On 28-05-2017 04:24, Jason Resch wrote:
On Saturday, May 27, 2017, Russell Standish <li...@hpcoders.com.au>
wrote:
On Thu, May 25, 2017 at 06:30:07PM -0700, Pierz wrote:
Recently I've been studying a lot of history, and I've often
thought about
how, according to special relativity, you can translate time into
space and
vice versa, and therefore how from a different perspective we can
think of
the past as distant in space rather than time: my childhood being
40 light
years away, rather than 40 years for instance. I can visualise my
own body
as a sort of long, four dimensional tendril through spacetime, of
which I
only ever see a three-dimensional cross-section. This is the
block universe
idea of course. What occurred to me recently was that the past,
in any
physical theory I know of, is "locked down". There is only a
single history
consistent with the present (ignoring the microscopic ambiguities
of
quantum interference effects), but the present is consistent with
multiple
futures.
This assumption is wrong. There are many histories (pasts)
consistent
with our present. If we don't know some fact about the past (eg
T. Rex's colour), then pasts with different colours of T.Rexes are
all
compatible with our present. Only when we make a measurement that
distinguishes between different facts about the past, do we
eliminate
some of those pasts from the compatibility list.
There are, however, arrows of time - past and future are
asymmetric,
the future is more uncertain than the past. But I don't see how you
can leverage that into support for the MWI.
I agree, there are multiple pasts compatible with our future. Some if
these can't be ruled out with any possible measurements, like in the
case if the quantum erasure.
That entropy increases does mean there are more futures than pasts.
Jason
Unitary time evolution implies that the number of states cannot change.
Entropy, when defined as the logarithm of the real number of states a
closed system (or the entire universe) can really be in, does not
increase it will always stay the same due to unitary time evolution.
Entropy as used in thermodynamics has to be defined using a coarse
graining procedure, this will then be the logarithm of the number of
microstates that have the same macroscopic properties as the system
under consideration (the coarse graining is then implied by the notions
of "macro" and "micro", as soon as you specify exactly how you draw the
line here).
But note here that saying that there are an X number of microstates
compatible with the macrostate of the glass of water on my table,
doesn't mean that the glass of water can really be in any one of the X
states. If I were to do a free expansion experiment where a gas
containing N molecules in a perfectly isolated cylinder had doubled its
volume, then the entropy increase of N Log(2) does not mean that after
the expansion there are really a factor of 2^N more possible states the
gas can be in.
The unitary time evolution of the original state when the boundary is
removed gives a one to one mapping between the initial and the final
states, therefore after the free expansion the gas can really only be in
exactly the same number of states. But there are then 2^N times more
other states that will have the same macroscopic properties as the real
states the gas really can be in. So, we have a number of fictitious
states of (2^N - 1 ) times the original number of states that we cannot
distinguish from the real states.
Unlike the real states, the fictitious states will most likely not
evolve back to the original volume under time reversal. But this is not
a property that's visible at the macroscopic scale.
One can then ask why entropy is a useful concept is it refers to the
number of fictitious states the system can actually not be in? What do
we make of the "equal prior probability postulate" used in statistical
physics if it is actually not true? The reason is that one is ultimately
doing statistics with the microscopic degrees of freedom, and in
statistics all you need is a representative sample. Taking averages over
a larger set will yield the same answer as computing the average over a
more restrictive set, provided the properties you are interested in are
statistically the same in that larger set. And mathematically it's
easier to compute the former.
Saibal
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