[Pmb]

That's wrong. I have already replied you (in a previous post of this or another similar thread, don't remember) that a photon is different because has zero mass.

I can see that you’re not one who is much for agreeing to disagree, huh? Okay.

For an electron, you can have non-zero momentum p even at very low speeds, because of its non-zero mass. Then De-Broglie relationship: = h/p tells that, in the limit h --> 0, = 0, that is, frequency should be infinite.

And since the product of wavelength and momentum has to remain the same in that relationship it means that it’s an improper limit since as ones going down, the other is going up.

In any case you keep forgetting that we’re treating it as a classical particle for which the relationship: = h/p ignored. Thus it means nothing in the classical sense to take a classical limit of a photon. JP and myself explained how it works in a classical sense.  You insist on ignoring its defining properties. It’s a classical description of a Fourier integral description of a sharp pulse of radiation. Since JP and I both have our convictions I’m wondering what it is that you hope to gain into continuing this? You certainly can’t change the textbooks or change the usage of the center of mass of a two photon system in the textbooks. As I have asked too many times now with no response – why do people insist in using the scenario I’ve described and never came to a wrong answer.

Please explain, in detail if you please, what it means when you say “You can’ do that!” when so many people do it, and very successfully too I might ad. You imply that you can’t draw a worldline of a photon in a spacetime diagram and yet physicists do it all the time. E.g. referring to finding the center of mass of two photons you claimed “You can't localize a photon, so you can't do that.” When in fact derivations based on the localizability of property of a photon that plays a crucial role in its use in the derivation, you know, the one you claimed can’t be done. While you’re at it please state in detail what you mean whey you say “You can’t localize a photon”.  Again you claimed that just because I was speaking about classical physics you claimed that I was speaking about quantum mechanics, again with no proof provided. I suggest that you take a look at the derivation again http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm just pas Eq. (. Nothing about a quantum nature about anything is mentioned in there. Easy as cake. Over and over again you keep making the unfounded assertion that you can’t localize a photon but then never state what that means in practice. Then you later claim that you “so you can’t speak of photons”. Then you go on an claim I don’t know a lot about QM just because you didn’t understand what I wrote and you didn’t appear to go back to JPs post to see the context in which I made the statement which makes you think I don’t understand QM. As JP says and I believe him Maybe there's a reason why you can't, but based on my (admittedly limited) understanding of the Standard Model, I don't see why this would be.

[lightarrow]

I can see that you’re not one who is much for agreeing to disagree, huh? Okay.

It depends. Because of my nickname, I like to talk about light and photons [], so I've studied this subject and discussed it in the forums, for several years.

For an electron, you can have non-zero momentum p even at very low speeds, because of its non-zero mass. Then De-Broglie relationship: = h/p tells that, in the limit h --> 0, = 0, that is, frequency should be infinite.

And since the product of wavelength and momentum has to remain the same

? We are making the limit h-->0, so it doesn't remain the same!

In any case you keep forgetting that we’re treating it as a classical particle for which the relationship: = h/p ignored.

But the point is that *you have to prove* treat it can be treated as a classical particle.

Thus it means nothing in the classical sense to take a classical limit of a photon.

Exactly! Read again what you have written here   []

JP and myself explained how it works in a classical sense.

JP wrote this:
<<Good point.  After reading that and a bit more thinking, I believe that what's going on with these "classical photons" is two limits.  If we have a field made of photons, the classical limit does not correspond to taking h->0, but rather to taking many photons.  In this limit, you recover Maxwell's equations, but you've lost information about the behavior of individual photons.

