Why does E=mc² give a nonzero mass for a photon?

[Sothh]

I know that a photon cannot have mass.

I know that a photon does carry energy, however.

So, just for fun I used E=mc², to find out how much mass a photo would have.

This was mainly just to play around with the equation, but I found the answer interesting.

1.11265005605e-31 kilograms.

That is the mass of a single photon, even though I know its not.

What I don't know is why its not.

 

[WannabeNewton]

E = mc^2 is only valid for objects in their rest frames. A photon has no rest frame so that equation is invalid for a photon. A photon has momentum and this translates to a momentum density and momentum flux for a bunch of photons but that is not the same as rest mass.

 

[Vanadium 50]

You are using the wrong equation. E = mc² is for a particle at rest, which a photon is not. For a particle in motion you need to use E² = (pc)² + (mc²)². Since for light E = pc, if you will solve you will get m = 0.

 

[Sothh]

Thanks!

I have always wondered about this.

If the photon transfers its energy to an object with a rest mass, then does it add mass to the object?

 

[Pengwuino]

Thanks!

I have always wondered about this.

If the photon transfers its energy to an object with a rest mass, then does it add mass to the object?

There are two things you might be interested in. http://en.wikipedia.org/wiki/Compton_scattering" occurs when a photon scatters off a particle and in turns, imparts some of it's energy to the particle and flies off with a smaller energy. However, the rest mass of the particle (What $E=mc^2$ really talks about) does not change; it simply gains kinetic energy.

There is also http://en.wikipedia.org/wiki/Pair_production" where high energy photons can actually create massive particles.

 

[ZapperZ]

I know that a photon cannot have mass.

I know that a photon does carry energy, however.

So, just for fun I used E=mc², to find out how much mass a photo would have.

This was mainly just to play around with the equation, but I found the answer interesting.

1.11265005605e-31 kilograms.

That is the mass of a single photon, even though I know its not.

What I don't know is why its not.

Please start by reading the FAQ thread in the General Physics forum.

Zz.

 

[edguy99]

Thanks!

I have always wondered about this.

If the photon transfers its energy to an object with a rest mass, then does it add mass to the object?

In Einstein's second paper on relativity in 1905, he explicitly concludes:

"Radiation carries inertia between emitting and absorbing bodies". It is important that not only does something receive a "kick" from the momentum of the energy, but the internal inertia (i.e., the inertial mass) of the body is actually increased. (from mathpages.com)

 

[Goldstone1]

I know that a photon cannot have mass.

I know that a photon does carry energy, however.

So, just for fun I used E=mc², to find out how much mass a photo would have.

This was mainly just to play around with the equation, but I found the answer interesting.

1.11265005605e-31 kilograms.

That is the mass of a single photon, even though I know its not.

What I don't know is why its not.

Among all this confusion, first $$E=Mc^2$$ is only good an an outdated concept of particles at rest - you need the relativistic formula $$E^2=M^2c^4+p^2c^2$$, but when I read your opening posts that photons cannot have a mass is simply wrong.

It does have a lower bound of mass at $$10^{-51}$$ g that is if one wants to believe it even has a mass of the ridiculously small length.

 

[edguy99]

I know that a photon cannot have mass.

I know that a photon does carry energy, however.

So, just for fun I used E=mc², to find out how much mass a photo would have.

This was mainly just to play around with the equation, but I found the answer interesting.

1.11265005605e-31 kilograms.

That is the mass of a single photon, even though I know its not.

What I don't know is why its not.

I fully agree that the photon has no mass. But, one way to "weigh" this photon is to consider a box of mirrors mounted on a scale facing each other. Assume the "weight" of the mirrors on the scale is 1 kilogram. Say a photon goes by and does not get trapped by the mirrors. The scale will continue to be say exactly 1 kilogram.

Now, say the photon gets trapped by the mirrors and bounces back and forth between them. The scale will change and show a "weight" of slightly more then 1 kilogram (specifically, the mass equivalent of the photons energy).

In this way, you can view matter as trapped energy, it may be a vortex, mirrors, black holes or who knows what.

 

[HallsofIvy]

Among all this confusion, first $$E=Mc^2$$ is only good an an outdated concept of particles at rest - you need the relativistic formula $$E^2=M^2c^4+p^2c^2$$, but when I read your opening posts that photons cannot have a mass is simply wrong.

It does have a lower bound of mass at $$10^{-51}$$ kg that is if one wants to believe it even has a mass of the ridiculously small length.

?
Where did you get that figure?

 

[Goldstone1]

?
Where did you get that figure?

I hope i said it in grams, but basically this is old-ish news:

http://aip.org/pnu/2003/split/625-2.html

 

[ZapperZ]

I hope i said it in grams, but basically this is old-ish news:

http://aip.org/pnu/2003/split/625-2.html

That's not a "lower bound mass". That's the UPPER limit of the mass, meaning that the photon mass, IF it exist, has to be lower than that.

Zz.