Do Photons Have Mass and Momentum?

[Garvi]

photon is a particle. then how come it does not have mass?

 

[1MileCrash]

The word "particle" doesn't imply mass. I couldn't think of a more vague word.

Furthermore, this is one of the reasons light is sometimes thought of a wave and sometimes thought of a particle. I'd rather it be a wave when talking about its lack of mass, and I'd rather it be a particle when talking about its momentum.

 

[Naty1]

Why should it have mass??

Anyway, nobody really knows...anymore than we know why an electron has the mass we observe...or the charge.

Or asking "Why is the Earth here?"

Some good related discussion here:

https://www.physicsforums.com/showthread.php?t=507973&highlight=photon+mass

 

[sophiecentaur]

Why should it have mass?
Look at what wiki has to say about the fundamental particles, how they interact and how the forces between particles can be accounted for. It's very involved.

But, personally, I think that referring to a photon as a particle is not helpful. There are many paradoxes involved if you want to look at is as a little bullet - like how big could it be? Would a photon of 200kHz radiation really be 1000 times 'bigger' than a photon of 200MHz radiation (bearing in mind that there would also have to be a thousand times as many 200kHz photons for the same power flow)?
I prefer to stick with an idea of a photon as being just a quantum of energy which only shows up when an em wave interacts with some system of charges, such as an atom, molecule or nucleus. That view doesn't actually run counter to the 'proofs' of it being a particle, such as the photoelectric effect and can save many sleepless nights, worrying about it.

 

[jishitha]

Photons possesses mass, when it is moving., and rest mass of photon is 0...

 

[DrDu]

In superconductors, photons are massive.

 

[sophiecentaur]

Photons possesses mass, when it is moving., and rest mass of photon is 0...

When is a photon not moving?

 

[DrDu]

When is a photon not moving?

In the case of massive particles, the mass is the energy of the particle at momentum 0 (divided by c^2). If one extends this definition to the case of photons in vacuo one has to set the mass of the photon to 0 as E=c p and therefore vanishes at p=0.

 

[sophiecentaur]

So when is a photon not moving? You haven't said. You have merely introduced a property of particles that do have mass. (A circular argument).
Measured mass of a photon, from wiki <1×10−18 eV/c2. Not 'measured' as zero because of the accuracy of the measurement that was possible - hence the upper limit is quoted.

The "non-zero mass" is referred to as "effective rest mass". That is hardly the same thing as mass. It's a bit like discussing semiconductor Holes. They are only a way of describing an observed conduction mechanism.

 

[DrDu]

So when is a photon not moving? You haven't said. You have merely introduced a property of particles that do have mass. (A circular argument).
Measured mass of a photon, from wiki <1×10−18 eV/c2. Not 'measured' as zero because of the accuracy of the measurement that was possible - hence the upper limit is quoted.

The "non-zero mass" is referred to as "effective rest mass". That is hardly the same thing as mass. It's a bit like discussing semiconductor Holes. They are only a way of describing an observed conduction mechanism.

I don't think this is circular. I just wanted to point out how the concept of (rest-) mass can be extended to objects which can't be at rest.

As to "effective rest mass" vs "true mass". Obviously it is something different to discuss propagation of light in vacuo vs in matter. But I don't think that there is a difference of principle. Electrons in vacuo aren't more fundamental than holes in solids. They both only describe an observed conduction mechanism, nothing more.

 

[sophiecentaur]

That's a fair enough comment. I rather shot myself in the foot there!
I still think that there is a (quantitative) difference between the behaviour of a photon under most conditions ( i.e., it exhibits no mass pretty much all the time ) and the 'effective' behaviour of a photon under special fringe-quantum conditions in which a mass-like nature reveals itself.
But, as with the Higgs Boson and other frontier-bashing concepts, it may turn out to be very relevant to our better understanding and development of a TOE.
My problem is that such inconsistencies can be taken out of context by the 'less well informed' and applied to everyday situations where they are not relevant and can introduce even more confusion. That little word "effective" can so easily be confused with "it's really there" and could be used in arm waving explanations of such things as Light Pressure, where Momentum is the relevant quantity.

 

[joyever]

Photons possesses mass, when it is moving., and rest mass of photon is 0...

so can we say light has mass?

 

[sophiecentaur]

Can someone tell me of a time when a photon is not moving? If not, then what has "rest mass" got to do with this discussion?

The one quoted situation when a photon may 'exhibit the property of mass', still doesn't imply that the photon is ever stationary. So where does that take us?

