# Julian Barbour on does time exist

by julian
Tags: barbour, exist, julian, time
Astronomy
PF Gold
P: 23,110
 Quote by sshai45 So does that mean there would be an absolute, universal time and simultaneity, and so Einstein was "wrong" in some sense? How does "only 'now' exists" jibe with "'now' depends on the observer"? How do the non-reality of the block universe and the relativity of simultaneity play with each other?
That's an intriguing question! I don't think introducing the (M,ω) picture and the corresponding state-dependent time flow on the algebra indicates that GR is wrong. But I want to take more time to answer.

Here's part of a short answer I gave to your question in post #144, with a clarifying addition in red:
 Quote by marcus Sshai, I will get back to your comment, time permitting. I think Einstein is still right. We still have observer time. Each observer has a different time (as A.E. said) and it is interesting to compare them. But also now we have a *state-dependent* time as well. It depends not on a particular observer but on the function omega that summarizes what we think we know (with various degrees of confidence) about the world. ...a new way to picture the world, as (M,ω) where M is a star algebra (observables) and omega (state) is a function from M to the complex numbers[giving correlations between observables]. Ordinary QFT (quantum field theory) has already been put in star algebra form. And there seems no reason that the dynamic geometry of GR should not also be put into that same form---thus combining the content of QM and GR, combining geometry with matter in a background independent or general covariant way. The (M, ω) is suitable for both. So this (M, ω) business is quite an interesting development... However in any case it does not say that "Einstein was wrong". It brings into existence yet ANOTHER version of time, which depends on the state we specify rather than on any particular observer. ...And it already seems interesting to COMPARE this time with that of a given observer because it has been shown that the ratio of rates of time-passage can be physically meaningful ...It also seems to be good for other things where you can't use observer-time...
Basically what we are discussing in this thread are theorists' response to what is called the problem of time in GR and also in quantum GR, where the problem is broader and more formidable. Here is the best short statement I know of the problem.
It is from page 4 of Chapter 1 of the 2009 book Approaches to Quantum Gravity, D. Oriti ed. published by Cambridge University Press ( http://arxiv.org/abs/gr-qc/0604045 )

==quote Chapter 1 of Approaches to Quantum Gravity==
... In special relativity, this notion of time is weakened. Clocks do not measure a universal time variable, but only the proper time elapsed along inertial trajectories. If we fix a Lorentz frame, nevertheless, we can still describe all physical phenomena in terms of evolution equations in the independent variable x0, even though this description hides the covariance of the system.

In general relativity, when we describe the dynamics of the gravitational field (not to be confused with the dynamics of matter in a given gravitational field), there is no external time variable that can play the role of observable independent evolution variable. The field equations are written in terms of an evolution parameter, which is the time coordinate x0, but this coordinate, does not correspond to anything directly observable. The proper time τ along spacetime trajectories cannot be used as an independent variable either, as τ is a complicated non-local function of the gravitational field itself. Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable. This does not mean that GR lacks predictivity. Simply put, what GR predicts are relations between (partial) observables, which in general cannot be represented as the evolution of dependent variables on a preferred independent time variable.

This weakening of the notion of time in classical GR is rarely emphasized: After all, in classical GR we may disregard the full dynamical structure of the theory and consider only individual solutions of its equations of motion. A single solution of the GR equations of motion determines “a spacetime”, where a notion of proper time is associated to each timelike worldline.

But in the quantum context a single solution of the dynamical equation is like a single “trajectory” of a quantum particle: in quantum theory there are no physical individual trajectories: there are only transition probabilities between observable eigenvalues. Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime, in the same sense in which the motion of a quantum electron cannot be described in terms of a single trajectory.
==endquote==

So the problem is on two levels, classical and quantum. Already at the classical level
there is no observable independent time variable that can be used to describe the evolution of a (general) relativistic system.

And at the quantum level the problem is even more severe, since one cannot realistically assume some fixed metric solution--i.e. a geometric "trajectory".

