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Julian Barbour on does time exist

by julian
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experimentum
#55
Nov18-12, 08:58 AM
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Time is not a result of Thought, if I don't want time that wont make it go away and thats what you are really asking is time a result of thought. No, thought is a result of time and thought patterns are undistinguishable to the thinker even if the timeline is different only the total amount of time differs by comparison. Thus proving time and thought are a constant.
marcus
#56
Nov18-12, 11:41 AM
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We've come quite a ways. I want to recap some of what was said on page 1 of this thread. Starting with Julian's post #1.
The gas in a box can be in equilibrium even though individual molecules are colliding and bouncing around. It depends on perspective. Micro-beings riding on the molecules can have a local idea of time based on motion of surrounding molecules. Their world doesn't look like it's in equilibrium to them, though it does to us. And also any thermal equilibrium state breaks Lorentz invariance and gives us an intrinsic macro idea of time This was what Rovelli was discussing as Julian pointed to in post #1. Here is the OP:
Quote Quote by julian View Post

I prefer Rovelli's explanation of evolution from a timeless universe which has to do with how we have limited information about the world - less depressing perhaps as it leaves room for change? Like England winning the world cup.
Quote Quote by marcus View Post
...If you have a particularly clear passage by him where he explains that idea, I'd be glad for a pointer to it. Are you perhaps thinking of this recent paper?
4059419]http://arxiv.org/abs/1209.0065
General relativistic statistical mechanics
Carlo Rovelli
(Submitted on 1 Sep 2012)
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the conventional ones in the non-relativistic limit, but remain valid for a general covariant theory. The formalism extends to quantum theory. The construction builds on the idea of thermal time, on a notion of locality for this time, and on the distinction between global and local temperature. The last is the temperature measured by a local thermometer, and is given by kT = h dτ/ds, with k the Boltzmann constant, h the Planck constant, ds proper time and dτ the equilibrium thermal time.
9 pages. A tentative second step in the thermal time direction, 10 years after the paper with Connes. The aim is the full thermodynamics of gravity. The language of the paper is a bit technical: look at the Appendix first

Quote Quote by julian View Post
It is in Rovelli's paper "Forget time" http://arxiv.org/pdf/0903.3832.pdf he talks about it:

"The time of our experience is associated with a number of peculiar features that make it a very special physical variable. Intuitively (and imprecisely) speaking, time “flows”, we can never “go back in time”, we remember the past but not the future, and so on. Where do all these very peculiar features of the time variable come from?

I think that these features are not mechanical. Rather they emerge at the thermodynamical level. More precisely, these are all features that emerge when we give an approximate statistical description of a system with a large number of degrees of freedom. We represent our incomplete knowledge and assumptions in terms of a statistical state..."

Yes this is related to his new paper. After posting the Barbour's intro I came across Rovelli's new paper. Exciting to see if there is progress as I remember the paper he wrote with Connes http://arxiv.org/pdf/gr-qc/9406019.pdf and finding it very interesting but that was a while ago. I'm having a look at them both now...
This idea of a THERMODYNAMIC TIME arising from a global equilibrium state comes out of the Connes Rovelli paper which Julian gave a link to. There is also the idea of LOCAL time emergent from motions or mechanics but these are reversible. Barbour shows how time emerges from local motions. but that local emergence doesn't explain everything, e.g. direction. So there is an idea of scale. What level of time are we talking about? Also Naty gave an interesting reference to a paper that says a lot about the problem of understanding time.

Quote Quote by Naty1 View Post
...
Rovelli: Unfinished revolution
Introductive chapter of a book on Quantum Gravity
The link to this is http://arxiv.org/abs/gr-qc/0604045. And Chronos concisely summed things up at the end of page #1 of thread.

Quote Quote by Chronos View Post
I can buy the idea that time is not fundamental, rather, it is an emergent property of the universe...
I want to add one idea to the discussion at this point. We have seen that time is "scale dependent"---it emerges from experience at different levels. Like temperature too. Temperature depends on at what scale you measure and it is emergent. It is very real! But it is emergent from more fundamental descriptors. Like Chronos said.

OK so time is emergent and scale dependent, now I want to add a footnote to that: The *expansion* of distances in the universe makes scale dependence very interesting. Geometry is dynamic you can have things staying in the same place but everything getting farther apart without any relative change in position.

