
#73
Nov2412, 06:23 AM

P: 165

I think that the central idea of Rovelli’s essay “Forget Time”; his proposed “thermal time hypothesis” ; is a “timely”, important and thought provoking reminder of an uncomfortable truth, namely that the way physicists describe reality (which is their job description!) is dominated by our anthro’centric perspective. We are a species distinguished by our peculiarly elaborate communication skills.
Rovelli persuasively argues that: What about situations where we are as yet unable to quantify entropy, but just trust the Second Law implicitly? As Rovelli says: “Time is ... the expression of our ignorance of the full microstate”. Is Rovelli suggesting that our concept of time is an statistical artefact of the scale we human beings inhabit? Just a tool; a parameter that physics uses to describe quantitatively our human circumstances, with thermodynamics as a sort of catchall background? Roll on the next chapter in this story. 



#74
Nov2412, 12:23 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

I've moved over to and am working from the Connes Rovelli paper, since it is the main source and considerably more complete than any of the other papers (including the wideraudience FQXi essay.) The C&R paper has 77 cites, over a third of which are in the past 4 years. It is the root paper that other thermal time papers (including by Rovelli) refer to for detailed explanation. So what I would propose as a "next chapter in the story" is to make sure we get the main points that C&R are making. I'll run down the main corroborative cases they give on page 22, in their conclusions. These are explained in the preceding section, pages 1621. == http://arxiv.org/abs/grqc/9406019 == ... • Classical limit; Gibbs states. The Hamilton equations, and the Gibbs postulate follow immediately from the modular flow relation (8). • Classical limit; Cosmology. We refer to [11], where it was shown that (the classical limit of) the thermodynamical time hypothesis implies that the thermal time defined by the cosmic background radiation is precisely the conventional FriedmanRobertsonWalker time. • Unruh and Hawking effects. Certain puzzling aspects of the relation between quantum field theory, accelerated coordinates and thermodynamics, as the Unruh and Hawking effects, find a natural justification within the scheme presented here. ... ==endquote== They also include three other supporting points. One that is not discussed in the paper and they simply mention in passing is the widely shared notion that time seems bound up with thermodynamics and there are indeed hundreds of papers exploring that general idea in various ways (far too numerous to list). Their idea instantiates this widely shared intuition among physicists. Another supporting point is that the thermal time formalism provides a framework for doing general relativistic statistical mechanics. Working in full GR, where one does not fix a prior spacetime geometry, how can one do stat mech? A way is provided here (and see http://arxiv.org/abs/1209.0065 ) The sixth point is the one they give first in their "conclusions" listI will simply quote: ==quote grqc/9406019 page 22== • Nonrelativistic limit. In the regime in which we may disregard the effect of the relativistic gravitational field, and thus the general covariance of the fundamental theory, physics is well described by small excitations of a quantum field theory around a thermal state ω⟩. Since ω⟩ is a KMS state of the conventional hamiltonian time evolution, it follows that the thermodynamical time defined by the modular flow of ω⟩ is precisely the physical time of non relativistic physics. ==endquote== There is one other supporting bit of evidence which I find cogent and which they do not even include in their list. This is the uniqueness. Have to go, back shortly. 



#75
Nov2412, 01:48 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

The way I see the uniqueness point is that once you have a C*algebra A of all your observables, and a (positive traceclass) state functional ρ representing what you think you know about the world, then there is only one time evolution that you can define from the given (A,ρ) without making any further choices.
It is the natural canonical flow of time, given the world as we know it. We know the world as a bunch A of observables/measurements that are interrelated by adding subtracting multiplying etc. that is what an algebra is. And as a probabilistic functional ρ defined on that algebra, representing our information about what values those observables take. Given those two things (A,ρ) there is a unique flow defined on the algebra, taking each observable along to subsequent versions of itself. I'm not entirely clear or comfortable with this, but it seems reasonable to try thinking along those lines. GR is timeless, QM says what counts are the measurements, we take those hints seriously and we say that the world exists (timelessly) as an algebra of observations A. Specifically a C* algebra (abstract form of von Neumann algebra) and such an algebra has a natural idea of state defined on it representing what we think we know and expect. So this pair (A, ρ) is the world. And that pair gives you a unique time flow. The oneparameter group of automorphisms on the algebra that takes any observable to the next, to the next, to the next. There is a natural builtin way to make the observables flow. That's time. Or one idea of it. 



