Electromagnetic Wave have momentum

[Ashish]

Well while reading a chapter on EM waves I got confused about EM have momentum.

 

This really little bit confusing because momentum can only be of them who has a mass and in EM waves there nothing like mass or there isn't any thing that can have mass.

 

So can anybody clear out my problem either I may wrong.

[Gilded]

Due to mass-energy equivalence ([math]E = mc^2[/math]) you could say that a photon has mass since it has energy, and thus it has momentum since it has a non-zero velocity. And anyway [math]p=mv[/math] is just a classical approximation. For example the momentum of photons is described by this equation:

 

[math]p = \frac{h}{\lambda}[/math]

 

where [math]h[/math] is Planck's constant and [math]\lambda[/math] is the wavelength of the photon.

[Severian]

That is a really horrible way to put it Gilded.

 

It is much better to use the general, non-rest frame, equation:

 

[math]E^2=p^2c^2 +m^2c^4[/math]

 

Then you can see that even if [math]m=0[/math] (as for a photon) the particle still has momentum from its non-zero energy [math]p=E/c[/math].

[Gilded]

That is a really horrible way to put it Gilded.

 

It is much better to use the general, non-rest frame, equation:

 

[math]E^2=p^2c^2 +m^2c^4[/math]

 

Then you can see that even if [math]m=0[/math] (as for a photon) the particle still has momentum from its non-zero energy [math]p=E/c[/math].

 

Well yeah I suppose it's more convenient as it has the E in there rather than the wavelength.

[NeonBlack]

Mass/Energy has nothing to do with it.

Even without [math]E^2=p^2c^2 +m^2c^4[/math], electromagnetic waves as predicted by Maxwell 50 years before Einstein carry momentum.

[Severian]

Mass/Energy has nothing to do with it.

 

They do. Maxwells equations are simply the equation of motion generated by the photon's kinetic term in the QED Lagrangian. Maxwell's equations obey the rules of relativity, including [math]E^2=p^2c^2+m^2c^4[/math], whether you like it or not. That was one of the things that led Einstein's to his theory.

[Klaynos]

Electromagnetism was the first relativistic theory...

[John Cuthber]

Glided's "horrible way of putting it" got DeBroglie a Nobel prize in 1927.

[swansont]

Glided's "horrible way of putting it" got DeBroglie a Nobel prize in 1927.

 

de Broglie's Nobel was "for his discovery of the wave nature of electrons" (and it was 1929)

 

I think the "horrible way" refers to saying the photon has mass.

[Severian]

de Broglie's Nobel was "for his discovery of the wave nature of electrons" (and it was 1929)

 

I think the "horrible way" refers to saying the photon has mass.

 

Yes, that's right - I wasn't meaning to diminish de Broglie's achievements.

 

Having said that, there have been plenty horrible Nobel Prizes. I hear Cabbibo is furious about this year's.

[Gilded]

While the photon mass-equivalent thing is an outdated concept I think it's an adequate analogy. I don't really mind that it's being gradually shifted out of textbooks though.

[am-tep]

Why do photons have momentum? Well...

 

As an example, consider the infra-red photons or even microwave radiation.EM-Radiation is capable of increasing the temperature of an object.Which means it can impart momentum to the molecules thereby changing their kinetic energies.Considering the fact that momentum is a conserved quantity, we are forced to conclude that radiation must possess momentum.

[Martin]

Well while reading a chapter on EM waves I got confused about EM have momentum.

 

This really little bit confusing because momentum can only be of them who has a mass and in EM waves there nothing like mass...

 

Have you heard of light pressure? Or of a type of space technology called the photon sail?

 

Light has measurable momentum and can impart momentum to something when it hits it (and bounces off or is absorbed). That is how the photon sail works. It captures momentum from sunlight.

 

If I remember right, the Japanese put one up not so long ago.

 

Mass isn't a completely simple concept. There are some different definitions. According to the most common definition, the mass of a photon is zero (as Severian says) and yet a photon carries a definite momentum (as he and others also say).

So it must be true that stuff can have momentum even though it does not have mass. In the case of a flash of light, the momentum is E/c.

You can calculate it. Take a one watt flashlight (electric torch) and flash it on for one second, so the energy of the light is one joule. Divide one joule by the speed of light. That will be some amount of momentum---the amount carried by that flash, in whatever direction you pointed it.

[am-tep]

Photons do have mass.The rest mass of a photon is zero. Which means that the photon will cease to exist at rest. However, a photon can never be brought to rest. The photon is even influenced by a gravitational field. As you may be aware light bends around a dent in the spatial fabric. It responds to the presence of mass,that is to gravity. Thus a photon can easily impart momentum for it has momentum.

[Klaynos]

Most people who work with relativity (certainly theorist) will agree that there is ONLY rest mass, that is mass, the one the only... The person who taught me special relativity in my second UG year who did his phd about general relativity (although he no longer works with relativity) actually got quite angry about people using relativistic mass.

