Julian Barbour on does time exist

marcus

Hi TD, Alain Connes and Carlo Rovelli have a definite proposal which they offer for consideration, called the "thermal time hypothesis". I'll excerpt a brief summary. (Someone else may be able to talk about what Barbour would say "must be done".)
As for C&R they are quite explicit already on page 2 of their paper. One just googles "connes rovelli" and gets http://arxiv.org/abs/gr-qc/9406019
==page 2==
In a general covariant theory there is no preferred time flow, and the dynamics of the theory cannot be formulated in terms of an evolution in a single external time parameter. One can still recover weaker notions of physical time: in GR, for instance, on any given solution of the Einstein equations one can distinguish timelike from spacelike directions and define proper time along timelike world lines. This notion of time is weaker in the sense that the full dynamics of the theory cannot be formulated as evolution in such a time.1 In particular, notice that this notion of time is state dependent.

Furthermore, this weaker notion of time is lost as soon as one tries to include either thermodynamics or quantum mechanics into the physical picture, because, in the presence of thermal or quantum “superpositions” of geometries, the spacetime causal structure is lost. This embarrassing situation of not knowing “what is time” in the context of quantum gravity has generated the debated issue of time of quantum gravity. As emphasized in [4], the very same problem appears already at the level of the classical statistical mechanics of gravity, namely as soon as we take into account the thermal fluctuations of the gravitational field.² Thus, a basic open problem is to understand how the physical time flow that characterizes the world in which we live may emerge from the fundamental “timeless” general covariant quantum field theory [9].

In this paper, we consider a radical solution to this problem. This is based on the idea that one can extend the notion of time flow to general covariant theories, but this flow depends on the thermal state of the system. More in detail, we will argue that the notion of time flow extends naturally to general covariant theories, provided that:
i. We interpret the time flow as a 1- parameter group of automorphisms of the observable algebra (generalised Heisenberg picture);
ii. We ascribe the temporal properties of the flow to thermodynamical causes, and therefore we tie the definition of time to thermodynamics;
iii. We take seriously the idea that in a general covariant context the notion of time is not state- independent, as in non-relativistic physics, but rather depends on the state in which the system is.
==endquote==

Note that this is presented as a hypothesis---it is proposed as one possible solution to be studied. They take the observable algebra. As given it is timeless. Any STATE is a positive functional on this algebra that gives expectations/correlations for all the observables. Then they offer a canonical way to derive a one-parameter group of automorphisms α_t of the observable algebra.
This is the modular group that you derive using the given state. Remarkably, it turns out to reproduce Friedmann time in cosmology if you use the cosmic microwave background to define the state. I have not examined the proof of this. They offer several indications that this modular group α_t corresponds to a satisfactory global idea of time. One can compare local observer-time to it and the comparison can have physical significance, which might be interesting. I have to go, back later. Thanks for the question!

TrickyDicky

Hmmm, that paper is almost two decades old, but I guess the concept hasn't changed much from then since you are linking it.
My question was trying to clarify what is the proposed practical implementation of considering the time coordinate "unnecessary". I guess they are not just suggesting to eliminate the time coordinate since that means doing away with Lorentzian manifolds and that seems quite wild. So is thermal time the new time coordinate?

marcus

Yes! I do think the Connes Rovelli paper is very well written. What they say there can probably not be said much better by anybody. But the idea has developed and the most recent paper is, as you may know, Rovelli's September 2012 "General relativistic statistical mechanics".

I think the point is this is a major outstanding problem that may be nearing the time when it is ripe to work on. In a general covariant theory there is no preferred idea of time, and so one cannot do thermodynamics or stat mech as we ordinarily think of it.

One can do these things on an arbitrary fixed curved spacetime, but that is not the full GR treatment. So eventually humans HAVE to do thermo and stat mech in full GR context. Or the quantum version of that. But researchers must use their efforts wisely and not work on problems which are not ready to be addressed. For a while they only slowly chip away, or prepare some ideas to start with. that is how i see it.

I think one should not immediately think of a 4D lorentzian manifold (just my private opinion) I think one should think of the observable algebra, possibly abstractly as a C*-algebra. And the state embodies what we think we know and expect about all the observations. The fine thing is that this state itself uniquely specifies a one-parameter flow on the observables---the modular group of automorphisms of the algebra---uniquely up to some equivalence relation.
that is very abstract, but then one can in various cases make it specific using the familiar tools of the Hilbertspace, the 4D manifold, the fields written on the manifold, and so on. Or (I don't know) maybe LQG tools and Hilbertspace. At the moment I do not see any suggestion of a connection with LQG, it seems like an entirely separate development. (Except for sharing the general covariant GR perspective.)

marcus

I must repeatedly stress that this is only a hypothesis put forward to be tested, but C&R just could have hit on the way to handle time in a generally covariant quantum system. Remember that all we actually have is an algebra of observables. A 4D differential manifold is sheer mathematical fiction, as far as anyone knows. All we really have are our observations, a finite number of them, of which we can multiply and add together some to predict others (because they form an algebra).

==quote http://arxiv.org/abs/gr-qc/9406019 page 14==
Let us now return to generally covariant quantum theories. The theory is now given by an algebra A of generally covariant physical operators, a set of states ω, over A, and no additional dynamical information. When we consider a concrete physical system, as the physical fields that surround us, we can make a (relatively small) number of physical observation, and therefore determine a (generically impure) state ω in which the system is. Our problem is to understand the origin of the physical time flow, and our working hypothesis is that this origin is thermodynamical. The set of considerations above, and in particular the observation that in a generally covariant theory notions of time tend to be state dependent, lead us to make the following hypothesis.

