What is the truth about photons and their mass?

[ImAnEngineer]

I had a discussion with my physics teacher. He claimed that photons have mass (although no rest mass), since they have energy and E=mc². I argued that having energy isn't the same as having mass, but that energy could be converted into mass which is a different thing (e.g. a photon can disintegrate into a positron-electron pair which have mass, but that doesn't mean the photon itself had mass). My second argument against the claim that photons have mass, is that (if v=c): m = m0 / sqrt(1-c²/c²) = 0 / 0 which is undefined.

Who is right?

 

[CompuChip]

Personally, I would favour the second view, although I don't think anyone is really wrong. You just have differing views, where you have two concepts called "(total) energy" and "mass" and he has two concepts called "rest mass" and "relativistic mass" (which is related to your total energy divided by c^2).

There are arguments for both approaches: on one hand they have different units; on the other hand, in many ways objects with higher energy behave like they are in fact more massive (e.g. you can write F = m a where m = m₀ γ is the relativistic mass and m₀ the rest mass, for the parallel (or was it perpendicular?) component of the force and acceleration).

Just my 2 cents here, perhaps others disagree.

 

[ZikZak]

Ask your teacher what he means by "mass."

Does it have something to do with inertia? If mass has something to do with inertia, then photons must have infinite mass, since you cannot accelerate them at all. Does that seem meaningful?

Does it have something to do with gravity? Photons do cause curvature of spacetime, true... but the curvature they produce is significantly different from that of a mass E/c^2 at rest, and you would get completely wrong ideas about it if you tried to plug E/c^2 into F=Gmm/r^2, for instance.

 

[ImAnEngineer]

Ask your teacher what he means by "mass."

Does it have something to do with inertia?

Yes

If mass has something to do with inertia, then photons must have infinite mass, since you cannot accelerate them at all. Does that seem meaningful?

Not really.

Moreover, he mentioned de Broglie wavelength:

\lambda=\frac{h}{mc}

Then
m_p_h_o_t_o_n=\frac{h}{\lambda c}= 3.97 * 10^-^1^9 kg if the wavelength is 500nm?
I also asked: do photons with different frequencies have different mass since E=hf?
He answered yes.

If the mass of a photon however is either 0 or infinite, then there shouldn't be any difference in mass. (infinity + a little bit is still infinity). Am I right?

I'm quite confused right now. Please enlighten me :P .

 

[ZapperZ]

You may want to start by reading the FAQ in the General Physics forum.

Zz.

 

[ImAnEngineer]

You may want to start by reading the FAQ in the General Physics forum.

Zz.

I read it now. What is in there is exactly what I thought!

So my physics teacher sucks? :P

 

[ImAnEngineer]

You may want to start by reading the FAQ in the General Physics forum.

Zz.

By the way, this link in the FAQ is broken:

You can read more about this at the Usenet FAQ.

 

[Bob S]

Ask your teacher what he means by "mass."

Does it have something to do with inertia? If mass has something to do with inertia, then photons must have infinite mass, since you cannot accelerate them at all. Does that seem meaningful?

Does it have something to do with gravity? .

First, accelerating a photon itself is difficult, but you can accelerate a particle or object that emits photons (like a radioactive source), and you will find that the forward emitted photons have higher energy (doppler shift) even though their velocity has not changed. So if the photon energy has increased, and the velocity has not increased, then its relativistic mass has increased.

Second, If you use an iron-57 source which emits 14.4 keV photons with a very narrow linewidth, and put it on the roof of a building, and measure the energy of these photons at ground level, you will find that the photon energy has increased due to the gravitational potential change. This is called the Mossbauer Effect experiment, which was done in 1959 at Harvard by Pound and Rebka.

 

[jnorman]

this is a long standing debate, with advocates on both sides of this issue. photons have no rest mass. however, E=MC2 does indeed imply that energy and mass are interchangeable, thus implying that the energy of photons does indeed represent a certain quantity of mass, which is born out by the fact that photons can impart momentum. the resolution revolves around (as mentioned above) the definition of mass used in the discussion.

 

[ImAnEngineer]

First, accelerating a photon itself is difficult, but you can accelerate a particle or object that emits photons (like a radioactive source), and you will find that the forward emitted photons have higher energy (doppler shift) even though their velocity has not changed. So if the photon energy has increased, and the velocity has not increased, then its relativistic mass has increased.

