Julian Barbour on does time exist

[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?

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"?

 

[marcus]

Now you are getting down to the basic similarities and differences with the earlier picture. These are good questions, I think.

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.

 

[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? 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)?

 

[marcus]

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.

 

[mattmars]

Hi Marcus,

Thank you very much for your reply. This is pretty much my 4th version of a reply to you, just trying to keep it short. I have so much to say on this subject that my posts often end up being far too long unless I’m very careful. So excuse me if I don’t address each of your points specifically. But re QM and SpaceTime, here is my angle.

I followed the links to the Do We Need a Physics of ‘Passage’? site, and looked at the Program of events. Very interesting , I`ll read through the abstracts.

re your posts, There seems to be problems reconciling QM with ‘time’ or space time etc. I know very little about QM, but I accept its essence. I have read, thought, written and spoken a lot about the idea ‘time’, from the angle that time may be a complete misunderstanding. And I think I can show how ‘time’ is a completely unfounded idea, and thus how it does not exist. (In the same way that ‘phlogiston’ or the ‘Aether’ are just unfounded ideas).

If I am correct in my view on time not existing, then we see there is no temporal direction and no temporal order to the universe. Seeing if this is the case, I assume that problems with QM such as Qm’s incompatibility with space time, the need for ‘retro’ causality to explain certain things – or energy being borrowed from ‘the future’ to make quantum leaps etc, can be seen in a new way by those who understand them.

The problem with space-'time'.

Einstein famously declared the distinctions between the past present and future to be illusions because he considered the validity of 'blocktime', in which 'before' and 'after' might be akin to 'over here' and 'over there' - so just as the distinction between 'here' and 'there' is arbitrary, so might be the distinction between 'times'. But I believe it can be shown that even blocktime is a highly misleading red herring. And that the distinctions between past and future simply do not exist because those places or concepts are simply invalid and nonexistent.

Einstein’s work does show us that moving machines (atoms, life etc) run slow. And this is astounding and unexpected. 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.

However, if ‘time’ happens to exist, then it is agreed Einstein's work tells us something about it, and the concept of space-time may be fully or partially correct.

But, if time does not exist, then Einstein’s SR only shows us is that ‘moving machines’ (etc) run slower than stationary ones.(And this is absolutely not the same as proving there is a thing called time, connecting past and future, who's passage can be dilated, such that thing 'sink into past' or 'surge into future' etc)

So – it may be the case thatthere may be space, and things moving in space, and those moving things may be changing more slowly than other ‘stationary’ things. And that is all! If so, then we should not be insisting ‘space’ and ‘time’ should always be talked about together, or that what is true of one must a have a bearing on the other – unless we have shown both exist.

‘space’ is clearly a bit tricky mentally to grasp, but I have no deep problem with it. ‘Space’, it is the gap between railing in my local park etc.

I have a big problem with ‘time’, because most people, seem to have the most paper thin logic for assuming the existence of a 4th dimension. Even someone of the stature of Stephen Hawking bases his belief that 'time' exists because...

"we remember the past but not the future"
(brief history of time p161)

While in fact , surely we just look at some of the contents of our minds and 'call' them 'the past', and construct the 'idea' there is a 'future', and say we can't 'remember' 'it'.

For a pattern to form and be fixed in your mind only requires that matter can exist, move , change and interact.

Just because we can form useful and interesting patterns in our minds as we observe events (memories) - does not imo prove the the universe also creates a record of all events in a place called 'the past' - and so is not a proof that 'the past' and thus 'time' exist.QM and space-time.

Therefore, what I am suggesting is this,

‘time’ does not exist. It is just a useful idea. If we have no reason or proof that ‘places’ such as the ‘past’ or ‘the future’ exist then we should not scientifically insist they do.

If ‘the past’ and ‘the future’ were to exist, then it would make sense to consider that there is a thing called ‘time’ that has a flow and a direction (or any other description of time one prefers, ‘blocktime’ etc).

But, If there is NOT a past and a future, then there is NOT a past and a future!

And, if there is NOT a past and a future, then there is no such thing as ‘time’, and no such thing as a flow or direction of ‘time’.

And, there is no such thing as ‘space-time’ to be compatible or incompatible with QM etc.