There's more to say, I'll try to get back to this later. The outstanding thing to notice about the (M,ω) format (for dynamic QG geometry and simultaneously for matter QFT) is that it DOES have an independent time variable that can be used to describe the dynamical evolution of geometry+matter. The point of the quote above is that any observer's time is NOT adequate since the observer's time depends on how the geometry evolves!

When you want to describe the dynamical evolution of a system you need a time variable which is not totally at the mercy of how the system happens to evolve. So observer-time is no good.

This is why the (M,ω) formalism has come up in the context of trying to devise a fully general relativistic treatment of thermodynamics and statistical mechanics. Imagine trying to do statistical mechanics with no possibility of a physically meaningful preferred time variable. That's why it has always been done on a fixed space-time, not in a fully general covariant way. I hope to get back to this. It really interests me.
 P: 175 ﻿I've been going through Jeffery Bub's paper that Marcus pointed to in his #141 post (http://arxiv.org/abs/1211.3062). It's about stuff that I'm not at all familiar with: statistics and simplex theory. My comprehension is strictly limited, to put it mildly. Perhaps there is someone here who can straighten my thinking out. It seems to me that Bub is trying to describing mathematically a world where the speed of information is limited and the observations that guide description are of a statistical nature --- as well as being causal, because they affect this world. He seems to show that observation inevitably generates loss of information, i.e. uncertainty, as is the case in quantum mechanics. I think he also establishes that entanglement is inevitably associated with such loss of information. He says that all this is an expected consequence of “probabilistic correlations, (and) the structure of information”; all that is needed, I suppose, to formulate a predictive description in a holistically statistical world. So are the mysteries of quantum mechanics forced on us because causality is a sort of statistical correlation? But what he doesn’t clarify is for me the central mystery: the magnitude of what sets the whole shebang up, namely Planck’s constant. Perhaps his interesting approach will eventually lead to our understanding why h is of order 10^-34 J.s.in our real world? I do hope so.
P: 63
 Quote by marcus This is why the (M,ω) formalism has come up in the context of trying to devise a fully general relativistic treatment of thermodynamics and statistical mechanics. Imagine trying to do statistical mechanics with no possibility of a physically meaningful preferred time variable. That's why it has always been done on a fixed space-time, not in a fully general covariant way. I hope to get back to this. It really interests me.
By a "preferred" time variable, does this mean that this time forms an "absolute time" in some sense (i.e. a "universal clock" that is not tied to a particular observer, sort of like in "old" pre-Einstein physics), or what?
Astronomy
PF Gold
P: 23,110
Paulibus, bravo for tackling Bub! I'll be interested to know what you make of it. So far what I can get is for the most part merely what delighted me so much in the introduction (and I quoted.) But I'm trying to do too many things at once (family Christmas letters, and our community chorus has given several performances of Moz. mass in c-minor!, not to mention physics-watching)
 Quote by sshai45 By a "preferred" time variable, does this mean that this time forms an "absolute time" in some sense (i.e. a "universal clock" that is not tied to a particular observer, sort of like in "old" pre-Einstein physics), or what?
Maybe we need a new word to use instead of "preferred". I think it's different from going back to "old" pre-Einstein time ideas. In the old days there was an absolute time and all observers clocks were supposed to follow it and agree on simultaneity and stuff.

Now we still have all the observer-times and a democracy of disagreeing clocks, but IN ADDITION we have one more clock, which we can COMPARE the various observer clocks with. The ratio of rates can even be physically meaningful, correspond to something measurable.

This one additional clock is distinguished by the fact that it is not observer-dependent it is, instead, state-dependent. It depends on what we think we know about the world--on our degree of (un)certainty about correlations amongst observations---what we posit to be the case, with varying degrees of confidence. If you like, picture the state as a density matrix defining a function on the observables.