So would a calculation as I posted in post#4 make sense?

 

[Count Iblis]

Lev Okun has explained it very well here:

http://arxiv.org/abs/0808.0437

 

[atyy]

http://focus.aps.org/story/v16/st1

 

[confinement]

I read it now. What is in there is exactly what I thought!

So my physics teacher sucks? :P

Yes, your teacher sucks at physics if they think that the mass of a photon is given by m = E / c^2.

 

[Fredrik]

He claimed that photons have mass (although no rest mass), since they have energy and E=mc².

My opinion is that the concept of "relativistic mass" is pointless, and I don't use it myself. Note that the formula E=mc² for photons isn't even a derived result. It's the definition of m.

I argued that having energy isn't the same as having mass,

It does make sense to think of a photon's energy as a "mass" expressed in different units. Consider e.g. a box that contains one photon, endlessly bouncing around between its walls. If you put this box on a (ridiculously sensitive) scale, you will see that it weighs more than an identical box that's empty. You can think of this as a consequence of the photon being blueshifted by gravity on the way down, and redshifted on the way up, so when it hits the floor it has more momentum than when it hits the ceiling.

The same box will also be slightly more difficult to accelerate than an empty box, for pretty much the same reason. Just replace the word "gravity" above with "acceleration".

And yes, the amount of momentum and energy gained during the trip from the ceiling to the floor depends on the energy of the photon, so a photon with higher energy changes the "mass" (as measured by the scale) by a larger amount.

My second argument against the claim that photons have mass, is that (if v=c): m = m0 / sqrt(1-c²/c²) = 0 / 0 which is undefined.

That particular formula is for massive particles, so it doesn't apply. The formula that holds for all particles is

E^2=\vec p^2c^2+m_0^2c^4.

When \vec p=m\vec v=\gamma m_0 \vec v, the right-hand side reduces to m^2c^4, but \vec p=\gamma m_0 \vec v only holds for massive particles.

 

[alxm]

this is a long standing debate, with advocates on both sides of this issue.

No, it is not a "long-standing debate". The definitions of 'relativistic mass' and 'rest mass' were made quite clear when special relativity was developed, as well as the fact that the 'm' in E=mc^2 is rest mass and nothing else.

I don't see where the 'debate' would be. Either you've understood SR, including its definitions, or you haven't.

 

[atyy]

http://books.google.com/books?id=udA0Gjq8vHIC&printsec=frontcover#PPA16,M1

 

[jostpuur]

No, it is not a "long-standing debate". The definitions of 'relativistic mass' and 'rest mass' were made quite clear when special relativity was developed,

I don't see where the 'debate' would be. Either you've understood SR, including its definitions, or you haven't.

There are those who understand that the definitions of relativistic mass and rest mass are only definitions, and then there are those who insist that relativistic mass is incorrect. This is where the debate originates.

as well as the fact that the 'm' in E=mc^2 is rest mass and nothing else.

Well that 'm' in that equation surely can be something else than the rest mass, since you did not emphasize that the energy means the rest energy by writing lower index E_0.

 

[Dmitry67]

I understnd that it is slightly belongs to the 'Beyond the Standard model'
But among different definitions of mass we should use the one which still correct when we go deeper and deeper.
So, mass of all prarticles is 0 and the observed mass is a result of interaction of these massless particles with the Higgs condensate. So, no particle can be observed in it's own rest frame. Hence, only reltivistic definition of mass in valid on the long run.

 

[ImAnEngineer]

It is clear to me that a photon has no rest mass. But can anyone come up with a watertight argument that it has no relativistic mass? And that calculating the mass by m=E/c² is wrong? I want to know how I can convince my teacher I am right :) .

Thank you

 

[robphy]

It is clear to me that a photon has no rest mass. But can anyone come up with a watertight argument that it has no relativistic mass? And that calculating the mass by m=E/c² is wrong? I want to know how I can convince my teacher I am right :) .

Thank you

This really depends on your definition of "relativistic mass".
Once properly defined, then you can probably answer your own question [with your definition].

To me, the real [physically-interesting] issue is likely
how would one use or misuse such a quantity.

 

[jostpuur]

It is clear to me that a photon has no rest mass. But can anyone come up with a watertight argument that it has no relativistic mass?

You are not right here, since photon has relativistic mass.

