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Natural Science Forum / Physics / Particle Physics / September 2004Do free particles have spin?
Is there any evidence for the existence of particle spin for free particles, that is, for particles not bound to atoms? If so, please give references or links.  SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf >Is there any evidence for the existence of particle spin for free >particles, that is, for particles not bound to atoms? If so, please give >references or links. Polarization of light? Werner and friends showed that a neutron really is a spinor. They split a neutron beam in an interferometer, and showed that the neutrons in one leg must be rotated by 4*pi to return to their original state. Polarizers and spin flippers are commonly used on neutron beam lines. Signature"You're not as dumb as you look. Or sound. Or our best testing indicates." -- Monty Burns to Homer Simpson > >Is there any evidence for the existence of particle spin for free > >particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 5 lines] > neutron beam in an interferometer, and showed that the neutrons in one leg > must be rotated by 4*pi to return to their original state. I seem to recall there is some macroscopic contruction involving string which shares this property. Do you know what I'm talking about? > Polarizers and spin flippers are commonly used on neutron beam lines. >> >Is there any evidence for the existence of particle spin for free >> >particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 9 lines] >string which shares this property. Do you know what I'm talking >about? If it's what I think you're talking about, the professor in one of my classes demonstrated it in cardboard and string. There was one peice of cardboard, and four students each holding a string, but I forget just how the trick goes. I wasn't sure how to relate it to the spin of an electron. Signature"When the fool walks through the street, in his lack of understanding he calls everything foolish." -- Ecclesiastes 10:3, New American Bible > >> >Is there any evidence for the existence of particle spin for free > >> >particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 14 lines] > cardboard, and four students each holding a string, but I forget just how > the trick goes. I guess I'll have to look for the details. I recall it did involve a solid object attached to fixed points by string. > I wasn't sure how to relate it to the spin of an electron. Well, as an off-the-wall conjecture from us aetherial types, one just might think it suggested that if a particle were connected to the rest of the universe, that this peculiar "return to itself after 4pi rotation" property just might be understandable in terms of a realistic model. Think of the particle as a topological defect in space with the same connectivity as this toy model. >>Is there any evidence for the existence of particle spin for free >>particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 7 lines] > > Polarizers and spin flippers are commonly used on neutron beam lines. Thanks Gregory. Do you know of any evidence in support of free charged particle spin? SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf >>>Is there any evidence for the existence of particle spin for free >>>particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 10 lines] >Thanks Gregory. Do you know of any evidence in support of free charged >particle spin? Neutrons are my thing, not charged particles. But Google has quite a lot to say about "polarized electron beam". Signature"Experiments are the only means of knowledge at our disposal. The rest is poetry, imagination." -- Max Planck >>Thanks Gregory. Do you know of any evidence in support of free charged >>particle spin? > > Neutrons are my thing, not charged particles. But Google has quite a lot > to say about "polarized electron beam". I searched Google under "polarized electron beam" and none of the links explained the difference between polarization and spin orientation. I know that, for a photon, they're different things. Is a polarized electron beam the same as a spin oriented electron beam? If so, how do you know if you are measuring polarization or spin? SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf >>>Thanks Gregory. Do you know of any evidence in support of free charged >>>particle spin? [quoted text clipped - 7 lines] >electron beam the same as a spin oriented electron beam? If so, how do >you know if you are measuring polarization or spin? To polarize something is to orient its spin. Back to the neutron world, a neutron polarizer is also called a spin filter, because the beam is polarized by removing the 50% whose spins are oriented in the wrong direction. Photons, with spin 1, have two orthogonal polarization directions, e.g. vertical and horizontal. (They're massless, so they can't be longitudinally polarized.) Neutrons, with spin 1/2, have two orthogonal polarization directions, e.g. up and down. Why aren't the neutron polarizations vertical and horizontal? Because that's not an orthogonal basis for spin 1/2. The number of polarization directions for a spin 1/2 particle