On Thu, Feb 26, 2015 at 04:44:25PM +1100, Bruce Kellett wrote: > Russell Standish wrote: > >On Thu, Feb 26, 2015 at 09:31:53AM +1100, Bruce Kellett wrote: > >>An eigenfunction in one basis is a superposition (potentially an > >>infinite superposition) in any other basis. Why do we not see > >>superpositions of positions? > >> > >>Bruce > > > >But we do! Whenever the two slit experiment is performed, for example, > >or perform a momentum measurement of a photon. > > > You seem to have missed the point I was making. The measurement in > the two slit experiment is the spot on the screen where the particle > lands. The slits themselves are not measurement devices. So the > eigenfunctions of the position measurement are (ignoring HUP > limitations for the moment) delta functions along the position > direction. But this is only one possible basis of the Hilbert space > for the position operator. We could take any arbitrary rotation in > this Hilbert space to form another, equally good, basis. In that new > basis our observed delta function would be a superposition. If that > new basis were preferred, our observed outcome would be a > superposition. But we observe position outcomes only as eigenvalues > and eigenfunctions in one particular basis. Why is that? What > selects that basis in the position Hilbert space? > > Bruce >
Your basis is not the position operator of the particle (which slit it went through in the 2slit experiment, or of the photon), but the basis of the measuring apparatus, which as classically conceived, is probably some sort of position basis (eg the needle of an analogue meter). Does a measuring apparatus always have to be eigenvalue of some position operator, though? What about variants of the experiment that record the results of the measurement as bits in a computer memory. Surely that would be in a basis that is eigenvalue of the charge of the memory cell transistor, not a position operator at all? Cheers -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics [email protected] 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 [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.
