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Do changes of spacetime geometry affect entropy?

  1. Jul 11, 2010 #1
    The backdrop against which cosmology is set is provided by the geometry of spacetime. As often pointed out in this forum, General Relativity has revealed that this geometry is not fixed and eternal, but changes as the structure of the universe evolves from an ultradense, ultrahot but formless plasma into the objects we now observe in our night skies. And much else.

    The second law of thermodynamics prescibes that during this evolution entropy must increase. Penrose, in his Road to Reality, Chap. 27 explains how an increase of entropy can occur (despite the random initial state of the universe) as gravitational degrees of freedom are taken up during structure formation. He presents and illustrates his arguments in terms of the coarse-graining of phase space, analagous to the coarse graining of the phase space of a perfect gas.

    Phase space is an abstract and convenient tool for simplifying the the evolution of a multi-component system (such as a gas) by representing its evolution as a single ergodically wandering curve in phase space.

    But phase space is derived from the coordinate spaces we use to quantify 'real space' (whatever that may be!) and, as with spatial sections of spacetime , these coordinate spaces must change and evolve, expand and locally distort, as the universe itself changes locally or globally, and evolves.

    When Chance, Nature or Something invents, deploys or activates (words are difficult here) autocatalytic tricks (I'm thinking of gravity or the much later inception of DNA) will this, together with the evolution of spacetime, not profoundly alter the coase-graning of phase space and with it, how entropy increases as the universe explores its future?
     
    Last edited: Jul 11, 2010
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  3. Jul 17, 2010 #2

    Fra

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    I have his book, and I've read some of it, but I am not a fan of Penrose perspective.

    My first counter-question with purpose of clarifying what we ask here is "entropy relative to which observer"?

    To just talk about entropy, without having the context clear is to me non-physical and a mathematical game without clear physical basis.

    I think the only sensible view, is to picture, what entropy an "inside observer" would have seen back in the early universe. And then one realizes that this question is inseparable from the structure of the observer itself - which in the real caes means structure of the matter existing back then (if we see these as the proto-observers, clearly we're not talking about humans or even biological observers).

    /Fredrik
     
  4. Jul 18, 2010 #3
    Thanks for these comments, Fredrik. I agree with your last statement, but I'm a bit puzzled about entropy being viewed as relative to an observer.

    Entropy, like its cousin temperature, is a more slippery concept than appears at first sight. In a simple-minded way I think of entropy as a concept that was invented (by Clausius) to serve human purposes in describing the Real World Out There, which I hope has an existence independent of ours.

    For instance, entropy distinguishes adiabatic curves on a P-V diagram for a gas in the same way that temperature distinguishes isothermals. It's also a simplifying concept that usefully describes the state of multicomponent systems that have many equivalent microstates -- lots of degrees of freedom that can change without affecting their macroscopically perceived state --- again as with a gas.

    Is it here that you view entropy as 'relative to an observer', because different observers might make different judgments of what are identical macroscopic states? (My cat insists that all interesting macroscopic systems must involve fish!) I agree that this is a puzzling aspect of defining entropy (which Penrose dismisses hand-wavingly dismisses as unimportant) but I'm unsure how important, for our purposes, such observer-dependent differences are.

    Entropy is now often discussed as a property of very complex systems, even of the Universe as a whole. I think this sweeps interesting things under the carpet. For example it seems reasonable to calculate the entropy of the early universe without taking gravity into account. Its state is then a hot dense gas. But once gravity is 'switched on' as a structure-forming agent, by a fall in temperature caused by expansion, the situation veers dramatically
    away from being the same gas.

    An autocatalytic process is now active --- gravitational condensation is a runaway positive-feedback process whose action promotes more condensation. This process must change the state space itself, the background against which entropy increases by ergodic wandering; change it also as spacetime expands and locally becomes distorted, and change how the state space is divided up into 'boxes", a la Penrose. I think this should affect the way entropy changes.

    The universe is now dramatically different from what it was 13.7 billion years ago. It now even has observers that worry about such questions --- all the result of another autocatalytic process starting up here quite recently -- the efflorescence of DNA. Do such 'tricks' speed up or slow down entropy change?
     
