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. Cheers -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au Latest project: The Amoeba's Secret (http://www.hpcoders.com.au/AmoebasSecret.html) ---------------------------------------------------------------------------- -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
