# Photons, energy and mass

#### erty

These are some of the very fundamental things about the wave/particle-duality, I do not understand:

1) Do photons have a mass?

2) Do particles have a frequency? $$E = hf$$, how do I interpret this?

3) $$E = mc^2$$ and $$E = hf$$. I've seen these two equations combined into $$mc^2 = hf$$, indicating that a photon does have a mass. I can't see why the to equations are combined, the E's in the equations are about something different.

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#### FunkyDwarf

Ok firstly, let me correct you grammar :) Its DO photons have mass, and the answer is: no.

they do not have mass because they move at the speed of light, or you could put the conditions the other way im not sure. Einstines equations prohibit anything with mass from traveling at c as it would require an infinite amount of energy to accelerate them to that velocity.

2.) They do, but not directly through that equation. Particles have, or rather i should say, the probability of finding a particle has a wavefunction which has a wavelength, known as the debroglie wavelength, if you look that up you will find some better answers than i could give you.

It is a common misconseption to think that a particle is spread over an area like a wave, it is not. A particle, when you measure its position, will be in one spot and one spot only. The probability however does resemble a wave, or has wavelike behaviour.

3.) Photons do not have mass but have an analog of mass which gives them a kind of inertia, i think, which gives rise to things like radiation pressure.

Hope this helps
-G

#### erty

Ok firstly, let me correct you grammar :)
Yes, I stand corrected. I changed "a photon/particle" to photons/particles, but forgot to correct the rest.

Its DO photons have mass, and the answer is: no.

they do not have mass because they move at the speed of light, or you could put the conditions the other way im not sure. Einstines equations prohibit anything with mass from traveling at c as it would require an infinite amount of energy to accelerate them to that velocity.
...
3.) Photons do not have mass but have an analog of mass which gives them a kind of inertia, i think, which gives rise to things like radiation pressure.
Then how do I validate $$hf = mc^2$$, if it can't be applied to something like photons: they do have energy, but not any mass.
Does this have something to do with the wave/particle duality? Electrons exhibit the same properties, but they do have a mass (but they don't move at the speed of light).

2.) They do, but not directly through that equation. Particles have, or rather i should say, the probability of finding a particle has a wavefunction which has a wavelength, known as the debroglie wavelength, if you look that up you will find some better answers than i could give you.

It is a common misconseption to think that a particle is spread over an area like a wave, it is not. A particle, when you measure its position, will be in one spot and one spot only. The probability however does resemble a wave, or has wavelike behaviour.
I will look it up. thanks so far.

#### notknowing

These are some of the very fundamental things about the wave/particle-duality, I do not understand:

1) Do photons have a mass?
The answer to that question depends on the definition of mass. Often, people mean by mass the rest mass or invariant mass. If this is meant, one can say that photons have no mass. Since a photon is never at rest, the "rest mass" is however an absurd quantity for a photon. In this case, it makes more sence to look at the "relativistic mass" definition, which correspond to the total, real, relativistic energy when the particle is moving. If this mass is meant, then a photon has definitely a mass. To find the mass, just take the relation between frequency and energy (E = h v(freq)). Then divide E by c^2 to find the mass of the photon.

PS : Note that the equation E=m c^2 is generally valid when m is the relativistic mass.

#### Hootenanny

Staff Emeritus
Gold Member
In this case, it makes more sence to look at the "relativistic mass" definition, which correspond to the total, real, relativistic energy when the particle is moving. If this mass is meant, then a photon has definitely a mass. To find the mass, just take the relation between frequency and energy (E = h v(freq)). Then divide E by c^2 to find the mass of the photon.

PS : Note that the equation E=m c^2 is generally valid when m is the relativistic mass.
A photon does not have mass, invariant or "relativistic". Which ever way you look at it, it is nonsensical for a photon to have any sort of mass. And the equation E = mc2 is not valid for any zero invariant mass particle, including the photon. I will say here as I have done many times before, the idea of "relativistic mass" is a fallacy, which is often used to teach special relativity at a very elementary level. Relativistic mass does not exist, i.e. the faster an object travels does not mean that it gains more mass; it simply means the momentum of an object increases at a greater rate than classically predicted.

#### anantchowdhary

hey the mass actually doesnt increase,but energy increases wich give an EFFECT of more mass

#### anantchowdhary

mass is a FORM of energy,a photon is a different form of energy.Mass and light energy are different due to energy density.

Is my understanding correct?

#### FunkyDwarf

Relativistic mass does not exist, i.e. the faster an object travels does not mean that it gains more mass; it simply means the momentum of an object increases at a greater rate than classically predicted.
Could you expand on this a little? My understanding, and that of my physics lecturer, is that the measured mass is more if something is moving relative to the observer, the phenomenon known as mass addition. Seems to make sense to me, am i missing something?

-G

#### marlon

A particle, when you measure its position, will be in one spot and one spot only.
Yes, but this is not true if we DON'T measure the position. In the latter case, a "particle" also has non particle like properties.

The probability however does resemble a wave, or has wavelike behaviour.
The probability has wavelike behaviour but for that to happen the "particle" must be expressed as a wave. So, it is not just a particle of which the probability of finding it has wavelike behaviour, which IS what you seem to be suggesting. Both the "particle language" and the "wave language" are equivalent in the QM formalism. You seem to be make a distinction between the particle and it's probability as a wave. This is INCORRECT. It is the physical object itself that is written either as a particle (in terms of momentum eg) or as a wave (in terms of a wavelength eg)

marlon

#### notknowing

A photon does not have mass, invariant or "relativistic".
This is not correct.
Which ever way you look at it, it is nonsensical for a photon to have any sort of mass. And the equation E = mc2 is not valid for any zero invariant mass particle, including the photon..
Again not correct. Consider an empty box with perfect mirrors on the inside and determine its weight by a balance. Then, "inject" a certain amount of photons into this box. Weigh the box again. Do you really think it will weigh exactly the same as before ? If not, photons can be considered to have mass.
I will say here as I have done many times before, the idea of "relativistic mass" is a fallacy, which is often used to teach special relativity at a very elementary level. Relativistic mass does not exist, i.e. the faster an object travels does not mean that it gains more mass; it simply means the momentum of an object increases at a greater rate than classically predicted.
Again not correct. Relativistic mass is (per definition) that mass you obtain by dividing its energy by c^2 and this mass takes into account the mass increase due to the relative velocity.

You can verify all these things in elementary books on special relativity.

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