# What is photon momentum?

1. Dec 10, 2014

### mac_alleb

While planing some simple experiments us encountered such a problem: what is exactly photon momentum?
p_ph = ?

2. Dec 10, 2014

### Vagn

The photon momentum, $p$ is the momentum carried by a photon and is related to the energy of the photon by the equation $E=pc$ where c is the speed of light in a vacuum.

3. Dec 10, 2014

### ZealScience

Even classically, radiation carries momentum. That's why you get radiation pressure. The whole formalism is derived from the Lorentz forces which implies that E-M field carries momentum. In fact, the quantum field theory of photon arises from covariant quantization of vector potential and therefore photons carry quantized version of the classical E-M field momentum.

4. Dec 10, 2014

### Johan0001

momentum is a vector .
Then in which direction does the E-M field travel , say in the case of Cosmic Background Radiation, which is all around us?

5. Dec 10, 2014

### bhobba

What direction does the microwave radiation in a cavity travel?

Thanks
Bill

6. Dec 10, 2014

### ZealScience

It is not the E-M field that travels, it is the energy that travels. For free space, poynting vector is in the same direction as the wave vector and thus the direction of momentum vector. I am not expert on Cosmic background radiation, but I think they should have momentum, even on the ground of relativity. If you are in some random frame, it is likely that some of the photons are redshifted and some are blueshifted. For comoving fundamental observers, the radiation is isotropic, but that does not mean individual photon does not have momentum.

7. Dec 10, 2014

### bhobba

The CBMR is radiation left over from the early of universe and behaves like blackbody radiation:
http://en.wikipedia.org/wiki/Black-body_radiation

The classical black-body is a kiln with a small hole in it so you can observe the radiation inside. As such direction is not a property of its radiation - if you view it as photons its like a gas that has reached thermal equilibrium - you cant really ascribe a direction to such a situation. In fact its the exact analogue of a gas except it obeys the Bose-Einstein statistics due to photons being indistinguishable and doesn't obey the Pauli exclusion principle of fermions.

The CBMR doesnt really have a direction - but recently there have been found small departures from uniformity that it is suspected to be left over from the early inflation phase of the universe.

Thanks
Bill

8. Dec 11, 2014

### ZealScience

Actually, I just attended a talk by a scientist from Astronomy department. He was analyzing some data from a ground based telescope which potentially indicate CMB polarization by the inflatory gravitational waves. Unfortunately, the data is heavily affected by galactic dust and they are currently trying to salvage the actual signal.

But I am no expert on it. I do not know the details.

9. Jan 4, 2015

### mac_alleb

So E = pc???
Is it E or p definition?
Could it be derived?

10. Jan 4, 2015

### bhobba

11. Jan 4, 2015

### dlgoff

bolded by me

First Direct Evidence of Cosmic Inflation

Toward an Understanding of Foreground Emission in the BICEP2 Region

12. Jan 4, 2015

### Staff: Mentor

Or think of a container with a gas inside of it, like air. Each individual molecule travels in some random direction. In what direction does the gas as a whole travel?

13. Jan 6, 2015

### mac_alleb

So, as easily seen, nobody knows what is photon momentum?? That's interesting, while how they calculating over all this experiments?

14. Jan 6, 2015

### bhobba

How you draw such a conclusion has me beat. It a good idea to not to jump to conclusions physicists don't know what they are talking about when the more likely explanation is you don't understand it.

You may like to acquaint yourself with Noethers Theorem:
http://en.wikipedia.org/wiki/Noether's_theorem

See also:
http://www.damtp.cam.ac.uk/user/tong/qft/six.pdf

See equation 6.16.

Its the conserved quantity associated with spatial symmetry like energy is the conserved quantity associated with time symmetry

Did you get what I said about the square in the relativistic equation?

Thanks
Bill

Last edited: Jan 6, 2015
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