Assuming the (LQC model) cosmological bounce---at the maximum energy density start of expansion, the universe was in thermal equilibrium. It was like the distribution of gas in a box, all flattened out under the regime of repellent gravitation (which is what causes bounce at extreme energy density in LQC model). So because GR is timeless (as therefore QGR must be also) the U is forever in equilibrium state.

So it has a thermal time, as Connes and Rovelli showed, which derives from any equilibrium state, its own global time. This is essentially the same as Friedmann universe time used by cosmologists, they get it by fitting data to model and calculating age of U, or they get it from CMB temperature. Same thing.

*But also expansion is like a zoom microscope* So compared with things at the start of expansion we are like the very small beings riding on the molecules in the box. So we see things around us that don't look like equilibrium. Stuff is happening. If you ran the whole show back to the start of expansion, it would look smooth and even, and it STILL IS in a sense if you adopt a cosmological perspective. But locally the individual molecules we are riding on are bucking and whirling splitting and merging.

Connes and Rovelli introduce the idea of a geometric temperature to coordinate these ideas of local and global time. It doesn't seem like a bad idea. Somebody named Tolman (at Oxford I think) had already discussed geometric temperature in the 1930s and C&R's idea turned out to recover Tolman's in the relevant case. So there is all this interesting stuff.
marcus
#57
Nov20-12, 07:40 PM
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I guess two obvious things everybody realizes but could be mentioned:

Obviously the free energy in a situation depends on the scale you're able to manipulate. If you are molecule-size and live in a box of gas, then you can lasso molecules and can harness them (or play the Maxwell demon with them), and get energy. But whatever you do with the energy makes no difference to a large outsider. He looks in and sees no free energy---because he can't see or manipulate or benefit at your scale. He sees a uniform "temperature" throughout, which you do not. Whatever you accomplish with the free energy you see doesn't make a damn bit of difference to him---it still looks like gas in a box. So free energy depends on the scale at which the observer is interacting with it, and likewise the Boltzmann distribution, depending as it does on the free energy. So the idea of EQUILIBRIUM depends on scale.

The second obvious thing to mention, since we are concerned with cosmology, is that cosmologists have coordinates called COMOVING coordinates where the separation between things does not change. Aside from little random individual jiggles, as thing's comoving coordinates do not change. Not substantially compared with the expansion process itself. So two hydrogen atoms are about as far apart now, in comov. dist., as they were when the universe was only a few years old. things do fall together and interact and recombine and split apart etc but that is a small percentage of their comoving distance from each other, which stays approximately constant.
So I suppose some of the analysis of the sort of things we were talking about could be done using comoving coordinates.

Interestingly, it seem if we imagine doing relativistic thermodynamics in a quantum cosmology context it might happen that the U is, and always has been, in a PURE STATE and that it also (at a certain scale) is in a state of THERMAL EQUILIBRIUM.
=================

The reason it's relevant is that several of us in the thread seem to agree on looking at time as real but *emergent* either from local motions or thermodynamics. In particular e.g. Julian Barbour in his prize-winning FQXi essay showed clearly how time is emergent from local motions, at a certain level. One does not have to treat it as a quasi-spatial "extra" dimension. One wants to be able to generalize on both Barbour's time and thermodynamic or "thermal" time (which may, at root, be the same thing as Barbour's) to understand the emergence of time in a variety of contexts and at various scales.
Paulibus
#58
Nov21-12, 01:13 AM
P: 175
Marcus: Your recent post #57 said things that really needed saying. I liked it a lot. Here are a few comments.

As Niels Bohr pointed out, Physics is a matter of what we say about stuff, not what stuff “is”. This justifies the use of inverted commas (here) and prolifically in your post, together with stars and upper case to distinguish words ( e.g.: is, emergent, temperature, equilibrium) that have context-sensitive meanings. To be trite; '"Obviously” physics just describes what we call reality. This description is perforce made in the context of common human experience, say of hot and cold, or the maintenance of a status quo. When we try to extend such descriptions beyond scales familiar to us, a qualification as “emergent” can be useful for broadening context. So is the quantitative and logical extension provided to ordinary language by mathematics.

