
#127
Dec1212, 07:44 PM

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PF Gold
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I think it's important to grasp what Rovelli says here, regarding time in General Relativity and the further weakening of the time concept that must accompany any quantum theory encompassing GR, on basic grounds regardless of what theory one considers. First one needs to appreciate this fact, repeated below in larger context:
" Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable." This is best understood in contextit 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/grqc/0604045 ) ==quote Chapter 1 of Approaches to Quantum Gravity== ... Before special relativity, one assumed that there is a universal physical variable t, measured by clocks, such that all physical phenomena can be described in terms of evolution equations in the independent variable t. 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 x_{0}, 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 x_{0}, 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 nonlocal 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 solutioni.e. a geometric "trajectory". 



#128
Dec1212, 08:34 PM

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PF Gold
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This is the logjam which the (M, ω) formulation breaks thru. I'm using the notation from the Princeton Companion to Mathematics article which I quoted back few posts. M is the *algebra of measurements/observations and ω: M→ℂ is a positive linear function defined on M, called the "state". It summarizes what we think we knowincluding statistical uncertaintiesabout the means variances and correlations of the elements of M. Physical theories and constants boil down to correlations among measurements. Uncertainty about the precise values of constants boils down to variancesall that is comprised in the state ω. Along with observational data and predictions.
The Companion article explains how a unique idea of TIME arises from (M, ω) as a oneparameter subgroup or flow defined on M, which in this thread I've been writing α_{t}: M→M. 



#129
Dec1212, 08:37 PM

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PF Gold
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I should gather together some of the main source links for thermal time (= Tomita flow time).
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/grqc/9406019 Here is Chapter 1 of Approaches to Quantum Gravity (D. Oriti ed.) http://arxiv.org/abs/grqc/0604045 Page 4 has a clear account of the progressive weakening of the time idea in manifoldbased physics, which I just quoted a couple of posts back. I see the inadequacy of time in manifoldbased 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....15671568.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 to 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...dtomitaflow/ Wide audience essaysthe 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 



#130
Dec1312, 12:46 AM

P: 165

The RovelliSmerlak reference (#6 of your list above) makes me wonder if thermal time might be distinguished from ordinary time experimentally by folk familiar with isotope enrichment via the centrifuge method. Could high centrifuge accelerations, combined with cryogenic temperatures, perhaps amplify the fractional difference between the two Times sufficently to alleviate the pesky 1/c^2 factor?
Some such connection between mathematical ratiocination and observation might also help to dissipate the frustration of theorists in general, engendered by many years of sterile string theory. 



#131
Dec1312, 03:19 PM

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PF Gold
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But that was just a passing remark, I wouldn't take it terribly seriously. There could be other regimes in which it is measurable. Putting that issue aside for the moment, I think you might enjoy the talk. Unfortunately it cuts off after 15 minutes. So we don't get the last 10 or 15 minutes of his presentation. Anyway, just in case you're interested, here's the link. http://vimeo.com/33363491 It's from a 2day workshop March 2011 at Nice, France. 



#132
Dec1312, 11:57 PM

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PF Gold
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#133
Dec1412, 12:04 AM

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PF Gold
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http://inspirehep.net/search?ln=en&a...=50&sc=0&of=hb That gets 428 quantum cosmology papers (2009 to present) about half of which are loop. And among them are quite a few phenomenologyabout observable effectsthough you have to look for them. There's a more selective link that is sometimes slow. I'll get that in a moment. http://wwwlibrary.desy.de/cgibin/s...tecount%28d%29 It just now timed out on me twice and then worked the third time. It came up with 66 recent Loop cosmology papers that are more consistently oriented towards observational testing. I would very much like to see the Loop cosmology bounce modeled using Tomita flow time. 