Then you take a second limit corresponding to wavelength->0 which gets you ray optics.  So essentially, your "classical photon" is an arbitrary packet of energy assigned to propagate along a ray.  It's related to real photons only insofar as the sum over many photons gets you the classical field, which you then use to define rays.>> 

So JP, essentially, says: OR you recover classical electromagnetism, and you have lost information about the behaviour of individual photons, OR you come up with the geometrical optics approximations and you can talk about packets of energy assigned to propagate along a ray.
But this is exactly what I've already written to you in previous posts  []

You certainly can’t change the textbooks

Sincerely I have never read "classical photon" in a book of physics.

or change the usage of the center of mass of a two photon system in the textbooks. As I have asked too many times now with no response – why do people insist in using the scenario I’ve described and never came to a wrong answer.
Please explain, in detail if you please, what it means when you say “You can’ do that!” when so many people do it,

"So many people" are able to localize a photon in flight? Forget it...

and very successfully too I might ad. You imply that you can’t draw a worldline of a photon in a spacetime diagram and yet physicists do it all the time.

How do you draw a photon's worldline between (0,0,0,0) and (1,1,0,0)? Just for curiosity.

E.g. referring to finding the center of mass of two photons you claimed “You can't localize a photon, so you can't do that.” When in fact derivations based on the localizability of property of a photon that plays a crucial role in its use in the derivation, you know, the one you claimed can’t be done. While you’re at it please state in detail what you mean whey you say “You can’t localize a photon”.  Again you claimed that just because I was speaking about classical physics you claimed that I was speaking about quantum mechanics, again with no proof provided. I suggest that you take a look at the derivation again http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm just pas Eq. (. Nothing about a quantum nature about anything is mentioned in there. Easy as cake. Over and over again you keep making the unfounded assertion that you can’t localize a photon but then never state what that means in practice. Then you later claim that you “so you can’t speak of photons”. Then you go on an claim I don’t know a lot about QM just because you didn’t understand what I wrote and you didn’t appear to go back to JPs post to see the context in which I made the statement which makes you think I don’t understand QM. As JP says and I believe him Maybe there's a reason why you can't, but based on my (admittedly limited) understanding of the Standard Model, I don't see why this would be.

I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.

[JP]

I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.

This sums it up nicely: you two disagree on what you call a photon.  Pmb's photons are not at all the quantized photons of quantum optics.  If I were writing the textbooks, I'd side with Lightarrow on this and reserve photon to mean a very specific thing in quantum mechanics that has no classical analogue: the state resulting from an exitation of hbar*omega of energy in the EM field.  However, as I'm not the President of Physics, I can't do this, and I've noticed that many physicists use the term in a sense similar to what Pmb is doing, and this works out pretty well.  The problem arises when compare the properties of these different uses of "photon" and realize they're talking about two completely different things with completely different properties, and that there is no classical limit of a single-photon Fock state.

Perhaps the solution should be to elect me the President of Physics and I'll rewrite all the textbooks to clear this up?   

[Pmb]

I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.

If that is your response then you weren't paying attention to what I was saying. You consistently keep forgetting the approximation and what it would mean to put the photon's position vector inside the area of uncertainty according to how the wave function would average the position. I gave you an example of a pixel of 0.001 mm in width a length and when it detects the photon then its localized in that area and the location of the photon is the location of the pizel) e.g. geometric center.

You youy insist on ignoring every single thing I've said regarding approximation then there is no use to continue this conversation. Why should I post something I know you're going to igore?

While you're at it it wouln't hut you to finally state what it is you mean by saying something can or can't be localized. E.g. find a QM texbook and quote the definition of "localized" or "localize" so you won't be vauge anymore.

[lightarrow]

I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.

If that is your response then you weren't paying attention to what I was saying. You consistently keep forgetting the approximation and what it would mean to put the photon's position vector inside the area of uncertainty according to how the wave function would average the position. I gave you an example of a pixel of 0.001 mm in width a length and when it detects the photon then its localized in that area and the location of the photon is the location of the pizel) e.g. geometric center.

You youy insist on ignoring every single thing I've said regarding approximation then there is no use to continue this conversation. Why should I post something I know you're going to igore?

While you're at it it wouln't hut you to finally state what it is you mean by saying something can or can't be localized. E.g. find a QM texbook and quote the definition of "localized" or "localize" so you won't be vauge anymore.

It's you that don't pay attention to what I wrote. I've already written that "saying to have exactly localized a photon is the same mistake of saying to have perfectly localized a particle' path in a cloud chamber".
And, again, you don't need to talk of photons, if you intend to make such coarse approximations, you can talk of pulses of light.