But let’s not kid ourselves that the words and mathematical descriptions we use have absolute eternal meanings; they just conveniently communicate concepts between us. Like the mysterious word “time” that everybody knows. Although we cannot yet claim to accurately understand and describe time, one thing does stand out: using time as a parameter to characterise change works wherever physics rules. This, it seems, is all over the Universe. Therefore: time can’t just be some local quirky emergent thing; it must be related to something universal, like the observed red-shift and its cause, namely “expansion”. Or is this also just an "emergent" aspect of the “reality” that we try to describe?
ImaLooser
#59
Nov21-12, 04:40 AM
P: 570
Quote Quote by Paulibus View Post
 Or is this also just an "emergent" aspect of the “reality” that we try to describe?
Emergent is rapidly becoming one of my less favorite words. It seems like a classy way to say I dunno.
experimentum
#60
Nov21-12, 08:31 AM
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Quote Quote by marcus View Post
I guess two obvious things everybody realizes but could be mentioned:

Obviously the free energy in a situation depends on the scale you're able to manipulate. If you are molecule-size and live in a box of gas, then you can lasso molecules and can harness them (or play the Maxwell demon with them), and get energy. But whatever you do with the energy makes no difference to a large outsider. He looks in and sees no free energy---because he can't see or manipulate or benefit at your scale. He sees a uniform "temperature" throughout, which you do not. Whatever you accomplish with the free energy you see doesn't make a damn bit of difference to him---it still looks like gas in a box. So free energy depends on the scale at which the observer is interacting with it, and likewise the Boltzmann distribution, depending as it does on the free energy. So the idea of EQUILIBRIUM depends on scale.

The second obvious thing to mention, since we are concerned with cosmology, is that cosmologists have coordinates called COMOVING coordinates where the separation between things does not change. Aside from little random individual jiggles, as thing's comoving coordinates do not change. Not substantially compared with the expansion process itself. So two hydrogen atoms are about as far apart now, in comov. dist., as they were when the universe was only a few years old. things do fall together and interact and recombine and split apart etc but that is a small percentage of their comoving distance from each other, which stays approximately constant.
So I suppose some of the analysis of the sort of things we were talking about could be done using comoving coordinates.

Interestingly, it seem if we imagine doing relativistic thermodynamics in a quantum cosmology context it might happen that the U is, and always has been, in a PURE STATE and that it also (at a certain scale) is in a state of THERMAL EQUILIBRIUM.
=================

The reason it's relevant is that several of us in the thread seem to agree on looking at time as real but *emergent* either from local motions or thermodynamics. In particular e.g. Julian Barbour in his prize-winning FQXi essay showed clearly how time is emergent from local motions, at a certain level. One does not have to treat it as a quasi-spatial "extra" dimension. One wants to be able to generalize on both Barbour's time and thermodynamic or "thermal" time (which may, at root, be the same thing as Barbour's) to understand the emergence of time in a variety of contexts and at various scales.
I cant even begin to understand everything in these posts. My math and even my vocabulary skills being well below the required level but I try because i still learn from the bits and peices I do pick up.
Theoretical physics I relize is very advanced even among the real physicists but let me check if I somewhat understand this.

I'm understanding it as the current laws for time are universal in this model the box is our 'universe' the gas filling the box is 'time' and any events it real time are represented as a temperature change so the model has a way of catagorizing integral parts of time us being assumedly on the hotter end of the scale. Is this right that I'm sub catagorizing us given any present moment in our timelines is not assumed but analitical. In my mind this gives us a convective effect on the gas.

I hope I'm getting it because if not its a real blow to my ego well, either way it kinda is cause I never would have bien able to come up with that myself :( and, I've just wasted everyones time! but hey, wait a minute, don't be such a hothead! lol!
marcus
#61
Nov21-12, 12:03 PM
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Hi Exper., Looser, Paulibus, thanks for your comments! This is a really important point. The idea of what is fundamental is comparative and provisional---depending on context some stuff is MORE fundamental than other stuff but we can't expect that anything is ABSOLUTELY fundamental.
Quote Quote by Paulibus View Post
...But let’s not kid ourselves that the words and mathematical descriptions we use have absolute eternal meanings; they just conveniently communicate concepts between us. ...
or ETERNALLY, like Paulibus says, fundamental. Because 10 years later physicists might discover something even more basic.

