know what other people have learned about this nexus of problems.

If you want a paper that is easy to read and quickly covers the material of that video, google "Mermin problem of the now". This defines a conceptual problem common to a lot of physics, notably (but not exclusively) classical. You might be interested in how Mermin resolves it.
That is a December 2013 paper---we're especially interested in recent work in this thread.

I want to mention some foundations connections between GR, StatMech, Thermodynamics, but will make a separate post of that so this one doesn't get too long.

2. Jan 12, 2014

### marcus

To help anyone new get their bearings, it's characteristic of an epistemic view that the 4D "Minkowski space" of special rel is a math device to help one understand, relate aspects of experience, relate measurements of distance, duration, motion, angle, area etc.
This 4D coordinatized device is extremely useful but we don't assume it is "reality" We don't imagine that this 4D thing with all its handy formulas EXISTS.

Likewise we don't assume that the curved 4D block universe of General Rel exists. Why should spacetime exist? GR is a useful 4D mathematical device that helps a person organize their experience and predict and find relations amongst measurements. Like of orbits and the angles of incoming starlight and the discrepancies of clocks.

So if you google "Freidel relative locality arxiv" you'll find articles about some new math model where there is no one single official spacetime but different observers construct their own. And experimental observations are proposed to decide if this picture is more accurate than usual GR.
Or if you google "Gielen Wise observer space" you get a different proposed replacement for GR which does not necessarily imply that a 4D continuum common to all observers exists. Those are classical constructions, that recover classical GR in the appropriate limit. If you haven't looked at the papers you might be interested in checking them out to see what the motivation or rationale is. These are 2012-2013 articles, in other words recent.

But that's not what I wanted to talk about in this post. In 1995 Jacobson showed a fundamental connection between GR and thermodynamics
Most people have seen this paper, I think, but if you have not then you are invited to google "Jacobson GR thermodynamics arxiv" and as the first hit you will get
Thermodynamics of Spacetime: The Einstein Equation of State which DERIVES the equation of GR from the fundamental relation connecting heat, entropy, and temperature. What is the heat of geometry? Can geometry be understood as a cloud of "molecules of geometry" that wiggle and jitter and recombine in various ways and thereby have geometric temperature and entropy?
If you google that "Jacobson GR thermodynamics arxiv" I suggested the second hit will be
Non-equilibrium Thermodynamics of Spacetime
A four page 2006 paper by Jacobson and two co-authors.
More could be said, but I don't want to make this post too long. It seems clear that the dynamics of changing geometry is not a separate subject from Thermodynamics. GR and Thermodynamics are two classical theories which are related at fundamental level in a way we do not yet understand.
So that leads to a mention of Rovelli's idea of thermal time and his 2012 paper on General relativistic statistical mechanics.
There are recent papers on epistemic quantum mechanics interpretation that we could also bring up in connection with this. However I hope other posters will contribute to this topic. Can you add some notices of recent research addressing foundational problems of GR/Thermo/StatMech/QM, perhaps suggesting connections among them, or a possibility of our getting a better understanding of one or several of them?

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3. Jan 12, 2014

### atyy

There is a technical problem. CBism is meant to be an analogy for QBism. However, take Freidel and colleagues' relative locality, for example, although spacetime does not exist constitute all of reality (mathematically defined below, so no arguments about it), there is still an overarching reality in the model, simply that local observers cannot reconstruct all of it. The Harrigan and Spekkens psi-ontic and psi-epistemic definitions also assume that there is reality. Now this is a technical discussion, because Harrigan and Spekkens, following Bell, did define reality in their paper as something that could be represented by the possibly very nonlocal, nonseparable hidden variables λ.

The problem is that Mermin and colleagues write in their QBist paper that λ is a discredited element of reality. This is why more than one person (including Mitchell Porter, RUTA), with good technical justification, has said that QBism assumes there is no reality. Therefore Freidel and colleagues' relative locality, and most psi-epistemic views which assume the existence of λ are not analogues of Mermin and colleague's QBism, if one takes all they say seriously (although the analogy is pretty good if one disregards these QBists' point about λ; and there are technical elements that are common in motivation such as Caves and Fuchs re-derivation of Hudson and Moody's quantum de Finetti representation http://arxiv.org/abs/quant-ph/0104088).