#134
Dec1412, 02:10 AM

P: 13

....hello all...a most fascination take on time, and for simplicity's sake the theory of time will give me endless hours of enjoyable argy bargy...it's the mathematics that seems to have to creep in ...and we all know that mathematics are the tools for proving a theory, but once again time will confound us on that account as there is no need to ''prove'' its existence....it will continue to pervade our lives and stridently make us have to grapple with it.....seeya




#135
Dec1412, 11:25 AM

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PF Gold
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The phrase "does time exist?" is just a way of getting attentionit's not a useful way to frame the discussionnot really what we're talking about. The main thing driving the discussion seems to be dissatisfaction with the (outmoded, I believe) way of imagining time mathematically as an "axis" i.e. as a pseudospatial dimension. The title of the Capetown conference, held this week, was Do we need a physics of 'passage'? IOW instead of a static picture with time as an AXIS (analogous to spatial coordinate axes) shouldn't we develop a mathematical picture in which it is a PROCESS OF CHANGE. For a substantial part of the last century the prevailing tendency was to geometrize timeput it on an axisleading to a static picture in which our experience of time's passage is apt to be disregarded or explained away as merely psychological. Now the pendulum seems to be swinging the other direction (away from the static geometrization of time.) I wouldn't disparage mathematics. The meat of the discussion here is actually about competing mathematical representations of time. Math can represent process in various ways, it's not restricted to describing location along a coordinate axis. You might be interested to read what the organizers of the "Passage" conference wrote about it: http://prce.hu/centre_for_time/jtf/passage.html http://prce.hu/centre_for_time/jtf/FullProgram.pdf In the html index page they quote some famous 19th and 20th century physicists to exemplify what they, the organizers, are NOT happy with and want to try to change. You might even like the tack they are taking. 



#136
Dec1512, 02:50 AM

P: 13

...thanks for the clarifications marcus .. could i pose this thought ....to a photon or any other massless object, time has no usefulness or relevance to their being, as their travelling at the speed of light renders time to stand still...
...when we start to include mass into the physics there is automatically a need to invoke the constant of time....but this leads us to at least two sets of rules, which is repulsive to a pure theory of time..... ....any thoughts?...i hope i'm not over simplifying things....cheers 



#137
Dec1512, 08:31 AM

P: 18

Hi Marcus,
Interesting discussion but I have to admit I don't follow the maths... I just wanted to say that I remember reading, about 25 years ago or more, in the New Scientist magazine (that was when it was worth reading!) an article relating to the idea of the flow of time as a phasechange. The general idea was that in a similar way to which a pond freezes over where you can imagine a layer of ice spreading across the surface so does time appear to us. By which I mean that to us the past is fixed (frozen) but the future is mutable and "now" is, of course, where that phase change occurs. This idea seems to me to be consistent with your Does this idea still sound viable as a layman interpretation of the current discussion? 



#138
Dec1612, 06:28 PM

P: 13

If time did not exsist, what would prevent everything from happening at once?




#139
Dec1612, 09:33 PM

P: 289

"Time is nature's way to keep everything from happening at once." John Wheeler.




#140
Dec1912, 01:33 PM

Astronomy
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PF Gold
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Thanks Julian, Paulibus, Exile, Detective and others for keeping us wondering about time!
There've been some more interesting papers posted on arxiv that bear on this, but first I want to recall a portion of the passage quoted in post #121, over ten days ago! ==quote page 4 http://arxiv.org/abs/grqc/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== IOW people have now developed some candidate QG theories, though it's still workinprogress and as yet there's no consensus as to which nature prefers. But even before we have a fully developed preferred QG theory we can still take the lessons seriously that GR and QM teach us. Our eventual QG theory will probably NOT be manifoldbased. It will not be about the geometry of a spacetime continuumthat would be a geometric *trajectory*. Instead it will be about probabilistic correlations between measurements. That is, the basic math object is probably to be (M,ω) a star algebra and a function from M to the complex numbers that gives the expectation values and correlations, rather than a continuum with fields defined on it. M="measurements" and ω="state" (what we think we know about the both past and future, and our statistical uncertainty therewith.) Our notions of physics THEORY are encompassed in ω, as correlations among possible measurements we might make, as are our ideas about physical constants, past observations, initial conditions etc. Now this gets into an area of QM foundations where a couple of researchers have recently posted new papers, so I want to quote their abstracts. Here are the links in case you want to check them out: http://arxiv.org/abs/1211.3062 http://arxiv.org/abs/1212.3606 I have to go out briefly but will try to get back 



