Understanding the Massless Photon

[Lelan Thara]

(I hope I've chosen the right sub-forum for this question...)

Hi folks - I've recently joined here to see if people who are more knowledgeable than me can help me understand some physics issues I have struggled with for a long time.

My current question is a pretty basic one about how it is possible for a photon to have no mass.

We have the famous equation, "E = mc squared" My math knowledge is very limited, but from what I know - if I assign the value "0" to m, and multiply 0 by c squared, the answer for E should be zero.

Yet a photon possesses energy, and is said to have no mass.

I can see 3 possibilities:

- "E = mc squared" is not a standard algebra equation, and assigning the value "0" to m doesn't result in E being zero.

- "E = mc squared" does not apply to photons - something that seems very unlikely to me.

- photons do, in fact, have mass, or conversely, have no energy.

Can someone help me understand this? I would be very grateful. Thanks!

 

[arivero]

You need quantum mechanics too... E=h f

 

[Thrice]

It's usually a good idea to start out on wikipedia before asking here.

http://en.wikipedia.org/wiki/E=mc²

 

[Lelan Thara]

It's usually a good idea to start out on wikipedia before asking here.

http://en.wikipedia.org/wiki/E=mc²

Actually I do usually start with Wiki, but it never occurred to me to look up "E = mc squared" there.

Thanks for the link - it answers my question.

That was easy, wasn't it? Carry on, carry on...

 

[RandallB]

Yet a photon possesses energy, and is said to have no mass.

Can someone help me understand this? I would be very grateful. Thanks!

If you’re just looking for a way to understand; there is a very simple way.
Don't thing of a photon as "possessing" energy --- thing of a photon AS energy.
Now when an atom absorbs a photon and moves one its electrons into a higher energy ‘obit’ it gains mass.
When it drops to a lower energy level the atom loses mass as a photon is emitted in some random direction.

Where was the mass? in the electron; or in the atom as whole – I’ll let you speculate.
But that mass cannot just appear and disappear; shouldn’t mass be “conserved”?
No conservation of mass and conservation of energy is “Old School”
In modern physics it is the net of Mass and Energy that is conserved.
So when a bit of mass disappears from an atom we can find it in the energy that escapes from it – we call it a photon.
When a lot of mass disappears very quickly we can describe it as a lot photons (aka energy) escaping – or more easily described as a nuclear explosion.

 

[Doc Al]

My current question is a pretty basic one about how it is possible for a photon to have no mass.

We have the famous equation, "E = mc squared" My math knowledge is very limited, but from what I know - if I assign the value "0" to m, and multiply 0 by c squared, the answer for E should be zero.

Yet a photon possesses energy, and is said to have no mass.

The complete relativistic expression for the energy of a particle is this:
E = \sqrt{p^2c^2 + m^2c^4}

Where p is the momentum. Note that for massive particles at rest (momentum = 0) that equation becomes the more familiar E = mc^2.

For a photon: the mass is zero, but the momentum and energy are non-zero. E = pc = hf.

 

[Thrice]

Actually I do usually start with Wiki, but it never occurred to me to look up "E = mc squared" there.

Thanks for the link - it answers my question.

That was easy, wasn't it? Carry on, carry on...

Glad I could help. I picked up this firefox extension to make sure I can't avoid searching on wikipedia.

https://addons.mozilla.org/firefox/2517/

 

[Lelan Thara]

Thanks agains to all. The most fundamental answer to my question is that E=mc squared is not as universally applied as I assumed it was, at least not in its familiar simple form.

There is something that still confuses me a bit, and that's the concept of "rest mass". I was under the impression that the only time mass could be at rest was at a temperature of absolute zero, which doesn't really exist in nature (like a perfect vacuum). The photon is also never at rest - is the difference that the photon can't conceptually be at rest?

I've also come across references to the "virtual mass" of a photon. Can anyone shed more light on that?

The larger question might be - is the massless photon massless by definition? In other words, "mass is a quality of matter, the photon isn't defined as matter despite being a particle, and therefore the photon can't have a quality of matter - mass"?

Or is it something more concrete - that the photon doesn't exhibit inertia, acceleration and deceleration, and other properties of mass?

Thanks again.

 

[selfAdjoint]

Thanks agains to all. The most fundamental answer to my question is that E=mc squared is not as universally applied as I assumed it was, at least not in its familiar simple form.

There is something that still confuses me a bit, and that's the concept of "rest mass". I was under the impression that the only time mass could be at rest was at a temperature of absolute zero, which doesn't really exist in nature (like a perfect vacuum). The photon is also never at rest - is the difference that the photon can't conceptually be at rest?

