# How to apply e=mc^2 to a photon?

## Main Question or Discussion Point

Hey can sum1 please tell me if we can apply e=mc^2 to a photon?
Also if the energy of a photon is relative

and speed of light isnt relative and e=mc^2*lorentz factor

then how is energy of a photon relative in the above Case?

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dextercioby
Homework Helper
We can, if we specify that the "m" is not the rest mass which is 0 for a photon. It's the the so-called "relativistic mass" (very troublesome term). The energy of a photon relative to what ? To velocity, to momentum, spin??

Daniel.

Relative to observers travelling at different velocities

and can we use the lorentz factor for a photons energy?As the apparent frequency might change!

dextercioby
Homework Helper
Yes, the energy is of course relative to the motion of various observers trying to measure the energy of the photon. If you know what a 4 vector and and a Lorentz boost are, then the explanation is obvious.

Daniel.

No i do not about Lorentz boost and 4 vector.Could you please explain them to me?

And does magnetism take place due to photon exchange?

Hootenanny
Staff Emeritus
Gold Member
No i do not about Lorentz boost and 4 vector.Could you please explain them to me?
Four vectors in relativity are just a particle's space-time coordinates or energy momentum expressed as a vector. For example, the energy and momentum of a particle could be expressed thus;

$$\vec{P}=\left[\begin{array}{c} E\\ p_{x}C\\ p_{y}C\\ p_{z}C \end{array}\right]$$

Or more succinctly;

$$\vec{P}=\left[\begin{array}{c} E\\ \vec{p} \end{array}\right]$$

The Lorentz boost is just a Lorentz transformation, which "boosts" in a given direction, For example a "boost" in the x-direction and can also be expressed in matrix form, thus;

$$\begin{bmatrix} c t' \\ x' \\ y' \\ z' \end{bmatrix} = \begin{bmatrix} \gamma&-\beta \gamma &0&0\\ -\beta \gamma&\gamma&0&0\\ 0&0&1&0\\ 0&0&0&1\\ \end{bmatrix} \begin{bmatrix} c t \\ x \\ y \\ z \end{bmatrix}$$

And does magnetism take place due to photon exchange?
Yes, in QED the electromagnetic exchange force arises from the exchange of virtual photons.

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photon, rest mass and relativistic mass

Hey can sum1 please tell me if we can apply e=mc^2 to a photon?
Also if the energy of a photon is relative

and speed of light isnt relative and e=mc^2*lorentz factor

then how is energy of a photon relative in the above Case?
The high frequency at which that question appears on the Forum, shows that we should not fully give up the concept of relativistic mass!

ranger
Gold Member
The high frequency at which that question appears on the Forum, shows that we should not fully give up the concept of relativistic mass!
The large degree of confusion caused by relativistic mass proves otherwise. The only mass we should talk about is invariant mass and only speak of how energy and momentum increases with velocity.

I do not understand how the lorentz factor can be applie to e=mc^2 for a photon,as the speed of a photon aint relative.And please tell me more about exhnage of virtual photon if possible!

The large degree of confusion caused by relativistic mass proves otherwise. The only mass we should talk about is invariant mass and only speak of how energy and momentum increases with velocity.
What is difference between
m=m(0)g(V)
E=E(0)g(V)
and
p=g(V)vE(0)/cc ?

Hootenanny
Staff Emeritus
Gold Member
Again, all these threads seem to drift back to invariant vs. relativistic mass. I agree here with ranger, relativistic mass only tends to add confusion to a subject, in particular when teaching/explaining such phenomena to a semi-mathematically literate audience. I will say however, that relativistic mass is can be used in SR if applied correctly. BUT relativistic mass certainly has no place in GR.

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relativistic mass

Again, all these threads seem to drift back to invariant vs. relativistic mass. I agree here with ranger, relativistic mass only tends to add confusion to a subject, in particular when teaching/explaining such phenomina to a semi-mathematically literate ordience. I will say however, that relativistic mass is can be used in SR if applied correctly. BUT relativistic mass certainly has no place in GR.
I fully aggree with that conciliatory point of view in SR. The problem is to apply correctly!

ZapperZ
Staff Emeritus
2018 Award
This has got to be THE most frequently asked question here on PF. It is obvious that even with the various FAQ's all over the 'net, this is STILL going to be asked on here.

Can I get a volunteer to write something to address this type of question for our own FAQ in the General Physics forum? It should be tailored to the level that people who often ask this type of question can understand (see the existing FAQ there), and it should be tailored for the specific type of issues that we continue to see on here.

This can be done either by an individual, or via collaboration. Please PM me if you're interested. This will not stop people from asking, but at least, we can point very easily to a link on here and not have to go through ALL of this "pain and suffering" again. :) At the very least we don't have to rewrite the same thing, and go on with a discussion beyond that.

Zz.

jtbell
Mentor
I do not understand how the lorentz factor can be applie to e=mc^2 for a photon,as the speed of a photon aint relative.
The momentum-energy four-vector transforms in the same way as the position-time four-vector. In Hootenanny's matrix version of the Lorentz transformation, simply replace the position-time four-vector with the momentum-energy four-vector:

$$\begin{bmatrix} E' \\ {p'}_x c \\ {p'}_y c \\ {p'}_z c \end{bmatrix} = \begin{bmatrix} \gamma&-\beta \gamma &0&0\\ -\beta \gamma&\gamma&0&0\\ 0&0&1&0\\ 0&0&0&1\\ \end{bmatrix} \begin{bmatrix} E \\ p_x c \\ p_y c \\ p_z c \end{bmatrix}$$

This works for any particle, including photons.

Photons dimensions

Is a photon 2d or 3d or 4d.As at c ,time shudnt pass for it.But when it goes thru a refracting medium,duz it enter time.Also

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Hey can sum1 please tell me if we can apply e=mc^2 to a photon?
Also if the energy of a photon is relative

and speed of light isnt relative and e=mc^2*lorentz factor

then how is energy of a photon relative in the above Case?
anant, if I understand what Einstein was thinking, then the potential of the photon would have linear velocity c and angular velocity c.

jtbell
Mentor
the potential of the photon
Eh, what? Sry i dont understand.A photon shud be travelling thru time wen its velocity<c and shudnt be aging wen its v=c.So pls explain.Im sry i didnt understand!

Hootenanny
Staff Emeritus
Gold Member
Sry i dont understand.A photon shud be travelling thru time wen its velocity<c and shudnt be aging wen its v=c.So pls explain.Im sry i didnt understand!
In which cases doesn't a photon travel at c?

In which cases doesn't a photon travel at c?
I can pull searches to reference a specific experiment which raises this question.
And since I am not doing so at this time does not allow me to comment on it.

When its in a refracting medium?

ZapperZ
Staff Emeritus