Each observer still gets to keep his own individual clock and nobody is presumed to be RIGHT, but there is this one additional clock, which has one particular advantage: the world can be analyzed as a fully relativistic system evolving according to THIS time.

Which is something you CAN'T do with some particular observer time, because the observer's history itself depends on how the system evolves---so there is a kind of logical circularity. The observer's time is not truly an independent variable.

So as I see it, this is not going back to the old picture, but instead is adding one more disagreeing clock to the general temporal madhouse and anarchy---which however has a nifty feature that you can do a fully general relativistic statistical mechanics and thermodynamics using IT as the independent time variable---something you cannot do with any other clock as far as I know. So it is subtly different from going back to the old picture and it does not imply that "Einstein was wrong". Or so I think.

Maybe instead of preferred we could say "distinguished" time variable. Distinguished by the fact that it can be used as independent variable in a fully general relativistic quantum statistical mechanics and suchlike fully relativistic analysis (rather than have to first choose a fixed solution to the Einstein equation and then do the analysis "on curved spacetime".) This gives the variable a definite "distinction" without applying that it is somehow "absolute" and the only right choice :big grin:
The key paper for understanding it in this light is http://arxiv.org/abs/1209.0065
But also maybe re-read the "Chapter 1" quote in post #145. It's short and to the point.
 P: 4 Dear Marcus Hi, Im new to this thread, and I think it is very well conducted, and please excuse my butting in. But I would like to respectfully say that I question/disagree with your view... “I think everybody in the thread would go along with the idea that time is real and vitally important---both in physics and in our everyday experience.” (post #135) ...at a fundamental level. If we take the simple working view that ‘time’ is apparently 'real', and thus something that in the most simple terms consists, at least, in some way of components described as ‘the past’ and ‘the future’ then at the most basic level we would need... A- some initial reason for suspecting or assuming the existence of these things/places ('past', 'future'), and, B- some proof / reason or experiment, to sensibly show how or why they exist. It seems to me that if the universe is such that it is just filled with a quantity of matter/energy that ‘just’ (as in ‘only’) exists, moves, changes and interacts, (without leaving a 'past' behind us, and without heading into a 'future'), then this would explain all that we think implies the existence of a past and future – if we misinterpret, or over extrapolate, what we observe. Specifically – if as that matter moves and changes, it also moves and changes the contents of our minds, we may look at some of the contents of our minds, and ‘call’ those contents ‘memories’, and add to this (possibly wrongly) that those contents (memories) are not just things that exist and prove that matter can exist, but are also proof that another thing called ‘the past’ -also- exists. (And thus also proof that a thing called 'time' exists). As such we may (imo wrongly) imply that some existing matter, in a particular formation, gave us good reason to suspect that as things move and change the universe ‘also’ creates and stores some kind of ‘record’ of all events in a place or a thing called ‘the past’. So – is it correct to say , either, 1- Matter just exists moves and changes, or 2- There is also a (temporal) past, and thus a thing called ‘time’ that also may be considered. Many people seem to assume that Relativity tells us something about the nature of a thing called ‘time’. From what I have read, as far as I can tell, relativity only seems to actually tell us about the way, and ‘rates’ at which things may move and change differently under various conditions. As far as I can tell no part of relativity ever proves or demonstrates the existence of things (or places etc) such as ‘the past’ or ’the future’. Although it is written in a way that seems to imply or suggest ‘time’ and these places naturally or obviously exist, or make sense. While relativity seems to correctly show that matter may intrinsically 'change at different/reduced rates' while at velocity, in acceleration, gravity, etc, I don't see any proof that such matter 'sinks into a past' or 'surges into a future', or that relativity indicates the existence of these concepts. I would suggest 'time' is not real, but only a false idea borne out of us incorrectly interpreting what the contents of our minds prove and do not prove. If I am wrong could you point me to a link that shows how the existence of these entities ( 'the' past and 'the' future) has been demonstrated (in relativity or otherwise), as opposed to have just been assumed and untested? Yours M.Marsden, London
 P: 63 So if I'm getting this right, then the difference between this and "pre-Einstein" universal time is that in the latter, everyone's clocks must agree with the universal time, but that is not the case for this kind of "universal" time. Does this time also have a rest frame associated with it? Also, I notice you mention that "omega" represents "our knowledge". Does this mean that as we get "more knowledge", then it further "refines" this universal time? However, I'm curious about that bit about "spacetime does not exist", the "block universe doesn't exist": I thought that the block universe was essentially necessitated by the fact that observers could disagree on what constituted the past, present, and future. So that all three would have to exist "eternally". How is this handled in this "spacetime-less" theory? If you replace "time as a dimension" with "time as 'change'", then that would mean there would have to exist a universal "now", no? And that "now" would be the only thing that exists, everchanging (as we have no spacetime, so the past and future don't eternally exist). And if that "now" is the only thing that exists, then how can some observer in it include events in the non-existent universal past as part of their "now"?
Astronomy
PF Gold
P: 23,110
Now you are getting down to the basic similarities and differences with the earlier picture. These are good questions, I think.
 Quote by sshai45 So if I'm getting this right, then the difference between this and "pre-Einstein" universal time is that in the latter, everyone's clocks must agree with the universal time, but that is not the case for this kind of "universal" time. Does this time also have a rest frame associated with it? Also, I notice you mention that "omega" represents "our knowledge". Does this mean that as we get "more knowledge", then it further "refines" this universal time?
M consists of all possible measurements, ever. I think you are RIGHT that we will want to use a different state function ω when we have improved physics theories and more precise estimates of the constants. ω is a probabilistic idea of the state---correlations between measurements also embodying uncertainties about the fundamental constants, earlier conditions and even what the applicable equations are.