[Pmb]

I pay close attention. You just never make any sense and you ignore all the derivations provided to you. You're the one who insists on refusing to explain how physicists, in physics journals none the less, do what you claim can't be done and yet get the correct results.

Is there a good reason why you keep refusing to provide a definition of the term "localized" as you insist on using it? I case your response is to claim that you already have please post the time and day of your response.

[JP]

Is there a good reason why you keep refusing to provide a definition of the term "localized" as you insist on using it? BTW photons are always localized when their position is measured

But a photon that's been measured is no longer a photon.  The entirety of this argument comes down to the fact that Lightarrow uses photon to mean a single photon Fock state, which cannot be localized by definition, and you're using photon to mean a classical pulse.  A measured photon is no longer in a Fock state, so it is no longer a photon by that definition.

[Pmb]

But a photon that's been measured is no longer a photon.

I’m aware of that, of course. I wasn’t sure he was aware that when a photon’s position is measured that it was localized.

The entirety of this argument comes down to the fact that Lightarrow uses photon to mean a single photon Fock state, which cannot be localized by definition, and you're using photon to mean a classical pulse..

Sorry, but I don’t know what a Fock state is.

In any case, that’s not what I meant by a “classical photon.” Recall the definition that I used. A classical photon is a particle whose inertial energy is related to its momentum by E = pc and interacts with charges via the electromagnetic interaction. There is no associated wavelength since that’s a quantum property just as a classical electron has no wavelength. By this definition it moves on a classical trajectory, has a position vector, etc.  This is what they use in the derivations for the mass-energy equivalence relationship where they use the conservation of the center of momentum. It’s also what relativists use when they draw a worldline of a photon.

It doesn’t matter at this point. I don’t want to discuss it anymore. I merely wanted to see what lightarrow thinks “localized” means. I've already had enough of his broken record responses.

[Pmb]

I checked all my texts on quantum mechanics and none of them mentioned Fock space. However a friend of mine just gave me his text Quantum Mechanics II: A Second Course in Quantum Theory by Rubin H. Landau.

I guess this is where this second quantinization stuff I hear about so often is addressed. I've never studied QM at this level before. Thanks for mentioning it. It'll give me a goal to reach after I refreshen my quantum mechanics in the next few months. 

[JP]

I guess this is where this second quantinization stuff I hear about so often is addressed. I've never studied QM at this level before. Thanks for mentioning it. It'll give me a goal to reach after I refreshen my quantum mechanics in the next few months. 

It's interesting stuff.  I've studied the basics, but haven't really applied it to anything.  A single Fock state can't be localized, but physics can and do write approximate photon wave functions when considering photons emitted by a source and absorbed by a detector.  I briefly read a section on this in Optical Coherence and Quantum Optics in Mandel and Wolf when this question came up previously, but I didn't have the time to really dig into the details.  Again, I'm not going to wade into the argument of whether we should call localized wave functions that aren't single-photon Fock states "photons," but some physicists definitely do so in practice.

[Pmb]

I guess this is where this second quantinization stuff I hear about so often is addressed. I've never studied QM at this level before. Thanks for mentioning it. It'll give me a goal to reach after I refreshen my quantum mechanics in the next few months. 

It's interesting stuff.  I've studied the basics, but haven't really applied it to anything.  A single Fock state can't be localized, but physics can and do write approximate photon wave functions when considering photons emitted by a source and absorbed by a detector.  I briefly read a section on this in Optical Coherence and Quantum Optics in Mandel and Wolf when this question came up previously, but I didn't have the time to really dig into the details.  Again, I'm not going to wade into the argument of whether we should call localized wave functions that aren't single-photon Fock states "photons," but some physicists definitely do so in practice.

What we were talking about was the position vector of a single photon in a system of only a few photons. Can that be done by using some sort of centroid?

[JP]

The short answer is yes.  I found part of the book I was talking about on Google books:

http://books.google.com/books?id=FeBix14iM70C&pg=PA480&lpg=PA480#v=onepage&q&f=false

They come back to the plane wave description I was giving earlier: if you have a single plane wave it is not localized in space and time, but if you have many added together, it can be localized. 