Trying to compute rest mass with m_0=E/c^2 would be wrong, while m_0=0 is right.

Computing relativistic mass with m_{\textrm{rel}} = E/c^2 is right.

And that calculating the mass by m=E/c² is wrong?

Here you are right, since "the mass" usually means the rest mass, and we are supposed to use the notation m=m_0 (right), and not the non-standard notation m=m_{\textrm{rel}} (wrong).

So m=E/c^2 would usually mean m_0=E/c^2 which is wrong.

 

[jnorman]

alxm - a rather terse and closed position for you to take here. the debate revolves around the basic concept of relativistic mass as applied to photons, and there are several threads about this in the archives. many people deny relativistic mass outright, while many others see merit in its application to photons. there is no reason to assume any kind of fixed opinion in QM, since even you must agree that nobody understands the underlying reality. we are all in kindergarten as far as i am concerned.

 

[MathematicalPhysicist]

I wonder how did they eventually built the H-bomb with this controvesy.

 

[lightarrow]

Relativistic mass already had another name: total energy. Why do people want to create another name?

 

[Count Iblis]

I wonder how did they eventually built the H-bomb with this controvesy.

The controversy was helpful. It meant that people who were not clever enough to see through it would drop out in college.

 

[ImAnEngineer]

This really depends on your definition of "relativistic mass".
Once properly defined, then you can probably answer your own question [with your definition].

Okay, so then what are different ways to define relativistic mass?

You are not right here, since photon has relativistic mass.

Trying to compute rest mass with m_0=E/c^2 would be wrong, while m_0=0 is right.

Computing relativistic mass with m_{\textrm{rel}} = E/c^2 is right.

Here you are right, since "the mass" usually means the rest mass, and we are supposed to use the notation m=m_0 (right), and not the non-standard notation m=m_{\textrm{rel}} (wrong).

So m=E/c^2 would usually mean m_0=E/c^2 which is wrong.

Okay, so m_r_e_l=E/c^2 can be used to compute the relativistic mass of photons.

Relativistic mass already had another name: total energy. Why do people want to create another name?

What other name?

 

[jostpuur]

Relativistic mass already had another name: total energy. Why do people want to create another name?

What other name?

The relativistic mass of some object is simply the total energy of the object divided by c^2, so they are almost the same thing. There is the concept which originally has the name "energy", and then it is given other name "relativistic mass" in a redundant manner. Some people believe that it is a useless alternative name for a concept which already had a name.

 

[ImAnEngineer]

The relativistic mass of some object is simply the total energy of the object divided by c^2, so they are almost the same thing. There is the concept which originally has the name "energy", and then it is given other name "relativistic mass" in a redundant manner. Some people believe that it is a useless alternative name for a concept which already had a name.

Ah ok, thanks! Now I understand.

 

[DrGreg]

It is clear to me that a photon has no rest mass. But can anyone come up with a watertight argument that it has no relativistic mass? And that calculating the mass by m=E/c² is wrong? I want to know how I can convince my teacher I am right :) .

Thank you

Everyone agrees a photon has no "rest mass". Everyone agrees a photon has "relativistic mass". What they disagree over is whether it has "mass", i.e. does "mass" mean "rest mass" or "relativistic mass"? This is just convention, but there's no convention that everyone agrees with. It seems most professional experts use "mass" to mean "rest mass" (and never refer to "relativistic mass"), but some don't.

Relativistic mass already had another name: total energy. Why do people want to create another name?

What other name?

Er, "relativistic mass". "Relativistic mass" and "total energy" are two names for the same thing (in different units). Why have two names when one will do?

 

[atyy]

There is the concept which originally has the name "energy", and then it is given other name "relativistic mass" in a redundant manner.

I agree with the science and understand the terminology here. Just curious whether the "originally" is historically correct - after all, isn't energy in special relativity a new thing? It only approximates the Newtonian one at low speeds, and I've heard it said that special relativity shows that "energy" is not conserved, but physicists like "energy" conservation so much, they redefined "energy" so that it is still conserved.

 

[ImAnEngineer]

Everyone agrees a photon has no "rest mass". Everyone agrees a photon has "relativistic mass". What they disagree over is whether it has "mass", i.e. does "mass" mean "rest mass" or "relativistic mass"? This is just convention, but there's no convention that everyone agrees with. It seems most professional experts use "mass" to mean "rest mass" (and never refer to "relativistic mass"), but some don't.

