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csmyth3025
2011-Jun-03, 09:19 PM
In another thread EigenState commented that:


The photon is completely described in terms of its momentum and spin angular momentum. The momentum is completely defined by the direction of propagation and the frequency. Thus frequency is an intrinsic property of a single photon...

I tried to get an idea of what this means but even the Wikipedia article on the photon is mostly over my head.

Empirically, I can sort of understand that the momentun (energy) of a photon is directly related to its frequency. A photon of blue light has more energy (momentum) than a photon of red light. In this sense I can imagine an experimental set-up that detects individual photons as they impinge on a surface (doped silicon?) to produce a momentary voltage spike. I'm guessing that by measuring the magnitude of this voltage spike, the energy (momentum, or frequency) of the photon can be determined.

Angular momentum (spin) is the concept that really has me stumped. At first I was thinking that it's directly related to the energy (momentum, or frequency) of the photon but I couldn't manage to fit the these ideas together.

To illustrate my confusion, this is the "simple" explanation Wikipedia offers:


In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0:

E^2 = p^2c^2 + m^2c^4.

The energy and momentum of a photon depend only on its frequency (ν) or inversely, its wavelength (λ):

http://upload.wikimedia.org/math/d/0/7/d07def13d6f88776fe72fd064c75f820.png

http://upload.wikimedia.org/math/5/e/c/5ec51e67be09073c9152f61fd03c885f.png

where k is the wave vector (where the wave number k = |k| = 2π/λ), ω = 2πν is the angular frequency, and ħ = h/2π is the reduced Planck constant.

Since p points in the direction of the photon's propagation, the magnitude of the momentum is

http://upload.wikimedia.org/math/3/8/2/382f8c0764c28cdcde234eb0d96268b1.png


The photon also carries spin angular momentum that does not depend on its frequency. The magnitude of its spin is http://upload.wikimedia.org/math/c/2/e/c2eb21daddf83cb0d85936e2d3b5f4b4.png and the component measured along its direction of motion, its helicity, must be ±ħ. These two possible helicities, called right-handed and left-handed, correspond to the two possible circular polarization states of the photon.

(ref. http://en.wikipedia.org/wiki/Photon) (Bold added by me)

I realize that I have a lot to learn before I can make sense out of the above passage. For right now, though, the thing that really puzzles me is the part that says: "...The photon also carries spin angular momentum that does not depend on its frequency..."

I'm left with two questions: How is a photon's angular momentum measured? and, Is there any analogy that can help me understand what the angular momentum of a photon is?

Chris

chornedsnorkack
2011-Jun-03, 09:40 PM
I think that single photon can be imagined as being circularly polarized.

Its angular momentum is independent of its frequency because angular momentum can be imagined as product of momentum of circular motion and applicable lever arm. Since the lever arm is photon´s wavelength (or a fixed fraction of it), the frequency cancels out.

loglo
2011-Jun-03, 10:11 PM
In another thread EigenState commented that:



I tried to get an idea of what this means but even the Wikipedia article on the photon is mostly over my head.

Empirically, I can sort of understand that the momentun (energy) of a photon is directly related to its frequency. A photon of blue light has more energy (momentum) than a photon of red light. In this sense I can imagine an experimental set-up that detects individual photons as they impinge on a surface (doped silicon?) to produce a momentary voltage spike. I'm guessing that by measuring the magnitude of this voltage spike, the energy (momentum, or frequency) of the photon can be determined.

Angular momentum (spin) is the concept that really has me stumped. At first I was thinking that it's directly related to the energy (momentum, or frequency) of the photon but I couldn't manage to fit the these ideas together.

To illustrate my confusion, this is the "simple" explanation Wikipedia offers:


(ref. http://en.wikipedia.org/wiki/Photon) (Bold added by me)

I realize that I have a lot to learn before I can make sense out of the above passage. For right now, though, the thing that really puzzles me is the part that says: "...The photon also carries spin angular momentum that does not depend on its frequency..."

I'm left with two questions: How is a photon's angular momentum measured? and, Is there any analogy that can help me understand what the angular momentum of a photon is?

Chris

Spin is one of the more obscure concepts in particle physics. It is not angular momentum but quantised angular momentum and is only loosely related to the everyday concept of spin.

EigenState
2011-Jun-03, 10:39 PM
Greetings,



I'm left with two questions: How is a photon's angular momentum measured?

All atomic and molecular electronic transitions require very specific changes in the combined angular momenta of the atom or molecule, and the photon. Those requirements are summarized by what are known as selection rules that specify the allowed changes in angular momenta under the different possible kinds of transitions (electric-dipole, electric-quadrupole, magnetic-dipole). The photon is a spin 1 particle such that the quantized value of the projection of the angular momentum onto the direction of photon propagation can assume the values of +1, 0, or -1.

Given that background, one can determine the angular momentum of a photon spectroscopically by judicious choice of atom and excited states to be probed. This might well require high resolution (Doppler-free) spectroscopic techniques that would resolve the different angular momentum states of the atom. The different angular momentum states of the photon can only induce specific transitions. For example: the atomic transition of interest requires a change in the total angular momentum of +1. That unit increase in the angular momentum of the atom must be supplied by the photon. If the angular momentum of the incident photon does not satisfy that condition, the transition will not be stimulated.


Is there any analogy that can help me understand what the angular momentum of a photon is?

As loglo pointed out above, there is no classical mechanical analog to quantized spin angular momentum. It is an intrinsic property of the particle.

Best regards,
EigenState

csmyth3025
2011-Jun-04, 08:30 AM
Spin is one of the more obscure concepts in particle physics. It is not angular momentum but quantised angular momentum and is only loosely related to the everyday concept of spin.
Spin is, indeed, one of the more obscure concepts in particle physics. I'll keep working on the more basic (simpler) stuff and, hopefully, I'll start to grasp the concepts behind the more obscure stuff.

Thanks for the replies.

Chris