The idea is, we have to go with the best ideas and knowledge we have, and predict the measurements that we consider to be in our future, based on our knowledge and the odds we ascribe to it.

So exactly as you say, as future humans refine ω so would this idea of time (the Tomita flow on M) be refined.

I do not think that the Tomita flow has any idea of simultaneity belonging to it. There is no distinguished time-slice associated with it, that you could somehow "date from".

this is jumping way ahead, but if LQC (with its bounce) were ever implemented in a (M,ω) model then it would acquire a reference time-slice, the bounce. But we already know that when standard Friedmann cosmology is implemented one recovers standard time used in cosmology. Cosmologists use a universe time or "Friedmann time" in their standard expansion model. And , no surprise, (M,ω) reproduces it. Tomita = Friedmann. but that's jumping ahead.

The basic answer is NO there is no reference timeslice in the (M,ω) picture. there is the Tomita flow but no universal starting place for it.

In a sense M takes the place of the 4D spacetime of GR. but it has no geometry. the measurements all embody uncertainty and can assume various values. We can only imagine making a FINITE NUMBER of measurements. Like knowing where a particle went but only at a finite number of points along the way---not knowing the entire continuous trajectory.

M is very different from a space-time with a metric describing its geometry, in the sense that we make only a finite number of measurements (of areas, of angles, of distances, of matter density, of charge, etc)---and make a finite number of predictions based on that---beyond that we don't presume. The geometry is obviously quantum and uncertain because the geometric measurements themselves are quantum observables. But more than that, we do not presume that an overall classical geometry even exists.

I'm trying to interpret from the Connes Rovelli paper http://arxiv.org/abs/gr-qc/9406019 as best I can, and also from the recent one
http://arxiv.org/abs/1209.0065

 However, I'm curious about that bit about "spacetime does not exist", the "block universe doesn't exist": I thought that the block universe was essentially necessitated by the fact that observers could disagree on what constituted the past, present, and future...
Yes we all want observers to be able to disagree! But does this actually necessitate a "block universe". I think that is only ONE POSSIBLE data structure that permits them to systematically disagree. I think you are asking an extremely good question and one which, since the (M,ω) way of representing the world is new to me, as is the Tomita flow idea of time, I cannot competently answer. I would like to see more examples.
the Connes Rovelli paper shows a bunch examples but I would like to be clearer. How do different observers disagree harmoniously within the (M,ω) context? A researcher at Perimeter Institute named Laurent Freidel has been working on something he calls "Relative Locality" in which no global spacetime exists but there is Lorentz symmetry locally. Could this be encompassed in the (M,ω) picture?

