tag:blogger.com,1999:blog-7897235423812277683.post6948457139256980242..comments2022-05-03T15:16:51.392+01:00Comments on Ramblings of a Short Fat Failed Physicist: Mathematics of two state systems 2: QuantumChris Fhttp://www.blogger.com/profile/03530660309554429226noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-7897235423812277683.post-24348799446462754182012-03-01T22:48:03.838+00:002012-03-01T22:48:03.838+00:00Hi and thank you for your reply however I would di...Hi and thank you for your reply however I would dispute a number of points, First I disagree with tour contention that you have never known a mathematician as opposed to a say a physicist with confusing a model with reality. Take two prominent examples Roger Penrose who I would call a mathematician and not a physicisit is definitely guilty of this. Also G H Hardy was an unashamed Platonist who thought that he was discovering some aspect of reality every time he proved a theorem of number theory or analysis. <br /><br />In contrast your 'average bog standard (of which I count myself' physicist who is quiietly calculating the energy levels or a solid or new molecule or even the scattering cross section of a new reaction involving exotic particles is prepared to see the framework with which they calculate the results that they use to make concrete predictions which they can go and correlate with measurement as no more than a useful device to achieve concrete predictions as observed in the lab and nothing more or nothing less. To quote Helmholtz Maxwell's theory is Maxwell's equations' nothing more nothing less. <br /><br />It seems to me we are in a similar situation vis a vis the interpretation of quantum mechanics. One can go down the route of saying the wave function represents something real and physical in which case you end up with all the alleged paradoxes namely the belief that a new universe really is created every time a meausurement is made. Cats really are in limbo between being alive or dead until someone opens a box. Particles really do split in two when passing through slits and then magically recombine when observed. (So why do we need CERN if that really happens and so forth). <br />On the other hand seeing the wave function as the complex square root of a probability distrubition function does <br /><br />a) Explain all the predictive power of quantum mechanics<br /><br />b) Cuts through all the balderdash associated with seeing the 'wave' function as a real field in either 3N+1 dimensions or many universes <br /><br />c) Provides the minimal extension to our 'common sense notion' of how we interact with reality sufficient to account for the empirical facts that quantum physics would seem to dictate.<br /><br /><br />As to your point about the physics being buried in the phase factor that is true to some extent but in situations whereby the origin of the phase factor is not clear the formalism I've shown applies to all 2 atate quantum system whether or not we can ascribe a physical significance to the phase factor. Any complex number with both real and imaginary parts will have some sort of phase factor associated with it by virtue of the exponential representation of a complex number. <br />Of course in some cases such as the two slit experiment or the beam splitter we can relate the phase factor to something physical but it's not clear that we can do this in all cases.Chris Fhttps://www.blogger.com/profile/03530660309554429226noreply@blogger.comtag:blogger.com,1999:blog-7897235423812277683.post-86934271716886182582012-02-28T18:28:26.631+00:002012-02-28T18:28:26.631+00:00Hi Chris, I found this from the links on the MS324...Hi Chris, I found this from the links on the MS324 forum. I'm a mathematician not a physicist but a few points struck me when reading the articles.<br /><br />First a general point. I have never known a mathematician ever confuse a model with reality. All that a mathematician requires of a model is that it's not too self-contradictory and useful in some way. If it can be calibrated to some external real-world data then so much the better.<br /><br />By contrast physicists seem to confuse their models with reality all the time - at least in their language. Maybe there's a clear distinction in their heads but I'm not so sure. This seems especially ironic as all modern physics is based on models only about a century old whereas mathematics from thousands of years ago is still perfectly valid today and always will be.<br /><br />OK now to a concrete point. You add the e^{-i\phi} phase multiplier term arbitrarily to one of the two probability states [of course with very reasonable physical grounds for doing so] and then claim the final probablity phase term depending on the phase factor has come from nothing(!) No it hasnt come from nothing, it's come directly from that tweaking of the state vector!<br /><br />Why do you make that adjustment? Because you know of course that light has a finite speed and a phase which leads to inteference when one path is longer than the other. But this is all knowledge of the external world which has been determined experimentally and has no origin within your mathematical model. So to answer your question "Where's the physics?", well here it is. Even the assumption that the probability amplitudes of S1 and S2 are mutually exclusive is based on the very reasonable principle of conservation of energy.<br /><br />Matt FletcherAnonymousnoreply@blogger.com