That's in quantum mechanics. Special Relativity CAN be interfaced to quantum mechanics, but when we talk about SR by itself we mostly mean the classical model, where things can be at rest. You are right about the photon though, it has no rest frame, even in the classical theory, and no mass.

Sidebar.
I am one of the ones who do not use "rest mass" because that implies there is some kind of distinguished non-rest mass, which I deny. There are are other posters on this forum who vehemently disagree, and in order to get maximal use out of your experience here you have to be clear in your mind so the disagreement (which is a tempest in a teacup as far as physics is concerned) doesn't confuse you. In my view a particle has one mass, no matter how it is moving in relation to you, and this mass is a "scalar", that is to say the same in every frame.

I've also come across references to the "virtual mass" of a photon. Can anyone shed more light on that?

I don't know this one. Did you mean virtual photons?

The larger question might be - is the massless photon massless by definition? In other words, "mass is a quality of matter, the photon isn't defined as matter despite being a particle, and therefore the photon can't have a quality of matter - mass"?

ST postulates that the speed of light is invariant, the same for all inertial frames. It is a mathematical deduction from that postulate that if light is carried by a particle then that particle must be massless. In fact the two concepts "Massless" and "Moves at the Speed of Light" are synonymous in SR. Gluons in the Standard Model also have this property.

Or is it something more concrete - that the photon doesn't exhibit inertia, acceleration and deceleration, and other properties of mass?

As far as we can tell, it takes no acceleration to get a massless particle up to the speed c. But the experimental evidence for the masslessness of the photon is mostly in another area. From classical wave theory it follows that if light were carried by a massive particle, it would exhibit longitudinal (compression type) waves. Whereas we only find transverse light waves. Experimentalists do tests with fantastically refined versions of this distinction to examine the possibility that there are some very weak compression waves, that would allow a tiny mass to the photon. They've been doing this, with ever increasing precision, for generations. They've never found anything.

Of course no experiment can ever proves that the mass is exactly zero; every experiment has error bounds, but the error bounds on these tests have gotten really tiny, off the top of my head I want to say + or - 10^-20 electron volts.

Thanks again.[/QUOTE]

 

[notknowing]

Thanks agains to all. The most fundamental answer to my question is that E=mc squared is not as universally applied as I assumed it was, at least not in its familiar simple form.

There is something that still confuses me a bit, and that's the concept of "rest mass". I was under the impression that the only time mass could be at rest was at a temperature of absolute zero, which doesn't really exist in nature (like a perfect vacuum). The photon is also never at rest - is the difference that the photon can't conceptually be at rest?

I've also come across references to the "virtual mass" of a photon. Can anyone shed more light on that?

The larger question might be - is the massless photon massless by definition? In other words, "mass is a quality of matter, the photon isn't defined as matter despite being a particle, and therefore the photon can't have a quality of matter - mass"?

Or is it something more concrete - that the photon doesn't exhibit inertia, acceleration and deceleration, and other properties of mass?

Thanks again.

You made a good point here. The concept of a "massless particle" is so familiar in present day physics that people forget that it is in fact not such a good concept at all. As you pointed out, the photon is indeed never at rest, and can not be, so why should one talk of rest mass ? It is really nonsense if you think about it and it seems to cause a lot of confusion to many people (judging from the forum questions).So, the photon is massless by definition only with the convenient result that one can insert m=0 into the complete relativistic expression, such that one obtains the correct relation between energy and impulse. Maybe it would be better to use the term "c-particle" to indicate that it is a particle which moves at the speed of light.

 

[robphy]

Maybe it would be better to use the term "c-particle" to indicate that it is a particle which moves at the speed of light.

There already is a term: "lightlike" particle.

 

[rbj]

Thanks agains to all. The most fundamental answer to my question is that E=mc squared is not as universally applied as I assumed it was, at least not in its familiar simple form.

it could be more universally applied if the m in E = m c^2 is always considered the relativistic mass and E is the total energy, kinetic energy plus rest energy. or the energy of the particle in the frame of the observer watching it whiz by. or the momentum of the particle divided by speed. assuming photons travel at the speed of the wavespeed of electromagnetic radiation, c, the (relativistic) mass of the photons is

m = \frac{E}{c^2} = \frac{h \nu}{c^2}

but here m is not the "rest mass" or "invariant mass". for particles that move more slowly that c, special relativity says their momentum is

p = m v = \frac{m_0 v}{\sqrt{1 - \frac{v^2}{c^2}}}

where m_0 is the rest mass (and E_0 = m_0 c^2 is the rest energy and the total energy E_0 = m_0 c^2 is the rest energy plus kinetic energy). so the relationship between rest mass and relativistic mass is

m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}

or turned around is

m_0 = m \sqrt{1 - \frac{v^2}{c^2}}

or

m_0 = \frac{E}{c^2} \sqrt{1 - \frac{v^2}{c^2}} .

now, no matter what finite energy that particle has, if it moves at the speed of light, that equation says that the rest mass of the particle has to be zero.

the equation

E = m c^2

is just as general as

E^2 = m_0^2 c^4 + p^2 c^2

if the rest mass m_0 is related to relativistic mass m as per the equation above and momentum is stiil the same p = m v.