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4. Jan 12, 2014

### atyy

Regard Jacobson's insight, the most recent progress has come from van Raamsdonk and colleagues' work, which is based on the thermodynamics of the modular Hamiltonian. The modular Hamiltonian is related to Rovelli's thermal time in the sense that the modular Hamiltonian defines a modular flow which is Tomita-Takesaki flow (as I learnt from marcus).
http://arxiv.org/abs/1308.3716
http://arxiv.org/abs/1312.7856

The Tomita-Takesaki flow also appears in Papadodimas and Raju's state dependent observables for the interior of a black hole. In some ways this is nice and very Rovellian since it coincides with a very strong (intuitive, non-technical) notion of background independence. On p42 they extend their construction to slightly out-of-equilibrium scenarios.
http://arxiv.org/abs/1310.6335

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5. Jan 12, 2014

### marcus

Atyy, thanks for the interesting observations and links! I forgot to mention something at the start of the previous post, which I'll put in now---the point that when one takes an epistemic view of of some mathematical model (a physics theory) one is not thereby denying the existence of a common reality which all observers/agents are engaged with.
This is the old point about not confusing the description with the reality.
Math is an evolving artificial human language that is continually sprouting new concepts and syntax as mathematicians see the need for them. It has no fixed essence or predetermined limits, so we don't know what math models will be like in the future, what the language will be able to say by way of modeling and explanation.

I personally believe strongly in a common shared reality that exists independently of any one person's mathematical description. The value and meaning of the model, for me, is found in its usefulness in relating different features of existence (measurements)--understanding and predicting. It's in that light that I said this earlier:

6. Jan 12, 2014

### friend

The fact that we can distinguish one point in spacetime from another means it exists. How could you distinguish or analyze non-existing things?

Yes, I've been thinking about this too. The connections I've notices are as follows: Spacetime is made up of "events" at every point in a manifold - "event" as used in the language of relativity. And more generally, events are situations describable with propositions. And a proposition is either true or false, so it carries the information of a bit. There, you have the information and entropy of bits connected to spacetime. I don't know yet how the curvature of spacetime would be connected to the entropy/information of the region enclosed. But there does seem to be a fundamental connection.

Thinking a bit further about this... What else can spacetime do besides bend and curve? And since spaces of different curvature are different from each other, different curvature has different amounts of information. I can't say by how much, yet.

Thinking even further... Curved spacetimes are contracted. In a sense, there is more spacetime in a curved spacetime than in a flat spacetime. So one should expect that there be more information/(entropy?) in a curved spacetime than in a flat spacetime. Perhaps a baseline of 0 entropy/information can be set for flat spacetime, and, what, an infinite entropy for a singularity. There is no such thing as negative entropy or information is there?

PS. I'd like to point out that there is nothing speculative about different things (different spacetime points) being described with propositions, or propositions carrying one bit of information. We assign bits to true/false logic states in electronic circuits. This is too basic to be speculative.

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7. Jan 12, 2014

### marcus

Hi Friend,
I want to be clear that although I don't want to get into private SPECULATION in this thread I want to point out that looking at conceptual gaps and mismatch in the foundations of various types of physics is currently stimulating some interesting professional research.

Foundations/interpretation has become a rich area that is breeding new physical models: e.g. the
Tomita time (= "modular flow") stuff that Atyy was just linking to. Or the Freidel and the Gielen-Wise papers that Strangerep linked to. There is plenty of new stuff to discuss within the purview of current professional research.

I should clarify the term epistemic by generalizing the blue highlight in post #2.

" A central issue is whether any mathematical model describes reality (the ontic view) or an agent's knowledge of reality (the epistemic view)."

The original highlighted quote from Mermin merely applied to "a quantum state" and I'm extending it to include classical states and physical models in general.