Emergent simply refers to something that is real and physical (maybe indispensable, necessary for our understanding) but NOT FUNDAMENTAL. Like temperature, or like the water level in a lake. If you zoom in too closely you won't see it. But it's real.

I guess you could say that all physical descriptors and features are elements of a mathematical language that we are trying to apply to nature. Some of those descriptors (the traditional name is "degrees of freedom") are more basic than others. We call them fundamental. And others are more COMPOSITE or DERIVED or only definable when we have a large unspecified number of basic objects, and we call them non-fundamental, or less fundamental, or emergent. Like the water level or the temperature.

All these things are elements of a (mathematical) language which is evolving to better fit nature.
And I have to admit the fit is astoundingly good in so many areas. But still, as Paulibus suggested, let's not confuse our descriptive/predictive language model with nature/reality itself.
=================

I think for the purposes of this thread, if someone wants to join the discussion, they should have looked at both the first--prize essays on this winners list:
http://fqxi.org/community/essay/winners/2008.1
In 2007-2008 FQXi (foundational questions institute) had an essay contest on The Nature of Time and they gave out two first prizes.
These essays are wide-audience, so some of the language in each essay is for non-specialists. And some is difficult mathematics.
The theme (what is time?) is not introductory physics. So if anyone is trying to teach themselves basic college physics this is definitely NOT a good place to start! The nature of time is one of the frontiers of physics where there is naturally the greatest confusion, disagreement, lack of clarity.

Both of the first prize essays took the position that time is NOT FUNDAMENTAL but is something you can derive from studying motion and change at a more basic level.
The two essays I'm suggesting people look at are Barbour's and Rovelli's (as a minimum, several other people in this thread have mentioned some other really good ones.)
marcus
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Nov21-12, 12:15 PM
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You can get an idea of Barbour's essay by looking at the brief summary, the "abstract" at the beginning:
===quote===
The Nature of Time
By Julian Barbour

Essay Abstract
A review of some basic facts of classical dynamics shows that time, or precisely duration, is redundant as a fundamental concept. Duration and the behaviour of clocks emerge from a timeless law that governs change.
==endquote==

In a nutshell, time is not needed as a fundamental concept. Time emerges. And he gives a careful concretely worked-out example of how time emerges from watching a specific system of bodies, like a solar system or a cluster of stars.
http://fqxi.org/community/essay/winners/2008.1

You can get an idea of Rovelli's essay from its abstract, or summary. Shown further down on the same list. It is also on the preprint archive: http://arxiv.org/abs/0903.3832
===quote===
Forget Time*
By Carlo Rovelli

Essay Abstract
Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role at all. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must "forget time", and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time.
==endquote==

There are actually two Rovelli essays to look at. A good non-specialists introduction is "Unfinished Revolution"
( http://arxiv.org/abs/gr-qc/0604045 ) because in about 3 pages near the beginning it takes you through the HISTORY of the gradual weakening of the idea of Newtonian time by 1905 special through 1915 general relativity to today's quantum gravity research. It is good to get that perspective. Notice that in quantum mechanics a moving particle does not have a continuous TRAJECTORY. You can only *observe* where it passed thru at some discrete locations. You cannot say what it did in between. In the dynamically evolving geometry of quantum relativity, a continuous 4D spacetime is the analog of a continuous particle trajectory. For the same reason, one cannot say that it exists. One can only make a finite number of observations of geometric observables and study/predict the correlations.

In that sense a spacetime is not any more fundamental than a continuous particle trajectory. Both are derived constructs.
Paulibus
#63
Nov22-12, 08:20 AM
P: 175
The essays of Barbour and Rovelli that you kindly highlighted, Marcus, illuminate nicely the dangers of assuming that familiar concepts (like time) are fundamental (although Rovelli contrarily notes that “...time is one of the fundamental notions in terms of which physics is built....”).

