[JP]

I believe a "classical photon" would be a ray.  You get ray optics from light waves using the same procedure that you can use to get particle-like electrons from a more thorough quantum wave theory.  But it sounds like Pmb's classical photons are like little bullets, not rays.  I'm not sure how to get to those from the wave theory.

[lightarrow]

Geometrical optics is the (classical) limit of em radiation when frequency goes to infinite. While this gives a perfect geometrical ray (no diffraction, possibility to create infinitely thin rays) it's a mistake talking of "classical photons" even in this case because you can never know where exactly the photon is along the ray.

[JP]

I agree that a ray isn't a photon.  You can hand wave a bit and define the ray as carrying a density of photons proportional to the power transported along it (divided by frequency, perhaps?), but I don't see how you can define a single photon in this way.

[Pmb]

Classical photons? Which movie is it?  []

I don't understand what you mean, "Which movie is it?"

lightarrow - Have you ever heard of the terms "classical photon" and "classical electron"?

"classical electron": yes
"classical photon": no. The reason is because of qm history: a classical electron was a starting point for Bohr and Sommerfeld when they described the atom. But a classical photon couldn't have any meaning, because m = 0 in this case.

A classical photon is defined as a point particle whose energy i related to its momentum by E = pc, whose speed is c, and whose momentum is p = Mv = mc where M = E/c^2. M is defined as the photon's inertial mass.

Worrying about m = 0 is confusing inertial mass (a pre-relativistic notion) with proper mass (a relativistic notion)

[Pmb]

I believe a "classical photon" would be a ray.  You get ray optics from light waves using
 the same procedure that you can use to get particle-like electrons from a more thorough
quantum wave theory.  But it sounds like Pmb's classical photons are like little bullets, not rays.
 I'm not sure how to get to those from the wave theory.

A ray would be approximated as a stream of classical photons. Picture a laser beam as an approximation
of a ray.

[JP]

But a beam isn't a point particle.  I understand that you can express a beam roughly as a density of classical point particle photons moving along raytrajectories at the speed of light, but the case of two classical photons seems a rather unphysical approximation to me.  Can you point out a case that is well approximated by two classical photons?

[lightarrow]

A ray would be approximated as a stream of classical photons. Picture a laser beam as an approximation of a ray.

It's the same mistake that one makes stating that an electron's track in a bubble chamber means that elementary particles have a precise trajectory. QM teaches us they actually don't have.

[Pmb]

But a beam isn't a point particle.

Since nobody suggested or inferred otherwise this comment confuses me. Can you elaborate please?

I understand that you can express a beam roughly as a density of classical point particle photons moving along raytrajectories at the speed of light, but the case of two classical photons ...

Where did you get the idea of using only two photons from?

[Pmb]

A ray would be approximated as a stream of classical photons. Picture a laser beam as an approximation of a ray.

It's the same mistake that one makes stating that an electron's track in a bubble chamber means that elementary particles have a precise trajectory. QM teaches us they actually don't have.

Hence the term "approximation". In classical mechanics we're most often concerned with physics only down to, perhaps, the micron level. At that level and over small distances such as a mile we don't much need to worry about the non-exact nature of the trajectory of the photons.
I've been thinkig of this stream of photons as a laser beam and when I studied ray optics as an undergrad I always had a laser beam in mind.
I never worried about the cross sectional area of the laser beam either.

This is getting off course of the reason I mentioned classical photons.

As I said, in relativity one uses classical photons, which is basically a point particle having a classical trajectory but zero proper mass. Such a thing can be localized.

I had in mind this notion when I was reading Exploring Black Holes and working with GR and SR and when they used photons. Never in that work does anybody ever worry about te photon being localized or it not having a classical trajectory.

Remember this is an analogy which, by definition, means that its alike in some ways and not alike in other ways.
Let is not forget why it was brought up rather than dwell on what each of us knows all to well about how real photons behave,shall we? Otherwise it gets over pedantic and that's when I go back to watch my brand new 60" plasma TV

[Pmb]

Heh

I can see you and Pete gearing up to a argument Lightarrow

Ain't gonna happen. I had several months of too much quite to come out and worry about such trivia.

There are many terms in physics for which you must know the context and perhaps the authors views in order to determine the precise definition of a term. E.g when some people use the term "weight" they refer to the quantity mg. Others refer to weight only when the object of mass m is being supported at rest in the field while only defining weight as mg could mean that a body in free-fall has weight.

Then there is the definition of momentum. In Newtonian physics it means p = mv. In analytical mechanics and quantum mechanics it means canonical momentum. And you have to know that when reading QM material - the authors won't just tell you.

So nope. Nore more debating things anymore for me. I have no desire to let people know the complete picture of things. If they think they're gonna get a complete picture on the internet then they deserve whatever it is they get.

[Pmb]

[quote author=PhractalityI'm wondering, now, if I should consider the center of the two-photons to be the center of energy; equivalent to center of mass. Applying inverse square law to the energy of each photon to get a ratio of each photon's distance from the center. My brain hurts; maybe I'll just play solitaire, instead. 
[/quote]
If you're speaking of the geometric center of the two photons then no. The center of enegy is not the same as the geometric center of the two photons.