 

You can formulate the whole of relativity using only mass (rest mass), and having things like momentum relativistic.

[Pete]

Well while reading a chapter on EM waves I got confused about EM have momentum.

 

This really little bit confusing because momentum can only be of them who has a mass and in EM waves there nothing like mass or there isn't any thing that can have mass.

 

So can anybody clear out my problem either I may wrong.

The answer to your question hinges on the definition of the term mass (the definition of which a controversial subject).

 

The answer to your question is forthcoming once you have the definition of mass in place. Simply put, mass is defined so that momentum p is conserved, i.e. mass is defined as the m in p = mv. Note: I use the symbol m to represent inertial mass (often referred to as relativistic mass). This should not be confused with proper mass which is often represented using the same symbol as Severian has above.

 

Strictly speaking one defines m so that mv is a conserved quantity in elastic collisions in an inertial frame of reference. One then defines this product as the momentum of the particle. That an em wave has momentum can be shown my demanding that the total momentum of a system be conserved in all processes, both mechanical and electromagnetic. I posted this derivation on my website at http://www.geocities.com/physics_world/em/momentum_of_radiation.htm

 

That an electromagnetic field behaves as if it has mass dates back as far as 1885 and was due to J.J. Thomson who noted that a charged conductor in motion behaves as if its mass increases.

That is a really horrible way to put it Gilded.

You can glean from my comments above that I disagree with this assertion.

 

To say that only rest mass is used in relativity is a bit misleading. Strictly speaking one cannot define mass in all generality as proper mass (aka rest mass) since it only works in special cases. As far as being out of date - That's a bit misleading too. In particle physics it is convenient to use the symbol m for proper mass and then symbol refer to it as “mass” just as one uses the symbol “T” for a particle’s lifetime and refer to it only as “lifetime” and not “proper lifetime.” There is basically a gentlemen’s agreement among practitioners that the “proper” is understood. Otherwise it’s a pain in the butt to have to keep adding the adjective “proper” before the terms. However when one is working in GR or cosmology one has to be a bit more careful. For example; if you were to look in Peeble’s cosmology text then one would see that inertial mass and gravitational mass are not the same as proper mass. In fact they are different. The former includes terms which take stress into account since stress has inertia and therefore mass.

The person who taught me special relativity in my second UG year who did his phd about general relativity (although he no longer works with relativity) actually got quite angry about people using relativistic mass.

Sounds like a jerk to me.

 

I agree with Martin. He was quite right when he said Mass isn't a completely simple concept. As Max Jammer wrote in Concepts of Mass in Contemporary Physics and Philosophy' date=' page 167

Thus, in spite of all the strenuous efforts of physicists and philosophers, the notion of mass, although fundamental in physics, is, as we noted in the preface, still srhouded in mystery.

Edited November 11, 2008 by Pete

[Martin]

I agree with Martin. He was quite right when he said Mass isn't a completely simple concept. ...

 

Pete, thanks for mentioning your agreement with me on that one point. I should make clear where I stand personally on the semantic issue. I disagree pretty much completely with you---I strongly prefer defining mass to be rest mass.

 

This is how the vast majority of physicists define mass, and use the concept. You are trying to promote a minority word usage, and I would recommend that you stop voluntarily, or that all links to your site be deleted.

 

The reason is that it is just a semantic issue, not physics. There is no physics content. So there is no reason NOT to go along with the majority. And on top of that, language is MORE EFFICIENT and communication is easier if everybody defines quantities the same way and uses words to mean the same thing.

 

The reason mass is not a completely simple concept (as we both agree) is that there are a few diehards who stubbornly persist in using the word differently from the majority, and this leads to apparent contradictions in discussion and tedious sterile argument.

 

... The person who taught me special relativity in my second UG year who did his phd about general relativity (although he no longer works with relativity) actually got quite angry about people using relativistic mass.

...

Sounds like a jerk to me.

On the basis of what evidence Klaynos presented no way was the guy a jerk, but was looking out for his students best interests.

 

If we are going to start identifying people as jerks...

Edited November 11, 2008 by Martin
multiple post merged

[Pete]

This is how the vast majority of physicists define mass, and use the concept. You are trying to promote a minority word usage, and I would recommend that you stop voluntarily, or that all links to your site be deleted.

Just because ~60% of physicist disagree with me doesn't mean anything other than they disagree with me. I am merely stating my personal opinion and what I choose to do. My opinion is firmly based on physics and a thourough study of the concept of mass in relativity. I am not alone in this view as evidenced in various physics texts and journal articles (e.g. American Journal of Physics). And this is not merely a semantic issue either since there is no way to define proper mass in all possible cases (proof provided upon request). Frankly most physicists who object to the idea of relativistic mass do so because they don't fully understand relativity in regards to the inertia of stress and the stress-energy-momentum tensor. And the link had nothing to do with this point since the material on that page is a derivation/justification of the expression of the momentum of radiation.