But I sympathise with Imalooser's irritation with the somewhat shopsoiled label “emergent”. It helps when an explanation is given of what the thing in question (here the time concept) emerges from, as in these essays. Barbour plumps for Newtonian mechanics, but I get confused about what "emerges" from which: time from physics or physics from usually being parameterised by time. Rovelli, on the other hand,
...thinks that (some puzzling features of time) are not mechanical. Rather they emerge at the thermodynamical level..... (they are) features that emerge when we give an approximate statistical description of a system with a large number of degrees of freedom.....We represent our incomplete knowledge and assumptions in terms of a statistical state ....Time is .... the expression of our ignorance of the full microstate.
Both essays offer lots of argument, but describe no verifiable predictions. For me they represent scientific curiosity biased by special pleading; for a Newtonian perspective in Barbour’s case; for a Loop Quantum Gravity perspective in Rovelli’s case ---, rather than describing a usual cycle of scientific progress.

Interesting indeed, but for me less exciting than the famous emergence of Ursula Andress from the ocean in the first Bond movie!
marcus
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Nov22-12, 10:27 AM
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Quote Quote by Paulibus View Post
... Barbour plumps for Newtonian mechanics, but I get confused about what "emerges" from which: time from physics or physics from usually being parameterised by time. Rovelli, on the other hand, ...
==Paulibus quoting Rovelli==
...thinks that (some puzzling features of time) are not mechanical. Rather they emerge at the thermodynamical level..... (they are) features that emerge when we give an approximate statistical description of a system with a large number of degrees of freedom.....We represent our incomplete knowledge and assumptions in terms of a statistical state ....Time is .... the expression of our ignorance of the full microstate.
==endquote==
Hi Paulibus, thanks for your comment! You have what is presented as a quote from that essay but I didn't understand it and couldn't find it in the essay so I figured it might be your paraphrase plus bits from several different pages taken out of context. I therefore went looking for the context. I think this is the main context, which may help me better understand what you are saying. I've highlighted some things I may want to refer to later.

==quote page 8 of "Forget time"==
This observation leads us to the following hypothesis.

The thermal time hypothesis. In nature, there is no preferred physical time variable t. There are no equilibrium states ρ0 preferred a priori. Rather, all variables are equivalent; we can find the system in an arbitrary state ρ; if the system is in a state ρ, then a preferred variable is singled out by the state of the system. This variable is what we call time.

In other words, it is the statistical state that determines which variable is physical time, and not any a priori hypothetical “flow” that drives the system to a preferred statistical state. When we say that a certain variable is “the time”, we are not making a statement concerning the fundamental mechanical structure of reality. Rather, we are making a statement about the statistical distribution we use to describe the macroscopic properties of the system that we describe macroscopically. The “thermal time hypothesis” is the idea that what we call “time” is the thermal time of the statistical state in which the world happens to be, when described in terms of the macroscopic parameters we have chosen.
Time is, that is to say, the expression of our ignorance of the full microstate.


The thermal time hypothesis works surprisingly well in a number of cases. For example, if we start from radiation filled covariant cosmological model, with no preferred time variable and write a statistical state representing the cosmological background radiation, then the thermal time of this state turns out to be precisely the Friedmann time [21]. Furthermore, this hypothesis extends in a very natural way to the quantum context, and even more naturally to the quantum field theoretical context, where it leads also to a general abstract state-independent notion of time flow. In QM, the time flow is given by
At = αt(A) = eitH0 Ae−itH0 . (19)
A statistical state is described by a density matrix ρ. It determines the expectation values of any observable A via

ρ[A] = T r[Aρ]. (20)

This equation defines a positive functional ρ on the observables’ algebra. The relation between a quantum Gibbs state
ρ0 and H0 is the same as in equation (14). That is ρ0 =Ne−βH0. (21)
Correlation probabilities can be written as WAB(t) = ρ[αt(A)B] = Tr[eitH0 Ae−itH0Be−βH0], (22)
Notice that it follows immediately from the definition that
ρ0t(A)B] = ρ0[α(−t−iβ)(B)A], (23)
Namely
WAB(t) = WBA(−t − iβ) (24)
A state ρ0 over an algebra, satisfying the relation (23) is said to be KMS with respect to the flow αt.
==endquote==

It may take me a little while before I can respond to your post, Paulibus. I can see you are making an effort to understand the thermal time idea and give a fair summary of it (as I am trying to do or would like to do myself!)
marcus
#65
Nov22-12, 01:41 PM
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You see Barbour and Rovelli's pictures as contrasting but I see an underlying similarity, both dispense with time (as a basic given) and derive it from what is the case, from the timeless reality of all our interrelated observations, perhaps one could say.