The model itself does not force any division into past present future. But how for example is Lorentz symmetry implemented? Wish I could do a better job answering.
 P: 63 Thanks for the response. I'm curious about that "bounce". Does it imply that the future of the universe is to recollapse ("Big Crunch") and bounce again? If so, how does that jibe with dark energy? Does dark energy disappear at some point, or does it "reverse" itself somehow (so as to become attractive instead of repulsive in effect)?
Astronomy
PF Gold
P: 23,110
 Quote by sshai45 Thanks for the response. I'm curious about that "bounce". Does it imply that the future of the universe is to recollapse ("Big Crunch") and bounce again? ...
Thanks for the interesting discussion. In fact it does not imply recollapse. The Penn State people run many different cases on the computer, including Λ = 0 so they get a variety of behavior including that cyclic behavior you mentioned. But when they put in a realistic positive cosmological constant then they get just one bounce. This is similar to the classical DeSitter universe which has Lambda>0 and only one bounce.

Personally I don't think of Λ > 0 as representing an "energy". I just think of Lambda as a constant which naturally occurs in the Einstein equation of GR (the symmetries of the theory permit two constants, G and Λ). And all the evidence so far is that Λ does not change over time.
So if you think of it as an "energy" that energy density would not be changing.

In the way it first appeared in the GR equation, Λ is not an energy density but simply a small inherent CURVATURE. That is to say, the reciprocal of an area. If you have a favorite force unit in mind you can always multiply reciprocal area by force and get a pressure and that is the same type of physcial quantity as an energy density. So you can convert Λ to an energy density by fiddling with it. Move it from left side (curvature) of equation to right side (matter) and make mysterious talk about "dark energy" but I think that is going out of style. More often now I hear cosmologists simply refer to the cosmo constant Λ. "Dark energy" is more for the media. All we know is there is this acceleration that appears exactly as if due to a constant curvature at the classical level.

