Why against Stern-Gerlach experiment photons are said to be spin 1?
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From: Tom Roberts on 8 Dec 2009 12:15 Jarek Duda wrote: > On 6 Gru, 17:59, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: >>> Does free (not moving) electron have angular momentum? I don't think >>> so ... >> Of course it does. The value of angular momentum depends on the point >> around which you calculate it; classically any moving object has nonzero >> angular momentum around any point not directly in line with its >> velocity. Quantum mechanically, a free electron is modeled as a plane >> wave, which when expanded in terms of angular momentum eigenfunctions >> has a nonzero amplitude for every term in the infinite series (this is >> true for any point used as the origin, and for any value of momentum, >> including zero). > I've written - not moving. > Electrons are mass particles - has velocities smaller than c - we can > choose coordinates in which its not moving, just saying in one point. > Does such electron (in its ground state) has angular momentum? Yes, as I said before. In non-relativistic quantum mechanics, an electron with a definite momentum p_u has a plane-wave wavefunction ~ exp[-i hbar p_u x^u]. Putting p_i=0 (i=1,2,3) means the wavefunction ~ exp[-i hbar E t]. Projecting that onto the angular momentum eigenstates {Y_lm} gives a nonzero amplitude for every one. [As is well known, such plane-wave wavefunctions are not normalizable.] In QFT things are more complicated, but still the states with nonzero angular momentum have nonzero amplitudes. >> Whether or not elementary particles are related to topological defects >> is an open question that is directly related to modern attempts to >> formulate a theory of quantum gravity. No success so far. But the >> "topological defect" due to spin would be a line, not a point, and is >> not observed for particles. There is more going on than just spin.... > Why do You think we don't observe them? Because we observe no line-like structure related to elementary particles, nuclei, or atoms. > saying that pure electron has angular momentum doesn't have > too much sense... It most definitely does in non-rel QM (see above). Ditto for QFT. > What it has is spin That, too. > spin is something simpler and so more fundamental than > charge! Hmmm. Spin is a representation of the Lorentz group, charge is an integer. I'm not sure "simpler" applies, but if it does I think an integer is "simpler". Note the integers for charge actually enumerate representations of the group U(1).... > And what photon can have is just angular momentum - traveling twist- > like excitation of the field - and there is no spin or charge needed > for that. Spin 1 is NECESSARY to model photons in agreement with experiments. So is charge 0. Both are determined experimentally to extremely high accuracy. I repeat: spin is not angular momentum. See my earlier postings for what they actually are, in our best models of EM and quantum phenomena. Tom Roberts
From: Jarek Duda on 8 Dec 2009 17:18 On 8 Gru, 18:15, Tom Roberts <tjrob...(a)sbcglobal.net> wrote: > Yes, as I said before. In non-relativistic quantum mechanics, an electron with a > definite momentum p_u has a plane-wave wavefunction ~ exp[-i hbar p_u x^u]. > Putting p_i=0 (i=1,2,3) means the wavefunction ~ exp[-i hbar E t]. Projecting > that onto the angular momentum eigenstates {Y_lm} gives a nonzero amplitude for > every one. (...) > In QFT things are more complicated, but still the states with nonzero angular > momentum have nonzero amplitudes. You focus on wave nature of particles, but there is also corpuscular one. I think about quantization procedure - going into Fock space, as a tool for perturbatve approximation. Let's focus on nonperturbative picture - in which electron is a corpuscle of nonzero radius - and so with some internal structure. Formalism You written usually forgets about this internal structure. It is taken into consideration in fitted abstract expansion terms in some abstract potential... but these terms only describes some parameters of the particle ... they don't answer to the most important question here: WHAT IS PARTICLE'S INTERNAL STRUCTURE? exp[-i hbar E t] formulation again completely ignores its internal structure. Better approximation of behavior is given by quantum rotation operator for spin particles and it says that there is made topological singularity there ... OK .. how to experimentally prove/disprove electron's internal angular momentum? Maybe through annihilation ... how does electron + positron annihilation results depends on their polarization? But my intuition suggests that before collision they should align their spins correspondingly - always in the same way... ? > Because we observe no line-like structure related to elementary particles, > nuclei, or atoms. What would You expect? Shining lines? :) They would be extremely small, very stable and so they could practically not affect photons ... If they would have energy density per length, while reconnecting this energy would be released ... what can be what is missing in current models of