Photons have momentum - they show it all the time. That doesn't imply mass.

 

[Khashishi]

jigarbageha: I don't think your physics are wrong. Your disagreement is stemming from a non-conventional definition of the term "mass". "mass" when used by itself is ambiguous, but is conventionally taken to mean "rest mass", which is the energy left over when you've subtracted all the kinetic energy and removing any potential well. If you prefer to mean relativistic mass, you'd better spell it out, but the term isn't used much because it's redundant with the term energy.

 

[DrGreg]

There are (at least) two competing definitions of "mass" within relativity. One definition is now used by almost all professional physicists; the other definition was used historically by physicists and is still used in some schools, and books aimed at the general public.

The old definition included an object's kinetic energy* as part of its mass (via E = mc²). Thus an object's "mass" (a.k.a. "relativistic mass") varied with velocity*; the object's mass when it was stationary* was called its "rest mass".

The new definition excludes the kinetic energy of the object and is therefore constant. In the old terminology it was "rest mass" and is now called just "mass".

It's unfortunate that both definitions are still in use, so if someone refers to "mass", you need to check whether they mean the old definition (="relativistic mass") or the new definition (="rest mass" or "invariant mass").

The equation relating mass (=rest mass) m to energy* E and momentum* p is<br /> E^2 = m^2 c^4 + |\mathbf{p}|^2 c^2<br />This applies to particles with non-zero (rest) mass, but also applies to photons if you set m=0. This justifies saying that the mass of a photon is zero (in the new terminology), or that the rest mass of a photon is zero (in the old terminology) even though a photon can never be at rest. This is one case where it was less confusing to use the term "invariant mass" instead of "rest mass".

So, the answer to the original question "do photons have mass?" is "no" under the modern definition, but "yes" under the old definition which some people still use.

There is some more about this in the relativity forum's FAQ https://www.physicsforums.com/showthread.php?t=511175 .

____
*relative to some frame of reference

 

[juanrga]

When is a photon not moving?

The concept of rest mass does not imply that a body is not moving. Electrons have rest mass but does not imply that are always at rest, neither that the concept of rest mass only applies when they are at rest.

 

[Hootenanny]

The concept of rest mass does not imply that a body is not moving. Electrons have rest mass but does not imply that are always at rest, neither that the concept of rest mass only applies when they are at rest.

Indeed this is only true, but that wasn't sophie's point. In order to define a non-zero rest mass for a particle, there must exist a fame in which the particle is stationary. There exists such a frame for an electron, but not the photon.

 

[sophiecentaur]

Wouldn't a finite rest mass imply infinite mass at c? Is that not a clincher?

 

[juanrga]

Indeed this is only true, but that wasn't sophie's point. In order to define a non-zero rest mass for a particle, there must exist a fame in which the particle is stationary. There exists such a frame for an electron, but not the photon.

Rest mass is not the mass that a particle has only when is at rest.

The rest mass of a particle is also well-defined for frames in which the particle is not at rest. Rest mass is one of the properties that defines the particle (together with spin, charge..) and those properties are frame-independent.

From a particle point of view, the rest mass can be obtained from the mass operator in the energy-momentum space.

Maybe the term "rest" is at the root of the confusion. Just substitute the term "rest mass" by invariant mass or simply mass for avoiding it.

 

[sophiecentaur]

Whatever sort of mass you are talking of, how would it not go infinite for a speed of c?

 

[dchris]

Hey, i have a question. Photons posses mass only when they are moving, so according to our actual laws of physics, shouldn't they reach an infinite mass by moving with the speed of light? Photons obtain mass while moving, and they are always in motion,so due to our laws of physics anything that obtains mass is not able to move with speed of light in vacumm because it would have an infinite mass, and to move an infinite mass you need infinite energy, and there is nothing in our universe that is infinite (well, maybe excpect the universe itself). So logically light shouldn't be able to move with c. Am i correct? Or is there something wrong with modern physics?

 

[Phrak]

"particle" is a word used to distingush one field from another having different quantum numbers. Why are we talking about particles as little bee-bees?

Or sometimes I see talk about "waves" as contrart to particles, as if there is some sort of particle-wave duality.

Throwing out these two conceptual crutches may improve ones thought processes.

 

[cmb]

If a photon's momentum is h/λ and it is traveling at c, then one might naively suppose its mass is h/cλ, no?

Perhaps the issue with the question is understanding what 'mass' means for relativistic particles?

 

[Hootenanny]

Rest mass is not the mass that a particle has only when is at rest.