8. Jan 12, 2014

### friend

marcus, I understand your concerns. So I made an effort not to cross the line into speculation. Your questions seem to be asking about how we can know on a foundational level that entropy was connected to spacetime. And since I had been thinking about this too, I thought I would revert to the most basic definitions of information and of spacetime. I believe what I've written is too basic to be speculative.

9. Jan 12, 2014

### atyy

To give some background linking your question of what may be an appropriate notion of entropy for spacetime, with the Jacobson papers in marcus's post #2 and the links in post #4, it may be the entanglement entropy. This goes back to Ryu-Takayanagi formua linking entanglement entropy and a notion of area http://arxiv.org/abs/hep-th/0603001, and has an intuitive picture pointed out by Swingle http://arxiv.org/abs/0905.1317.

The links in post #4 take a generalization of this to be the appropriate notion of thermodynamics indicated Jacobson's paper mentioned in post #2. From this the Einstein equations are derived at linear level. There is still much work to be done to recover the full nonlinear Einstein equations, but these seem like steps in the right direction.

For a point of view supporting the relationship between entanglement entropy and spacetime that was co-authored by LQG and string people, see Bianchi and Myers's http://arxiv.org/abs/1212.5183. In another thread, marcus pointed out this talk by Bianchi, which I found helpful: Entanglement, Bekenstein-Hawking Entropy and Spinfoams http://pirsa.org/13070048/.

Edit to add a note on terminology:
entanglement entropy ~ entanglement thermodynamics
entanglement Hamiltonian = modular Hamiltonian
modular flow = Tomita-Takesaki flow

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10. Jan 12, 2014

### marcus

Good! I'm glad Atyy was alert to that and able to pick up on it. This is getting interesting, thanks both.

11. Jan 12, 2014

### marcus

A little note on the word "Bayesian" which is apt to come up in discussion. Here's an excerpt from the wikipedia article

==quote http://en.wikipedia.org/wiki/Bayesian_probability ==
…The term "Bayesian" refers to the 18th century mathematician and theologian Thomas Bayes, who provided the first mathematical treatment of a non-trivial problem of Bayesian inference.[3] Nevertheless, it was the French mathematician Pierre-Simon Laplace who pioneered and popularised what is now called Bayesian probability.[4]

...The term Bayesian refers to Thomas Bayes (1702–1761), who proved a special case of what is now called Bayes' theorem in a paper titled "An Essay towards solving a Problem in the Doctrine of Chances".[8] In that special case, the prior and posterior distributions were Beta distributions and the data came from Bernoulli trials. It was Pierre-Simon Laplace (1749–1827) who introduced a general version of the theorem and used it to approach problems in celestial mechanics, medical statistics, reliability, and jurisprudence.[9] Early Bayesian inference, which used uniform priors following Laplace's principle of insufficient reason, was called "inverse probability" (because it infers backwards from observations to parameters, or from effects to causes).[10] After the 1920s, "inverse probability" was largely supplanted by a collection of methods that came to be called frequentist statistics.[10]
==endquote==

A good way to make the idea of subjective degrees of certainty concrete is to think of a rational bettor, a bookie IOW whose profession is to buy and sell bets. If he thinks something is a sure thing (100% probability) he will BUY any bet for $1 that pays$1.01 if it happens, or indeed any payoff greater than \$1. I suppose the name "bookie" comes from the alleged professional practice of keeping a "dutch book" containing a consistent listing of bets the bettor considers rational according to his subjective degree of certainty.

Other posters have given or can give a clearer explanation. I don't want to do more than touch on this, since it is a term that may come up in the discussion. It can apply in CLASSICAL settings (where a physicist may have absolute 100% certainty about an hypothetical outcome, law, or pattern) as well as, of course, in QUANTUM settings.

In any case in an epistemic view probability is not accorded physical existence as one might real fluid substance that flows around in the real world. It is a feature of the assessment made by an agent/observer/physicist. The subjective estimate is part of the agent's knowledge and it gets revised or updated as he acquires more information.

Just as a fanciful side comment, I wonder if in a Bayesian perspective "Now" should be defined as the moment when past bets are paid off and future bets are made. I.e. when the croupier says "Mesdames et messieurs, les jeux sont faits."