Er, "relativistic mass". "Relativistic mass" and "total energy" are two names for the same thing (in different units). Why have two names when one will do?

Thanks for clearing it up. I get it now!

I agree with the science and understand the terminology here. Just curious whether the "originally" is historically correct - after all, isn't energy in special relativity a new thing? It only approximates the Newtonian one at low speeds, and I've heard it said that special relativity shows that "energy" is not conserved, but physicists like "energy" conservation so much, they redefined "energy" so that it is still conserved.

Interesting question, I would like to know that as well.

 

[ZikZak]

The problem with "Relativistic Mass" is how it is used and abused by high school and college science teachers, such as the one you are having this debate with.

After a semester of discussion about the Newtonian ideas of what mass is, defining it as the inertia of a particle in F=ma, and also its gravitational charge in F=Gmm/r^2, your teacher now smugly declares that photons have mass m=E/c^2, and so there. But this is exceedingly disingenuous. Yes, the photon has "relativistic mass" E/c^2, but what does that "mean" now? Clearly, it's not the m in F=ma NOR in F=Gmm/r^2 any longer. Not when you're looking up close at the photon. So what is it? Your teacher has just given you a meaningless and misleading bit of information. This situation could be resolved by your teacher actually sitting down and explaining to you the senses in which the energy of the photon actually behaves in ways we think of as "massive," such as carrying momentum (but not momentum mv) and generating gravity (but not Gmm/r^2). But instead, he decided (unfortunately, and like many teachers who lack deep understanding of the theory) to simply "wow" you with this cool thing, that photons have mass, which has had the predictable result of confusing you because you actually want to understand what he means by that.

Even worse would have been the standard tactic of defining for you the relativistic mass m=\gamma m_0, making you do multiple problems finding relativistic masses, and then declaring that this increase in mass is what prevents you from accelerating massive particles to c (since after all, the mass=inertia is increasing, right?). The implication being that the relativistic mass is the inertia of the particle. Wrong. If you accelerate a particle from rest with a constant force, measure its coordinate acceleration, and then find the mass using m=F/a, you do NOT find that the "mass" defined this way is the relativistic mass of the particle.

So this is a concept that not only already has a name ("total energy") and is not in need of a new one, but is a concept that is explicitly misused to confuse newcomers. That is why some of us object to its use at all.

 

[atyy]

http://books.google.com/books?id=ipY8onVQWhcC&printsec=frontcover#PPA83,M1

 

[ImAnEngineer]

...
So this is a concept that not only already has a name ("total energy") and is not in need of a new one, but is a concept that is explicitly misused to confuse newcomers. That is why some of us object to its use at all.

If one objects to use the concept of relativistic mass, then what would be said about the mass of a photon? Simply that the mass is zero (i.e. the rest mass)?

And if photons have energy which they do, and E=mc², then what could be said about m? It is certainly not the rest mass. Or would this equation not be used at all?

 

[ImAnEngineer]

http://books.google.com/books?id=udA0Gjq8vHIC&printsec=frontcover#PPA16,M1

What about it?

I do own Richard Feynman's lectures on physics and it includes special relativity.

 

[lightarrow]

If one objects to use the concept of relativistic mass, then what would be said about the mass of a photon? Simply that the mass is zero (i.e. the rest mass)?

Yes.

And if photons have energy which they do, and E=mc², then what could be said about m? It is certainly not the rest mass. Or would this equation not be used at all?

They already answered you. You can use equations if you know their meaning; in E = mc² what is E? Is the total energy? Is the rest energy only?
The answer is the second.
The correct equation for total energy, as already written by others is:

E² = (mc²)² + (cp)²

The other, simpler equation is just a specific case of this (that is, the case in which p = 0).

 

[ImAnEngineer]

Yes.
The correct equation for total energy, as already written by others is:
E² = (mc²)² + (cp)²
The other, simpler equation is just a specific case of this (that is, the case in which p = 0).

But photons do have momentum, so then it doesn't make sense to write E=mc² for photons at all?

Instead you could write, however:
m=\sqrt{\frac{E^2}{c^4}-\frac{p^2}{c^2}}

Then how would one that objects to use the concept of relativistic mass call this m?

 

[Count Iblis]

But photons do have momentum, so then it doesn't make sense to write E=mc² for photons at all?