There is something that still confuses me a bit, and that's the concept of "rest mass".

particles moving past an observer at very high speeds "appear" to that observer to have a larger mass than they do if the observer is moving alongside the particle. the mass that the particle has in the same reference frame of the particle is the rest mass.

I've also come across references to the "virtual mass" of a photon. Can anyone shed more light on that?

dunno if it means

m = \frac{h \nu}{c^2}

of if it means that the jury might be out as to whether photons, the particle manifestation of light, travels as fast as the wavespeed of light. some have posted is upper bound for the rest masses of photons (if i recall this upper bound was somewhere around 10^-52 kg which is virtually nothing. so the difference in speeds are not measureable if there is such a difference at all. if it turns out that photons are known to travel at precisely the speed of light (waves), then the rest mass of the photons would have to be zero.

The larger question might be - is the massless photon massless by definition? In other words, "mass is a quality of matter, the photon isn't defined as matter despite being a particle, and therefore the photon can't have a quality of matter - mass"?

it's because they (are believed to) move at the speed of light that their rest mass has to be zero.

Or is it something more concrete - that the photon doesn't exhibit inertia, acceleration and deceleration, and other properties of mass?

it exhibits inertia, but no acceleration or deceleration if it always flies by at a speed of c, no matter who the observer is (this is a postulate of special relativity). they have momentum of

p = m v = \frac{h \nu}{c^2} v

which, if they move at speed v = c, then the momentum is

p = \frac{h \nu}{c}

they have non-zero momentum if that is what you mean by "inertia".

i know that i am presenting this from a POV that is discouraged in modern physics pedagogy (i don't think that Doc Al will like it), but it's correct given the definition of relativistic mass.

 

[Lelan Thara]

Thank you, folks.

I wish I could tell you where I saw the "virtual mass" for a photon mentioned. Most of my physics reading is books for laymen, but once I did try to wade through articles by physicsts themselves in the library - I think it might have be in an article by Bohr where I saw it.

Here's a related question - if a photon has no mass, what pushes a solar sail? Is it other forms of radiation, as opposed to photons?

 

[robphy]

Here's a related question - if a photon has no mass, what pushes a solar sail? Is it other forms of radiation, as opposed to photons?

Photons have momentum, as well as energy.

 

[pmb_phy]

(I hope I've chosen the right sub-forum for this question...)

Hi folks - I've recently joined here to see if people who are more knowledgeable than me can help me understand some physics issues I have struggled with for a long time.

My current question is a pretty basic one about how it is possible for a photon to have no mass.

We have the famous equation, "E = mc squared" My math knowledge is very limited, but from what I know - if I assign the value "0" to m, and multiply 0 by c squared, the answer for E should be zero.

Yet a photon possesses energy, and is said to have no mass.

I can see 3 possibilities:

- "E = mc squared" is not a standard algebra equation, and assigning the value "0" to m doesn't result in E being zero.

- "E = mc squared" does not apply to photons - something that seems very unlikely to me.

- photons do, in fact, have mass, or conversely, have no energy.

Can someone help me understand this? I would be very grateful. Thanks!

The answer to your question regards your confusion as to the definition of the term "mass." Sometimes the term is used to refer to a particles proper mass while sometimes its used to refer to inertial mass (aka relativistic mass). The photon has zero proper mass and an inertial mass m = E/c². For details please see

http://www.geocities.com/physics_world/mass_paper.pdf

Best wishes

Pete

 

[pervect]

Note that Pete's paper, with the URL given above, while mostly correct, has not been peer reviewed, and that some of us (like me) have disagreements with him on certain technical points and usages. Most of these are rather "fine" points, though.

 

[Lelan Thara]

Pervect - given what you said above, my question would be - do you agree with Pete that photons have inertial mass?

 

[Garth]

Photons have momentum and carry energy.

Garth

 

[pervect]

Pervect - given what you said above, my question would be - do you agreew ith Pete that photons have inertial mass?

I would say that photons have a zero invariant mass. If pressed, I would admit that they have a non-zero "relativistic mass", though I would be quick to point out that I personally did not like relativistic mass.