This means that every bit of matter in the universe is just, ‘always’ somewhere, doing something ‘now’ (to use a thus redundant term).

This means that causes do not have effects in a ‘temporal’ direction, but they very simply have effects in physical directions. A tennis racket hitting a ball has an effect in that direction, the opponents racket has an effect in the opposite physical direction. An explosion has effects in all directions.

Likewise there are no ‘relativistic tilted planes of simultaneity’ to be accounted for. (if a spaceship is heading at speed to ‘Andromeda’, then that’s what it’s doing – all its machines (‘clocks’) etc may be running slower than those on Andromeda, but nothing is ever experiencing a different ‘now’.

So, if there is a discrepancy or conflict between QM and space-time, I suggest people go over what is and is not proven in Relativity, and double check, and be very, very clear as to whether there is space, motion, and a thing called ‘time’, to be accounted for. Or just space and motion to be accounted for. And these are very different positions.

where you say...

This does not mean that TIME AS A PROCESS OF CHANGE isn't real.

- I agree, but also think things are even simpler that this, there may not be a thing called ‘time’ which is a process of change. There may just be change. Giving change a second name is confusing, and misleading. (I also think I have worked through every basic aspect of Relativity, and shown how does not describe a thing called 'time', but still makes full sense as a theory only describing the finer aspects of 'change').

What I am trying to suggest, (given the title of this discussion is ‘... does time exist’), is that one should be very careful and very clear as to the specific terms we use in any discussion aimed at clarifying some deep confusion, and precisely what we mean by them.

I would agree that things ‘change’ – that is ‘things’ exist, and move, collide, interact, transform from matter to energy etc etc etc, and so the term ‘change’ is legitimate.

But to say ‘time’ as a process of change is real, (for me) is to say ‘the process of change is (also) called time’

But using the word ‘time’ suggests a plethora of other mysterious, deep and intangible, ethereal and unseen ‘places or things’ also exist. E.g. a place or thing called the future, a place or thing called the past, a thing called time that flows between these mysterious places, and which may be slowed by motion, or possibly traveled through etc etc etc. (while change just means existing stuff may be moving and changing shape or place etc, simply, always just ‘here’ ‘now’)

So, I am saying, consider that change is JUST change. Period.

re
So the QG program is aimed at constructing and verifying the most fundamental picture of the world. If you cannot incorporate a block space-time in QG, then that is as much to say a block spacetime does not exist, and time is not a 4th dimension.

I can see the aim is to construct and verify the most fundamental (i.e. simplest sensible working model that addresses all observations without adding unnecessary 'frills') - and I think the picture I have reached does this in every way I have tested it.

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.
or a thing that 'proves the existence of a thing called time'. imo there is just change, and, if you can see the heart of this (and if i am correct) then we see there never 'is' or 'was 'a past', and never 'is' or 'was' a 'future'. These are both purely and only useful ideas. Deeper still we may see that if there is no past and no future, then there is no time, and specifically no 'direction' to a thing called time.

This also means there is no 'temporal order'. As a simple example of this consider - With the idea of time fixed in our minds, and us habitually trying to make the idea of temporal progression fit what we see, it seems obvious that (say) the 'Wright Flyer' existed 'before' the jumbo jet. And thus it seems clear there is temporal order, temporal progression, and thus time.
But with the idea that "perhaps everything is always just here 'now' and happening 'now' ", we can see a way to at least consider that the atoms that make the Write Flyer, are always doing something as are the atoms that make up jumbo jets. As are the laws of physics that allow write flyers and/or jumbo jets to work, always present. And thus the atoms that make the flyer are never doing something 'before' or 'after' the atoms that make a jumbo jet - and vice versa.

Instead things, wherever they are, are just there, moving and changing, (not over a thing called time) but just where they are and in whatever physical direction they are heading in, with no ‘future’ ahead of them and no ’past’ behind them, i.e. timelessly so to speak.

This is easier to see on a large scale, but perhaps various problems with QM may be seen in a different light if this directional ‘linear’ straight jacket of an idea of ‘time’ is seen to be completely dissolved.
I say all of this because this physics form is specifically about the question ‘...does time exist’, and I think it can be shown ‘time’ does not exist, other than as a useful idea.