Instead you could write, however:
m=\sqrt{\frac{E^2}{c^4}-\frac{p^2}{c^2}}

Then how would one that objects to use the concept of relativistic mass call this m?

This is called the invariant mass, or just mass.

 

[ImAnEngineer]

This is called the invariant mass, or just mass.

I really lost you guys. I understood that people who object to the use of relativistic mass use the rest mass instead (same thing as invariant mass?).

But when m is calculated with the last equation I gave, it doesn't give zero which is the rest/invariant mass of a photon...

My guess is that people who object to relativistic mass just wouldn't use it (and express it in terms of energy instead) and have no other name for (relativistic) mass, is that correct?

 

[Count Iblis]

I really lost you guys. I understood that people who object to the use of relativistic mass use the rest mass instead (same thing as invariant mass?).

But when m is calculated with the last equation I gave, it doesn't give zero which is the rest/invariant mass of a photon...

My guess is that people who object to relativistic mass just wouldn't use it (and express it in terms of energy instead) and have no other name for (relativistic) mass, is that correct?

The energy of a photon is E = p c. So, you see that m = 0 for a photon.

 

[ZikZak]

If one objects to use the concept of relativistic mass, then what would be said about the mass of a photon? Simply that the mass is zero (i.e. the rest mass)?

One says that the mass of a photon is zero, because the mass of a body is its energy at rest, and photons are never at rest.

But photons do have momentum, so then it doesn't make sense to write E=mc² for photons at all?

No, it does not make sense to write that, because E=mc^2 is only generally true for bodies at rest. The correct general equation is E^2=mc^2+(pc)^2, from which you obtain the next expression:

Instead you could write, however:
m=\sqrt{\frac{E^2}{c^4}-\frac{p^2}{c^2}}

Then how would one that objects to use the concept of relativistic mass call this m?

But when m is calculated with the last equation I gave, it doesn't give zero which is the rest/invariant mass of a photon...

The m found this way is the invariant rest mass. For a photon, it is in fact zero.

 

[ZikZak]

http://books.google.com/books?id=ipY8onVQWhcC&printsec=frontcover#PPA83,M1

So... "If it's good enough for Feynman, then it should be good enough for anyone?" You appear to be arguing from authority.

 

[jnorman]

i think most people who object to "relativistic mass" tend to view systems in terms of total energy rather than invoking mass terminology at all. mathematically, it is much cleaner.

 

[ImAnEngineer]

...

The m found this way is the invariant rest mass. For a photon, it is in fact zero.

Ah, I see. If E² is substituted by (pc)² the result is zero, so it is consistent to call it just (non-relativistic) mass . I think everything is clear to me right now.

Thanks to everyone!

 

[delplace]

Recent experiments showed that photons are not wave and not particles. They are something different. From these results, photons could be a fragment of spac-time detached from the continuum. In that way their mass does not exist because space-time continuum has no mass. But it is clear that this subject often called "The nature of light" remains one of the greatest question of physics.

 

[Vanadium 50]

Recent experiments showed that photons are not wave and not particles.

Reference, please? Of course light has both wave and particle properties, but this has been known for more than a century.

From these results, photons could be a fragment of spac-time [sic] detached from the continuum.

Reference, please?

In that way their mass does not exist because space-time continuum has no mass.

Even if the premise were true, and the conclusion is true, I don't think this argument is valid.

 

[Vanadium 50]

I have no desire to continue this discussion via PM. I posted my question here, and would like the answers here. (Note however, that PF rules do impose some limitations on the kinds of references that can be posted)

 

[ImAnEngineer]

Why would you discuss it via PM? I was waiting for the answers here in this thread.

 

[delplace]

I have no desire to continue this discussion via PM. I posted my question here, and would like the answers here. (Note however, that PF rules do impose some limitations on the kinds of references that can be posted)

ok, I give you the reference in a well known journal reviewed by peers :

S. Gleyzes et al., Nature, 446, 297, 15 march 2007

Concerning the second point, the paper is in a review process, so I will wait a little bit

Best regards

FD

 

[delplace]

Why would you discuss it via PM? I was waiting for the answers here in this thread.

sorry but I was not aware that people don't like PM discussions. I give you the reference :

S; Gleyzes et al., Nature, 446,297, 15 march 2007

Best regards

FD