On Tue, Jan 7, 2014 at 11:14 AM, John Clark <[email protected]> wrote:
> On Mon, Jan 6, 2014 at 2:36 PM, meekerdb <[email protected]> wrote: > > > he assumed this time asymmetry was fundamental, not a mere statistical >> effect related to the low entropy of the initial conditions of the >> experiment. >> > > A mere statistical effect?? I would argue that the second law of > thermodynamics is much more fundamental than the first. The first law, the > idea that matter and energy can not be created or destroyed is not a > logical necessity it's merely a empirical observation, up to now we've just > never seen that law violated and we use induction to conclude that we never > will. Induction is a very good rule of thumb but it you wait long enough it > can sometimes lead you astray. I don't expect it to happen but I can at > least conceive of the idea that someday we will find a circumstance where > the first law is untrue. > > But the second law is not like that, conceiving of a world where entropy > doesn't increase with time is like imagining what the world would be like > if 2+2=5. The second law is not based on observation but on pure logic and > the fact that there are just more ways to be disorganized than organized. > Science always changes but if I had to pick one thing that would still be > valid in a thousand or even a million years it would be the second law. > Are you disputing the "statistical effect" part, or the "mere" part? Because while it's true that the second law can be derived theoretically from some fairly broad assumptions, this derivation is itself a statistical one which assigns a nonzero probability to spontaneous decreases in entropy. Also, I think it's going too far to say that imagining a world where entropy doesn't increase is like imagining a world where 2+2=5, since you do need *some* assumptions about the laws of physics to derive the second law. For example, in a world where volume in phase space wasn't conserved by the dynamics (Liouville's theorem in classical statistical mechanics), so a collection of initial states occupying a large region of phase space could all converge on a smaller number of later states occupying a smaller region of phase space (meaning that information can be lost, since multiple initial states can lead to the same later state leaving you with no way to determine what the initial state was), you could well have consistent decreases in entropy with time. Even with the laws of physics we know, if you don't assume the universe *starts* in a state of low entropy, then the 2nd law should actually be time-symmetric, given that the fundamental laws of physics themselves are time-symmetric (or CPT-symmetric in quantum field theory). With time-symmetric laws, if you are given the state of an isolated system at some time t, the laws which allow you to predict the future state later than t can just as easily be used to "retrodict" the past state at times earlier than t. So if you at some time t you find a system in a macrostate of lower-than-maximum entropy, and you retrodict its past in this way, exactly the same statistical reasoning tells you its entropy is far more likely to have been higher in the past of t, rather than lower as we might intuitively expect. This may seem strange, but to see why it makes physical sense, imagine you have an isolated system (a box of gas, say) that is known to have reached maximum entropy at some time in the past. Then if you choose a random time to observe it and find the entropy to be lower-than-maximum, it actually is most likely that you are looking at the local minima of a random entropy-decreasing statistical fluctuation, which means that entropy should be symmetrical higher both shortly before and shortly after the observation time. So, to explain the asymmetry between past and future--the "arrow of time"--the 2nd law alone won't do it. You need to either assume low-entropy conditions at the Big Bang (which might themselves have some explanation in an "eternal inflation" theory, see for example Sean Carroll's theory which he summarizes in a blog post at http://preposterousuniverse.blogspot.com/2004/10/arrow-of-time.html and also in the paper linked to there, and further in his book "From Eternity to Here"), or some basic time-asymmetry in the fundamental laws of physics, although I get the sense that the second is not a very popular approach to explaining the arrow of time among physicists (and it's not really clear to me what the connection would be between time-asymmetry in some new theory like quantum gravity, and the failure of the 2nd law to apply in reverse). Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
