Why Photon Spin on Z Direction Must be +1 or -1

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Discussion Overview

The discussion centers on the nature of photon spin, specifically why photons, as spin-1 bosons, can only exhibit two projections of spin along the z-direction: +1 or -1. Participants explore whether this can be explained through quantum mechanics or if it is merely a well-justified assumption based on experimental evidence.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that photons can only have spin projections of +1 or -1, as a spin projection of 0 would imply a rest frame for the photon, which contradicts its massless nature.
  • One participant references Wigner's theory, stating that elementary particles correspond to irreducible representations of the Poincare group, classified by mass and spin. They note that photons are described by a direct sum of two massless irreducible representations with helicities -1 and 1, but the reason for this remains unknown.
  • Another participant seeks clarification on the term "helicity," suggesting it may refer to the projection of spin along the direction of motion.
  • A later reply defines helicity for massless particles as the projection of angular momentum on the direction of motion, indicating that in the 1-photon Hilbert space, the helicity operator has only two eigenvalues: -1 and 1.
  • One participant briefly mentions U(1) gauge symmetry as a relevant concept in this context.

Areas of Agreement / Disagreement

Participants generally agree on the restriction of photon spin projections to +1 and -1, but the underlying reasons and implications remain contested and not fully resolved.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about mass and rest frames, as well as the dependence on the definitions of helicity and spin for massless particles.

paweld
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Why photn (boson with spin 1) can have only two projections of spin on z direction +1 or -1
(0 is not allowed). Is it possible to explain this in terms of quantum mechanics or is it
only our assumptions well justified by experiment.
 
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paweld said:
Why photn (boson with spin 1) can have only two projections of spin on z direction +1 or -1
(0 is not allowed). Is it possible to explain this in terms of quantum mechanics or is it
only our assumptions well justified by experiment.

The photon spin projections +1 and -1 correspond to the different helicities of the photons, that is, the projection of their angular momentum on their direction of travel. The two states are equivalent to right and left circularly polarized light.

As I understand it, if a photon had a spin projection of zero on its direction of travel, then one could construct a reference frame where it was at rest. In order for this to happen, it would have to have a non-zero rest mass. This would then make it a virtual photon, which basically means that we could never detect it experimentally.
 
It is not possible to have a photon with spin zero because if it did, the the photon, at a stand still, would have no mass and therefore is basically non-existent.
 
paweld said:
Why photn (boson with spin 1) can have only two projections of spin on z direction +1 or -1
(0 is not allowed). Is it possible to explain this in terms of quantum mechanics or is it
only our assumptions well justified by experiment.

According to Wigner's theory, each elementary particle corresponds to an irreducible unitary representation of the Poincare group. (the best reference is S. Weinberg, "The quantum theory of fields" vol. 1) Such irreducible representations are classified by two parameters - mass and spin (or helicity). If the mass is zero then helicity can take any integer value: ...-2, -1, 0, 1, 2, ... (there are other more exotic possibilities, but they have not been seen in nature). In fact, photon is not represented by a single irreducible representation (so it is not a true elementary particle, according to Wigner). Photon is described by a direct sum of two massless irreducible representations with helicities -1 and 1. Why this is the case? Nobody knows. That's just the way it is.

Eugene.
 
meopemuk said:
Photon is described by a direct sum of two massless irreducible representations with helicities -1 and 1. Why this is the case? Nobody knows. That's just the way it is.

Could you explain what do you mean by helicity. Is it simply projection of the spin on direction of motion.
 
paweld said:
Could you explain what do you mean by helicity. Is it simply projection of the spin on direction of motion.

Operator of spin can be defined only for massive particles. For massless particles helicity is the projection of the angular momentum on the direction of motion (momentum) (\mathbf{J} \cdot \mathbf{P})/P. In the 1-photon Hilbert space this operator has only two (eigen)values: -1 and 1.

Eugene.
 
Because of the U(1) gauge symmetry.
 

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