magnetic reconnections... which are far form observed in Sun's corona ... But generally in lower temperatures they would prefer to be very short - for example making loop joining two particles and explaining why they prefer to couple on atom orbitals or as Cooper pairs ... Do You have a better explanation for Cooper pairs? Collective deformation waves of the lattice is not enough to hold two repelling electrons together ... This picture also explains why while deexcitation spin is usually changed by one - topologically to break such loop, the simplest way is to twist one electron 180 deg and reconnect (fig. 7 I wanted You to at least to look at ... ) You will probably say that it can be also explained by that there is some usually conserved abstract mathematical property - parity ... but ... why?? do You really have not mathematical, but physical intuition about this property? > > spin is something simpler and so more fundamental than > > charge! > > Hmmm. Spin is a representation of the Lorentz group, charge is an integer. I'm > not sure "simpler" applies, but if it does I think an integer is "simpler". You have to think about spin through Dirac equations ... but they are only some general tool to operate on something spin-like ... They again don't see particle's internal structure! Particle is a corpuscle also ... especially when it just stays in one place and don't move ... > Spin 1 is NECESSARY to model photons in agreement with experiments. Which experiment do You refer???? The reason of this thread was to hear answer for that question ... and after 200 posts I still didn't heard any concrete experimental argument... > I repeat: spin is not angular momentum (...) I agree ... and do You agree that photons can carry angular momentum? If yes - how to cope these two sentences? ... Generally I apology for not referring to Your whole posts - I read them all, but I see the standard picture I know well and which after a lot of thinking brought me to more and more doubts I try would like to understand - I ask because standard answers don't satisfy me. best, jarek
From: Tom Roberts on 10 Dec 2009 15:04 Jarek Duda wrote: > On 8 Gru, 18:15, Tom Roberts <tjrob...(a)sbcglobal.net> wrote: >> Yes, as I said before. In non-relativistic quantum mechanics, an electron with a >> definite momentum p_u has a plane-wave wavefunction ~ exp[-i hbar p_u x^u]. >> Putting p_i=0 (i=1,2,3) means the wavefunction ~ exp[-i hbar E t]. Projecting >> that onto the angular momentum eigenstates {Y_lm} gives a nonzero amplitude for >> every one. (...) >> In QFT things are more complicated, but still the states with nonzero angular >> momentum have nonzero amplitudes. > > You focus on wave nature of particles, but there is also corpuscular > one. Hmmm. I described this in terms of non-rel QM, and mentioned how it extends to QFT. Your concept of there being "wave" and "corpuscular" descriptions is not contained in either of them. You need to get a real QM/QED textbook, not a comic book. > I think about quantization procedure - going into Fock space, as a > tool for perturbatve approximation. Those are words of the technical vocabulary, but they don't really go together like that. Get a real textbook. Study it. You ask > WHAT IS PARTICLE'S INTERNAL STRUCTURE? In non-rel QM the electron has no structure. In QED the bare electron has no structure, and the dressed particle's structure is described in the perturbative approximation by summing the appropriate diagrams to all orders. >> Spin 1 is NECESSARY to model photons in agreement with experiments. > Which experiment do You refer???? > The reason of this thread was to hear answer for that question ... and > after 200 posts I still didn't heard any concrete experimental > argument... You have to ask the question to get an answer; until now you haven't asked this particular question. All of atomic spectroscopy, including its transition rules, directly implies that emitted photons must have spin 1. There are literally zillions of experiments summarized in that one sentence. The angular dependence of pair production implies the photon has spin 1. The angular dependence of Compton scattering implies the photon has spin 1. For essentially every decay or interaction of an elementary particle, if the photon had no spin there would be no selection rule preventing the emission of an arbitrary number of photons in addition to the other decay products. This is not observed. Those are what comes to mind in a minute or two. There are surely others.... Spin is pervasive, essential, and subtle. You cannot expect to understand it without a serious study of QM, QED, and QFT. Tom Roberts