http://arxiv.org/abs/1002.3966

However one likes to think of it, including constant Λ > 0 in the picture with either classic DeSitter or Loop QC, you get a universe history with just one bounce.
 Astronomy Sci Advisor PF Gold P: 23,110 Hi Matt, I looked over your post and it seems to me it could be clearer and more compact if your words were anchored to definite mathematical objects. Physics is a mathematical science which means people are looking for the simplest best fit model (in math language). When we talk with English words there is normally some underlying math the words can be reduced down to, or can be anchored to. It may be very simple but there is usually some nonverbal foundation. Talking English can be convenient and bridge people with different technical upbringing and help speed up acquiring intuition, but the verbal description is seldom the whole story. So you say HAVING TWO WORDS IS REDUNDANT AND CONFUSING we shouldn't have separate words "time" and "change". That makes a certain amount of sense on a purely verbal level. But the Tomita math model of time has a use for both words. This is because of a subtle difference in the way we TREAT intervals of time and the changes that correspond to them, mathematically. There is an algebra M consisting of all possible measurements or observations. It is an algebra because you can add two measurements X+Y and multiply them XY. And there is an extremely useful object alpha-sub-t called a ONE PARAMETER GROUP OF AUTOMORPHISMS. αt is the change corresponding to an interval of time of length t. For every real number t there is a change αt which stirs M around, it sends every element of M to a new element. X → αt(X) And ADDING TWO TIMES corresponds to doing first one change and then the other. If there are two real numbers s and t. then the change corresponding to s+t is what you get by changing by αs and then changing by αt. Doing one change and then the other change is thought of as group multiplication and so we write αs+t = αsαt The alphas would normally be large MATRICES of complex numbers, or something analogous. Their actual written form would vary depending on the problem. The matrix entries would depend on the time parameter t. So it is useful to have two words: time is the additive parameter, and you add time intervals together. Changes are matrices that stir the world around, and you multiply two matrices together to see what happens when you do one change and then the other. Changes correspond to passage of a certain amount of time. That is what a one parameter group of transformations is, or a one parameter group of automorphisms, or changes, is. Time is the additive real number parameter t, and αt is the change. From a math standpoint it would be inconvenient and confusing to have only one word. The words are NOT redundant, from a math standpoint. But you have written a purely verbal essay arguing that we should reform the way we speak and have only one word, because from your verbal perspective the two words are redundant. I hope I've clarified the difficulty somewhat.
P: 175
 Quote by Mattmars ﻿But just ‘‘calling’’ a machine a clock, then saying that a ‘‘clock’’ is a thing that measures a thing called ‘‘time’’, and then claiming this is a proof that ‘‘time’’ exists, is imo absolutely not a proof that a thing called ‘‘time’’ exists.
And "exists" is also a wooly word. Of course. I agree. But these are just nice words; remember 40 years of fruitless speculation about string theory! To connect words, or squiggles on paper (as Hardy called mathematics) with memorable physics, one needs to suggest something practical we can actually do with new ideas. Making something that can reveal part of the future, like a time machine, would be good! Even correctly predicting the fall of cards in a poker game would draw attention.

So far in this thread no one, sadly including myself , has come anywhere near making such a useful suggestion. So far, it’s a futile story.
 Astronomy Sci Advisor PF Gold P: 23,110 Hi Paulibus, glad to see you! Personally I think the topic has a certain beauty and excitement because of the prospect of doing general relativistic statistical mechanics (and thermodynamics) something not hitherto possible. You probably have seen the Einstein field equation dozens of times---relating curvature quantities on the left side to matter and energy quantities on the right side. Back in the 1990s Ted Jacobson DERIVED that equation from some thermodynamic law, some fact about entropy. That to me is a very mysterious thing. they seem like utterly separate departments of physics. The connection remains puzzling and incomplete to this day. this is one reason that I view the