Re: use of real numbers in mathematics and physics

From: Ed Fredkin (edfredkin_at_yahoo.com)
Date: 10/12/04 

Date: Tue, 12 Oct 2004 15:49:37 +0000 (UTC)

"robert j. kolker" <nowhere@nowhere.net> wrote in message news:<2svm8gF1lo6eoU1@uni-berlin.de>...
> Tobias Fritz wrote:
> >
> > 2) Do you think that the real numbers are the appropriate system for
> > formulating a unified physical theory? What about quantization of
> > spacetime?
> >
>
> My guess is that a purely discrete theory to describe physical reality
> will be mathematically intractable. We have a dillema. The mathematics
> we can use, cannot be literally true of reality. The mathematics that
> can be literally true of reality we cannot use because of its difficulty.
>
> Go figure.
>
> Bob Kolker

We don't have to have a dilemma. Both physics and mathematics reveal
the fact that the world of integers and continuity can coexist.
Differential equations work very well modeling discrete phenomena:
nuclear reactors, fluids, electric charge and currents all involve
discrete quantities yet differential equations work just as well as
would be the case if the atomic theory was false.

There are totally discrete space-time-state systems, such as Cellular
Automata on a Cartesian lattice, whose gross behavior is well modeled
by differential equations. Further, it is possible to design such
systems so that the representations of many physical quantities, such
as momentum, spin or charge are conserved exactly. Noether's theorem
states that for every such conserved quantity there is a corresponding
continuous symmetry. In the case of a CA model, we must assume that
there is an apparent continuous symmetry that occurs as one looks at
scales far enough above the scale of the lattice.

One advantage of up from the bottom totally discrete models of
physical systems (if we can find one) is that what occurs at the
bottom would be easy to understand exactly! Further, it would be
possible to derive analytically the differential equations we know and
love. Today, in many areas where we have math that works, it is
accompanied by a total lack of understanding as to what is actually
going on at the bottom. QM is the best example, the math works but no
one knows why and no one understands what is actually going on.

Some may be satisfied to have the math and nothing more, but I side
with Hilbert, "Wir müssen wissen, wir werden wissen." We must know,
we will know!

Ed F

Relevant Pages

  • Re: use of real numbers in mathematics and physics
    ... >> mathematics we can use, cannot be literally true of reality. ... towards the infinitely small set by quantum physics when he in 1925 ... there is no reason at all to replace the continuum by means of discrete ...
    (sci.physics.research)
  • Re: Neural netss (was Re: death of the mind.)
    ... > All that I am trying to say is, the brain is analog, but discrete, as ... The question is, for brain studies, do you need to go all the way to ... > b) some bio molecules have macro-scale quantum effects as Penrose ... physics, ...
    (sci.cognitive)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... |> your statement "there can be no such thing as continuum in the ... world is discrete. ... | discrete, e.g. quantum physics. ... A lot of the arguments that are put forth in favor of nature ...
    (comp.theory)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... |> your statement "there can be no such thing as continuum in the ... world is discrete. ... | discrete, e.g. quantum physics. ... A lot of the arguments that are put forth in favor of nature ...
    (sci.math)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... |> your statement "there can be no such thing as continuum in the ... world is discrete. ... | discrete, e.g. quantum physics. ... A lot of the arguments that are put forth in favor of nature ...
    (sci.logic)