#76
Nov2412, 07:29 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

I think perhaps the essential thing about timeordering is it makes a difference which measurement you do first. All these differences are encoded in the noncommutativity of the algebra of observations, so timeorderings are already latent in the algebra. We shouldn't be too surprised that an algebra of observables, helped by a timeless state function to define the world, would have a preferred flow.




#77
Nov2512, 03:46 AM

P: 165

What are simple folk like me to think if Connes and Rovelli's approach turns out to be right? Time is part of the flexible spacetime geometry responsible for gravity. Time curves as one of the four dimensions described by the Riemann tensor. So I've understood. Or is it ct, which dimensionally is spacelike, that curves? Or perhaps just c that changes from place to place, so bending light around galaxies? Strange thoughts pass by. 



#78
Nov2512, 04:44 AM

Astronomy
Sci Advisor
PF Gold
P: 22,796

And it may be right! This approach proposed by Connes and Rovelli may be wrong. It is just an hypothesis which they argue should be thought through. You put the mental dilemma very preciselyand the business of light bending around galaxies and clusters of galaxies is very beautiful. As well as being essential to observational cosmology nowadaysthey depend on the magnification produced by lensing. The whole business of 4D geometry is compellingly beautiful... It's a challenge to hold two contradictory ways of thinking, at least for a while, in one's head. I can't say it any better than you just did. 



#79
Nov2512, 10:42 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

Paulibus, I don't want to raise false hopes. But I am beginning to find thermal time understandable and (for me) it comes of reading pages 16 and 17 of the Connes Rovelli paper. I'm comfortable with ordinary operator algebra on ordinary hilbertspace. this is undergrad math major level. there are many steps of algebra but you just have to go thru them patiently. IFF you also are comfortable it might work for you. Then you wouldn't have to feel mystified by it. Maybe in a day or two I will try to make INTUITIVE sense of the 20 or so steps of algebra on those pages. In case you don't like vectors and matrices and would find it tedious to work thru.
What it does is go thru the NON relativistic case where there is already a hamiltonian and it shows that the jazzy new thermal time flow RECOVERS the conventional hamiltonian time evolution. IOW the jazzy new idea of time specializes down to the right thingit is a valid generalization of what we already think of as timeevolution flow. So for me, the pages 16 and 17 are the core of the Connes Rovelli paper and at least for now the core and the whole business. It's not so unintuitive now. 



#80
Nov2512, 11:49 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

here ( grqc/9406019 pages 16,17) we have a conventional situation with hilbertspace H and hamiltonian H. Of course we have the algebra A of observables, the operators on the HAnd the quantum state ω is a density matrix: that's what we want to study and finesse a time evolution from. And of course we have the algebra A of observables, the operators on the H
Imagine it in positive diagonal form, we'll need its square root k_{o} = ω^{1/2}. Now the trick is the "GNS construction" which is like obviously a bunch of matrices can themselves form a vectorspace! You can add two and get another matrix. You can multiply by a scalar. If we want to think of k_{o} as an operator we write it k_{o}. If we want to think of it as a vector in a vectorspace where the vectors are actually matrices we write it  k_{o}> This (which appears kind of dumb at first sight) is actually the cleverest thing on the whole two pages. I've seen this in math before, something that looks utterly pointless turns out not to be. It is so pointless that it takes clever people like Gelfand Naimark Segal to think of it. We can make a mixed state (a matrix) into a pure state (a vector) in a "higher" hilbertspace this way. Now all the operators A which used to act on H can act on vectors like k_{o}, call a generic such "vector" k. The key analytic condition is that k k* have finite trace (equation 30). Define the new action of any operator A by A k> = Ak> It's obvious. k WAS an operator, so A by k is another operator so Ak> is a vector. It is the vector which k> gets mapped to. So now we can do something a little interesting. We can define the set { A k_{o}> for all A} I think I've seen that called the "folium" of k_{o}>. Anyway the set of all vectors that k_{o}> gets mapped to, using all possible operators in the algebra. that is a vectorspace and it has k_{o}> as a "cyclic" vector. I don't like the term "cyclic" for this but it has historical roots and is conventional. Call it seed or generator if you want. It generates the whole vectorspace when operated on by the algebra A. Above all algebra requires patience, now we are at the top of page 17, where things begin to happen. I'll continue later. k_{o}> is going to play the role of a "thermal vacuum state". the vanilla state from which the thermal time arises. the authors say a little about it at the top of page 17 that could provide extra intuition. But I'll continue this later. 