In the same way, if you have a single Fock state, it cannot be localized, but if you add many single-photon Fock states together, it can be.  But since this is quantum, the addition of many Fock states can be a single-photon state, since each Fock state represents a configuration of a photon, and the whole state describes the probability of finding that photon in each configuration.

But as they say, you have to be careful when interpreting "localized" photons, since they are defined from second quantization of the field, and do not have all the properties of a particle such as an electron, which can be described in terms of first quantization of a particle.

[Pmb]

Thanks JP. Speaking about electrons, I just read an iteresting comment in French and Taylor's QM text on page 9

Millikan demonstrated very directly what he called the "unitary nature of electricity," the fact that electric charge is quantized and transferred in multiple integrals of e.

So lightarrows attempt to use the term "quantized" as part of the definition of photon has the defining "quantum mechanical" property is flawed since we know that referred only to it being a discrete amount of something and not as "quantum mechanical" also finds its use as in the defining property of the electron as well. In fact they use it to first describe the electron and only much later to describe the photon. As I said before, you have to be careful of how you interpret the use of the term "quantized" or "quantum." For the most part it refers to discrete lumps of matter more that it does to the name of a theory.

[Pmb]

Recall the definition that I used. A classical photon is a particle whose inertial energy is related to its momentum by E = pc and interacts with charges via the electromagnetic interaction.

This has been bothering me recently. It appears to me now that such a classical photon cannot interact with other particles in such a way that it would change its energy E. There’s no way for such a particle to change its energy so when a charged particle interacts with it it can’t change its energy. So a classical photon can’t change its kinetic energy, since E = kinetic energy. A quantum photon can change its kinetic energy by changing its wavelength. So a classical photon cannot change its speed.

Since the uses I've seen for such a particle never invoke a change of energy this isn't a serious limitation.

[AndroidNeox]

Put a kilogram of matter and one of antimatter into an impregnable box, like a Schrödinger cat box, and the mass of the box (any category of mass you care to choose) will not change when the contents annihilate each other. Even if the box only contains light, the mass(es) will not change.

Correct, but it doesn't confirm your statement.
By the way, there is no need of matter and antimatter and not even of light in a box,  two photons are enough, because such a system have a non-zero mass (I mean invariant mass, not relativistic mass), I have already showed it in a recent thread and in several others, during the years.

It's both correct and does prove my statement.

[Pmb]

Put a kilogram of matter and one of antimatter into an impregnable box, like a Schrödinger cat box, and the mass of the box (any category of mass you care to choose) will not change when the contents annihilate each other. Even if the box only contains light, the mass(es) will not change.

Correct, but it doesn't confirm your statement.
By the way, there is no need of matter and antimatter and not even of light in a box,  two photons are enough, because such a system have a non-zero mass (I mean invariant mass, not relativistic mass), I have already showed it in a recent thread and in several others, during the years.

It's both correct and does prove my statement.

Forget what he's been saying. He has a way of confusing the poperties of mass with those of proper mass. There are three aspects of mass given three names and each are merely just called "mass" because they all have the same value

(1) inertial mass - m = p/v. The higher the inerial mass the harder it is to change its momentum.

(2) passive gravitational mass - The property of matter to respond to a gravitational force.

(3) active graivtational mass - The property of matter to generate a gravitational field.

proper mass (i.e. what lightarrow is always referring to when he sees the word "mass") has little or nothing to do with the defining characteristics of mass. A photon has zero proper mass but has inertial mass, passive gravitational mass and active gravitational mass.

[JP]

proper mass (i.e. what lightarrow is always referring to when he sees the word "mass") has little or nothing to do with the defining characteristics of mass.

That's because you're defining mass to preclude the use of invariant mass.  Plenty of physicists (mostly in high energy physics) use "mass" to mean invariant mass, which also has desirable properties. 
(1) Invariant mass properly satisfies m=p/v when you use 4-momentum and 4-velocity, while inertial mass doesn't
(2) Invariant mass is invariant when you change inertial reference frames, which is a very elegant property.

