
#145
Dec2112, 12:48 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

Here's part of a short answer I gave to your question in post #144, with a clarifying addition in red: 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/grqc/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 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". 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 observertime 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 spacetime, not in a fully general covariant way. I hope to get back to this. It really interests me. 



#146
Dec2212, 02:59 AM

P: 165

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. 



#147
Dec2212, 04:36 AM

P: 55





#148
Dec2212, 10:12 AM

Astronomy
Sci Advisor
PF Gold
P: 22,809

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 cminor!, not to mention physicswatching)
Now we still have all the observertimes 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 observerdependent it is, instead, statedependent. It depends on what we think we know about the worldon our degree of (un)certainty about correlations amongst observationswhat 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 evolvesso 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 anarchywhich however has a nifty feature that you can do a fully general relativistic statistical mechanics and thermodynamics using IT as the independent time variablesomething 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 reread the "Chapter 1" quote in post #145. It's short and to the point. 



#149
Dec2212, 01:35 PM

P: 4

Dear Marcus
Hi, I`m 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 importantboth 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 



#150
Dec2212, 01:57 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

Hi Matt, welcome to PF and thanks for contributing to this discussion. I'll try to respond...
I think your critique is mainly focused on the 4D "block universe" idea. You offer reasons to be skeptical about the existence of time as a DIMENSION, extending back into past and forward into future. You are skeptical of the idea that pastpresentfuture exists as a kind of 4D crystal with time as a kind of pseudospatial dimension. That's how I read what you say. You seem dubious regarding the presumed real existence of SPACETIME. You are certainly in good company as far as that goes. There was even a conference in Capetown South Africa this month bringing together people critical of the 4D block spacetime idea. We discussed that earlier in this thread. Your message also doesn't seem basically at odds with what I've been saying. You may have misunderstood what I've been trying to get across about time as a real process of change, rather than a spacetime dimension. I think the best argument against the actual existence of spacetime was given in Chapter 1 of that book, also available online at "arxiv.org". I gave the link in post #145, and quoted a passage that comes on page 4 of the essay. A 4D block spacetime seems incompatible with quantum uncertainty. You have to fiddle around with the concepts too much to get them to live with each other. Look back at post #145 right on this page, where it says: Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime... Which is to say, because we are talking about what is the best most fundamental mathematical description of the world, spacetime does not exist. This does not mean that TIME AS A PROCESS OF CHANGE isn't real. The math representation of a process of change is as a flow defined on the set of all observations. That is where transition probabilities and correlations between measurements (now and a few seconds later or a few years later) are defined. When you treat time as a process the math formalities are not as familiar to most people as when you treat it as a dimension, but that just takes getting used to. There is an observable algebra M consisting of all the possible measurements, and a numerical function ω giving correlations amongst the possible measurements, representing our knowledge. It's more abstract than most people are used to, but maybe that will change. (M, ω) is one possible formulation of any quantum theory about the world. John von Neumann is the main person who developed that approach back in 1930s. It does not necessarily assume a spacetime. And then given (M, ω) as the world, TIME is represented as a process that stirs M around. This kind of picture can be constructed using matrices of numbers. People can build examples of what I'm referring to. Already did this in the 1930s. von Neumann again. and others. Nowadays you can put this kind of model of the world into a computer and run it. Time becomes a process of change defined on M, and is itself represented by matrices of numbers that you multiply other stuff by to change it. It may be that the "spacetime" or block universe picture simply is not realistic enough and people will have to go with this (M, ω) picture of the world, where time is not a pseudospatial dimension of a block of eternity but is a process of change instead. That block may simply not be realistic enough (with its eternally existing past present future.) That is what was being argued in that quote I mentioned where it says Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime. Quantum gravity means quantum *geometry*, the quantum theory of the geometry in which matter and everything else lives. So the QG program is aimed at constructing and verifying the most fundamental picture of the world. If you cannot incorporate a block spacetime in QG, then that is as much to say a block spacetime does not exist, and time is not a 4th dimension. So we have to see how the QG research program goes, and how it turns out. 



#151
Dec2212, 04:00 PM

P: 55

So if I'm getting this right, then the difference between this and "preEinstein" 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 "spacetimeless" 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 nonexistent universal past as part of their "now"? 



#152
Dec2212, 05:20 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

Now you are getting down to the basic similarities and differences with the earlier picture. These are good questions, I think.
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 timeslice 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 timeslice, 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 waynot knowing the entire continuous trajectory. M is very different from a spacetime 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 thatbeyond 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/grqc/9406019 as best I can, and also from the recent one http://arxiv.org/abs/1209.0065 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. 



#153
Dec2212, 05:33 PM

P: 55

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)? 



#154
Dec2212, 05:41 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

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. 



#155
Dec2312, 12:35 PM

P: 4

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 spacetime 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 cant '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 spacetime. 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 ‘spacetime’ 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 space ship 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 spacetime, 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 travelled 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 spacetime 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. 



#156
Dec2412, 02:03 AM

Astronomy
Sci Advisor
PF Gold
P: 22,809

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 alphasubt 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_{s}α_{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. 



#157
Dec2412, 02:13 AM

P: 165

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. 



#158
Dec2412, 02:21 AM

Astronomy
Sci Advisor
PF Gold
P: 22,809

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 timesrelating 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 timethe 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=ZOf...20math&f=false 



#159
Dec2412, 05:05 AM

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). 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 



#160
Dec2412, 11:50 AM

Astronomy
Sci Advisor
PF Gold
P: 22,809

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 moleculeit 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
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 meaningbecome undefined or inapplicableas you go to smaller and smaller scale. Concepts can be scaledependent, observerdependent, contextdependent, statedependentthere is a lot of nuance in physics (as in other branches of language! ) 



#161
Dec2412, 12:16 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

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/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 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...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 ==endquote== Interestingly, Tomita flow time is the only independent timevariable available to us if we want to study a general relativistic system. Observertime is not welldefined 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 worldline. Tomita time is independent of the observer. It depends only on what we think we know about the worldthe 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 2day workshop March 2011 at Nice, France. The link just missed being included in the above list. 



#162
Dec2412, 01:09 PM

Astronomy
Sci Advisor
PF Gold
P: 22,809

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 universallydefined Tomita flow becomes available. So the problem contains the seeds of its own solution. This passage gives a concise motivation for the staralgebra statedependent way of treating time evolution. ==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== In the (M,ω) picture, M —essentially the set of all measurements— functions as a quantumcompatible 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/grqc/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 nonrelativistic 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 mechanicsstat mech and thermodynamics INCLUDING GEOMETRY. The temperature and entropy of the geometry as well, not merely of matter distributed on some prearranged 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. 


Register to reply 
Related Discussions  
Does time exist?  General Discussion  56  
First post: "End of Time" by Julian Barbour  Science & Math Textbook Listings  0  
[SOLVED] Julian Barbour's "End of Time"  Science & Math Textbook Listings  2 