current interest in this Tomita time---the only universal time flow I know of (the cosmologist's Friedmann model time being a special case of it arising under simplifying assumptions)---as far from futile. I see it as pretty exciting. Another exciting thing has to do with what Matt just said: "Change is not a thing that happens ‘over a thing called time’, and change is not a thing intrinsically linked to a thing called time." When you read the Princeton Companion to Mathematics treatment of Tomita flow you see that the change matrix is a certain root matrix raised to the t power where time is measured in natural (Planck) units. So one can say time is the exponent of change. There is a matrix, or more generally a unitary operator S such that the automorphism corresponding to the passage of time t (in nature's units) is given by the matrix/operator St. This is why adding times corresponds to multiplying change (or doing one, followed by the other). That is how exponents behave. You always have Xs+t=Xs Xt. What this illustrates, to me, is that the world is more intrinsically unified at a math level than it is at a verbal level. Because Matt says "change is not intrinsically linked to time" but when I look at the world with Tomita's eyes I see immediately that TIME IS THE LOGARITHM OF CHANGE Time is the real number that you have to raise the Tomita base to, to get a given change process. (a stirring around or automorphism of the world M of measurements). Here is where the Princeton Companion describes how to find the Tomita base (like the number e, the base of the natural logarithms), it is what you raise to the power t to get the change corresponding to that passage of time. http://books.google.com/books?id=ZOf...20math&f=false
 P: 4 Hi Marcus, Thank you very much for that reply. Thanks for clarifying the 'subtle difference in the way we TREAT intervals of time and the changes that correspond to them'. I see what you are saying + I will have to read up on this and some of the other details you mention to address them properly. (no point just blindly replying :) However, the essence of my point is that with the question '... does time exist' there may be some very simple basic 'truth' that is consistently missed -because- the mathematics works, and the science it leads to is so practical and useful. That is to say we may be confusing the usefulness of the mathematics with what it actually does and does not prove. For example, of course accountancy maths and scientific maths are somewhat different, but nonetheless, consider that no matter how perfectly one might balance the books of a multinational conglomerate, it would be foolish to think this high level of accuracy, or the usefulness of what you had done, related in anyway at all to how well you had proved that " 'Money' really is a thing that actually exists", (other than as a useful idea). Im trying to show that we may be making the same error with high level mathematics and the notion of 'time'. Thanks again for your reply, you've given me a couple of things to think about. Ill make sure I've understood your points then respond. mm
Astronomy
PF Gold
P: 23,110
Matt you might be interested in some earlier parts of thread. Whether or not a concept emerges as meaningful useful real can depend on contextual things like e.g. SCALE. So we were talking earlier about how time could be emergent rather than fundamental. Like temperature of a gas, which is real enough but does not exist at the level of a single molecule---it is a property of the collective when you look largescale. Or the waterlevel in a pond, which is real enough at a large scale but at microscale the pond does not have a welldefined surface it is a wild fuzzy dance of molecules. So things can be emergent rather than fundamental (to use a verbal shorthand). I'll recall part of that earlier discussion. This is post #57
 Quote by marcus ... 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 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 said he liked some of post #57 but he didn't fully agree, and he made several other interesting points. I'll quote portions of his post #58.
 Quote by Paulibus .. As Niels Bohr pointed out, Physics is a matter of what we say about stuff, not what stuff “is”. ...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?
In the part I highlighted, Paulibus italicized the word works. That's key. In physics, as Niels Bohr indicated, we are less interested in what exists than in accurate consistent statements, predictions---the simplest best-fit model, testable stuff, measurements. As Paulibus just said: "exist" is a fuzzy word. You can waste a lot of time talking about whether this or that "exists".

