-------- Original Message --------
Replies to Stan Kelly-Bootle and James Studdard intercalated
below, for those interested in carping about physics.
--- On Fri, 8/1/08, Stan Kelly-Bootle <skb@BOOTLE.BIZ> wrote:
[Skipping points I agree with about knowledge and "reality"
and about not insisting that words mean the same thing at
all "times".)
SKB: > (Entropy is a measurable statistical value that NEVER
> decreases in a closed system
JF: Well... hardly ever.
JF: I appreciate your caveat below, but I think this point
is crucial. The Second Law of Thermodynamics is
almost tautological: it's more probable that less probable
states will evolve /in time/ into more probable states
than the other way around. But this is hard to separate
from a definition of time and causality.
JF: On the macroscopic level, of course, there's no problem.
We can identify when a film is run backwards because we
can tell, without calculation, when the Second Law is
being violated.
SKB: > and therefore gives an _objective_ non-cultural
> > meaning to the PASSING ONE-WAY flow of (thermodynamic)
> time.
JF: But things get a little more problematic when we look at
finer detail, and entropy may seem less objective when
we recall that it's defined in terms of macroscopically
indistinguishable states and we start thinking about the
instruments that let us see microscopic "reality".
SKB: > I'll test you on
> > this, so pay attention.) On a technical point: even
> when t is a physically
> > discrete variable, it can often be usefully treated as
> continuous, as, say,
> > when we differentiate ds/dt to get velocity. Recall
> the Planck time is so
> > terribly small that in many equations it might as well
> be infinitesimal.
> > Nevertheless, JA, I can assure that when your car
> comes to rest from 30mph, IT
> > DOES NOT PASS THROUGH EVERY SPEED FROM 30 TO ZERO mph.
> It slows down in tiny discontinuous increments.
JF: You mention the Uncertainty Principle below. If you
start thinking about looking at the elementary particles
in a car on scales of the Planck time and far smaller
lengths (30 mph times the Planck time), you'll see that
the uncertainty in speed is enormously greater than those
tiny increments you're talking about. I can't see any
picture of the speed ratcheting down discontinuously.
JF: Heck, at that scale you'd have a very hard time defining
what's part of the car and what's a passing co(s)mic ray.
SKB: > > This fact may not alter your world-view or driving
> > habits (why should it?), but it's as TRUE as er er
> ... VN remaining my favourite novelist.
JF: Maybe an excellent analogy. It would be quite
reasonable for you to become less certain of who your
favorite novelist is the more you try to pin it down.
JF: (Skip summary that I don't want to quibble with.)
SKB: > > Caveat: this email would require more precision were I
> writing for MAA or ACM.
--- On Fri, 8/1/08, james studdard <studlaw2000@YAHOO.COM> wrote:
> Planck time is the time that it would take a photon
> travelling at light speed, in a vacuum, to cross a distance
> of Planck's length. Since this would represent crossing
> the shortest possible distance at the fastest possible
> speed, this gives us the smallest meaningful unit of time.
JF: I don't see why you assume this (and if SKB is assuming the
same thing, I don't see why he does either). The Planck mass
is certainly not the smallest possible mass.
JF: My understanding is that at the scale of the Planck length
and time, energy fluctuations have the scale of the Planck
mass that the current tentative theories of quantum gravity
suggest that spacetime (there it is again!) looks radically
different from our picture of it, maybe multiply connected
or "foamy". But I don't see such pictures as saying that
these are the shortest possible lengths and times. Indeed
this unimaginably complicated picture seems incompatible
with simple time-steps--as is relativity, since the shortest
length to one observer looks even shorter to another.
Jerry Friedman