12. Jan 12, 2014

### marcus

If you google "introduction QBism" the top hit will be this November 2013 paper by Fuchs Mermin Schack http://arxiv.org/abs/1311.5253
An Introduction to QBism with an Application to the Locality of Quantum Mechanics
We give an introduction to the QBist interpretation of quantum mechanics. We note that it removes the paradoxes, conundra, and pseudo-problems that have plagued quantum foundations for the past nine decades. As an example, we show in detail how it eliminates quantum "non locality".
11 pages.

I don't think that's an empty claim and it signals a kind of change in the weather around quantum foundations and interpretation. Basically they say "let's put the agent (the subject, the physicist) into the picture instead of pretending that there's only the objective real world, and let's acknowledge that agents can communicate about their common reality." There is a kind of common sense realism here, I find.

This paper is one of two which for me personally characterize an epistemic view of QM. Bear in mind that there is more to this than merely Quantum Mechanics. There are significant epistemic developments in GR, StatMech, Thermodynamcs and in the interconnections among these fields. But just looking at QM for the moment, the OTHER paper personally significant for me is what you get when you google "relational EPR"

If you google "relational EPR" the top hit will be this April 2006 paper by Smerlak and Rovelli:
http://arxiv.org/abs/quant-ph/0604064
Relational EPR
We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of 'non-locality', when viewed in the context of this interpretation. The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.
10 pages
==excerpt==
... It is far from the spirit of RQM to assume that each observer has a “solipsistic” picture of reality, disconnected from the picture of all the other observers. In fact, the very reason we can do science is because of the consistency we find in nature: if I see an elephant and I ask you what you see, I expect you to tell me that you too see an elephant. If not, something is wrong.
But, as claimed above, any such conversation about elephants is ultimately an interaction between quantum systems. This fact may be irrelevant in everyday life, but disregarding it may give rise to subtle confusions, such as the one leading to the conclusion of non-local EPR influences.
In the EPR situation, A and B can be considered two distinct observers, both making measurements on α and β. The comparison of the results of their measurements, we have argued, cannot be instantaneous, that is, it requires A and B to be in causal contact. More importantly, with respect to A, B is to be considered as a normal quantum system (and, of course, with respect to B, A is a normal quantum system). So, what happens if A and B compare notes? Have they seen the same elephant?
It is one of the most remarkable features of quantum mechanics that indeed it automatically guarantees precisely the kind of consistency that we see in nature [6]…
==endquote==

Both these papers are so thematically similar that I continue to find it odd that the November 2013 one does not cite the April 2006 one as a reference! In any case both have helped to form my own views and thinking about this topic.

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13. Jan 12, 2014

### atyy

To sharpen the discussion, let's ask specifically: if QBbist and RQM interpretations are successful in defending locality, why do they not fall under the purview of Bell's theorem? If they do fall under the purview of Bell's theorem, they cannot be successful interpretations.

http://www.drchinese.com/Bells_Theorem.htm
"No physical theory of local Hidden Variables can ever reproduce all of the predictions of Quantum Mechanics."

Bell's theorem excludes local variables, hidden or not, and which can conceivably even be quantum states: http://arxiv.org/abs/1303.3081, http://arxiv.org/abs/0901.4255.

Many-worlds evades Bell's theorem, because the theorem assumes that each measurement has one definite outcome, whereas in many-worlds a measurement has multiple definite outcomes.

I will note that interpretations known as psi-epistemic (a technical term introduced by Harrigan and Spekkens http://arxiv.org/abs/0706.2661) do fall under the purview of Bell's theorem, but make no claim of locality: http://arxiv.org/abs/1201.6554, http://arxiv.org/abs/1303.2834.

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14. Jan 12, 2014

### strangerep

More than once, over the years, I've mentioned on PF that the usual proof of Bell's thm breaks down when the set of independent hidden variables is infinite. Suppose there are N hidden variables $\lambda_1, \cdots, \lambda_N$. There is a point in the Bell proof that relies on an ordinary Lebesgue integral like
$$\int \cdots d^N \lambda ~.$$But for $N\to\infty$, the measure does not exist. (There is no translationally-invariant Lebesgue measure in infinite dimensions.)

