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

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