It's been known since the 1970s that arbitrarily efficient computers
could be constructed that could perform an infinite number of
computations with a finite amount of energy, but only if the
computations done on that computer are logically reversible.
Performing a non-reversible computation results in an increase in
entropy for the system and thus would not be sustainable. (see
The physical interactions that occur in this universe are also
reversible. e.g. An electron can accept a photon and move to a higher
energy state or an electron can emit a photon and move to a lower
energy state. Does reversible physics imply that a computational model
of said physcis would involve entirely reversible computations? I
believe that if past states of the universe could be calculated from
future ones, then those computations would have to be reversible.
I don't think the calculation has to be reversible in order to be the
calculation of a reversible phenomena. We use irreversible computations all
the time to calculate simple Newtonian processes which are certainly reversible.
Assuming the above is true, it would have consequences for any
civilization in a universe like this one (with finite energy); it would
mean that said civilizations could only simulate universes using purely
reversible computations without exhausting the finite amount of useful
energy in their universe.
They could simulate a smaller or simpler universe, which is what, for example,
a computer game does. The irreversible computation just dumps entropy into the
universe which is far below it's maximum entropy (thanks to inflation). This
of course depends on a a coarse-grained view of entropy. At the microscopic
level, if we could keep track of all the quantum entanglement we'd presumably
see that the fine-grained entropy doesn't increase.
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