On Tue, Jan 7, 2014 at 11:14 AM, John Clark <johnkcl...@gmail.com> wrote:

> On Mon, Jan 6, 2014 at 2:36 PM, meekerdb <meeke...@verizon.net> 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

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