The physical time depends on the state. When the system is in a state ω, the physical time is given by the modular group αt of ω.

The modular group of a state was defined in eq.(8) above. We call the time flow defined on the algebra of the observables by the modular group as the thermal time, and we denote the hypothesis above as the thermal time hypothesis.

The fact that the time is determined by the state, and therefore the system is always in an equilibrium state with respect to the thermal time flow, does not imply that evolution is frozen, and we cannot detect any dynamical change. In a quantum system with an infinite number of degrees of freedom, what we generally measure is the effect of small perturbations around a thermal state. In conventional quantum field theory we can extract all the information in terms of vacuum expectation values of products of fields operators, namely by means of a single quantum state |0⟩. This was emphasized by Wightman...

...Given the quantum algebra of observables A, and a quantum state ω, the modular group of ω gives us a time flow α_t. Then, the theory describes physical evolution in the thermal time in terms of amplitudes of the form
F_A,B(t) = ω(α_t(B)A) (26)
where A and B are in A. Physically, this quantity is related to the amplitude for detecting a quantum excitation of B if we prepare A and we wait a time t – “time” being the thermal time determined by the state of the system.

In a general covariant situation, the thermal time is the only definition of time available. However, in a theory in which a geometrical definition of time independent from the thermal time can be given, for instance in a theory defined on a Minkowski manifold, we have the problem of relating geometrical time and thermal time. As we shall see in the examples of the following section, the Gibbs states are the states for which the two time flows are proportional. The constant of proportionality is the temperature. Thus, within the present scheme the temperature is interpreted as the ratio between thermal time and geometrical time, defined only when the second is meaningful.⁶

We believe that the support to the thermal time hypothesis comes from analyzing its consequences and the way this hypothesis brings disconnected parts of physics together. In the following section, we explore some of these consequences. We will summarize the arguments in support the thermal time hypothesis in the conclusion...
==endquote==

C&R are telling us that in a fully generally covariant system without making some additional arbitrary choices, *the modular group flow is the only definition of time we've got*.
Further, it gives us transition amplitudes.
Further, if we go ahead and arbitrarily make a choice of geometry (e.g. Minkowski) then we can compare that time with the inherent modular group time, and the ratio can have a physical meaning.

Paulibus

 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: (My emphasis.) Thermal time is taken as the variable that the system is “in equilibrium” with respect to. In the case of say, a gas, his thermal time, I gather, reduces to our ordinary time (to within a proportionality factor). Since our macroscopic-scale description of equilibrium hinges on the statistically and thermally defined concept of temperature, in this case “thermal” is a very appropriate label.

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 catch-all background?

Roll on the next chapter in this story.

marcus

Your post raises several interesting issues, I'm focussing on one right now---the cases where thermal time "reduces to our ordinary time". It seems important to list those offered in the Connes Rovelli paper, since the good consequences of the thermal time hypothesis (TTH) support one's suspicion that it is possibly right and worth investigating.

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 wider-audience 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 16-21.
== http://arxiv.org/abs/gr-qc/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 Friedman-Robertson-Walker 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" list---I will simply quote:
==quote gr-qc/9406019 page 22==
• Non-relativistic 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.

marcus

The way I see the uniqueness point is that once you have a C*-algebra A of all your observables, and a (positive trace-class) 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 one-parameter group of automorphisms on the algebra that takes any observable to the next, to the next, to the next. There is a natural built-in way to make the observables flow. That's time. Or one idea of it.

marcus

I think perhaps the essential thing about time-ordering is it makes a difference which measurement you do first. All these differences are encoded in the non-commutativity of the algebra of observations, so time-orderings 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.

Paulibus

Sounds sensible to me, put this way (barring C* algebra; new to me). But for a long time I've thought of time as a "dimension", one of four absolutely mysterious and fundamental such items in the "Universe Lucky Packet" that when unwrapped, started stuff off with a singular bang, or a softer bounce, neither of which we understand properly yet.

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 space-like, that curves? Or perhaps just c that changes from place to place, so bending light around galaxies? Strange thoughts pass by.

marcus

I imagine we're all rather much in the same fix as you describe, or at least I am. Geometrizing time as a pseudo-spatial dimension works so well! It's become part of how we think.

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 precisely---and the business of light bending around galaxies and clusters of galaxies is very beautiful. As well as being essential to observational cosmology nowadays---they 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.

marcus

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 thing---it is a valid generalization of what we already think of as time-evolution 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.

marcus

here ( gr-qc/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.

rjbeery

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.

marcus

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

rjbeery

Ahh, thanks marcus. I was too lazy to work through 4 pages of comments. Also, there wasn't much mention of Block Universe that I could see (even in your referenced posts).

This is because an observer in the "now" has access to information which has been stored in some manner accessible to the observer in the current state; this information gets stored via entropic processes. What this means is that entropy doesn't increase with time, but rather information is available for storage as entropy is increased. Any observer in the "now" might naturally conclude that states to which he has information (i.e. the past) are of a different character than those states which reveal how many essays you have or will read, but that isn't the case (IMHO).

marcus

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 time-flow 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 pseudo-spatial dimension or as something fundamental. It arises from more basic stuff. In this case it arises as a one-parameter 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.

marcus

Sources
http://arxiv.org/abs/gr-qc/9406019 pages 16,17
WikiP: "Gelfand-Naimark-Segal construction"
WikiP: "KMS state"
WikiP: "Tomita-Takesaki 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_tA 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_tA, for every timeparameter number t.