More recently, Warren Leffler noticed something very similar! He wrote a paper about how Path Spaces in Quantum Systems evade Bell's Thm, and produced some counter-examples to Bell's thm to illustrate the point. Here's the abstract:

Edit: I just noticed that he has another more recent paper, which I have not yet studied. Here's the abstract:

BTW, this sort of thing also gives a hint why Bohmian mechanics seems to be a counter-example to Bell's thm, at least from some people's viewpoint.

(Marcus: I'm not sure if all this is on or off your topic, so I leave it to you to decide.)

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15. Jan 12, 2014

### atyy

Yes, that seems very plausible. The minor technical point is I don't understand why one should not assume a translationally-noninvariant Lesbesgue measure.

The major technical point is that if the were how FMS were evading Bell's theorem, they would still be self-contradictory by claiming that λ does not exist, since this method of evading the theorem says that λ does in fact exist, but it is infinite dimensional.

16. Jan 12, 2014

### strangerep

Since (surprisingly!) no one has ventured a reply to my last post over in the Tomita-time thread, I'll ask here: what is the definition of "modular Hamiltonian".
I suspect a lurking circularity.

(Afaict, it's simply a generator that you can get by exponentiating a nonpure state operator.)

17. Jan 12, 2014

### atyy

Afaict, it is exactly that for the simple cases I understand. Why is it circular?

There is, as you probably know, an extension of the Tomita flow/modular flow language to infinite dimesional spaces (but I don't understand that at all).

18. Jan 12, 2014

### strangerep

Then one must say what the other measure is. Indeed, people often use Gaussian (Wiener) measure when trying to make sense of path integrals. But this needs Wick rotation, analytic continuation and all that, and they must show at the end that their limits do indeed exist.

In this case, Gaussian measure would imply that some values of the hidden variables are "less important" than others. So that must be justified on physical principles.

FMS are apparently unaware of Leffler's work. It may take a while before the ramifications play out fully. I haven't yet analyzed possible interplays that might lead to modifications their ideas.

19. Jan 12, 2014

### strangerep

When someone tells me how the nonpure fiducial state operator is chosen, I might have more to say on that.

20. Jan 12, 2014

### atyy

Ok, I'm not going to get this quite straight, but roughly the nicest example is to take the ground state of a CFT in Minkowski spacetime. The reduced density matrix of the half the space at t=0, when written in exponentiated form so that it looks thermal, yields a "modular Hamiltonian" that is the Rindler Hamiltonian. Since the causal development of the half space is the Rindler wedge, this is a nice heuristic for why the Rindler observer sees thermal radiation. Since I'm not very sure I got that right, let me refer to p2 of Swingle & Senthil's http://arxiv.org/abs/1109.1283 or p19 of Connes & Rovelli's http://arxiv.org/abs/gr-qc/9406019 (I dont understand the Connes-Rovelli paper, the simple presentation of Swingle-Senthil was easier for me).

BTW, physicists know this is not the proper way to prove Unruh radiation, but the heuristic is pretty sweet. http://arxiv.org/abs/1108.0320

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21. Jan 12, 2014

### strangerep

Let's take this in steps. First, one does not need to be heuristic for this. One can just perform the transformation from an inertial frame to a frame applicable to a uniformly-accelerated observer, and use this to derive the Unruh effect: that by this transformation the inertial vacuum gets transformed into a new (accelerated) vacuum (I'm using the Schrodinger picture here) that turns out to have an energy-momentum distribution similar to classical blackbody radiation, hence may be interpreted as a nonpure thermal state. But then the "thermal Hamiltonian" just comes from the acceleration parameter. [Edit: just saw your edit, but I might as well leave this paragraph as-is.]