(ok, I’ll stop here, that’s 1000 words, I never can keep this short :)

M.Marsden.

 

[marcus]

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. α_t is the change corresponding to an interval of time of length t.

For every real number t there is a change α_t which stirs M around, it sends every element of M to a new element. X → α_t(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 α_s and then changing by α_t. Doing one change and then the other change is thought of as group multiplication and so we write
α_s+t = α_sα_t

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 α_t 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.

 

[Paulibus]

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.

 

[marcus]

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 S^t.

This is why adding times corresponds to multiplying change (or doing one, followed by the other). That is how exponents behave. You always have X^s+t=X^s X^t.

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=ZO...6AEwAw#v=onepage&q=minoru tomita math&f=false

 

[mattmars]

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).

I`m 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. I`ll make sure I've understood your points then respond.

mm

 

[marcus]

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

...
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.

..
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! )

 

[marcus]

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=ZO...6AEwAw#v=onepage&q=minoru tomita math&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/C/Class%20Quantum%20Grav_vol.10_1993_pp.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.c...time-hamiltonians-kms-states-and-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.

 

[marcus]

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.

 

[mattmars]

Hi Marcus,

Thanks for those posts and I appreciate those links, I’ll look through them. (in particular the ‘emergent’ aspect etc). I want to air all my thoughts on many of the points you raise (because I genuinely think I have a meaningful answer to each of them), but that would create a massive post. So as I read up on the areas you’ve pointed to I`ll post some thoughts on a select few.

I`m drawn to this post ‘Julian Barbour on does time exist’, because of it’s title, and because like Julian I have also written a book (eBook) on the nonexistence of time – but from a significantly different and far simpler angle. ( search for ‘A Brief History of Timelessness’ + you`ll find the site/videos/book etc)

I appreciate your ‘angle’ on mathematics, but I really think the essence of the ‘problem’ can be expressed in simple plain English, and, what I see throughout all the discussions about ‘time’ I have read, (which is a lot), is the more sophisticated the conversation gets the more the basic issue gets irretrievably obscured. Effectively people end up considering questions that cannot be answered – because they may be based on very basic incorrectly made assumptions.

(For example if we ask the question which is probably the more correct view of time, Newton’s fixed and universal time, or Einstein's dilatable space time? Many people would start considering that obviously Einstein's view of time has been theoretically and practically proven to be more correct. However, I would say both are ‘completely’ wrong in that there is no such thing as time, at all, period. Einstein's work is clearly correct and proven in many ways, (Mercury’s advancing perihelion, gps etc), but (imo) it is not about a thing called ‘time’, it is just and only about the way things move (‘now’ to use a redundant and slightly misleading word).

Normally saying Einstein's view is better than Newton’s doesn’t matter. But if people assume this thus means it is a forgone conclusion that a thing called ‘time’ in some way exists, and Einstein's view of it is more refined, and now we just need to refine the view further- then they may never recheck the fact that the existence of the thing actually isn’t proven by either view. And I’ve got a stack of books all about time, virtually all of which are written as if ‘time’ exists, built on the idea that Einstein's work in some way proved times existence.

For example, as I say I`m drawn to this post because of the title, ‘Julian Barbour on does time exist’. I read Mr Barbours very well written and comprehensive book (‘The End of Time’) as careful as I could, in case his point was the same as mine, but it’s not.

The End of Time p143, Mr Barbour says ‘The block universe picture is in fact close to my own’,(I think)... he then describes a kind of ‘phase space of infinite dimensions’ in which all possible configurations of all the matter in the universe constantly, and statically exist. And in which all possible ‘historys’ statically exist – such that as we ‘move’ through particular paths in this infinite phase space it appears to each of us that ‘time’ with a past and future exist.

(Note that is just my own very rough understanding of what I think Julian is saying, the maths etc in the book is out of my league so I may have got that wrong).

In my opinion, this is an example of just how complicated things get if we have incorrect, unchecked assumptions at the core of a ‘theory’, and, if we ‘follow’ the maths searching for an answer to a problem that does not exist.

My approach...

My approach very briefly (I’ve expressed the whole thing on the website), to me the idea of “’time’ being explained by all possibly histories constantly existing’, or the question ‘”is ‘time’ emergent (or not)?” become redundant and moot if we just consider the following question very carefully (as I mentioned in my 1st post)

Do we actually have any legitimate reason to even suspect that (say) the term ‘the past’ in any way at all actually relates to some ‘thing’?

