On 22 Oct 2014, at 11:37, Richard Ruquist wrote:
Brent,
That is certainly true for Schrodinger's equations,
but is it also true for matrix theory?
Re: real and complex numbers.
Why would it be different for the matrix. In non relativistic QM, the
position observable in a continuous matrix of complex (and thus couple
of real numbers), same for momentum.
In a quantized space-time, that might be different. But we don't find
good quantization for space-time, I think. Loop gravity seems to be
refuted on this point.
Note also that if Brent is right that QM assume real numbers, it does
not imply that nature (whatever that is) needs them. All what we can
measure are rational numbers. Is there a circle in nature. I think
plausible that circle exists only in the mind of machine in
arithmetic, or they exists as infinite collection of natural numbers
with some relations, etc. Well, it has to like that if we assume
computationalism, and don't eliminate consciousness to save a primary
matter that nobody has seen or even can defined ...
Bruno
Richard
On Wed, Oct 22, 2014 at 1:30 AM, meekerdb <meeke...@verizon.net>
wrote:
On 10/21/2014 8:05 PM, LizR wrote:
On 22 October 2014 08:40, Russell Standish <li...@hpcoders.com.au>
wrote:
On Tue, Oct 21, 2014 at 11:14:14AM -0400, John Clark wrote:
> On Tue, Oct 21, 2014 at 8:45 AM, Bruno Marchal
<marc...@ulb.ac.be> wrote:
> >
> >> So you don't assume the real numbers exist?
> >>
> >
> >
> > Indeed.
> >
>
> Interesting.
>
In Bruno's TOE, real numbers don't exist in the same way as integers,
much in the spirit of Kronecker's famous quote:
http://en.wikipedia.org/wiki/Leopold_Kronecker
Quantum theory would appear to support Kronecker.
Quantum mechanics assumes real and complex numbers.
Brent
Relativity is more concerned with real numbers, not to mention
continua - but I have a feeling that most physicists would bet on
QM as being closer to reality than GR, if pushed.
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