But you asked about "inertial mass". I'm not quite sure what you mean by "inertial mass". At a guess, you are trying to divide the momentum of a photon by its speed (which is always 'c') and come up with a number. This number will depend on the frame of reference - it will not be a property of the photon alone.

My general remark would be this: photons carry momentum and energy. This should be clearly understood. The idea of "mass" is actually somewhat of an "umbrella concept" - the name "mass" is an "umbrella" which covers a large number of closely related, but different, concepts. You'll really need to learn about mass in Newtonian mechanics, mass in special relativity (invariant mass and perhaps relativistic mass) and mass in general relativity (ADM mass, Bondi mass, Komar mass) separately. To quote Max Jammer, "Mass is a mess".

For some online reading, samples of Max Jammer's two books on mass are available on Google. They appear to be some of the better non-technical references out there.

http://books.google.com/books?q=max+jammer+mass&btnG=Search+Books&as_brr=0

You can find the remark about "mass is a mess" at http://books.google.com/books?vid=I...x+jammer+mass&sig=rvmUlL1YxTTmzI_MxSEwoJB7fzo

The umbrella analogy is AFAIK mine, however.

 

[pmb_phy]

Pervect - given what you said above, my question would be - do you agree with Pete that photons have inertial mass?

That question cannot be answered until you have a definition of inertial mass. A.P. French in his SR text defines "inertial mass" as the ratio of the particle's momentum to its speed. Many others use this definition as well. So according to Frenchl anything that has momentum has speed. Therefore mass, just like momentum, will be dependent on the observer.

Best wishes

Pete

 

[ZapperZ]

That question cannot be answered until you have a definition of inertial mass. A.P. French in his SR text defines "inertial mass" as the ratio of the particle's momentum to its speed. Many others use this definition as well. So according to Frenchl anything that has momentum has speed. Therefore mass, just like momentum, will be dependent on the observer.

Best wishes

Pete

OK, using that definition, please tell me what is the "speed" of a crystal momentum.

Zz.

 

[pmb_phy]

OK, using that definition, please tell me what is the "speed" of a crystal momentum.

Zz.

That is very different usage of the term "momentum." It isn't even used in classical physics and this is a forum on cassical mechanics, not quantum mechanics. You will also note that I used the term "partcle" which a crystal is not.

Best wishes

Pete

 

[ZapperZ]

That is very different usage of the term "momentum." It isn't even used in classical physics and this is a forum on cassical mechanics, not quantum mechanics. You will also note that I used the term "partcle" which a crystal is not.

Best wishes

Pete

So according to Frenchl anything that has momentum has speed.

Then something is amiss here because in QM, the momentum operator is one of the central observable of our world.

And note that the word "crystal" here isn't what you you think it means. If you don't care for it, then let me ask you to replace "crystal" with, for example, "momentum of conduction electron in metals". Would that qualify as "particles" in your book?

Zz.

 

[vanesch]

Oh, puleeze, not another thread-war on relativistic mass versus rest mass

To the OP:

There are different ways to define "mass". All of them are motivated in one way or another and they are not always equivalent. So the best way to get confused is to take values or formulas for one, and use them as another. There are religious wars going on over what is the "right" way to define mass.

As Doc Al pointed out, there is a universal "dispersion relation" which links energy and 3-momentum of a particle, and it is given by:

E^2 = k^2 c^4 + c^2 p^2

with E the energy, c the light speed and p the norm of the 3-momentum of the particle. k turns out to be a constant which depends only on the type of particle. Consider that this form of the relationship between momentum and energy is experimentally established. We call this constant k the "rest mass", and usually write it like m_0 or the like.
Turns out that certain particles have this constant equal to 0. In that case, the relationship simplifies to E = |p| c
It turns out that these things can only travel at light speed.
For other particles, where the constant m_0 turns out to be a non-zero number, it turns out that they can travel at any speed below c. In the specific case where they are at rest (which is possible), the momentum is 0 too, and the relationship becomes E = m_0 c^2
But mind you that this is only 1) in the rest frame of the particle and that 2) only particles with non-zero m_0 can have a rest frame.

Now, in how much it is a good or a bad idea to call this m_0 the "rest mass" in the case of m_0 = 0 is a matter of semantics.

There are people who are fond of the relation E = m c^2 even in cases where we are not in the rest frame, and there are some good reasons to do so. The number m, which is nothing else but E / c^2, is called "relativistic mass". Clearly, it is another name for "energy" (in other units).
It has some good uses in extending Newton's second law into the relativistic domain.

There are people who are fond of the relation p = m v. The number m (which is different from the number m representing "relativistic mass") is called "inertial mass".

