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Newsgroups: sci.physics.research
From: Arnold Neumaier <Arnold.Neuma...@univie.ac.at>
Date: Fri, 4 Jan 2008 00:36:21 -0500 (EST)
Local: Fri, Jan 4 2008 12:36 am
Subject: Re: EM field of photon
CarlB schrieb:
> On Dec 22, 3:35 pm, Arnold Neumaier <Arnold.Neuma...@univie.ac.at> Her name is Hawton, not Hawkins... > wrote: > ... >> But (as she says in the abstract), her position operator does >> not transform as a vector, hence everything, including the >> probability of observing a photon in some region of space, >> is orientation dependent. This makes her construction unphysical. > Perhaps a better reference for Hawkins' method is the 6-year-old I can't find her reasoning convincing and suspect that it is faulty. > Baylis and Hawkins write: (on p.30) >> However, the photon (as well as other massless particles of spin S > 1/2 ) This is strange terminology which she uses repeatedly. Her position >> has only two linearly independent spin states, and in these states the spin >> is coupled to the momentum. As a result, its position operator is a matrix >> that does not commute with the spin. operator is a 3x3 matrix, not a vector as one would reasonably demand? On closer inspection it turns out that it is a 3-vector with 3x3 matrix components. Moreover, it is not clear what the argument is supposed to be. >> Different selections of the function This means that it does not contain the physical information about >> p () generally give different position operators, so that the position >> operator is not unique and does not transform under J as a simple vector. localization required of a position operator. One can construct arbitrary objects and give them names that sound interesting, but this does not give them physical content. The probability of being in a nonspherical domain cannot depend on the coordinate system used. I believe (and argued the reason in my FAQ) that this implies that the position vector must satisfy the standard commutation rules (3) with the angular momentum, which is violated, as she says explicitly on p.5. >> However, the eigenvectors of any one of these unitarily equivalent position Try to compute the probability of the photon being in some nonspherical >> operators gives a basis of localized states with unique eigenvalues that >> are independent of helicity, and there is consequently no disagreement >> as to the actual position of the photon. > In other words, the effect of a change in orientation is just a gauge region, or the expectation of some spherically nonsymmetric function of position. I predict that you'll find that these depend on the gauge and hence are unphysical. She discusses the effect of the phase too superficially (on p.28) > Indeed the method does not gives a position wave function Is this phase a number or also a 3x3 matrix? If it is the latter, > in the manner of the Schroedinger wave equation (as described > in your FAQ linked above). Such a scalar wave function could > be turned into a vector position operator that would meet your > requirements. > Instead, the method gives a position wave function that uses which is most likely (I doidn't wade through all details of the 42 page paper) the gauge transform will change probabilities. If the position operator has commuting components, it can be But angular momentum apparently is not represented as in a Finding d and exhibiting the nonstandard action of the angular > I suspect that the photon position operator will be a more Do you mean because the phase disappears? > natural object as a density matrix / density operator > density. But this only happens if the phase is a pure number, which I suspect isn't. If the density operator is gauge dependent, as I suspect, Hawton's construction is faulty. I also prefer treating quantum mechanics directly via density Arnold Neumaier You must Sign in before you can post messages.
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