I've been thinking on a problem. Namely, after the heat death has
occurred, can any state of the universe _possibly_ happen? And if the
universe survives eternally after the heat death has occurred, _will_
every state of the universe exist, as a statistical fluctuation? For
instance, after the heath death, will a shoe by chance appear and then
disappear?
I've been thinking along the following lines. Assume that the heat death
can be defined as when all potentials are levelled. (Is this a good
definition?) Then after the heat death the path of the universe in the
space of all configurations of the universe has no direction: The
universe is performing a random walk in the configuration space. (Is
this correct?)
Now, we know thing about random walks. For instance, we know about when
a random walk is recurrent and when it is not. If the random walk of the
universe (walking in the configuration space) is recurrent, then at some
point a shoe _will_ (probably) appear, assuming the universe exists
forever. (Am I right?)
A random walk is recurrent only in one and two dimensions and the space
of all configurations of the universe have tremendously many dimensions,
witch indicate that it is not recurrent at all. But this assumes that
the configuration space is infinite in more than two dimensions. But is
it? If every particle, quanta or whatever can have only a finite amount
of quantum states, locations in space, locations in time, etc, what happens?
Is this apperoach a good one? Is this problem solved already? Has anyone
argued along these lines before, in the same or a nearby problem?
(Please give me a pointer to such a work!)
Regards / Daniel Janzon, Sweden
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