  5. Jul 18, 2010 #4

    Fra

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    To connect back to Smolin's arguments. He argued that the current scheme of timeless laws and statespaces works fine in a special condition: when we are studying small subsystems!

    This applies geneally to "particle physics", but certainly not when one considers things like the "wavefunction of the universe".

    Smolin's argument is that the extreme success of the current scheme, has blinded us. And that applying the same logic/scheme to cosmology is a fallacy. Smolin labeled this the cosmological fallacy if remember correct.

    (Here is one talk http://pirsa.org/08100049/)

    However, Smolin does not go as far as Unger does. But the problem is then that Smoling is the physicist, not Unger. So I still expect some development here.

    The way _I_ see it: there is MORE to this than what's clear from the above arguments of smolin. This also touches unification (something that smolin never to my knowledge touched in his talks).

    The thing is that if you expect (á la entropic forces) that the action of each system is rational in the sense that it simply follows the entropic flow; then if you combine that with that each observer has it's own assessment of this flow, different observers would appearc to have "inconsistent" actions if you think there was an objective entropic flow, but this is exactly the mechanis that is the origin of interactions/forces! But this is my vision. I have not yet seen anyone else making this statement. But if Unger can have some more influence on smolin, this is what I hope will come up. This is also the one reason why I try to follow smoling and unger. Unfortunately their last talk didn't show much deveclopment as compare to the ones a couple of years ago.

    Also Smolins scattered papers on other things makes me think smolin is still very far from this vision.

    /Fredrik
     
  6. Jul 18, 2010 #5

    Fra

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    I should add that these are my own ideas in which I have great confidence, they are not current conventional wisdom in any sene. But to reiterate one of the core points of my vision.

    The measurable difference, is that two observers, both acting as per a "rational action conjecture" (this is what I call a generalisation of entropic action), then the variation of the entropy between two observer reflect their action!

    Think about human and social interactions, or poker games even. Clearly, the action of each player (given that he is rational) is determined by his assessment of his environment. Pleaes note the most important point here: this is true EVEN if his assessement is "wrong"! "right" or "wrong" is a non-issue here.

    Edit: The conclusion here should be that the classification of interaction types (forces) then becomes closely related to the classification of the population of observers. In theory one would think that this leads to arbitraryness and that a werid observer could see weird laws. While that is in principle ture, it is not aq problem as not all observers are viable and persistent.

    So evolution of law, and evolution/development of matter goes hand in hand. It's NOT that law RULES or FORCES the deveclopment of matter, that are just two side of the coin. And _maybe_ this could be exploited to reduce alot of parameters in the standard model, unify gravity with other forces etc.

    /Fredrik
     
  7. Jul 19, 2010 #6
    I agree with Smolin's views as you report them. Here, unfortuately, I don't have enough bandwidth to watch videos or listen to talks via the internet. Has Smolin said similar things on the Arxiv?

    It seems to me a bit crazy to accept the dynamic spacetime of GR but make do with timeless state spaces, which are but abstractions constructed from a changing space-coordinate geometry. By doing so one is ignoring our present understanding that almost everything we observe is a product of evolution, whether it be astronomical objects, geomorphology, or the biosphere of which we are a part.

    But perhaps asking physics to be concordant with evolution is just too difficult, even if only in accommodating changes in state space wrought by mass condensations.

    Here you're losing me; does anyone know what matter 'is' (other than a spacetime-distorting agent), let alone how it arises?
     
  8. Jul 19, 2010 #7

    Fra

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    Smolin has said similar things in various places, but how about downloading an mp3 and listen offline? there is no need to listen live. You can download both the videos, and the smaller mp3. I don't have a paper on the top of my head but maybe I can find one.
    A common reason to doubt this evolutionary picture, is that although it may seem plausible and sensible, so far we lack exact mathematical framework to formulate it. So it sure isn't easy, but somehow it's not a convincing argument.
    I don't mean to raise the question of what matter IS, in that sense, I actually just claim that spacetime without matter makes no sense, but also matter without spacetime makes no sense. With this I express a few things...

    - to even consider quantum gravity of "pure gravity" is very unlikely to make any sense; the argument here is that it's like considering a measurement theory without observers - it just makes no sense from the point of view of coherent reasoning.