I can't comment on your points (3) and (4), since I'm not up to speed on my general relativity.  They probably don't matter much to most particle physicists, since they don't deal with gravity.

It's also important to note that we all agree on the properties of mass in the non-relativistic limit, but all these definitions of mass agree in that limit, so we can't use that as a basis for picking the "best" one. 

There is legitimate controversy in the teaching of physics over which definition to use.  It's my impression that invariant mass is generally winning insofar as it's being adopted in introductory textbooks.  http://en.wikipedia.org/wiki/Mass_in_special_relativity#Controversy

[Pmb]

proper mass (…) has little or nothing to do with the defining characteristics of mass.

That's because you're defining mass to preclude the use of invariant mass.

Not at all. I’ve chosen to state the definitions (not to define them since they were defined waaaay before I was even a gleam i m'daddy's eye! lol!) of mass that describe dynamics. I’m not choosing one particular definition of mass over another to state because I wish to preclude the use of invariant mass. Invariant mass is quite useful. I’d hate to try to work out your typical particle physics problems without it. Proper mass is also a defining property of a particle in that it is the unique limit of inertial mass for low v, i.e. m = M(v) as v->0.

Plenty of physicists (mostly in high energy physics) use "mass" to mean invariant mass, which also has desirable properties. 
(1) Invariant mass properly satisfies m=p/v when you use 4-momentum and 4-velocity, while inertial mass doesn't
(2) Invariant mass is invariant when you change inertial reference frames, which is a very elegant property.

Absolutely (Noting that #1 fails for all luxons). Please don’t misinterpret my comments to mean that proper mass is not useful. That would be an outrageously inaccurate assumption.

I can't comment on your points (3) and (4), since I'm not up to speed on my general relativity.  They probably don't matter much to most particle physicists, since they don't deal with gravity.

Its my opinion that there are many more particle physicists than other kinds of users of relativity so that the majority of use is mass = proper mass. However that is merely a game of numbers and what’s currently a popular area of research.

It's also important to note that we all agree on the properties of mass in the non-relativistic limit, but all these definitions of mass agree in that limit, so we can't use that as a basis for picking the "best" one. 

Except when it comes to photons where there is no such limit, of course.

There is legitimate controversy in the teaching of physics over which definition to use. 

Oh yes. That horse has been thoroughly beat upon in virtully every physics forum on the internet ever time the subject of mass comes up. Its become a virus which derails most threads merely because when people say “mass depends on speed” the non rel-mass people have to change it to debate against rel-mass rather than jus think to themselves  “Okay. By ‘mass’ that person means rel-mass.” and then moves on with the discussion. Never happens in practice thought. The problem is that it causes tons of confusion because you then have to explain why light can generate a gravitational field. When it comes to defining mass density for a uniform magnetic field it becomes very dicey.

By the way, I’ve changed my mind on the only properties of a classical photon being its energy and momentum. It’s mass is the real physical property. While in QM the wavelength changes giving a corresponding change in energy in classical mechanics it’s the mass that changes giving a corresponding change in energy, same as in QM but phrased in terms of classical properties.

[JP]

proper mass (…) has little or nothing to do with the defining characteristics of mass.

That's because you're defining mass to preclude the use of invariant mass.

Not at all. I’ve chosen to state the definitions (not to define them since they were defined waaaay before I was even a gleam i m'daddy's eye! lol!) of mass that describe dynamics. I’m not choosing one particular definition of mass over another to state because I wish to preclude the use of invariant mass.

I'm just taking issue your one line above that I quoted.  Invariant mass has plenty to do with the definition of mass, since it agrees completely with non-relativistic mass in the non-relativistic limit, just as inertial mass does.  It's all a matter of the way you choose to extend that definition into a relativistic framework, and both invariant and inertial mass are useful extensions.

[Pmb]

I'm just taking issue your one line above that I quoted.

I smell a debate about proper mass vs rest mass in the air. That's when I must leave the room. Methinks it be bad juju!