The word "state" has the unfortunate mental associations that come from having heard countless times the phase "state at a given time". what one really needs is a word for the timeless state of the world. Something like what one gets from the first chapter ("Proposition 1") of Wittgenstein's Tractatus:

Proposition 1

1 The world is all that is the case.
1.1 The world is the totality of facts, not of things.
1.11 The world is determined by the facts, and by their being all the facts.
1.12 For the totality of facts determines what is the case, and also whatever is not the case.
1.13 The facts in logical space are the world.
1.2 The world divides into facts.
1.21 Each item can be the case or not the case while everything else remains the same.
=============

I don't see Barbour's vision as Newtonian because Newton's vision had an absolute time. He was closer to a 4D block spacetime in which the time coordinate had real physical meaning, was observable.
In GR the "time" coordinate is not observable and has no physical meaning, it is merely conventional. Barbour's observer derives time from watching motions. As he suggests, the idea of time as fundamental is unnecessary---I think one word for that would be "epiphenomenon".
Both Barbour and Rovelli seem in step with GR, perhaps a little out in front.

When you pass to a quantum version of GR the "state" (or "world") can no longer be a 4D continuum, for essentially the same reason that a particle cannot have a continuous trajectory. We only make a finite number of observations. We can have no mathematical representation of what is "in between" those observations. We simply have those observations and the correlations among them. The compact way to say that is with a C* algebra plus a positive (traceclass) operator ρ which represents what we think we know about it. Our knowledge and non-knowledge expressed probabilistically---as Rovelli says, "our ignorance".

Interesting stuff. Barbour's picture would ALSO need to be probabilistic since he doesn't know whether or not a neutron star is going to hurtle thru the solar system he is watching and disrupt his concept of time. He rightfully assumes it very unlikely but he talks as if it is completely ruled out. He sees and accounts for every body in the system, which in truth one cannot do with perfect certainty. So Barbour's picture also represents our knowledge/ignorance, just doesn't make that mathematically explicit.

I see their two visions of epiphenomenal time as somewhat akin to each other.
FalseVaccum89
#66
Nov22-12, 07:50 PM
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In Barbour's book The End of Time, he talks about the probabilities associated with QM being represented as densities of a "fog" in Platonia (the configuration space).
Paulibus
#67
Nov23-12, 03:30 AM
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Thanks for responding so fully to my sketchy post, Marcus. I agree that Barbour and Rovelli come to similar conclusions. I was thinking of Barbour’s emphasis on ephemeris time (a Newtonian concept used by astronomers), not of Newton’s absolute time. I also
confess I find both essays quite hard to understand, and in linking bits (as you correctly suspected) from Rovelli’s essay into a single quote I was trying to pick out the gist of his radical proposal.

Their tampering with our innate take on time won’t be easily accepted; it’s a central feature of our finite lives, and I guess our faith in its practical utility as a measure of life passing will be hard to shake. I wish Barbour and Rovelli success and look forward to the “time” when their ideas gain the gravitas conferred by testable predictions.
Maybe someone will build:
Quote Quote by H.G. Wells in 1895
....a glittering metallic framework, scarcely larger than a small clock... (with) ivory in it, and some transparent crystalline substance
that could demonstrate Time Travel!
TrickyDicky
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Nov23-12, 11:58 AM
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Quote Quote by marcus
...
In GR the "time" coordinate is not observable and has no physical meaning, it is merely conventional...
So what are Rovelli and Barbour suggesting that must be done with the time coordinate?
marcus
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Nov23-12, 12:48 PM
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Quote Quote by TrickyDicky View Post
So what are Rovelli and Barbour suggesting that must be done with the time coordinate?
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 αt 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 αt 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
#70
Nov23-12, 01:28 PM
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Quote Quote by marcus View Post
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".)
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?
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Nov23-12, 02:02 PM
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Quote Quote by TrickyDicky View Post
Hmmm, that paper is almost two decades old, but I guess the concept hasn't changed much from then since you are linking it...
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.)
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Nov23-12, 04:33 PM
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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 αt. Then, the theory describes physical evolution in the thermal time in terms of amplitudes of the form
FA,B(t) = ω(αt(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.


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