Note - See http://home.comcast.net/~peter.m.brown/sr/center_of_mass.htm

I see that this is where all this photon stuff started. This was a discussion of a classical photon and not a quantum mechanical one. Don't sweat the small stuff. Look how far off track it took this thread even though everyone knew what was meant by a classical and quantum photons.

In relativity we speak of point particles such as electrons, protons etc. even when we're speaking about classical relativity (since there is no quantum theory of relativity yet). When talking classical relativity and one is speaking of photons then what is being discussed is trivially simple: A classical particle having a well-defined trajectory, having its energy related to its mometum by E = pc and whose mass is given by p = mv = mc or E = mc^2.

This is how we speak of all particles in relativity. If you see a relativity text or article speaking of electrons, protons etc then they are treating them as classical particles. There is no difference with photons.

[lightarrow]

It's the same mistake that one makes stating that an electron's track in a bubble chamber means that elementary particles have a precise trajectory. QM teaches us they actually don't have.

Hence the term "approximation". In classical mechanics we're most often concerned with physics only down to, perhaps, the micron level.

No. When interactions among elementary particles are involved, you have to use the full wavefunctions treatize of QM, so: diffraction, interference, non existence of an exact trajectory. Ask particle physicists. Classical limits are used in macroscopic system *of non zero mass*, so singular photons are excluded by definitions. About lasers, you are using the geometrical optics approximation, so you are not talking of singular photons by definition.

--
lightarrow

[Pmb]

No. When interactions among elementary particles are involved, ...

Then you have to use QM. You did understand, didn't you, that I was speaking about classical relativity? I wasn't speaking of quantum relativity since it doesn't exist yet. If you have a problem which requires QM then you have to use QM. The context of my post tells you that I was referring to classical mechanics problems, not QM problems.

In relativity one speaks of light cones. In a 2-D spacetime diagram a photon moves on a straight worldline, i.e. a straigh in spacetime. We don't speak about quantum trajectories in classical relativity. When QM is required then we've gone outside the realm of classical relativity. In classical relativity one assumes that whatever we are speaking above can be approximated to move on worldlines, and that includes elementary particles too.

Clearly, when one is speaking of a particle moving on a null geodesics one is thinking about classical luxons. And that's what I've been explaining here.

[lightarrow]

No. When interactions among elementary particles are involved, ...

Then you have to use QM. You did understand, didn't you, that I was speaking about classical relativity?

So you can't speak of photons...

I wasn't speaking of quantum relativity since it doesn't exist yet.

You are joking! It was created in the 30' of the previous century, one of the first was Dirac, have you haver heard of "Dirac equation"? Have you ever heard of QED quantum electrodynamics?
Maybe you intended "quantum gravity", that is, a theory who would unify quantum mechanics and *general* relativity. But we are talking of laser beams, so we don't need gravity here.

Clearly, when one is speaking of a particle moving on a null geodesics one is thinking about classical luxons. And that's what I've been explaining here.

Don't know what they are, but certainly they are not photons.

[Pmb]

So you can't speak of photons...

While I disagree with you last post I've decided to end my contribution of quantum/photon thing since I've basically lost interest (of course I'm always available inPM for anything).

Plus I don't like endless debates on subjects, especially when most of it contains rephrasing of statements already made.

I'll end this with one reference: Inertia of energy and the liberated photon by Adel F. Antipa, Am. J. Phys., Vol (44) No.(9) Sep. 1976

Abstract
We follow through the different variants of Einstein's intuitive photon-in-a-box derivation of the inertia of the inertia of energy, then  end with a very simple "radiating atom" derivation

See section 7. The Radiating Atom

This article is basically a modern derivation of Einstein's famous "Photon in a Box" experiment. See my web site at
http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm

In the first section I outline Einstein's derivation. In the later section I outline Atipa's derivation.

Einstein uses a pulse of radiation to prove the mass-energy relation while Antipa uses an atom and a photon.
In both cases the center-of-mass is calculated and used.

The more general definition of center of mass of radiation is given in my web page at
http://home.comcast.net/~peter.m.brown/sr/conservation_laws.htm

The center of mass is in Eq. (15).

[Pmb]

I had another thought. In the physics literature one runs into terms like "classical electron" etc. In fact Fritz Rohrlich's book is called Classical Charged Particles. I know that saying "Classical Photon" caused some confusion here. But I'd like to end my contribution of this side bar by saying that in classical relativity one works with three classes of particles. They are defined as follows

(1)   If the speed of the particle is always v < c then the particle is classified as a Tardyon.
(2)   If the speed of the particle is always v > c then the particle is classified as a Tachyon.
(3)   If the speed of the particle is always v = c then the particle is classified as a Luxon.

There shouldn't be any problems now since these are well defined terms and used in the classical relativity literature.

[JP]

Would you folks be interested if I started and/or split off a thread with a title along the lines of "Is there such a thing as a "classical" photon?" or are you OK with this thread being used for discussion?

[Pmb]

Would you folks be interested if I started and/or split off a thread with a title along the lines of "Is there such a thing as a "classical" photon?" or are you OK with this thread being used for discussion?

Makes no difference to me, JP. I think we’ve all said what we wanted to say and learned what we wanted to learn at this point. But if you want to start a new thread on it then please feel free to do so.

[lightarrow]

I think Pmb has explained what he intended with that term in its previous post, so I can stop here too.

[JP]

Fair enough.