    - I think that matter, and spacetime are emergent simultaneosly. But several other people have epxressed the same view. Olaf Dreyer has make this explicit claim as well, that some of hte "problems" with QG, is that we don't acknowledge this tight connection.

    My view is that "matter" ENCODES the laws of physics, as well as state spaces, as well as information measures (entropy), and that when matter interacts, the interactions are a direct result of the conflict between the subjectivity of the measures. This is however very similar the idea between observers gauges and gauge interactions but it's taken another step. For example the different view, two relativistic observers have on a charge, is in fact responsible for certain forces. The interaction is directly inferrable from the differing "views" of observers. What is new is that I claim that also the transformation group that NORMALLY restores a fixed state space, is subjective an evolving. Therefore there is an hiearchy of the transformations, that in the low complexity limit is unification. But there are undecidable elements in this, that is important for understanding the interactions. The undecidability is why a very low-complexity observer (think TOE SCALE) can not distinguisha between the forces. They are just the same.

    In all this, space should ideally be emergent as a way for observer to relate to each other, and assign "distances" to them that relate to the a priori degree of correlation - this is an idea also raise by Ariel caticha, and part of information geometry. That two remote bodies are doesn't have a low degree of correlation because they are far apart, rather it's the low degree of correlation that DEFINES the distance.

    /Fredrik
     
  9. Jul 20, 2010 #8

    Fra

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    Oldman, the mp3 from "On the reality of time and the evolution of laws" Smolin:
    http://pirsa.org/index.php?p=media&...b1c7-70e498081c43.mp3&pirsa=08100049&type=MP3

    The mp3 from "Laws and time in cosmology" Smolin/Unger:
    http://pirsa.org/index.php?p=media&...bbd7-490c1c3adac2.mp3&pirsa=10050053&type=MP3

    The files are some 20-30 Mb I think, so even if you have a modem you can download and listen offline. It's what I've done as well. I typically listen to them on trips. If I remember right they are of the order of an hour or so.

    Both this talks are from perimeter institude and are philsophical and conceptual in nature. They are presenting a point of view to attack the problem of quantum gravity and is thus formally speculative, they are not presenting the full mathematical solution (because there is none yet as it's an open problem). Both the talks raises many question as well. But they provide some good arguments and they are worth listening to.

    /Fredrik
     
  10. Jul 20, 2010 #9

    Chronos

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    Personally, I think entropy is more fundamental than any other force in this universe. I believe most scientists, including einstein, hold this same belief.
     
  11. Jul 20, 2010 #10

    Fra

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    With this, do you mean that you believe there is an objective observer independent measure of missing information?

    /Fredrik
     
  12. Jul 20, 2010 #11
    Thanks for this tip, Fredrik. I'll see if this works for me.

    Just two quibbles, Chronos; but thanks for the comment:

    Quibble 1. Entropy isn't a force.

    But just what it is is not at all clear to me; Could be:

    A measure of missing information? --- maybe, but this is too vague. What happens when a person like Einstein dies quietly? Information that was there is quite suddenly no longer available. Does entropy change? This definition could be messy.

    A measure of the randomness of a situation? Better if one can quantify this easily. Often one can't.

    A measure of unavailable work in a thermodynamic system? Yes, but no quantum stuff here to play with! Too old fashioned?

    A logarithmic count of available microstates? Well, first, identify your microstates please.

    As for the concept of entropic force, like the polymer case used by Verlinde:

    Just because you see something strange happening, like a polymer molecule rolling itself up in a solution, doesn't mean that a force, say like elasticity, is involved. Watch being denied a lottery win when your number doesn't come up out of all those dancing, numbered balls in the draw? Is some malevolent entropic force busy thwarting you?

    Looks to me as if some simple-minded soul has a great opportunity to explain the concept of entropic force more clearly than Verlinde could , or those polymer chemists he's latched on to.

    Perhaps Penrose has it right when he says that entropy is just a convenience. Like all those other convenient concepts we use in physics --- convenient for we chattering African apes to occupy ourselves with, that is!

    But you may well be correct in saying that it is very fundamental.

    Quibble 2: Einstein may have believed this too. But he's dead and its hard to establish whether he still believes this.
     