It seems to me that the only reasons we even consider that a thing called ‘time’ might exist (or be emergent) is because we think our ‘memories’ indicate some kind of a ‘past’. But if we see that there is absolutely no reason at all to suspect that our ‘memories’ are anything at all other than ‘a collection of ions and electrons etc in a particular formation in our heads’ – then we can see that there is no reason at all to suspect ‘a (temporal) past’ exists in any way at all.

And if we are wrong to think there is ‘a past’, then we have no reason to suspect there is ‘a future’. And thus wrong to suspect there is a thing called ‘time’, or that ‘it’ has a flow or a direction. i.e (imo) it just does not exist and we are wrong to think it may.

Instead – the world is just as it appears to be – full of stuff moving in organised and/or chaotic ways. Whatever is true of QM is true of QM, but it needn’t have any component of a thing called time mixed in it. The universe may be expanding and heading for a heat death (or not) – but that may be ‘just’ what it is doing. Just because the universe is expanding in an ‘irreversible’ way, doesn’t mean there ‘is’ a past or a ‘future’ – or time, or an arrow of time.

Likewise , if things ‘just’ move and change etc , then ‘time’ is not emergent... things jjust move and change. Calling this ‘time’ and asking if it is emergent is (to me) like asking if ‘movement is emergent from movement’.

I appreciate what you say about the ‘Tomita flow time’ (tho I haven’t read up on it yet to be honest), but when I consider the ..

“subtle difference in the way we TREAT intervals of time and the changes that correspond to them”

My position is that there are no ‘intervals’ of ‘time’. We can sit in front of a motorised hand that is rotating around a numbered dial (a clock) – but just because we are breathing and that hand is rotating does not prove that there are such things as ‘intervals of time’ – or that a thing called ‘time’ is ‘passing’.

Its a odd concept to see if we are deeply ingrained that ‘time’ makes sense in some way, but if there's no past and no future, then there’s no time and ‘passage’ or intervals of it. And useful as the maths is, we may say t1+t2 =t3, and if time exists this may be valid, but in itself I don’t think this shows that ‘time’ exists,

-ok, i’ve hit 1000 words again, and i`m duplicating points, so i`ll stop. Please don’t think i`m ignoring the things you have pointed to, these are just my views at the moment – having written my book on the subject.

Sorry I haven’t. Addressed the issues you pointed to directly, I will read them in detail, and you're right I should (will) read earlier points of the thread, (just busy due to xmas), I just wanted to send this post before I take the xmas break.

Matt marsden (brief history of timelessness)

 

[marcus]

Interesting thing about Barbour is if you look at what he is actually saying, e.g. http://arxiv.org/abs/0903.3489
he shows that a time variable does not have to be put in "by hand" at the beginning of the analysis, but can be DERIVED from observation.

In this case he derives the evolution parameter from observing a dynamical system---a bunch of planets, or other bodies---stars, satellites, whatever.

This derivation us purely classical = non-quantum. The Tomita method is analogous in the sense that the evolution parameter is DERIVED (from correlations among observations) rather than put in by hand at start of analysis. However it is not limited to classical systems--can be applied to quantum ones as well.

As I think I said earlier in thread, I don't think "time does not exist" is an accurate headline for what Barbour and Connes-Rovelli are saying. "Exist" is a kind of fuzzy word anyway---more philosophy than science. Time remains a crucial indispensable and all-important element in their analysis, what they show is that it can be derived from other stuff.

In a sense that makes time all the more real because you cannot avoid it. It is implicit in what we observe.

As I said earlier, the headline "time does not exist" would be primarily an attention-getter, not an accurate summary of what Barbour or the others are saying. Perhaps a better (but less strikingly worded) summary would be "time is inherent in natural processes and can be derived from observation".

Since I'm currently very interested in the strategies used to derive time from observations, it actually does NOT get my attention to say "time does not exist". It may work for other people, though.

I think a frank answer, by Barbour, to the question does t exist (in thread title) would be YES INDEED it exists and it is very interesting how one can mathematically derive it!

 

[berkeman]

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