The rest mass of a particle is also well-defined for frames in which the particle is not at rest. Rest mass is one of the properties that defines the particle (together with spin, charge..) and those properties are frame-independent.

From a particle point of view, the rest mass can be obtained from the mass operator in the energy-momentum space.

Maybe the term "rest" is at the root of the confusion. Just substitute the term "rest mass" by invariant mass or simply mass for avoiding it.

If you carefully re-read what I wrote, you will find that I never said that the rest mass is only defined when a particle is at rest, nor did I say that the rest mass does no exist in a frame moving relative to the particle.

What I said is that there must exist a frame in which the particle is at rest. In other words, you must be able to associate a frame of reference with the particle. These statements do not mean that the rest mass is undefined in a moving frame.

Do you follow?

 

[Drakkith]

Hey, i have a question. Photons posses mass only when they are moving, so according to our actual laws of physics, shouldn't they reach an infinite mass by moving with the speed of light? Photons obtain mass while moving, and they are always in motion,so due to our laws of physics anything that obtains mass is not able to move with speed of light in vacumm because it would have an infinite mass, and to move an infinite mass you need infinite energy, and there is nothing in our universe that is infinite (well, maybe excpect the universe itself). So logically light shouldn't be able to move with c. Am i correct? Or is there something wrong with modern physics?

In the equation E=MC^2 the M is equal to an objects REST mass. For a photon this is 0 and the equation is invalid because it is an abbreviated form of the whole equation and is applicable to objects with no velocity or momentum. The rest of the equation adds in the energy due to an objects momentum. In relativity ALL energy contributes to gravity, and so a photon has 0 mass yet it does have gravity and it can, and does, travel at c to the best of our knowledge. Check out wikipedia for more.

If a photon's momentum is h/λ and it is traveling at c, then one might naively suppose its mass is h/cλ, no?

Perhaps the issue with the question is understanding what 'mass' means for relativistic particles?

Unfortunately the term "mass" is taken to refer to both invariant and relativistic mass. To avoid confusion it is usually advised to only use the term mass when referring to the invariant mass. The post I quoted above is a perfect example of this confusion.

 

[juanrga]

If you carefully re-read what I wrote, you will find that I never said that the rest mass is only defined when a particle is at rest, nor did I say that the rest mass does no exist in a frame moving relative to the particle.

What I said is that there must exist a frame in which the particle is at rest. In other words, you must be able to associate a frame of reference with the particle. These statements do not mean that the rest mass is undefined in a moving frame.

Do you follow?

I think that you missed my point again. As said in the message that you are replying, rest mass of a particle (i.e. its mass) is frame-independent, as is also any other property that defines a particle (I cited spin and charge, above). This independence means that you do not need "to associate a frame of reference with the particle".

 

[Hootenanny]

I think that you missed my point again. As said in the message that you are replying, rest mass of a particle (i.e. its mass) is frame-independent, as is also any other property that defines a particle (I cited spin and charge, above). This independence means that you do not need "to associate a frame of reference with the particle".

I think that we have crossed wires here. My point was merely this: A necessary and sufficient condition for a particle to have a non-zero rest mass is that there exists a valid frame in which the particle is at rest.

Do you disagree with that statement?

 

[dchris]

In the equation E=MC^2 the M is equal to an objects REST mass. For a photon this is 0 and the equation is invalid because it is an abbreviated form of the whole equation and is applicable to objects with no velocity or momentum. The rest of the equation adds in the energy due to an objects momentum. In relativity ALL energy contributes to gravity, and so a photon has 0 mass yet it does have gravity and it can, and does, travel at c to the best of our knowledge. Check out wikipedia for more.



Thanks Drakkith, now i understand. So a photon always has 0 mass, so its gravity comes from its energy, not mass. But now i have another question. So why does a photon restrict itself to c and not to higher speeds? IS the law that an object at c gains infinite mass somehow similar to energy? I mean can energy be so great at c that in becomes infinite? (meaning that E=M)

 

[Drakkith]

Thanks Drakkith, now i understand. So a photon always has 0 mass, so its gravity comes from its energy, not mass. But now i have another question. So why does a photon restrict itself to c and not to higher speeds? IS the law that an object at c gains infinite mass somehow similar to energy? I mean can energy be so great at c that in becomes infinite? (meaning that E=M)

Why? Not sure. All we can say is that it simply does. Maybe all the math says more but I don't know. I just know that c is the absolute limit that anything can travel at.
As for energy becoming infinite at c, that only applies for objects with mass.