From: Jarek Duda on 11 Dec 2009 02:01 On 10 Gru, 21:04, Tom Roberts <tjrob...(a)sbcglobal.net> wrote: > Hmmm. I described this in terms of non-rel QM, and mentioned how it extends to > QFT. Your concept of there being "wave" and "corpuscular" descriptions is not > contained in either of them. You need to get a real QM/QED textbook, not a comic > book. So in Your picture for example while electron-position creation, there appears (come from where? another dimension or something?) two points of infinite energy density ... with some magical labels containing their commutation relations ? I agree that one of us should return to reality ... No - we have only 4 dimensions of some field which has some special local solutions - particles. They have finite energy density and so nonzero radius. So they have some internal structures which results in their mathematical parameters. > Those are words of the technical vocabulary, but they don't really go together > like that. Get a real textbook. Study it. (...) > In non-rel QM the electron has no structure. In QED the bare electron has no > structure, and the dressed particle's structure is described in the perturbative > approximation by summing the appropriate diagrams to all orders. These theories are not physics, but some APPROXIMATIONS - mathematical models which allow us to calculate some properties, estimate some probabilities ... You cannot just blindly recite holy words of physics, but You sometimes also have to think in self-aware, critical way ... and in discussions at least looking at the second side's arguments would be nice, even if they are inconvenient to Your faith .... > All of atomic spectroscopy, including its transition rules, directly implies > that emitted photons must have spin 1. There are literally zillions of > experiments summarized in that one sentence. If You would try sometimes also to look at my posts, You would realize that in half of them I'm referring to this argument ... These rules says that spin up electron is changed into spin down - it can be done not only by magically transforming Your magical points, but also by just rotating them 180 deg and in this case photon has only to carry angular momentum! > The angular dependence of pair production implies the photon has spin 1. Yes - that one have one angular momentum and the second opposite because of momentum conservation ... > The angular dependence of Compton scattering implies the photon has spin 1. It only says that this process depends on photon's angular momentum ... > For essentially every decay or interaction of an elementary particle, if the > photon had no spin there would be no selection rule preventing the emission of > an arbitrary number of photons in addition to the other decay products. This is > not observed. So these processes comes in a few quick steps and each of them is 'summarized' by produced photon to fulfill conservation laws. I agree that photons (don't have to, but) can carry angular momentum. Please explain how these experiments shows that they also need to carry spin?
From: Tom Roberts on 11 Dec 2009 23:48
Jarek Duda wrote: > On 10 Gru, 21:04, Tom Roberts <tjrob...(a)sbcglobal.net> wrote: >> Hmmm. I described this in terms of non-rel QM, and mentioned how it extends to >> QFT. Your concept of there being "wave" and "corpuscular" descriptions is not >> contained in either of them. You need to get a real QM/QED textbook, not a comic >> book. > > So in Your picture for example while electron-position creation, there > appears (come from where? another dimension or something?) two points > of infinite energy density ... with some magical labels containing > their commutation relations ? Whatever makes you say that? The electron-positron pair is created, from the energy in the photon. They are "brand new", and "came" from nowhere -- they were CREATED, which is why they come in pairs with all their additive quantum numbers having exactly opposite values. And "energy density" is not infinite -- these are QUANTUM OBJECTS (they don't have sharp positions). The intrinsic properties of the e+ and e- are part and parcel of them, including properties modeled by commutation relations. > I agree that one of us should return to reality ... No hope -- neither you nor I know what "reality" is, so a "return" is not possible. All we have are MODELS. And yes, those models are not complete. > These theories are not physics, but some APPROXIMATIONS - mathematical > models which allow us to calculate some properties, estimate some > probabilities ... Your first statement is wrong, as physics _IS_ constructing models of the world, which necessarily involve approximations. > [...] > I agree that photons (don't have to, but) can carry angular momentum. Photons with definite momentum have non-zero angular momentum in any basis and relative to any origin. They are QUANTUM OBJECTS, not pointlike classical particles as you seem to think. They don't have sharp locations, which is why the projection of their wavefunction onto angular momentum eigenfunctions has nonzero amplitude for every one (when they have a definite momentum, as was the case being discussed). > Please explain how these experiments shows that they also need to > carry spin? The angular dependence of photon interactions directly implies they are spin 1. I repeat: you need to STUDY QM and QFT before you have any hope of understanding spin. Or why the wavefunction for quantum objects with definite momentum has nonzero amplitude for all possible angular momenta. This is getting overly repetitive. Don't expect me to respond unless you actually LEARN something about the subject. Tom Roberts |