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

[anantchowdhary]

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 isn't relative and e=mc^2*lorentz factor

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

 

[dextercioby]

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.

 

[anantchowdhary]

Relative to observers traveling at different velocities

 

[anantchowdhary]

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

 

[dextercioby]

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.

 

[anantchowdhary]

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

 

[anantchowdhary]

And does magnetism take place due to photon exchange?

 

[Hootenanny]

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;

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

More information can be found http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/vec4.html"

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.

 

[bernhard.rothenstein]

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 isn't 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]

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.

 

[anantchowdhary]

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!

 

[bernhard.rothenstein]

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]

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.

 

[bernhard.rothenstein]

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]

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]

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.

 

[anantchowdhary]

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

please tell me about its dimensions

 

[Schrodinger's Dog]

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

please tell me about its dimensions

There are two threads which will answer these questions.
https://www.physicsforums.com/showthread.php?t=150500&highlight=Photon+time

And the other is on FAQ.

It's the fourth FAQ.

https://www.physicsforums.com/showthread.php?t=104715

If you still have the same questions after reading those, ask again.

 

[Jimmini]

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 isn't 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]

the potential of the photon

Eh, what?

 

[anantchowdhary]

Sry i don't understand.A photon shud be traveling thru time wen its velocity<c and shudnt be aging wen its v=c.So pls explain.Im sry i didnt understand!

 

[Hootenanny]

Sry i don't understand.A photon shud be traveling 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?

 

[Jimmini]

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.

 

[anantchowdhary]

When its in a refracting medium?

 

[ZapperZ]

When its in a refracting medium?

You should read the FAQ in the General Physics forum before claiming that.

Zz.

 

[MeJennifer]

You should read the FAQ in the General Physics forum before claiming that.

Zz.

Clearly anantchowdhary is asking not claiming.

 

[ZapperZ]

Clearly anantchowdhary is asking not claiming.

That "question" was a followup to the statement he made in Msg. #21.

Zz.

 

[anantchowdhary]

Hey i didnt understand the FAQ explanation.Can u please explain in layman's language and give me a definite answer to my question about the constancy of the speed of a photon:Yes/NO?

Thnx

 

[Hootenanny]

Hey i didnt understand the FAQ explanation.Can u please explain in layman's language and give me a definite answer to my question about the constancy of the speed of a photon:Yes/NO?
Thnx

JesseM has given what amounts to a definitive answer in a previous thread of yours;

In terms of local inertial coordinate systems (defined in terms of measurements made by freely-moving observers in a small region of space and time) the speed of light is always c. But in terms of nonlocal coordinate systems in curved spacetime it doesn't have to be, and likewise, if you use a non-inertial (accelerating) coordinate system in flat spacetime it also may not be c.

Now, I quote directly from the FAQ authored by ZapperZ, just to be sure that you have read the correct section;

A solid has a network of ions and electrons fixed in a "lattice". Think of this as a network of balls connected to each other by springs. Because of this, they have what is known as "collective vibrational modes", often called phonons. These are quanta of lattice vibrations, similar to photons being the quanta of EM radiation. It is these vibrational modes that can absorb a photon. So when a photon encounters a solid, and it can interact with an available phonon mode (i.e. something similar to a resonance condition), this photon can be absorbed by the solid and then converted to heat (it is the energy of these vibrations or phonons that we commonly refer to as heat). The solid is then opaque to this particular photon (i.e. at that frequency). Now, unlike the atomic orbitals, the phonon spectrum can be broad and continuous over a large frequency range. That is why all materials have a "bandwidth" of transmission or absorption. The width here depends on how wide the phonon spectrum is.

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.

Don't worry about what phonons are, just make sure that you get the 'gist' of the explanation.

 

[anantchowdhary]

Hey,is it that the photon's time to cover that distance thru a refracting medium gets prolonged in comparison to its normal time taken to pass thru a distance?Im sry I am in a mess

 

[Hootenanny]

I'll try and paraphrase what Zz posted in order to make it easier to understand. Solids are made up of a network of ions (charged particles, in this case atoms) and electrons. Imagine that the atoms are balls, evenly spaced forming a cubic lattice, with springs connecting one atom to the next something like http://www.teachmetuition.co.uk/Chemistry/Chemicalstructureandbonding/cubeionstotal.gif" . These lattices have vibrational energy levels, similar to the energy levels in an atom. Now, when a photon enters a solid, it can interact with these energy levels; if the photon has an energy equal to one of the lattice vibrational energy levels, then the photon is absorbed. However, if the photon has an energy greater than any of the lattice vibrational energy levels the lattice will absorb the photon, but since there is too much energy for the lattice to absorb, it releases the energy in the form of another photon. However, there is a time delay between the lattice absorbing the first photon and emitting the second while the lattice tries to absorb the photon energy. A photon may 'hop' between springs while traveling through a solid, so although photons always travel at c in a solid they 'appear' to slow down while they are absorbed and re-emitted by the energy levels.

Does that make sense?

Caveat lector - much of this (in fact the majority of it) is not scientifically accurate, but does convey the 'gist' of the mechanisms.

 

[anantchowdhary]

Im getting a hang of wat ur saying.But can u please answer my previous question based on the time taken by a photon to traverse the same distance in a refracting medium and also in vacuum.Thank you

 

[Hootenanny]

Hey,is it that the photon's time to cover that distance thru a refracting medium gets prolonged in comparison to its normal time taken to pass thru a distance?Im sry I am in a mess

Yes, in general it will take light longer to travel through a refracting medium than through free space. Although please note that photons travel at c through the refracting medium. And there's no need to apologise, we're all here to learn.

 

[anantchowdhary]

Hey so if it takes a longer time then isn't Fermat's Principle of least time being violated
Also so a photon has to be two dimensional as viewed by us,is it?Cuz it ha no length also it duznt travel thru time?

 

[Hootenanny]

Hey so if it takes a longer time then isn't Fermat's Principle of least time being violated

Not if you correctly understand the principle.

Also so a photon has to be two dimensional as viewed by us,is it?Cuz it ha no length also it duznt travel thru time?

From our point of view photons do experience time.