From: Hal Finney (hal@finney.org)
Date: Wed Mar 27 2002 - 17:29:50 MST
Scerir writes:
> [Anton Zeilinger]
> > > That is to say, information is quantized.
>
> [Hal]
> > Actually, information is not quantized.
>
> Zeilinger was speaking about the 'physics'
> of information, I suppose, and not about
> information, or knowledge.
Maybe so. But he seemed to be saying, the universe is quantized, which
is a mystery; and we know that information is quantized, because it
comes in discrete bits; therefore we might look at information for an
explanation of why the universe is quantized.
This begs the question of whether information is really quantized
and discrete. Perhaps you can create a physical form of information
where this is so, but I don't think it would be the same as our usual
definition of information. In cryptography, which is closely related
to information theory, we deal in fractional bits all the time.
If you have to introduce some new "physical" kind of information then
chances are it is going to be based on quantum theory rather than
vice versa. So far nobody can give me a handful of raw bits.
> A spin 1/2 system has an information capacity =
> 1 bit. But a spin 1/2 system has an infinite
> number os states (see the 'Poincarč sphere').
> Hence an infinite amount of information could,
> in principle, be coded in a spin 1/2 system!
Not really. If you start with a system that has a large amount
of information and then try, through reversible quantum-mechanical
transformations, to transfer the information into the state of a spin
1/2 system, you will fail. You will not be able to reversibly pack
all the information into the spin 1/2 molecule, erasing it from your
original system. Because, of course, if you could, you could reverse
the process and unpack all that data from the spin 1/2 back into your
original, which as you note is impossible.
I agree that it is paradoxical that a system can have an infinite number
of possible states, each distinct at least in theory, and yet it can hold
only one bit of information. I don't have a good explanation of this,
other than that maybe you could say that the number of bits per internal
state is infinitisimal. I don't know if that really works, but it
suggests another place where fractional bits come into play.
Hal
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