 

[Tim_BandTech]

The simplest way to assign the mass of a photon is to marry
e = h v
with
e = m c c
which gives
m = ( h v ) / ( c c )
but this is typically called the 'rest mass' and photons do not seem to rest. Neither do electron's seem to rest, but that does not prevent a claim of measure of the electron's rest mass.

Like the consideration of mass, the consideration of wavelength as a real geometrical factor in the quality of a photon is not confronted within modern physics. The photon model must be oversimplified, and any who are happy with the current state ought perhaps to reconsider this position. The subject is alive and open for new interpretations, though these new interpretations will obviously conflict with the old principles. These old principles are inherently conflicted, such as particle wave duality, and the fact that we treat such terms as fixed and truthful principles exposes a human weakness: we are in danger of making physics into a religion. The subject must remain open to new interpretations. Keep going with your questioning and keep it first order as much as possible.

 

[sophiecentaur]

C and 0Kelvin needn't be regarded as ' barriers ' in the same way as Escape Velocity and the Sound Barrier. They are 'soft' limits that just require more and more effort as you want to get closer.
They are more like 'definitions' than boundaries to be conquered. Wherever you are and however fast you think you're going, something colder can be overtaking you.

 

[dchris]

Why? Not sure. All we can say is that it simply does. Maybe all the math says more but I don't know. I just know that c is the absolute limit that anything can travel at.
As for energy becoming infinite at c, that only applies for objects with mass.

You seem very certain about the speed limit, and i understand it. But what do you think about the discovery about those neutrinos that traveled 60 nanoseconds faster than light? Do you think its some kind of mistake or error? Or maybe a revolution?

 

[Vanadium 50]

I think that we have crossed wires here. My point was merely this: A necessary and sufficient condition for a particle to have a non-zero rest mass is that there exists a valid frame in which the particle is at rest.

Do you disagree with that statement?

It's true, but I don't think it's helpful to think of it as necessary. Rest mass is the norm of the energy-momentum four vector. This extends the concept seamlessly to massless particles, because even if you can't boost to a frame where the particle is at rest, every four vector has a norm.

 

[phinds]

You seem very certain about the speed limit, and i understand it. But what do you think about the discovery about those neutrinos that traveled 60 nanoseconds faster than light? Do you think its some kind of mistake or error? Or maybe a revolution?

First, I would caution you to develop a habit of not being sloppy in your phrasing of any statement purported to discuss science. "60 nanoseconds faster than light" is a meaningless phrase. What was observed was that neutrinos SEEM to have traveled over a certain distance in an amount of time that was 60 nanoseconds less than what it would have been had they been traveling at the universal speed limit (which is a speed limit that light obeys).

There has not as yet been any discovery that neutrinos travel faster than light. What there HAS been is a large number of experimental trials that give a result that the people who made the observations seem pretty convinced is an observational error, but they have tried six ways from Sunday to figure out where the error is and have not been able to do so, so they published their results with the specific request that other physicists (that is other than the 160 of them that had participated in the trials) see if they can figure out where the error is.

The popular press immediately pounced on this with such inanities as showing a picture of Einstein upside down and claiming a revolution in physics.

It certainly remains an open question until either the error is found or it is concluded that there is no error, in which case, THEN you can talk about faster than light, but it seems likely that an error will be found.

 

[jetwaterluffy]

A photon does not have mass, but it does have energy, and gravity works on anything that has energy (I think).

 

[Low-Q]

so can we say light has mass?

No.
Say that you have a flashlight that radiates X Watt of light. Say you put frictionless wheels on the flashlight. The flashlight weights Y Newton. Now after a given time, the flashlight should now roll a given distance due to the energy from the light. Since the flashlight actually don't move at all, it cannot be mass in the light that push the flashlight away.

Vidar

 

[Cantab Morgan]

No.
Say that you have a flashlight that radiates X Watt of light. Say you put frictionless wheels on the flashlight. The flashlight weights Y Newton. Now after a given time, the flashlight should now roll a given distance due to the energy from the light. Since the flashlight actually don't move at all, it cannot be mass in the light that push the flashlight away.

Vidar

Why do you contend that the flashlight will not roll? Of course, a real flashlight will not, but in your thought experiment, the flashlight with frictionless wheels will enjoy an impulse from the light.

 

[ZapperZ]

You seem very certain about the speed limit, and i understand it. But what do you think about the discovery about those neutrinos that traveled 60 nanoseconds faster than light? Do you think its some kind of mistake or error? Or maybe a revolution?