corresponds to the number of values m_z can take: -1/2 or 1/2. The number for a massive spin 1 particle would correspond to m_z = -1, 0, 1. Classically speaking, it's related to the way a field transforms. Electromagnetism is a vector field, neutrons or electrons would correspond to a spinor field. Gravity in general relativity is a tensor field that would correspond to a graviton with spin 2. SignatureIrony: "Small businesses want relief from the flood of spam clogging their in-boxes, but they fear a proposed national 'Do Not Spam' registry will make it impossible to use e-mail as a marketing tool." http://www.bizjournals.com/houston/stories/2003/11/10/newscolumn6.html > To polarize something is to orient its spin. Are you saying that once something is polarized in a particular direction, its spin is then oriented in that direction? > Photons, with spin 1, have two orthogonal polarization directions, e.g. > vertical and horizontal. I'm assuming that you mean that the orthogonal polarization directions are in a plane perpendicular to the direction of motion of the photon. > (They're massless, so they can't be > longitudinally polarized.) By longitudinal I'm assuming you mean along the direction of motion. But if what I've read is correct, a photon's spin orientation is in the direction of its motion (longitudinal). So the polarization and spin orientation of a photon are orthogonal to each other, since the polarization is orthogonal to the direction of motion. From your comments above, however, you seem to be saying that spin orientation and polarization are one and the same thing. Obviously, that can't be true for a photon, since its spin orientation and polarization are in different directions. > Neutrons, with spin 1/2, have two orthogonal > polarization directions, e.g. up and down. Up and down relative to what? Are you saying that the polarization direction is the same as the spin orientation? SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf >> To polarize something is to orient its spin. > [quoted text clipped - 11 lines] > >By longitudinal I'm assuming you mean along the direction of motion. Yes. >But >if what I've read is correct, a photon's spin orientation is in the [quoted text clipped - 5 lines] >for a photon, since its spin orientation and polarization are in >different directions. Horizontal and vertical are one basis for photon polarization. Another basis is left and right circular. They're related. |left,right> = (|vertical> +,- |horizontal>)/sqrt(2) or something like that. Recall that a rotation is described by finding the axis of rotation and applying a convention (the right-hand rule) to define the direction it points. So the motion of the hands of a clock are "pointing" into the wall, even though the hands move about the face. One way to change from a transverse to a circular polarization is to pass a transversely polarized beam through a birefringent plate, one that has different indices of refraction for different polarization directions, at 45 degrees, with a thickness so that one projection advances 1/4 wavelength ahead of the other. >> Neutrons, with spin 1/2, have two orthogonal >> polarization directions, e.g. up and down. > >Up and down relative to what? Are you saying that the polarization >direction is the same as the spin orientation? Up and down relative to whatever direction you choose, it's defined by your arrangement of apparatus. Up and down are just conventional labels, they're also called |+> and |->, referring to the z-direction. Parallel and antiparallel to the beam are the usual choice. A common technique is to use a supermirror to polarize the beam, which is a series of glass plates coated with magnetized nickel, which strongly absorbs neutrons of one polarization but reflects those of another. And the plates are bent so that there is no direct line of sight through the device. Signature"The average person, during a single day, deposits in his or her underwear an amount of fecal bacteria equal to the weight of a quarter of a peanut." -- Dr. Robert Buckman, Human Wildlife, p119. >>But if what I've read is correct, a photon's spin orientation is in the >>direction of its motion (longitudinal). So the polarization and spin [quoted text clipped - 19 lines] > 45 degrees, with a thickness so that one projection advances 1/4 > wavelength ahead of the other. I don't know enough about the Dirac notation to know if you are saying that spin orientation and polarization are one and the same thing. Could you please answer yes or no to that question and explain why? And if they aren't the same thing, how does the measurement of the polarization of a free particle confirm the existence of its spin? SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf >>>But if what I've read is correct, a photon's spin orientation is in the >>>direction of its motion (longitudinal). So the polarization and spin [quoted text clipped - 25 lines] >they aren't the same thing, how does the measurement of the polarization >of a free particle confirm the existence of its spin? They're the same thing. The |kets> label states, they're like basis vectors. I'll go classical. When a light