Why do QM particles with l<S vanish in a classical radiation field?

In summary, the classical radiation field with integer spin S and zero rest mass can be resolved into spherical harmonics, or multipole moments. Any components with l<S will disappear, while those with l>=S will remain, regardless of the source. This is because the number of degrees of freedom for oscillation in a quantized field is determined by the spin of the particle. This explains why long ranged forces, such as electromagnetic and gravitational forces, correspond to dipole and quadrapole moments, respectively, since they are mediated by particles with spin 1 and 2.
  • #1
Sourabh N
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Off pg 977 MTW Gravitation :

Consider a classical radiation field whose associated quantum mechanical particles have integer spin S, and zero rest mass. Resolve that radiation field into spherical harmonics - i.e. into multipole moments. all components with l<S will vanish; in general those with l>=S will remain; and this is independent of the nature of the source!

Can anyone reason me why l<S would vanish?
 
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  • #2
The polarization or the multi pole moment of a radiation field is given by the number of degrees of freedom the field is capable of oscillating in. When the field is quantized the these degrees of freedom are identified with spin of the particle.

The long ranged forces EM and gravitation are dipole and quadrapole respectively. Correspond to to the fact that they are mediated by photons(spin 1) and gravitons(spin 2) particles.
 

FAQ: Why do QM particles with l<S vanish in a classical radiation field?

Why do quantum mechanical particles with l

The reason for this is because of the concept of quantum superposition. In quantum mechanics, particles exist in a state of superposition, meaning they can exist in multiple states simultaneously. However, in a classical radiation field, the particles are forced to interact with the field and their superposition states collapse, causing them to vanish.

What is the significance of l

l

Can particles with l

Yes, particles with l

How does the concept of quantum entanglement relate to the disappearance of particles with l

Quantum entanglement is the phenomenon where two or more particles become connected and share a correlation, even when separated by large distances. In a classical radiation field, the entangled particles may interact with the field in a way that causes one particle to vanish while the other remains intact.

Is the disappearance of particles with l

Yes, the uncertainty principle in quantum mechanics states that it is impossible to know both the position and momentum of a particle simultaneously. In a classical radiation field, the particles' interactions with the field disrupt their position and momentum, making it impossible to predict their behavior and causing them to vanish.

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