There should be NO discussion on the OPERA results outside of the existing thread in the Relativity forum. Please confine the discussion only to on-topic subject.

Zz.

 

[phinds]

In superconductors, photons are massive.

Huh? Could you expand on that?

 

[jetwaterluffy]

No.
Say that you have a flashlight that radiates X Watt of light. Say you put frictionless wheels on the flashlight. The flashlight weights Y Newton. Now after a given time, the flashlight should now roll a given distance due to the energy from the light. Since the flashlight actually don't move at all, it cannot be mass in the light that push the flashlight away.

Vidar

It would move. That's how solar sails work. Light has momentum, but no mass.

 

[Hootenanny]

It's true, but I don't think it's helpful to think of it as necessary. Rest mass is the norm of the energy-momentum four vector. This extends the concept seamlessly to massless particles, because even if you can't boost to a frame where the particle is at rest, every four vector has a norm.

You are of course right. Defining the mass as the norm of the energy-momentum vector is more convenient. Perhaps necessary is was too stronger word, I was merely trying to expand on sophie's point for the OP's benefit, who I fairly sure would benefit more from a physical explanation, than a more formal one.

 

[Phrak]

Do photons have mass?-

On shell photon fields have mass. Off shell fields have nonzero mass.

 

[sophiecentaur]

On shell? What shell?

 

[dchris]

First, I would caution you to develop a habit of not being sloppy in your phrasing of any statement purported to discuss science. "60 nanoseconds faster than light" is a meaningless phrase. What was observed was that neutrinos SEEM to have traveled over a certain distance in an amount of time that was 60 nanoseconds less than what it would have been had they been traveling at the universal speed limit (which is a speed limit that light obeys).

There has not as yet been any discovery that neutrinos travel faster than light. What there HAS been is a large number of experimental trials that give a result that the people who made the observations seem pretty convinced is an observational error, but they have tried six ways from Sunday to figure out where the error is and have not been able to do so, so they published their results with the specific request that other physicists (that is other than the 160 of them that had participated in the trials) see if they can figure out where the error is.

The popular press immediately pounced on this with such inanities as showing a picture of Einstein upside down and claiming a revolution in physics.

It certainly remains an open question until either the error is found or it is concluded that there is no error, in which case, THEN you can talk about faster than light, but it seems likely that an error will be found.

Thanks for pointing out my mistake. But also keep in mind I am just 15 years old.

 

[sophiecentaur]

But also keep in mind I am just 15 years old.

Perhaps you could also bear that in mind when you feel tempted to jump in with both feet. You can expect to get a good kicking, sometimes, if you appear to be making unfounded assertions. OK as long as you have a thick skin - if you're 'ard enough.

 

[phinds]

Thanks for pointing out my mistake. But also keep in mind I am just 15 years old.

I was not aware of that and I'd say you're doing GREAT for a 15 year old, but as sophiecentaur pointed out, this is not a forum for the thinskinned and while I'm very serious in saying that you're doing well for a 15 year old, I would further caution you that if you want to play in the deep end of the pool you need to keep in mind that it was your own idea. Your statement "Thanks for pointing out my mistake. But also keep in mind I am just 15 years old." would really have been better as just "Thanks for pointing out my mistake". We ALL here make mistakes and part of playing in the deep end of the pool is to just fess up to them when we make them. You'll find my posts littered with them.

 

[sophiecentaur]

Yes. You may notice that people who start to start to 'wax lyrical' and 'alternative' very often get jumped on, here. There are always ways of saying things that avoid a bad response, at least initially. Asking questions rather than making statements and loads of IMHO's and things will help to oil the wheels. Remember, you may well be conversing with someone who knows a fair bit more about the particular topic than your teacher at School. And you would, of course, be verrrrry respectful about your teacher's knowledge.

There is a fair smattering of BS, too. You get to distinguish, soon enough, though.

 

[Low-Q]

It would move. That's how solar sails work. Light has momentum, but no mass.

OK. I did not take that into account, but you're right. However the force is very very weak. Vidar

 

[sophiecentaur]

Maxwell had all this sorted out before anyone discovered photons, you might be interested to know. My old classical electromag theory book derives the amount of 'light pressure' on a surface by just using the fields and how the surface modifies them. Surprise, surprise, old JCM got the same answer as the QM crowd. I bet that made the new boys pretty happy and relieved.

 

[Phrak]

On shell? What shell?

http://en.wikipedia.org/wiki/On_shell_and_off_shell"