The reason mass is not a completely simple concept (as we both agree) is that there are a few diehards who stubbornly persist in using the word differently from the majority' date=' and this leads to apparent contradictions in discussion and tedious sterile argument.

[/quote']

While that may be your opinion it sure isn't Jammer's. If you actually read Jammer's book, especially his views on relativistic mass, you'd know that your assumption about his remarks are false.

 

If you insist on forcing your opinions on me then I find I will be forced to leave this board. Please let me know if this is the case. I have no desire to post at a place where I will be censored and insulted. When I came here I thought I found a place where this kind of thing wouldn't happen. Was I wrong?

Edited November 11, 2008 by Pete

[swansont]

If you insist on forcing your opinions on me then I find I will be forced to leave this board. Please let me know if this is the case. I have no desire to post at a place where I will be censored and insulted. When I came here I thought I found a place where this kind of thing wouldn't happen. Was I wrong?

 

You really can't play the insulted card if you call someone a jerk, with or without the smiley. And the threat to leave the board carries little weight — either you do or you don't. Bringing it up multiple times quickly becomes unpleasant noise. Stick to the physics, please.

[Severian]

And this is not merely a semantic issue either since there is no way to define proper mass in all possible cases (proof provided upon request).

 

Proof requested.

[Mr Skeptic]

Proof requested.

 

Seconded. Hopefully, I'll learn something interesting.

[Pete]

Proof requested.

Mass is defined according to momentum. In the case of proper mass m₀' date=' its defined in the limit where v -> 0 as in m[sub']0[/sub] = limit (v->0) p/v. This assumes that the limit exists and is independant of the state and orientation of the body. When the body has stress in it then the limit will depend on the orientation of the body. In such case there is no unique value that can be assigned to the limit since it would depend on the orientation of the body. I derived an example in this page

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

 

See equation 4. What I'm saying here isn't anything new. Its just not a well known fact. But it can be found in treatments such as Rindler's SR text or perhaps Mollers. One might attempt to define proper mass according to the magnitude of the stressed bodies 4-momentum but when a body is not isolated it will not have a 4-momentum (i.e. the quantity (E,p) will not be a 4-vector).

Edited November 12, 2008 by Pete

[Severian]

Mass is defined according to momentum. In the case of proper mass m₀, its defined in the limit where v -> 0 as in m₀ = limit (v->0) p/v.

 

No, its not. Putting aside minor subtleties (caused by renormalization in quantum field theories) mass is the invariant length of the momentum four vector.

 

Proof invalid!

[Martin]

What I'm hearing in Pete's alleged 'proof' (whether it is valid or invalid). is that in order for the mass of a body to be defined it has to be isolated. Please see if this makes sense, or is at all helpful in context:

 

The root meaning of mass is inertia.

 

Granted with all real-world measurements the ideal conditions can only be approximated. A real body will only be approximately isolated and approximately at rest in the measurement frame---the more perfectly the conditions approximate ideal the better the measurement.

 

I'd put it this way: the mass of an isolated body is defined to be its inertia at rest (equivalently, in its rest frame).

 

=====================

 

I guess it hasn't been mentioned yet, but a major reason mass is defined as inertia at rest is because the inertia of a moving body cannot logically be expressed as a single number---the transverse inertia differs from the longitudinal (i.e. the inertia along the direction of motion). Once an object starts moving in the reference frame, its inertia, as a single quantity, ceases to be well-defined. This point is apt to eventually come up in these types of discussions, so it may as well be remarked here.

[Pete]

No, its not.

Yes. It is. Please do more than merely say "No its not." since merely objecting helps nobody. My guess is that you're used to seeing people define the mass of an object according to the magnitude of the object's 4-momentum. That doesn't work in general since such a 4-vector doesn't aways exist, as I already indicated.

Putting aside minor subtleties (caused by renormalization in quantum field theories) ..

When are you restricting the definition to a the very specific case of elementary particles rather than being as general as possible? Especially in those cases when a body is under stress as in the example I gave. Its good to do so especially since that has even appeared in a problem sections in a relativity text I had. Its good to learn relativity in a way such that one can solve any problem that could ever be posed to them.

..mass is the invariant length of the momentum four vector.

That is incorrect as I already indicated in the example I gave of a body under stress, i.e. (E,p) does not form a 4-vector. Is there a reason you ignored that portion of my response?

Proof invalid!

The example I gave is quite valid. In fact you didn't even post a proof otherwise. All you did was to claim it was wrong. That kind of response is of no use to anybody. Merely claiming something is wrong can never be considered a proof.

 

Martin - Since you ignored my question then I'll have to assume that you intend on censoring what I post on this topid from herein. As such I will will simply PM the person rather than post in the thread.

Edited November 12, 2008 by Pete
multiple post merged