Photons have momentum so they have mass?

[Prometheus]

So i just learnt that momentum is equal to plank's constant over wavelength,[math] p= \frac{h}{\lambda} [/math], and that this applies to photons. So if photons have momentum why is it said they do not have mass?

 

Has this got something to do with relativistic mass and if so is there any way of understanding it without general relativity (i might be able to cope with special relativity).

 

Cheers.

[swansont]

Because the relativistic equation governing momentum, mass and energy is E² = p²c² +m²c⁴

 

E = pc, so m = 0

 

You can also see that when p = 0 this reduces to the famous E = mc² but that it only holds for things at rest. So when people introduce relativistic mass, this is a new description, and not the mass being used in other equations.

[timo]

Special relativity is sufficient to describe massless photons. Giving a "reason" why they have momentum but no mass is tricky: What would be the reason that you need mass to have momentum? In non-relativistic physics, there is the relation p=mv, which sais you cannot have non-zero momentum when you have zero mass. That equation no longer applies in relativity. Hence, there is no (mathematical) reason why something with momentum would need to have a non-zero mass.

 

As for the "relativistic mass": The relativistic mass is defined as the energy divided by the squared speed of light. Photons do have non-zero "relativistic mass". But the term "mass" usually does not refer to "relativistic mass" (which is just the energy expressed in different units). The concept that "mass" usually refers to is the mass defined in the equation Swansont posted (the relating equation between energy and momentum). There, a photon's mass is zero.

Edited September 29, 2016 by timo

[Prometheus]

So in very simplistic terms mass and relativistic mass are different concepts?

 

Is relativistic mass a generalisation of classical mass?

[Strange]

Relativistic mass is a (misleading) way of describing energy.

[edguy99]

The equation Swansont posted tells the correct story.

 

To relate photons to "usual" or "classical" mass you need some way to "weigh" them. Ie. you put them on a scale, or you see how much resistence they put up when they are thrown.

 

This is hard to do, but if you trap a bunch of photons in a box that perfectly reflects the photons and keeps them inside, then throw the box full of photons, you would find that the box full of photons is harder to throw then the empty box, as if the photons had "classical" mass.

 

If you put the box full of photons on a scale in a gravitational field, it would "weigh" more then the empty box.

[Tim88]

So in very simplistic terms mass and relativistic mass are different concepts?

 

Is relativistic mass a generalisation of classical mass?

 

They use somewhat different definitions. An elaboration can be found in the well known "Physics FAQ".

(disclaimer: I influenced some of the corrections in the update).

[MrDr]

The interaction between an xray photon and an electron in Compton scattering suggests some kind of momentum transfer as in the collision of billiard balls. Though it may not be possible to measure for the much higher wavelength of visible light, how is the energy transfer calculated in the collision of any wavelength photon with an electron?

[swansont]

The interaction between an xray photon and an electron in Compton scattering suggests some kind of momentum transfer as in the collision of billiard balls. Though it may not be possible to measure for the much higher wavelength of visible light, how is the energy transfer calculated in the collision of any wavelength photon with an electron?

 

 

The momentum of a photon is E/c = h/lambda

 

The Compton scattering formula will give you the wavelength change so you can deduce the energy and momentum of the photon, and conservation of either will give you the information about the electron.