wave is vertically polarized, the electric field at a particular point in space will look something like, with the first component an x value and the second a y value, third is z, E_v = E0 (sin(wt), 0, 0) If horizontally polarized, E_h = E0 (0, cos(wt), 0) E_h doesn't need a cosine, it could have been a sine, but you'll see the reason I chose that phase. Circular motion, in Cartesian coordinates, is given by (sin(wt), cos(wt), 0) It's a vector sum of horizontal and vertical motion. The "direction" is given by the axis of rotation, which is mutually perpendicular to the two components. That's what I tried to express above. Circular polarization can be expressed as a combination of two transverse polarization modes. The field of a circularly polarized light wave doesn't point in the direction of propagation, but a vector that describes how the field rotates (clockwise or counterclockwise) points along the direction of propagation. Signature"We don't grow up hearing stories around the camp fire anymore about cultural figures. Instead we get them from books, TV or movies, so the characters that today provide us a common language are corporate creatures" -- Rebecca Tushnet > It's a vector sum of horizontal and vertical motion. The "direction" is > given by the axis of rotation, which is mutually perpendicular to the two [quoted text clipped - 5 lines] > of propagation, but a vector that describes how the field rotates > (clockwise or counterclockwise) points along the direction of propagation. But the polarization is always transverse to the direction of propagation, not in the direction of propagation like the spin orientation is, even for circularly polarized light. Just because you can describe the rotation of the field by a vector perpendicular to the plane of rotation doesn't mean that the polarization is now in the direction of that vector. The direction of polarization is changing, but it's always transverse to the direction of propagation. So even for circularly polarized light, polarization and spin orientation are not in the same direction, so they can't be the same thing. If the spin is described by the same vector that describes the rotation of the field, then what about linearly polarized light? That vector would be the zero vector, since the field is not rotating. Does that mean that in the case of linear polarization the photon has no spin? SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf >> It's a vector sum of horizontal and vertical motion. The "direction" is >> given by the axis of rotation, which is mutually perpendicular to the two [quoted text clipped - 15 lines] >circularly polarized light, polarization and spin orientation are not in >the same direction, so they can't be the same thing. It's customary to use the axis of rotation as the "direction" of a rotation, even if the electric field will never point in that direction. Yes, polarization and spin orientation are the same thing, and they're in the same direction. When spin orientation is rotating, it's also customary to use the axis of rotation to describe its direction. When you go to fancy math like wedge products, a rotation is no longer described by the axis because in four or higher dimensions, there are an infinite number of lines that are mutually perpendicular to a plane of rotation. It's described rather by specifying two vectors that define the plane of rotation. So instead of e_z, you'd call it e_x^e_y. But we usually don't do that in physics, we just give an axis of rotation. >If the spin is described by the same vector that describes the rotation >of the field, then what about linearly polarized light? That vector >would be the zero vector, since the field is not rotating. Does that >mean that in the case of linear polarization the photon has no spin? In the case of linearly polarized light, it is not the custom to use an axis of rotation. Signature"I'm giving you the chance to look fate in those pretty eyes of hers and say, 'Step off, bitch. This is my party and you're not invited.'" -- Chris Shugart, _Testosterone Magazine_ > > It's a vector sum of horizontal and vertical motion. The "direction" is > > given by the axis of rotation, which is mutually perpendicular to the two [quoted text clipped - 9 lines] > propagation, not in the direction of propagation like the spin > orientation is, even for circularly polarized light. The direction of the electric and magnetic field vectors is perpendicular to the direction of propagation. These are not the circular polarisation vector. The circular polarisation vector is parallel or antiparallel to the direction of propagation. Note that for an EM wave with no orbital angular momentum about the direction of propagation, the angular momentum density is fully described by the polarisation and intensity. Note that this angular momentum density can be mathematically and experimentally be shown to be spin density. > If the spin is described by the same vector that describes the rotation > of the field, then what about linearly polarized light? That vector > would be the zero vector, since the field is not rotating. Does that > mean that in the case of linear polarization the