But a forever-accelerating Rindler observer example is unphysical. Passing to the less-obviously-unphysical case of curved spacetime one gets the similar feature of Hawking radiation -- caused by the fact that free field modes (Poincare irreps) cannot sensibly be global in a curved spacetime, and one must Bogoliubov-transform between unitarily-inequivalent reps from point to point. These transformations (dependent on the curvature for their details) eventually yield a nonpure vacuum state operator. But to get the curvature one must know the energy-momentum details, and solve the Einstein equations. However, some of those other papers you linked bignote themselves about how they get the (linearized) Einstein equations out of AdS/CFT duality. Here lurks one possible circularity, istm.

[Again: Marcus: tell us to stop if this is off-topic.]

22. Jan 12, 2014

### atyy

As I understand, the papers claim to get the linearized Einstein equations from a CFT in flat spacetime (and some additional assumptions, but spacetime of the CFT is flat). Let's link http://arxiv.org/abs/1308.3716 and http://arxiv.org/abs/1312.7856 for easy reference.

I believe the major unproven assumption used is the Ryu-Takayanagi formula and its covariant generalization.

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23. Jan 13, 2014

### TrickyDicky

Regarding the epistemic view, I like these words by Einstein:

"How does it happen that a properly endowed natural scientist comes to concern himself with epistemology? Is there no more valuable work in his specialty? I hear many of my colleagues saying, and I sense it from many more, that they feel this way. I cannot share this sentiment. ... Concepts that have proven useful in ordering things easily achieve such an authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they come to be stamped as 'necessities of thought,' 'a priori givens,' etc.
The path of scientific advance is often made impassable for a long time through such errors. For that reason, it is by no means an idle game if we become practiced in analyzing the long-commonplace concepts and exhibiting [revealing, exposing? -Ed.] those circumstances upon which their justification and usefulness depend, how they have grown up, individually, out of the givens of experience. By this means, their all-too-great authority will be broken
." Einstein, 1916.

In science epistemology in the sense of questioning the foundations of a discipline judging the knowledge in itself, clarifying how the different concepts help in understanding the construction of the theory abstracted from the ontic object of this knowledge is usually a healthy exercise when used to disentangle possible sources of confusion.
Your example about the 4D spacetime geometry construct ¡s a nice example of how to employ epistemology in physics, but I suspect it might be a too strong starting point.
I suggest that maybe an easier concept to start analyzing physical foundations in GR/QM under the epistemic view could be(perhaps I'm wrong) the useful concept of fundamental particle, the understanding of matter as composed of "fundamental blocks", that has been very practical so far but that as it is suggested of the common 4D geometric concept might have become an obstacle to achieve a more complete understanding.
See for instance:
http://arxiv.org/abs/1204.4616
http://arxiv.org/abs/0807.3930

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24. Jan 13, 2014

### atyy

I don't know if this is related (apart from the general idea that infinite dimensional spaces are weird), but there is an open problem called Tsirelson's problem as to whether the nonlocality one gets from quantum mechanics (locality via tensor product Hilbert spaces) is the same as in completely rigourous quantum field theory (locality via noncommutativty of spacelike operators). Apparently Tsirelson's problem is related to an embedding problem of Connes's. Not that I understand it (since my philosophy is finite lattice models only!), but just in case you are interested.

http://www.tau.ac.il/~tsirel/Research/bellopalg/main.html

http://arxiv.org/abs/1008.1142
Connes' embedding problem and Tsirelson's problem
M. Junge, M. Navascues, C. Palazuelos, D. Perez-Garcia, V. B. Scholz, R. F. Werner

http://arxiv.org/abs/1008.1168
Tsirelson's problem and Kirchberg's conjecture
Tobias Fritz

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25. Jan 14, 2014

### strangerep

But.. (I was under the impression that...) the "Rindler Hamiltonian" is just the Poincare boost generator $K$, restricted to one of the wedges(?).

Thanks for reminding me of the Rovelli+Smerlak paper, which I had only skimmed previously. I've now studied it more closely, and I quite like it.

But,... umm,... you do realize (yes?) that Rovelli+Smerlak basically show that attributing the thermal-like spectrum perceived by an accelerated detector has nothing to do with reducing the full density matrix by tracing out the states on the wrong side of the Rindler wedge, even though the latter is a common explanation? (Corollary: the heuristic is not sweet, but misleading.)