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

In summary: 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 ir
  • #1
paweld
255
0
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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) [tex] (\mathbf{J} \cdot \mathbf{P})/P [/tex]. In the 1-photon Hilbert space this operator has only two (eigen)values: -1 and 1.

Eugene.
 
  • #7
Because of the U(1) gauge symmetry.
 

1. Why is the photon spin on the Z direction always either +1 or -1?

The spin of a photon is a fundamental property of the particle and is determined by its intrinsic angular momentum. This intrinsic angular momentum, also known as spin, can only have two possible values, +1 or -1, in the Z direction. This is due to the fact that photons are massless particles and have no rest frame, so their spin cannot be in any other direction.

2. How is the spin of a photon experimentally determined?

The spin of a photon can be experimentally determined through a process called polarization measurement. This involves passing the photon through a series of polarizing filters and observing the changes in intensity or direction of the photon's electric field. By measuring the changes in polarization, the spin of the photon can be determined.

3. What is the significance of the photon's spin on the Z direction?

The spin of a photon on the Z direction is significant because it plays a crucial role in determining the particle's behavior and interactions. For example, the spin of a photon affects its polarization, which in turn affects how it interacts with other particles. Additionally, the spin of a photon determines its helicity, which is an important property in quantum mechanics.

4. Can the spin of a photon be changed?

No, the spin of a photon cannot be changed. As mentioned earlier, the spin of a photon is a fundamental property of the particle and is determined by its intrinsic angular momentum. This means that the spin of a photon is fixed and cannot be altered through any external means.

5. How does the spin of a photon relate to the concept of quantum superposition?

The spin of a photon plays a crucial role in the concept of quantum superposition. In the quantum world, particles like photons can exist in multiple states simultaneously, known as superposition. The spin of a photon, being a quantum property, can also exist in a superposition of both +1 and -1 states. This allows for interesting phenomena such as entanglement, where the spin of one photon can affect the spin of another, even at great distances.

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