#81
Nov2612, 01:31 PM

P: 266

Here's my two cents;
IF: 1) All observers share a reality and 2) There is some definition of "state" or "now" describing physical existence which extends beyond those observers (which utilizes the concept of Time in any way) and 3) We consider what Relativity does to our usual definitions of Time THEN: Applying the definition of #2 for all observers in #1, taking #3 into consideration, we conclude that the entirety of the history/future of the Universe eternally exists as a physical representation in what is literally a static 4D Block Universe; the flow of time and the concept of becoming are emergent properties of being sentient. 



#82
Nov2612, 01:59 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

Hi RJ, block universe was discussed some earlier in posts #50 and 52 of this thread. Here is a link to post #52
http://physicsforums.com/showthread....32#post4140332 



#83
Nov2612, 02:32 PM

P: 266





#84
Nov2612, 04:13 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

If one accepts GR then the decay of a radioactive nucleus will affect the geometry of the universe (as the distribution of mass always does, in GR) and according to QM the time when the nucleus will decay has not yet been determined (unless you postulate "hidden variables") and cannot in principle be predicted. Thus the geometry (the metric) of the universe is not predetermined.
So if one accepts ordinary physics (GR and QM) there can be no block universe. George Ellis put this amusingly in his FQXi essay that I linked to above. He described a massive rocket powered sled zooming back and forth along a track under the control of a radioactive decay (Schrödinger Cat) mechanism that tells it when to go east and when to go west. In ordinary GR, the "coordinate time" is not physically meaningful. Not measurable. One needs to break general covariance by introducing an observer, or e.g. a uniformly distributed gas of particles, as is done in cosmology. A good discussion of the status of time in modern physics is provided in a few pages of the Rovelli essay that Naty linked to earlier in this thread. It is called "Unfinished Revolution" and was posted on arxiv in 2006 or 2007. Google "rovelli revolution" and you should get it. It is wide audience. I don't personally know of any working physicist who takes the traditional block U idea seriously. The prevailing question is where do we go from here. ========================= What I've been gradually working thru, in the past few posts, is the idea that there IS an intrinsic timeflow on the space of observables, which arises from specifying a STATE ω of the universe. This is akin to what Barbour has been saying: time is certainly real but not as a pseudospatial dimension or as something fundamental. It arises from more basic stuff. In this case it arises as a oneparameter group of transformations of the space of observables. What I'm trying to understand better is how this socalled "modular group" α_{t} or "flow" arises from specifying the algebra of observables A and the state ω. The formalism we are working with here is compatible with BOTH QM and GR, it is used to delve into "general covariant statistical quantum mechanics" which definitely seems interesting. 



#85
Nov2612, 05:20 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

Sources
http://arxiv.org/abs/grqc/9406019 pages 16,17 WikiP: "GelfandNaimarkSegal construction" WikiP: "KMS state" WikiP: "TomitaTakesaki theory" (not so good I think, but at least article exists) WikiP: "Polar decomposition" (article exists, I haven't used or evaluated it) The basic situation that general covariant quantum physics deals with is an algebra A of observables. That's the world. After all QM is about making measurements/observations. And a temporal flow α_{t} is a oneparameter group of automorphisms of that algebra. automorphism means it maps an observable A onto another observable α_{t}A which you can think of as making the same observation but "t timeunits later". oneparameter group means that doing α_{s} and then doing α_{t} has the same flow effect as doing α_{s+t}. the parameter t is a real number. And automorphism means it preserves the algebra operations, it is linear etc etc. Observables are in fact an algebra because you can add and multiply observables together to predict other observables or to find how they correlate with each other. The statistical quantum state of the world is represented by a positive functional on the algebra which we can think of as a density matrix ω and its value on an observable A can be written either as ω(A) or as trace(Aω). The state ω is what gives the observables their expectation values and their correlations. A nice thing about a density matrix ω is that it has a square root ω^{1/2}. Think of writing it as a diagonal matrix with all positive entries down the diagonal, and taking the square root of each entry. More about this later. From an algebra A and a state of the world ω it is possible to derive a unique flow α_{t} on the algebra. Taking each observable A into a progression of "later" evolved observables α_{t}A, for every timeparameter number t. 



#86
Nov2612, 05:21 PM

P: 266

I emboldened the words in your post which show that we have problems thinking without a "flow of time". Technically, neither GR nor QM have any mechanism for a FLOW of time whatsoever. They are completely timesymmetric theories, yet you are suggesting that one direction is preferred over the other. The time parameter is only a marker along the 4D Block Universe in my view. 



