I had always thought of this as sort of a pseudo-problem. After all, I would think, why shouldn't the dynamical laws be symmetric wrt time-reversal. As John Baez stated in a review of H. D. Zeh's The Physical Basis of the Direction of Time (which I haven't read) http://math.ucr.edu/home/baez/time/time.html: "Our world is evidently in a state that is not even approximately invariant under time reversal; there are many processes going on whose time-reversed versions never seem to happen. But this is logically independent from the question of whether the dynamical laws of physics admit time reversal symmetry." Which seemed to reinforce my notion that the time reversal asymmetry of the world isn't necessarily in conflict with the time reversal symmetry of dynamical laws. But at the end of the review he states: "The main remaining mystery, then, is why the state of the universe is grossly asymmetric under time reversal, even though the dynamical laws of physics are almost - but not quite! - symmetric." Did I miss something in Baez' review. If the time reversal asymmetry of the world and the time reversal symmetry of the dynamical laws are logically independent, then what exactly is the problem? Is it that physics doesn't offer an underlying general dynamic for the apparently pervasive time reversal asymmetry of the physical universe? Or is it more complicated than that? Thanks in advance for any comments.
I might have found the answer I was looking for here: http://en.wikipedia.org/wiki/Loschmidt's_paradox Any comments are welcomed.
Even ignoring the fact that there are time asymmetric laws of physics the point is that the laws of physics do not alone determine the evolution of a system. You also must also specify the boundary conditions. Even time symmetric laws will demonstrate asymmetric evolution from an extremely asymmetric boundary condition (like the Big Bang). Also, I think it is fundamentally wrong to ignore the asymmetric laws as is so often done in such discussions, i.e. Baez' description as "one small exception". It is asymmetric and it is a law of physics, the classification as "big" or "small" is purely aestetic.
Thanks DaleSpam. Another aspect of this pseudo-problem that I've seen is the question of why we don't see advanced waves. Also, I'm not comfortable with statements (vis statistical thermodynamics) that it's just very very unlikely, but not impossible, for (say) broken cups to reassemble themselves, or fried eggs to unfry themselves, etc. It would be nice if there was some sort of fundamental physical dynamic that made these 'possible' events, which are so improbable that they'll never happen, actually impossible. Do you forsee the formulation of any such fundamental physical law? Do you think that that is even possible?
I have always wondered about that. If we jiggle a charge we get a retarded wave moving outward in the characteristic dipole fashion. If we have a dipole wave moving inward towards a charge won't it jiggle and isn't that what an advanced wave is? I am pretty sure this means that the asymmetry of advanced and retarded waves is also just due to boundary conditions.
I was thinking of an advanced wave as a wavefront that contracts toward its source rather than expanding away from it -- like a circular disturbance suddenly appearing on the surface of a smooth pool of water and then contracting to a rock that suddenly appears and then rises from the water. We never see that. And it's not explained by the boundary conditions. It's not explained by the 2nd law of thermodynamics either, because it's not a dynamical law. Is there a fundamental dynamic regarding the evolution of our universe that makes it impossible for advanced waves to happen?
I was thinking a little more about this topic today. The second law of thermo is clearly time asymmetric, so we don't expect time symmetry in any process where it is involved. However, the 2nd law of thermo is often attributed purely to the boundary conditions (as I have done) and essentially relegated to a statistical rule-of-thumb on the micro-state of a system. However, is it possible that, due to the statistical nature of quantum particles the microstate itself is statistical and cannot be defined to arbitrary precision even in principle? That could potentially refute the usual "if you reverse the initial velocity of every particle you would get the broken cup repairing itself" and establish the 2nd law of thermo as more than just a rule-of-thumb. I cannot assert the validity of this argument as I lack the QM background. Take it for what it is, very rough and unsubstantiated preliminary musings.
You asked if I was sure about boundary conditions not being an explanation. Well ... no, I'm not. (I've been spending as much time as possible researching stuff I should already have learned.) I was thinking of boundary conditions as being more or less arbitrary constraints. Anyway, I'm not sure about anything (being somewhat semantically challenged when it comes to physics) -- that's why I ask questions here, and appreciate it when I get replies. Yes, the 2nd LoT says that systems will evolve from states of lower to higher entropy, or, using phase space modelling, from states of lower to higher probability, toward equilibrium (the most probable state). But this is just kinematics. There's no underlying dynamic, or deeper kinematics, that can be said to necessitate that behavior, afaik. So, it's possible, however remotely, that a highly improbable evolution, such as an expanding surface wave spontaneously contracting, can happen. Nevertheless, the normal practice is to act as if certain evolutions really are impossible, not just highly improbable, because all observations suggest that that's the most reasonable belief. So, why not assume that the arrow of time, wrt any behavioral scale, is an unalterable and necessary fact of nature? Then the question is, what's the underlying dynamic that makes it so? Can the cosmological arrow of time be used? Which is deeper, the large scale or the quantum scale behavior of the universe? In principle wrt what? In principle wrt the principles of any theory constrained by the randomness of individual experimental results (and therefor necessarily statistical). It would, except that the terms random and statistical don't apply to microstates but rather to the accumulation of the data that's used to support (or falsify)inferences regarding them. I thought that's what I was doing. Welcome to the party! Any further thoughts (or corrections to anything that I myself have mused) you might have on this or related topics -- please post them.