Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?

From: Ralph Hartley (hartley_at_aic.nrl.navy.mil)
Date: 02/03/05 

Date: Thu, 03 Feb 2005 08:39:08 -0500

examachine@gmail.com wrote:
> I think the evidence for a discrete world far outweighs the evidence
> for a continuous world, which is basically non-existent.

Then why is it that physicists use real numbers and continuous functions
more than anyone else? They *invented* those things! (or discovered, or
whatever...)

> If the world were continuous, then there might be a way to store a real
> number as a physical property. However, all storage devices have to
> rely on fundamental properties in the atomic world which are _all_
> discrete, e.g. quantum physics.

Quantum physics is not as discrete as you seem to think. I have even seen
arguments that quantum theory cannot be correct because it is not discrete.

Consider a single qbit (e.g. the spin of an electron). In a sense, this is
as discrete as any quantum system can ever be. If you use it to store
classical information, its capacity is just one bit.

However, its behavior cannot be perfectly reproduced by a discrete system
of *any* finite size. It can be approximated to arbitrary precision, but so
can a continuous system. To even *approximate* a collection of interacting
spins seems to require a discrete system that grows exponentially as the
number of spins increases.

Also, fully discrete approximations to quantum phenomena are very contrived
and complicated - they are not good as physical theories.

Quantum physics requires a continuum, even though it may be discrete in the
sense of not allowing a real number to be stored exactly (I don't know for
sure if it does or not).

> Why
> would I believe that something exists beneath the Planck scale, while
> our physics tells us that you cannot physically subdivide the Planck
> scale. There is no such thing, as far as I can tell, as to measure time
> or space in fractions of the Planck scale.

I have never heard such a thing from an actual physicist (from science
journalists yes), and I follow work on quantum gravity. I know that there
is *no* consistent physical theory with an indivisible unit of space or
time. There are discrete theories of gravity (none good enough to test),
but they are not discrete in *that* way.

> The only "evidence" for a continuous world is classical and
> relativistic physics cast in the language of geometry which makes use
> of real-valued numbers, that is they are no evidence. (How can a
> "theoretical assumption" be an evidence?) If we take particle physics
> seriously, which we should, we cannot say that they are equal ways of
> describing the world.

So we should take quantum theory, but not general relativity, seriously? I
certainly take them *both* seriously!

> but the wave function is
> continuous right? Right. Does the wave function exist? I don't think
> so. It is merely another theoretical instrument.

But the discrete features of quantum theory are just "theoretical
instruments" too. If you accept quantum theory, as anyone who is serious
about physics must, you have to accept it all. There are alternate
formulations of quantum mechanics that have no "wave function", but they
all contain *some* continuous parts.

There are also alternate "interpretations" of quantum theory (just as there
are alternate interpretations of probability theory). They are irrelevant
to the question at hand.

Ralph Hartley

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