photon has no spin? The average value of the photon spin is zero. The spin of the EM field is zero. Note what happens when the beam is incident on a circularly-polarising beamsplitter (ie a 1/4 wave plate and polarising beamsplitter). SignatureTimo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/ Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html > Note that for an EM wave with no orbital angular momentum about the > direction of propagation, the angular momentum density is fully described > by the polarisation and intensity. > > Note that this angular momentum density can be mathematically and > experimentally be shown to be spin density. Could you show me how mathematically and experimentally this is done, or give me a reference or (preferably) a link that shows it? Thanks, Timo. SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf > > > > Note that for an EM wave with no orbital angular momentum about the [quoted text clipped - 6 lines] > Could you show me how mathematically and experimentally this is done, or > give me a reference or (preferably) a link that shows it? Thanks, Timo. First, note that the momentum density of a plane EM wave is parallel to the direction of propagation. Hence the orbital angular momentum density in the direction of propagation is zero. Secondly, calculate the torque per unit volume in the direction of propagation exerted by a circularly polarised plane wave on an absorbing medium. Compare this torque with the rate of decrease of energy density in the direction of propagation. What, then, must be the relationship between the energy density and the angular momentum density? Note well that the component of the torque density found is independent of the choice of origin, and is therefore spin angular momentum. A similar calculation for a birefringent medium gives the relationship between spin density and polarisation. OK, that's the simple calculation for a simple case. Problems 7.27 and 7.29 in Jackson, 3rd ed, also treat this case. For a more thorough treatment of the maths, you'll need to resort to a good book on field theory. Soper, Classical Field Theory has the best and clearest treatment of this that I've seen. Jauch & Rohrlich, Theory of Photons and Electrons is also OK. Beware missing "if the fields fall off sufficiently quickly so that we can neglect surface terms"! The classic paper is J. Humblet, "Sur le moment d'impulsion d'une onde électromagnétique", Physica 10(7), 585-603 (1943). Another early paper of note is J. H. Poynting, "The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light", Proc. R. Soc. Lond. A 82, 560-567 (1909) Also check: S. J. van Enk and G. Nienhuis, "Commutation rules and eigenvalues of spin and orbital angular momentum of radiation fields", Journal of Modern Optics 41(5), 963-977 (1994) Stephen M. Barnett, "Optical angular-momentum flux", Journal of Optics B: Quantum and Semiclassical Optics 4, S7-S16 (2002) James H. Crichton and Philip L. Marston, "The measurable distinction between the spin and orbital angular momenta of electromagnetic radiation", Electronic Journal of Differential Equations Conf. 04, 37-50 (2000) http://ejde.math.swt.edu/ Bruno Piccirillo and Enrico Santamato, "Light angular momentum flux and forces in birefringent inhomogeneous media", Physical Review E 69, 056613 (2004) As for experimental demonstrations, one must start with Richard A. Beth, "Mechanical detection and measurement of the angular momentum of light", Physical Review 50, 115-125 (1936). Our own measurement are available on arxiv: http://www.arxiv.org/abs/physics/0402021 http://www.arxiv.org/abs/physics/0310003 http://www.arxiv.org/abs/physics/0308113 http://www.arxiv.org/abs/physics/0309122 Also: V. Garcés-Chávez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, "Observation of the transfer of the local angular momentum density of a multiringed light beam to an optically trapped particle", Physical Review Letters 91(9), 093602 (2003), http://www.st-andrews.ac.uk/~atomtrap/pub.htm SignatureTimo [snip] Thanks Timo, and thanks to everyone else for your help in this thread. I think I'll take some time and try to digest all the information you've given me. Bye for now. SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf > >>Thanks Gregory. Do you know of any evidence in support of free charged > >>particle spin? [quoted text clipped - 7 lines] > electron beam the same as a spin oriented electron beam? If so, how do > you know if you are measuring polarization or spin? Spin is has both magnitude and direction. Polarization indicates the spin direction. > Dave Rutherford [Old Man] [snip] > Do you know of any evidence in support of free charged > particle spin? The experiments in which the anomalous magnetic moments of electrons and muons are measured. Bye, Bjoern > Is there any evidence for the existence of particle spin for free > particles, that is, for particles not bound to atoms? If so, please give > references or links. Hey stooopid: TV picture tubes. Polarized accelerator e-beams. SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf > Is there any evidence for the existence of particle spin for free > particles, that is, for