#141
Dec1912, 03:40 PM

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PF Gold
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I guess the main point to be made in connection with the TIME theme of this thread is that once you have specified (M, ω) i.e. the world of observations/measurements and what we think we statistically know about it, then we automatically get a standard time.
We can compare our own local observer time with that standard time. Sometimes the ratio of rates is physically meaningful. The standard time is not a pseudospatial "fourth dimension", but rather it is a FLOW defined on the star algebra M. That is a one parameter group of automorphisms mapping M → M. "Time" is simply the real number parameter t that parametrizes that flow. I want to get a quote from one of those QM foundations papers I mentioned. The one by Jeffrey Bub. Here's his introduction paragraph: This paper is intended to be serious, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, insofar as a theory of information is essentially a theory of probabilistic correlations— not about energy being quantized in discrete lumps or quanta, not about particles being wavelike, not about the universe continually splitting into countless coexisting quasiclassical universes, with many copies of ourselves, or anything like that. To make this clear, it ... Bub is distinguished prof at U Maryland, same place as Ted Jacobson (topnotch expert on GR and QG, and profoundly original). IMHO with people like Bub and Jacobson you take seriously what they say even if it sounds unusual, or especially if it sounds unusual. He is saying that the Hilbert space doesn't matter and all that paraphernalia, what matters is the structure of correlations. The Hilbert space is just a convenient mathematical device to represent the structure of correlations, and it's not the only possible such framework. http://en.wikipedia.org/wiki/Jeffrey_Bub born 1942, PhD Uni London 1966, > 100 papers, several books, interpretation of qm and related. http://carnap.umd.edu/philphysics/bub.html 



#142
Dec2012, 05:54 AM

P: 55

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 nonreality of the block universe and the relativity of simultaneity play with each other?




#143
Dec2012, 10:30 AM

P: 165

Marcus: your post #141 gave me a belated (by one day) birthday present.
Your reference to Jeffery Bub in his paper "Bananaworld: Quantum Mechanics for Primates", to the effect that: '.....The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, insofar as a theory of information is essentially a theory of probabilistic correlations— not about energy being quantized in discrete lumps or quanta, not about particles being wavelike, not about the universe continually splitting into countless coexisting quasiclassical universes, with many copies of ourselves, or anything like that...', together with your comment that: Thanks for this. I plan to comment later, when I've better absorbed this gem of physics philosophy. 



#144
Dec2012, 12:12 PM

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PF Gold
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I'm so glad you were intrigued by Jeffrey Bub's ideas too!
I'm a bit disappointed in myself that I have a hard time following when I get into the middle of the paper. Even though he discusses in very basic terms (bananas, primates) and I'm convinced he has clear important insight, I'm still struggling. Still, it is kind of a fine Christmas present for me too! My wife likes Bill Bryson's books, and just read "At Home". She passes savory tidbits on to me. He is a good writer and outstanding as a researcher. ============== I also will have to comment later. 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 *statedependent* 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. Thanks to certain mathematicians of the second half of the 20th we have a chance at 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. 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 formthus 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. Of course it is hard to get used to because such a new approach. 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 timepassage can be physically meaningful (corresponding to a geometric temperature discovered by Tolman already in the 1930s and written about in his classic GR treatise). So it can be interesting to compare this version of time with the observer's time. It also seems to be good for other things where you can't use observertime. I'll try to get back to this later. 


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