On Tue, Jan 7, 2014 at 11:00 AM, Jesse Mazer <[email protected]> wrote:
> > > 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, That is interesting. Is it the same idea that David Layzer uses here http://www.informationphilosopher.com/problems/arrow_of_time/ to use the expansion of the universe to explain the increasing room for explaining how the room for possible entropy grows faster than energy and matter equilibration? Jason -- 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.