#87
Nov2612, 05:29 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

How about you read a few pages of Rovelli's wideaudience essay Unfinished Revolution, that I suggested you look at earlier? Section 1.2 "Time" is less than a page long. It starts at the bottom of page 3 and covers part of page 4. Google "rovelli unfinished revolution" and you get the arxiv version: http://arxiv.org/abs/grqc/0604045 



#88
Nov2612, 05:39 PM

P: 266





#89
Nov2612, 05:47 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

http://fqxi.org/community/essay/winners/2008.1 go there, scroll down to "second community prize", there is Ellis's abstract and a link to the PDF. I already explained the incompatibility using the same example Ellis did, radioactive decay changes the distribution of massEllis's rocket sled just makes it more colorful. 



#90
Nov2612, 06:07 PM

Astronomy
Sci Advisor
PF Gold
P: 22,796

I need to plug ahead with how time (as a flow on the observable algebra) emerges. For continuity, here are the essentials of the last post:
Given an algebra A of observables and a state of the world ω it is possible to derive a unique flow α_{t} on the algebra. Taking each observable A into a progression of "later" evolved observables α_{t}A, for every timeparameter number t. A nice thing is that this "thermal time" construct RECOVERS ordinary time when we start with a conventional Hamiltonian H and hilbertspace H. this is what Connes Rovelli show on pages 16 and 17 of their paper. See link: Sources http://arxiv.org/abs/grqc/9406019 pages 16,17 WikiP: "GelfandNaimarkSegal construction" WikiP: "KMS state" WikiP: "TomitaTakesaki theory" (not so good I think, but at least article exists) WikiP: "Polar decomposition" (article exists, I haven't used or evaluated it) The basic situation that general covariant quantum physics deals with is an algebra A of observables. That's the world. After all QM is about making measurements/observations. And a temporal flow α_{t} is a oneparameter group of automorphisms of that algebra. automorphism means it maps an observable A onto another observable α_{t}A which you can think of as making the same observation but "t timeunits later". oneparameter group means that doing α_{s} and then doing α_{t} has the same flow effect as doing α_{s+t}. the parameter t is a real number. And automorphism means it preserves the algebra operations, it is linear etc etc. Observables are in fact an algebra because you can add and multiply observables together to predict other observables or to find how they correlate with each other. The statistical quantum state of the world is represented by a positive functional on the algebra which we can think of as a density matrix ω and its value on an observable A can be written either as ω(A) or as trace(Aω). The state ω is what gives the observables their expectation values and their correlations. A nice thing about a density matrix ω is that it has a square root ω^{1/2}. Think of writing it as a diagonal matrix with all positive entries down the diagonal, and taking the square root of each entry. The observable algebra (think matrices) IS a vector space. You can add matrices entrywise and so on. The celebrated GNS construction makes a vectorspace out of ω^{1/2}⟩ together with all the other density matrices and their like which you can get by applying elements A of the algebra to that root vector. that is called the FOLIUM of ω Aω^{1/2}⟩ for all A in A It is a hilbertspace. The special good things about this hilbertspace (they give it a name, K) is that the algebra acts on it, after all it was MADE by having the algebra act on the single root vector ω^{1/2}⟩ and seeing what you get, and the other thing is just that: it has what is called a "cyclic vector", a root or generator: the whole hilbertspace is made by having the algebra of operators act on that one ω^{1/2}⟩, as we have seen. ω(A) = ⟨ω^{1/2}Aω^{1/2}⟩ Now what C&R do is they construct an operator, by giving its polar decomposition. This is what happens on page 17. And the operator obtained by putting the polar decomp. together has the effect of doing a matrix transpose, or mapping A → A*. They call this operator S. SA ω^{1/2}⟩ = A* ω^{1/2}⟩ There is some intuition behind this (there is already something about it on page 7 but I'm looking at page 17). It is like swapping creation and annihilation operators. Undoing whatever an operator does. Partly it is like getting your hands on what is implicitly an infinitesimal timestep, except there is no time yet. More importantly, transpose is tantamount to commuting (AB)* = B*A* So if we can just take the antiunitary part out of the picture it's almost like swapping order: AB → BA. Yes very handwavy, but there is some underlying intuition, will get back to this. We are going to build from that swapping or reversal operator S. In particular we will use the positive selfadjoint part of the polar decomposition. More about this later. 


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