  13. Jul 21, 2010 #12

    apeiron

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    Check Charley Lineweaver's papers on cosmological entropy...

    http://www.mso.anu.edu.au/~charley/papers/LineweaverChap_6.pdf

    http://www.mso.anu.edu.au/~charley/papers/EganLineweaverApJOnline.pdf

    http://www.mso.anu.edu.au/~charley/papers/LineweaverEgan2008v2.pdf

    And when you say autocatalytic processes, you perhaps mean dissipative structures or entropy degraders?

    http://www.redfish.com/research/SchneiderKay1995_OrderFromDisorder.htm
     
  14. Jul 21, 2010 #13
    This is exactly the sort of stuff I should have been reading. I'll spend some time on these papers. Thanks very much for pointing them out to me, Apieron.

    I mean something a bit more specific than dissipative structures or entropy degraders, which could be simple processes involving say, only friction.

    I meant a process that once active, makes it easier for a repetition of the same process to occur again. An obvious example is the flow of water down an initially smooth but erodable slope. When flow starts there are no flow channels. But once erosion begins, flow is directed into previous paths. A complex but characteristic pattern of flow eventually develops as streams, rivers etc. capture each other and the pattern deepens and evolves source-ward; hence lots of geomorphology. It's a pattern-forming trick in nature's repetoire, as it were, that starts evolving as soon as water flows downhill. Other such 'autocatalytic' tricks, like the inception of DNA and reproductive life, seem to take longer to get going from 'the beginning'. Gravity itself could be thought of as such a trick, active in the early universe when condensed masses begind to stimulate gravitational condensation.

    I'll check the papers you mentioned to see if it is thought that such tricks play any role in stimulating entropy increase. If not, perhaps it's time they were considered. Nature is clever and we're here......
     
  15. Jul 21, 2010 #14

    apeiron

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    There is a ton of jargon in this area because so many people have arrived at the same place from different backgrounds, each creating their own terminology.

    Autocatalytic was Stuart Kauffman I believe. You might also be interested in Bejan's Constructal Theory as the recent fashionable twist - http://en.wikipedia.org/wiki/Constructal_theory
     
  16. Jul 22, 2010 #15

    Chronos

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    Entropy is what prevents everything from happening all at once everywhere in the universe.
     
  17. Jul 22, 2010 #16
    My skill in math is the only thing worse than my spelling but if entropy as defined by Rudolf Clausius
    as
    1 CI = 1 Cal./*C = 4.1868 Joules/Kelvin and a joule may be defined as

    (1kg - m2) / s2 then time and distance are a function entropy.
    So on the surface why not.

    Wikipedia states as follows

    The philosopher Kelley L. Ross argues in "Time Travel Paradoxes" that in an ontological paradox scenario involving a physical object, there can be a violation of the second law of thermodynamics. Ross uses Somewhere in Time as an example where Jane Seymour's character gives Christopher Reeve's character a watch she has owned for many years, and when he travels back in time he gives the same watch to Jane Seymour's character 60 years in the past. As Ross states
    "The watch is an impossible object. It violates the Second Law of Thermodynamics, the Law of Entropy. If time travel makes that watch possible, then time travel itself is impossible. The watch, indeed, must be absolutely identical to itself in the 19th and 20th centuries, since Reeve carries it with him from the future instantaneously into the past and bestows it on Seymour. The watch, however, cannot be identical to itself, since all the years in which it is in the possession of Seymour and then Reeve it will wear in the normal manner. It's [sic] entropy will increase. The watch carried back by Reeve will be more worn that [sic] the watch that would have been acquired by Seymour."
    On the other hand, the second law of thermodynamics is understood by modern physicists to be a statistical law rather than an absolute one, so spontaneous reversals of entropy or failure to increase in entropy are not impossible, just improbable (see for example the fluctuation theorem). In addition, the second law of thermodynamics only states that entropy should increase in systems which are isolated from interactions with the external world, so Igor Novikov (creator of the Novikov self-consistency principle) has argued that in the case of macroscopic objects like the watch whose worldlines form closed loops, the outside world can expend energy to repair wear/entropy that the object acquires over the course of its history, so that it will be back in its original condition when it closes the loop.[69]

    so maybe. I would also believe that the farther back in time the more probable the effect of space time geometry on entropy becomes as the complexity of the system may be reduced.
     
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