----- Original Message ----- 
From: "Wei Dai" <[EMAIL PROTECTED]>
To: <everything-list@googlegroups.com>
Sent: Tuesday, April 11, 2006 01:46 AM
Subject: Re: why can't we erase information?

> Saibal Mitra wrote:
> > How would an observer know he is living in a universe in which
> > is lost? Information loss means that time evolution can map two
> > initial states to the same final state. The observer in the final state
> > thus
> > cannot know that information really has been lost.
> If the universe allows two different states to evolve into the same final
> state, the second law of thermodynamics wouldn't hold, and we would be
> to (in principle) contruct perpetual motion machines.
> I don't know why you say this can't be detected by an observer. In theory
> all we have to do is prepare two systems in two different states, and then
> observe that they have evolved into the same final state. Of course in
> practice the problem is "which two different states?" And as I suggest
> earlier, it may be that for anthropic reasons one or both of these states
> very difficult to access.

Yes, in principle you could observe such a thing. But it may be that generic
models exhibiting information loss look like model that don't have
information loss to internal observers. 't Hooft's deterministic models are
an example of this.

I'm also skeptical about observers being able to make more efficient
machines. The problem with that, as I see it (I haven't read Lloyd's book
yet) is as follows.

Consider first a model without information loss, like our own universe. What
is preventing us from converting heat into work with 100% efficiency is lack
of information. If we had access to all the information that is present then
you could make an effective Maxwell's Daemon.

Lacking such information, Maxwell's Deamon has to make measurements, which
it has to act on. But eventually it has to clear it's memory, and that makes
it ineffective.

To get rid of this problem Maxwell's Daemon would have to be able to reset
its memory without changing the state of the rest of the universe. This
could possibly be done in an universe with information loss, but that could
only work if the Daemon has control over the information loss process. If
information loss interferes with the actions of the Daemon, then it isn't
much use.

You could also think of the possiblity of some ''physical process'' which
would be sort of a ''passive Maxwell's Deamon'' that could reduce the
entropy in such universe. Using that you could create a temperature
difference between two objects. To extract work you now need to let heat
flow between the two objects. So, at that stage you need an entropy to
increase again.

So, to me this doesn't seem to be a generic world in which you have
information loss, rather a world in which it is preserved but where it can
be overruled at will. The benefits come from that magical power.


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