particles not bound to atoms? If so, please give > references or links. SLAC's collider has been firing polarized electrons at each other for some time now. PD >>Is there any evidence for the existence of particle spin for free >>particles, that is, for particles not bound to atoms? If so, please give >>references or links. > > SLAC's collider has been firing polarized electrons at each other for some time now. Thanks Paul. From what I've read, at least for photons, polarization and spin are two different things. For photons, the spin axis is in the direction of travel and the polarization axis is perpendicular to the direction of travel. Is that also true for electrons? SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf > >>Is there any evidence for the existence of particle spin for free > >>particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 6 lines] > direction of travel and the polarization axis is perpendicular to the > direction of travel. Electromagnetic waves, which consist of photons, can have linear transverse polarization. A photon cannot. A photon has only circular polarization, either in the direction of propagation, or opposed to it, as indicated by the direction of its spin vector. Is that also true for electrons? A massive particle is allowed to have a transverse spin component. > Dave Rutherford [Old Man] >Electromagnetic waves, which consist of photons, >can have linear transverse polarization. A photon >cannot. A photon has only circular polarization, >either in the direction of propagation, or opposed >to it, as indicated by the direction of its spin vector. What if I prepare a photon in the state (|right>+|left>)/sqrt(2)? Signature"Are those morons getting dumber or just louder?" -- Mayor Quimby > >Electromagnetic waves, which consist of photons, > >can have linear transverse polarization. A photon [quoted text clipped - 3 lines] > > What if I prepare a photon in the state (|right>+|left>)/sqrt(2)? That's two photons, isn't it ? Or is it a superposition of orthogonal states of a single photon ? In the second case, one can never observe such a state. One will observe either |left> or |right>. Old Man isn't positive on any of this. Please clarify. [Old Man] >> >Electromagnetic waves, which consist of photons, >> >can have linear transverse polarization. A photon [quoted text clipped - 9 lines] >observe either |left> or |right>. Old Man isn't positive >on any of this. Please clarify. Just one photon. Photons can be in a superposition of states. It would correspond to vertical polarization. It can be prepared and observed with transverse polarizers, or reflection at Brewster's angle. Remember the "spooky" thing about QM is all the wave mechanics is in play even if the photon are coming one at a time. Signature"Then they placed the ark of the Lord on the cart; along with the box containing the golden mice and the images of the hemorrhoids." -- 1 Samuel 6:11 > >Electromagnetic waves, which consist of photons, > >can have linear transverse polarization. A photon [quoted text clipped - 3 lines] > > What if I prepare a photon in the state (|right>+|left>)/sqrt(2)? After the above reply, Old Man looked in "Quantum Electrodynamics" by Landau & Lifshitz: They say that, (|right>+|left>)/sqrt(2) is a legitimate single photon wave function. However, they also say that it doesn't represent a "pure" quantum state, as do the helicity states, and that, under axial symmetry, only helicity is conserved. So, Old Man is simply wrong. Evidently a linear polarizing "filter" or a reflector (which don't possess axial symmetry) can absorb a circularly polarized photon and re-emit it in a mixed state, such as psi = (|right>+|left>)/sqrt(2), as Gregory suggested. So, what happens if one attempts to detect linearly polarized photons with a detector possessing axial symmetry along the photon's propagation vector ? [Old Man] >> >Electromagnetic waves, which consist of photons, >> >can have linear transverse polarization. A photon [quoted text clipped - 12 lines] >the helicity states, and that, under axial symmetry, >only helicity is conserved. I don't understand what a "pure" quantum state means in this context. Whatever quantum state you have, to express it you must first pick your basis. What is diagonal in one basis won't necessarily be diagonal in another, but so what? If the spin of a neutron is (|+z>+|-z>))/sqrt(2), is that a pure state? Doesn't look like it. But switch to a basis S,m_x and the neutron polarization is |+x>. Now it looks pure. And if your neutron beam has the polarization |+x> it will pass unimpeded through a spin filter that passes neutrons in the state |+x> (e.g. a glass cell filled with polarized 3He pointing in a direction transverse to the beam). You could still say the spin filter passes neutrons in the state (|+z>+|-z>)/sqrt(2), but that's clumsy. >So, Old Man is simply wrong. Evidently a linear >polarizing "filter" or a reflector (which don't possess [quoted text clipped - 5 lines] >polarized photons with a detector possessing axial >symmetry along the photon's propagation vector ? |vertical> = (|right> + |left>)/sqrt(2) (With a possible sign or sqrt(-1) error.) P = |<right|vertical>|^2 = 1/2 Half of them will get through. Signature"In any case, don't stress too much--cortisol inhibits muscular hypertrophy. " -- Eric Dodd > >>Is there any evidence for the existence of particle spin for free > >>particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 6 lines] > direction of travel and the polarization axis is perpendicular to the > direction of travel. Is that also true for electrons? I think you are confusing the polarization axis with the polarization plane. They are perpendicular. Besides, spin can really only be defined to be a good quantum number if it points in the direction of motion (or opposite to it). This is required for commutation of angular and linear momentum operators. >>>>Is there any evidence for the existence of particle spin for free >>>>particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 9 lines] > I think you are confusing the polarization axis with the polarization > plane. They are perpendicular. From what I've read, the polarization axis is commonly taken to be in the direction of the electric field, which is in the polarization plane, i.e. the plane perpendicular to the direction of propagation of the electromagnetic wave (or beam of light). Here's an excerpt from "An Introduction to Quantum Physics", by A. French and E. Taylor, pg. 233: "In terms of the classical wave description, a beam of light is linearly polarized if its electric vector lies in a single plane that includes the beam ... . The polarization axis is defined as the line in this plane along which the electric vector lies at any point. Because electromagnitic waves are transverse, the polarization axis is always perpendicular to the direction of propagation." > Besides, spin can really only be > defined to be a good quantum number if it points in the direction of > motion (or opposite to it). This is required for commutation of > angular and linear momentum operators. Then polarization cannot be the same as spin orientation, since they are not in the same direction. SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf > >>>>Is there any evidence for the existence of particle spin for free > >>>>particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 24 lines] > polarization axis is always perpendicular to the direction of > propagation. > > Besides, spin can really only be > > defined to be a good quantum number if it points in the direction of [quoted text clipped - 3 lines] > Then polarization cannot be the same as spin orientation, since they are > not in the same direction. But the only way you can define a plane vectorially is by a vector perpendicular to it. There is a lot going on in the polarization plane. There is an electric and a magnetic field, both of which can rotate within the plane. This is the property that essentially leads to spin. And on top of that, there has been a lot of talk lately about orbital angular momentum degrees of freedom associated with EM waves. But in the end, all of these things are occuring in the polarization plane, their angular momenta will always point perpendicular to the plane, in the same direction as a unit vector defining the plane. > Is there any evidence for the existence of particle spin for free > particles, that is, for particles not bound to atoms? If so, please > give references or links. Rutherford doesn't want references. He's trolling and want's to argue. Old Man is willing to play for awhile. 0) The magnetic moment of the muon is predicted via QED to within experimental error. 1) NMR: depends upon composite nuclear magnetic moment; only peripherally dependent upon atomic properties. 2) The magnet moment orientation of lepton and fermion spin states can be sorted via a non-uniform magnetic field. 3) Electron-positron annihilation generates either two (total S = 0) or three (total S = 1) photons,and the ratio thereof is accurately predicted by the statistics of spin sttates. 3) The only difference between a neutrino and an anti-neutrino is the direction of its spin vector WRT its propagation vector. consistent with observations of nuclear electron and positron decay. For muon neutrinos, see 0) above. [Old Man] > > Is there any evidence for the existence of particle spin for free > > particles, that is, for particles not bound to atoms? If so, please [quoted text clipped - 13 lines] > spin states can be sorted via a non-uniform magnetic > field. Oops !! that's for atoms. You don't need a non-uniform field for free particles. > 3) Electron-positron annihilation generates either two (total > S = 0) or three (total S = 1) photons,and the ratio thereof [quoted text clipped - 6 lines] > > [Old Man] [Old Man] > Is there any evidence for the existence of particle spin for free > particles, that is, for particles not bound to atoms? If so, please give > references or links. Spin is an intrinsic property of particles, independent of whether they interact or not. An electron has always spin 1/2 no matter what happens to it, it can not be changed. If you want to go into the details, check out the representations of the Poincare group (1-particle states) and/or a QFT book. Friendly, Kostas. >>Is there any evidence for the