So we have this working distinction between more or less fundamental and emergent, and the notion that the reality or usefulness of concepts can depend on scale. Temperature can be very important at largescale and gradually lose meaning---become undefined or inapplicable---as you go to smaller and smaller scale.

Concepts can be scale-dependent, observer-dependent, context-dependent, state-dependent---there is a lot of nuance in physics (as in other branches of language! )
 Astronomy Sci Advisor PF Gold P: 23,110 I'll repost a set of links useful for this discussion, mostly sources on thermal time (= Tomita flow time). ==from post #129== This is to page 517 of the Princeton Companion to Mathematics http://books.google.com/books?id=ZOf...20math&f=false It's a nice clear concise exposition of the Tomita flow defined by a state on a *-algebra. For notation see the previous post: #128. Here's the article by Alain Connes and Carlo Rovelli: http://arxiv.org/abs/gr-qc/9406019 Here is Chapter 1 of Approaches to Quantum Gravity (D. Oriti ed.) http://arxiv.org/abs/gr-qc/0604045 Page 4 has a clear account of the progressive weakening of the time idea in manifold-based physics, which I just quoted a couple of posts back. I see the inadequacy of time in manifold-based classical and quantum relativity as one of the primary motivations for the thermal time idea. The seminal 1993 paper, The Statistical State of the Universe http://siba.unipv.it/fisica/articoli....1567-1568.pdf This shows how thermal time recovers conventional time in several interesting contexts. Here's a recent paper where thermal time is used in approaches to general relativistic statistical mechanics and general covariant statistical QM. http://arxiv.org/abs/1209.0065 It can be interesting to compare the global time defined by the flow with a local observer's time. The ratio between the two can be physically meaningful. http://arxiv.org/abs/1005.2985 Jeff Morton blog on Tomita flow time (with John Baez comment): http://theoreticalatlas.wordpress.co...d-tomita-flow/ Wide audience essays--the FQXi "nature of time" contest winners: http://fqxi.org/community/essay/winners/2008.1 Barbour: http://arxiv.org/abs/0903.3489 Rovelli: http://arxiv.org/abs/0903.3832 Ellis: http://arxiv.org/abs/0812.0240 ==endquote== Interestingly, Tomita flow time is the only independent time-variable available to us if we want to study a general relativistic system. Observer-time is not well-defined unless we already have settled on a particular fixed geometry. If the underlying geometry is dynamic and undecided we can't specify an observer's world-line. Tomita time is independent of the observer. It depends only on what we think we know about the world---the correlations among measurements that embody physical theory and presumed initial conditions, along with our degree of confidence/uncertainty. That is, it depends on the state. In Bohr's words: "what we can SAY". As Wittgenstein put it: "The world is everything that is the case." Here's a Vimeo video of part of a talk on Tomita time by Matteo Smerlak: http://vimeo.com/33363491 It's from a 2-day workshop March 2011 at Nice, France. The link just missed being included in the above list.
 Astronomy Sci Advisor PF Gold P: 23,110 But at my back I always hear Time's wingèd chariot hurrying near; And yonder all before us lie Deserts of vast eternity. Andrew Marvell, around 1650 I also want to recall this other passage, which is crucial to the discussion. This concisely summarized one of the troubles with time in a classical GR context. And indicates how the problem appears to get even more severe when one goes to a quantum version. But it is just at this point that the (M, ω) picture with its universally-defined Tomita flow becomes available. So the problem contains the seeds of its own solution. This passage gives a concise motivation for the star-algebra state-dependent way of treating time evolution. ==quote page 4 http://arxiv.org/abs/gr-qc/0604045 == ... Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable. This does not mean that GR lacks predictivity. Simply put, what GR predicts are relations between (partial) observables, which in general cannot be represented as the evolution of dependent variables on a preferred independent time variable. This weakening of the notion of time in classical GR is rarely emphasized: After all, in classical GR we may disregard the full dynamical structure of the theory and consider only individual solutions of its equations of motion. A single solution of the GR equations of motion determines “a spacetime”, where a notion of proper time is associated to each timelike worldline. But in the quantum context a single solution of the dynamical equation is like a single “trajectory” of a quantum particle: in quantum theory there are no physical individual trajectories: there are only transition probabilities between observable eigenvalues. Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime, in the same sense in which the motion of a quantum electron cannot be described in terms of a single trajectory. ==endquote== In the (M,ω) picture, M —essentially the set of all measurements— functions as a quantum-compatible replacement for spacetime, doing away with the need for it. Uncertainty, including geometric uncertainty, is built into every measurement in the set. And there's another very clear explanation of the problem here (to get the original paper just google "connes rovelli" ): ==page 2 of http://arxiv.org/abs/gr-qc/9406019 == 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== So they describe the problem, and they propose a solution. The problem is "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." But we HAVE to have a preferred time flow if we are going to do general relativistic statistical mechanics--stat mech and thermodynamics INCLUDING GEOMETRY. The temperature and entropy of the geometry as well, not merely of matter distributed on some pre-arranged fixed geometry. These and other types of analysis require a time flow. We want to comprehend the whole, including its dynamic geometry, not merely a part. The proposed solution was clearly a radical departure, namely to roll all you think you know about the world up into one ball of information, called the state function, and make that give you an inherent distinguished time flow. Make it do that. Force it to give you an intrinsic flow on the set of all observations/measurements. Tomita, a remarkable Japanese mathematician, showed how. For some reason this reminds me again of Andrew Marvell's words: "Let us roll all our strength and all our sweetness up into one ball" and basically just blast on through "the iron gates of life." It is a bold move. He was talking about something else, though.

 Related Discussions General Discussion 56 Science & Math Textbooks 0 Science & Math Textbooks 2