If you do that, the capacity of the memory store would only grow as the
log of the volume. Is it possible to do better, or is there an upper bound
of M*log V on the entropy of an isolated system? (Well that is clearly not
true since a black hole has entropy proportional to M*V^(1/3), but perhaps
the bound holds when M is small compared to V?)
Another problem is once you've stored information as the position of a
particle, how do you then retrieve it?
> In The Physics of Immortality, Frank Tipler argues that open universes
> impose limits on calculation. Unfortunately his argument is not technical.
> Here is what he says, on page 139 (chapter 3, section "Experimental Tests
> of the Omega Point Theory"):
> "As I discussed in Chapter III, Freeman Dyson pointed out that, although
> the energy is available in open and flat universes, the information
> processing must be carried out over larger and larger proper volumes.
> This fact ultimately makes impossible any communication between opposite
> sides of the 'living' region in a flat universe, because the redshift
> implies that arbitrarily large amounts of energy must be used to signal,
> and Dyson showed that only a finite amount of energy is availble.
> On the other hand, open universes expand so fast in the far future that
> it becomes impossible for structures to form of sufficiently larger and
> larger size to store a diverging amount of information."
I don't understand why it would be impossible to form larger and larger
structures. I imagine that a structure would be gravationally bound and
contain a reserve of free energy to expand as needed.
> He may be saying that at some point there won't be enough energy in
> the whole universe to create a single photon of enough energy to signal
> from one side of the computer to the other. Apparently there is only a
> finite amount of energy in the (accessible?) universe. But I'm not sure
> that there is a threshold energy which would be necessary to create the
> signalling photon; perhaps photons can have arbitrarily small energies,
> as long as they are hotter than the background.
If your computer is reversible, you shouldn't have to use up any energy
for computation, so this situation shouldn't come up.