existence of particle spin for free >>particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 4 lines] > it, it can not be changed. If you want to go into the details, check out the > representations of the Poincare group (1-particle states) and/or a QFT book. Thanks Constantine. I know that, theoretically, free particles have spin, but I'm interested in experimentally confirmed properties of particles, not theoretical properties. SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf > >>Is there any evidence for the existence of particle spin for free > >>particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 8 lines] > spin, but I'm interested in experimentally confirmed properties of > particles, not theoretical properties. I don't understand what you mean by "experimentally confirmed properties of particles, not theoretical properties". Spin can be measured and has been, for every particle (elementary or composite). It's value is not affected by interactions. Friendly, Kostas. >>>>Is there any evidence for the existence of particle spin for free >>>>particles, that is, for particles not bound to atoms? If so, please give [quoted text clipped - 19 lines] > I don't understand what you mean by "experimentally confirmed properties of > particles, not theoretical properties". The only experiment said to confirm electron spin that I knew of before I posted my OP was the Stern-Gerlach experiment. That experiment used atoms (silver, I believe), not free electrons. I was wondering if there had been any spin experiments where they used free electrons (or other particles). SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf > The only experiment said to confirm electron spin that I knew of before > I posted my OP was the Stern-Gerlach experiment. That experiment used > atoms (silver, I believe), not free electrons. I was wondering if there > had been any spin experiments where they used free electrons (or other > particles). I see what you mean. How about all the high energy experiments (using collliders) utilising electrons? SLAC, DESY, the old LEP (gone now)... Friendly, Kostas. >>The only experiment said to confirm electron spin that I knew of before >>I posted my OP was the Stern-Gerlach experiment. That experiment used [quoted text clipped - 4 lines] > I see what you mean. How about all the high energy experiments (using > collliders) utilising electrons? SLAC, DESY, the old LEP (gone now)... I don't know anything about these, I'll have to look into it. Thanks Constantine. SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf > I don't know anything about these, I'll have to look into it. Thanks > Constantine. You are welcome. > Is there any evidence for the existence of particle spin for free > particles, that is, for particles not bound to atoms? If so, please give > references or links. The SLC and SLAC made and studied polarized electron beams for several years: http://mitbates.mit.edu/pesp2002/talks/Clendenin_SLACPES.ppt Muon spin precessions are studied in detail in g-2 experiments: http://www.g-2.bnl.gov/index.shtml Muon and tau spin is verified by their decay distributions (start by reading a decent textbook, like Halzen and Martin, then reading the about the corresponding measurments). Compton scattering is highly dependent on the polarization states of both the target particle and the photon beam. (Google "Compton Polarimetry" = 296 hits). The list of confirmations of particle spin is almost literally endless. Perhaps if you ask a more specific question, someone can give you a better answer. -E >> Is there any evidence for the existence of particle spin for free >> particles, that is, for particles not bound to atoms? If so, please [quoted text clipped - 18 lines] > endless. Perhaps if you ask a more specific question, someone > can give you a better answer. I'm still not convinced that polarization and spin are the same thing. What are the directions of the spin and polarization of an electron in quantum mechanics? SignatureDave Rutherford "New Transformation Equations and the Electric Field Four-vector" http://www.softcom.net/users/der555/newtransform.pdf Applications: "4/3 Problem Resolution" http://www.softcom.net/users/der555/elecmass.pdf "Action-reaction Paradox Resolution" http://www.softcom.net/users/der555/actreact.pdf "Energy Density Correction" http://www.softcom.net/users/der555/enerdens.pdf "Proposed Quantum Mechanical Connection" http://www.softcom.net/users/der555/quantum.pdf >>> Is there any evidence for the existence of particle spin for free >>> particles, that is, for particles not bound to atoms? If so, please [quoted text clipped - 22 lines] > What are the directions of the spin and polarization of an electron in > quantum mechanics? For Fermions, like elections, polarization is basically the net average spin direction of a group of fermions. The relationship is a little more complex for photons because polarization is defined in terms of the electric field vector, which, while related to the spin state, is not synonymous. There's a bit of a discussion here: http://www.mathpages.com/rr/s9-04/9-04.htm -E |
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