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FQXi FORUM
CATEGORY: Essay Contest
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TOPIC: Whither Time's Arrow? by Gavin E Crooks
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The voting deadline has been extended to January 1, 2009.
Please vote for your favorite essays soon!
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Essay Abstract
In our everyday lives we have the sense that time flows inexorably from the past into the future; that time has a definite direction; and that the arrow of time points towards a future of greater entropy and disorder. But in the microscopic world of atoms and molecules the direction of time is indeterminate and ambiguous.
Author Bio
Gavin Crooks is divisional fellow in Physical Biosciences at Lawrence Berkeley National Laboratory. He obtained his Ph.D. from the University of California, Berkeley. His current research interests include the thermodynamics of molecular machines and solar energy capture. http://threeplusone.com
Download Essay PDF File
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Hello Gavin!
Thanks for the essay!
Consider a Hydrogen atom that emits a photon. The photon propagates as a spherically-symmetric wavefront of probability expanding at c, never to return (or not very likely). This seems to define an arrow of time at the atomic level, for radiation exists at the atomic level, and thus the radiative arrow of time manifests itself at the atomic level.
Best & thanks,
Dr. E (The Real McCoy)
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Huw Price discusses this issue in his great book "Time's Arrow and Archimedes' Point", chapter 3. The radiative arrow is due to time-asymmetric boundary conditions, and ultimately reduces to the thermodynamic arrow.
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Dear Dr. Crooks,
May I try to answer the question in the title of your essay.
In your essay "Whither Time's Arrow?", you wrote: "Neither Newtonian mechanics, special or general relativity, quantum mechanics, nor quantum field theory picks a preferred direction in time, anymore than these theories picks out a preferred direction in space."
The apparent "expansion" of space due to the so-called 'dark energy from empty space' (L. Krauss, reference available upon request) does not pick up any preferred direction in space either, simply because this "direction" is omnipresent -- there is no direction in which space does NOT expand. The latter is ultimately needed as a reference direction w.r.t.w. we could discover another, preferred direction of space expansion.
Notice that such task is banned in GR by default, because it would require that GR determines the evolution of the lapse function and shift vector, along the "arrow" of the spacetime foliation. But as the lapse and the shift are gauge functions, any convertion into some Dirac observables would inevitably expose an *observable* absolute reference frame, and the ether will come back.
Hence many people at this Forum claim that we should "forget" time, but somehow avoid the driving force of the cosmological time arrow, and also the drastic contradiction between the predictions of their theories and all astronomical evidence of the cosmological time. As Thomas Thiemann acknowledged in astro-ph/0607380 v1:
"Why is it that the FRW equations describe the physical time evolution which is actually observed for instance through red shift experiments, of physical, that is observable, quantities such as the scale parameter?
"The puzzle here is that these observed quantities are mathematically described by functions on the phase space which do not Poisson commute with the constraints! Hence they are not gauge invariant and therefore should not be observable in obvious contradiction to reality."
In shorth, to answer the question posed in the title of your essay, the direction of time arrow is the one in which the amount of dynamic dark energy (DDE) is increasing -- the more time elapses along the cosmological time arrow, the more DDE we wind up with.
I tried to explain this paradoxical situation to my teenage daughter as follows: Suppose you accelerate a car, but the fuel gauge shows that you're actually gaining more fuel by accelerating the car. That's the ultimate 'free lunch' provided by DDE, only physicists cannot explain it.
A penny for your thoughts! It may be worth of billions, since we're talking about the cleanest and truly unlimited energy source.
Regards,
Dimi Chakalov
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Dimi Chakalov:
The issues you raise have to do with the cosmological origin of the arrow of time. On the other hand, the central topic of the essay is the other end of the scale, small systems and short times, where the ambiguity in time's arrow has quantitative consequences for modern, non-equilibrium thermodynamics. For molecular scale systems the origin of the large scale time-asymmetry of the universe is immaterial, although the consequences of time-asymmetry are vast.
GEC
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Gavin:
The issues I raised are indeed related to the cosmological origin of the arrow of time. Bottom line here is the quantum vacuum as the prime candidate for Einstein's cosmological constant proposal from February 1917. Hence "the other end of the scale", as you put it, is automatically involved.
I wonder how you would comment on my answer to the question posed in the title of your essay.
Dimi
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Dear Dr. Crooks,
In your essay, you explain very well the arrow of time. The arguments and the experiments presented show that the time’s arrow is local, depends on scale, and its “length” can be almost zero or negative, being thus neither fundamental nor absolute. Congratulations for the well-written essay.
Best regards,
Cristi Stoica
Flowing with a Frozen River
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Dear Dr. Gavin Crooks,
Thermodynamic entropy can never decrease. It is impossible for the exchange of energy it describes to reverse its direction. The definition of thermodynamic entropy is precise. It is defined under ideal conditions. It does not include any system for which any part can vary from its average temperature. We very closely approximate it by restricting the analysis to infinitesimal changes. The fact that these conditions cannot exist in the real world does not allow for loosening its definition. If it is given a notation for averaging, then it is not thermodynamic entropy. The new process may look similar, but it has become something different, something else. Thermodynamic entropy does not refer to a general process of achieving thermal equilibrium. Thermal equilibrium will eventually be achieved for other closed systems. Intervening conditions of disequilibrium do not affect the ultimate outcome. Yet, the kind of process they undergo is not the kind of process defined by thermodynamic entropy. Yes, in a system that is not in equilibrium, energy can flow in various directions at various points within the system. However, that kind of system is not telling us what thermodynamic entropy is telling us. It cannot tell us, location by location or instant by instant, about the direction of time. Thermodynamic entropy does tell us that its process, including our approximation of it using infinitesimals, moves forward as time moves forward.
Respectfully,
James Putnam
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Dear James Putnam,
Respectfully, in the microscopic realm entropy can both increase and decrease. This makes sense theoretically and has been observed experimentally. If you are used to thinking about entropy in terms of macroscopic thermodynamics, it takes some time to get used to the idea that entropy is statistical, fluctuates, and is not a property of equilibrium systems alone.
Gavin Crooks
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Dear Cristi Stoica,
You may also be interested in my recent PRL paper with Ed Feng, "Length of time's arrow". The FQXi essay attempts to give a basic introduction to relevant results in non-equilibrium, small system thermodynamics, but inevitable glosses over many details of the theory. The paper goes into much more depth.
http://threeplusone.com/pubs/fulltext/Feng2008a.pdf
Gavin Crooks
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Gavin:
I think "hypotheses non fingo" can hardly be justified, since your essay would then cover (at best) only 4 per cent from the stuff in the universe. As to the "cosmological questions", every time you contemplate about entropy in the microscopic realm, you are -- willingly or not -- implying the nature of time and its driving force. It's a package.
Have a nice white Christmas.
Dimi
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