There are still other ways to define "mass".
They have different values, they have different meanings, and they are used in different formulas.

 

[lightarrow]

There are people who are fond of the relation p = m v. The number m (which is different from the number m representing "relativistic mass") is called "inertial mass".

Why? It should be the same.

 

[vanesch]

Why? It should be the same.

Uh, yes. You're right.

I wanted to point out that there was a difference in definition (starting point), and then wrote something silly.

 

[pmb_phy]

Then something is amiss here because in QM, the momentum operator is one of the central observable of our world.

And note that the word "crystal" here isn't what you you think it means.

I think it means what it is defined to mean as defined in Wikipedia.

If you don't care for it, then let me ask you to replace "crystal" with, for example, "momentum of conduction electron in metals". Would that qualify as "particles" in your book?

It does.

I don't understand your confusion. Are you telling me that you don't know what momentum or speed is?

By the way, when I wrote "So according to Frenchl anything that has momentum has speed." It as a gross error on my part. That should have read "So according to French anything that has momentum and speed has inertial mass." Perhaps this is the source of your confusion??

This is not a unique place to see the term "inertial mass" defined in this way. Schutz also uses the term in the same way as French.

Oh, puleeze, not another thread-war on relativistic mass versus rest mass

No such war has taken place here in quite some time. People come here and always ask ther same, or similar, questions and the answer lies in definitions. The most reasonable thing to do is to provide the definitions. The "war" that you speak of has to do with how the term "mass" should be defined or someone whining about the way someone else uses the term.

Re - The statement Clearly, it is another name for "energy" (in other units). may be wrong. Please see

http://www.geocities.com/physics_world/sr/mass_momentum_density.htm
http://www.geocities.com/physics_world/sr/rd_paradox.htm
http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

Best wishes

Pete

 

[rbj]

But you asked about "inertial mass". I'm not quite sure what you mean by "inertial mass". At a guess, you are trying to divide the momentum of a photon by its speed (which is always 'c') and come up with a number. This number will depend on the frame of reference - it will not be a property of the photon alone.

that isn't true, is it? the speed of the "massless" photon is always c no matter the frame of reference but, if you define the mass of a particle as momentum divided by speed, then that mass does not depend on the frame of reference and is a property of the photon, namely

m = \frac{p}{c} = \frac{h \nu}{c^2}

hmmm, i guess because the frequency \nu of the wave is a function of frame of reference (doppler effect), but then also the momentum p = \frac{h \nu}{c} of the photon is dependent on the frame of reference in the same manner and no one is saying that photons have no momentum.

Oh, puleeze, not another thread-war on relativistic mass versus rest mass

No such war has taken place here in quite some time.

i dunno. i try to get a few licks in.

People come here and always ask ther same, or similar, questions and the answer lies in definitions. The most reasonable thing to do is to provide the definitions. The "war" that you speak of has to do with how the term "mass" should be defined or someone whining about the way someone else uses the term.

 

[pmb_phy]

that isn't true, is it? the speed of the "massless" photon is always c no matter the frame of reference but, if you define the mass of a particle as momentum divided by speed, then that mass does not depend on the frame of reference and is a property of the photon, namely

m = \frac{p}{c} = \frac{h \nu}{c^2}

hmmm, i guess because the frequency \nu of the wave is a function of frame of reference (doppler effect), but then also the momentum p = \frac{h \nu}{c} of the photon is dependent on the frame of reference in the same manner and no one is saying that photons have no momentum.

Frankly I don't see why being observer dependent is a problem or concern to anyone in relativity. Many things are observer dependent such as energy and the lifetime of a particle, value of electric/magnetic field, relative velocity of on object relative to an observer etc. etc. etc.

Best wishes

Pete

 

[pmb_phy]

i dunno. i try to get a few licks in.

There is plenty of discussion of it yes. But nobody getting angry at another poster. There are posters who get angry when the subject comes up, e.g. Oh, puleeze, not another thread-war on relativistic mass versus rest mass. vanesch makes it sound as if when a subject is discussed a few times it shouldn't be discussed again. However he doesn't seem to realize that we get newcomers all the time and referring them to an old thread is rather like blowing the OP off by pasting a reference to such post. I respond as simply as I can as a matter of curtisy the precise point/solution to their problem regarless if somene thinks I should or shouldn't speak about "that" subject. Otherwise what could be a short simple answer gets trampled on by someone who doesn't like the topic to come up. I recall one time that a poster was upset with me because I didn't say how many people use what in their work etc. Frankly that's a matter of statistics. However there is a paper which does give some statistics if anyone is curious.

Pete