On 23 October 2014 13:35, Russell Standish <[email protected]> wrote:
> On Wed, Oct 22, 2014 at 05:23:38PM +0200, Bruno Marchal wrote: > > > > 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 ... > > > > To reiterate on Bruno's point, observables corresponding to x or d/dx > do not exist in reality. Every measurement made is done to some finite > precision - the number of digits of a numerical readout, or the needle of > an analogue meter lying between one graduation and the next. > > Consequently, the actual observables have eigenvalues and eigenvectors > drawn from the rational complex numbers. Reals do not exist except as > an approximation that is convenient for doing calculations. And even then, > countable models of the reals' axioms exist, by virtue of the > Löwenheim–Skolem theorem. These countable models exist in Bruno's > ontology, and suffice for any practical purpose QM is put to. > > Um, does that mean you agree with me? :-) -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
