Why against Stern-Gerlach experiment photons are said to be spin 1?
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From: Jarek Duda on 26 Nov 2009 13:22 On 26 Lis, 18:14, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > I repeat: spin does not imply any sort of topological singularity. So please describe mathematically behavior of quantum phase around nonzero spin particle. Tip: look what quantum rotation operator does.
From: Tom Roberts on 26 Nov 2009 17:15 Jarek Duda wrote: > On 26 Lis, 18:14, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: >> I repeat: spin does not imply any sort of topological singularity. > So please describe mathematically behavior of quantum phase around > nonzero spin particle. > Tip: look what quantum rotation operator does. You're not listening - go back and READ what I wrote. The "quantum rotation operator" is a red herring: there is NOTHING rotating in a photon (or an electron, or...). A photon is spin 1 because we must use a spin-1 representation of the Lorentz group to model it. The representation is part of the vertex function, not the propagator -- we know the photon's spin because of the way photons interact, not from the way they propagate. Tom Roberts
From: Jarek Duda on 26 Nov 2009 20:10 On 26 Lis, 23:15, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > You're not listening - go back and READ what I wrote. The "quantum > rotation operator" is a red herring: there is NOTHING rotating in a > photon (or an electron, or...). A photon is spin 1 because we must use a > spin-1 representation of the Lorentz group to model it. The > representation is part of the vertex function, not the propagator -- we > know the photon's spin because of the way photons interact, not from the > way they propagate. Quantum mechanics is a tool (less precise than QFT) to estimate probabilities of results of experiments. You are probably talking about Dirac equation - extension of QM to operate on objects with something 'spin-like' ... but this mathematical tool is very universal - should be similar when operating with something 'twist-like' ... To summarize: Your argument is - in some cases we can use the same mathematical model for waves carrying ANGULAR MOMENTUM and SPIN so these properties are equivalent. It's like saying that we can similarly describe electrostatics and Newton's gravity, so they are the same ... Please use a better argument than similarity of our formalisms.
From: Darwin123 on 27 Nov 2009 01:39 On Nov 26, 4:01 am, Jarek Duda <duda...(a)gmail.com> wrote: > What we need is for example field of vectors which prefers nonzero > length - kind of quantum phase which prefers to choose some phase > (angle) in practically all points. I am not sure what you mean by a field of vectors that prefers nonzero length. >It can have some gauge invariance. > This property allows it to create topological singularities - spins - > for example quantum phase making rotation around spin axis. Warning, I know very little about topology. However, this talk of topology made me of the Moebius strip. So maybe we don't want a topological singularity, whatever that is. Maybe we want holes in loops of paper. My first experience with topology (age 14) was making Moebius strips (single loops) and the associated more usual double loops. So maybe I will start to think of electrons as the single loops (Moebius strips) and the photons as double loops (convectional loops). So allow me to conjecture a little bit on the relationship between electrons and Moebius strips. I think a Moebius strip has some of the properties that I have read with respect to fermions. For instance, an electron supposedly has to to be rotated about its axis twice before it returns to its original state. That is supposedly the basic of the 1/2-spin. A Moebius strip has to be rotated twice before it comes back to its original state. Make a Moebius strip at home with paper and tape. Draw a picture anywhere on the Moebius strip. One has to roll that figure around the strip twice before it comes back to its original position. The polarization of a light wave is often imagined as an polarization vector that rotates around the wave vector axis. The polarization field vector only has to roll around its axis once to get back to its original direction. Now think of the polarization of an electron wave (or the wave of any fermion) as being some polarization vector that has to move in a pattern resembling a Moebius strip. The polarization vector has to rotate around the axis twice to gt back to the original position. This is an all wave picture of an electron. Alternatively, we can use an all particle picture. Think of the electron as a particle being in the shape of a Moebius strip. Then the particle has to turn around its axis twice before returns to its original shape. I suddenly heard a distant voice say "Idiot- snip." I must be hallucinating!
From: Tom Roberts on 27 Nov 2009 11:31
Jarek Duda wrote: > On 26 Lis, 23:15, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: >> You're not listening - go back and READ what I wrote. The "quantum >> rotation operator" is a red herring: there is NOTHING rotating in a >> photon (or an electron, or...). A photon is spin 1 because we must use a >> spin-1 representation of the Lorentz group to model it. The >> representation is part of the vertex function, not the propagator -- we >> know the photon's spin because of the way photons interact, not from the >> way they propagate. > > To summarize: Your argument is - in some cases we can use the same > mathematical model for waves carrying ANGULAR MOMENTUM and SPIN so > these properties are equivalent. NOT AT ALL! Go back and READ what I wrote. Translating what I said into the terms you used here: Since spin is modeled DIFFERENTLY from angular momentum in QFT, they are different aspects of a system. As I have said several times, spin is INTRINSIC to a particle, but angular momentum is not -- that's QUITE DIFFERENT, in both classical and quantum theories. In QFT, spin is modeled with a definite-spin representation of the Lorentz group, but angular momentum is modeled with eigenfunctions of the angular momentum operator -- that's QUITE DIFFERENT. > It's like saying that we can similarly describe electrostatics and > Newton's gravity, so they are the same ... No. It's much more like saying that Newtonian gravity couples to mass while electrostatics couples to charge, so they are DIFFERENT.... Extending the analogy: both electrostatic and (Newtonian) gravitational forces affect the trajectory of an object subject to both; both spin and angular momentum combine to form the total angular momentum of a system. The combination is not at all simple addition -- Clebsch- Gordon coefficients are involved. L=1 orbital a.m. and a spin-1/2 particle combine into four J=3/2 states and two J=1/2 states. Note this is QUITE DIFFERENT from the behavior of spin in classical mechanics (where spin IS angular momentum). AFAIK there is no good and accurate classical model of spin as we know it in quantum systems. Note that this ANALOGY does not capture the similarities and differences completely.... > Please use a better argument than similarity of our formalisms. Please actually READ what I write. Tom Roberts |