[Bill S]

JP, as a "hitch-hiker" where science is concerned, I got a bit bogged down in this thread.  In general, I find your explanations reasonably easy to follow, as long as you don't wax too technical, so if you are going to say a bit more about the idea of "classical photons" I'll follow with interest.

[Pmb]

JP, as a "hitch-hiker" where science is concerned, I got a bit bogged down in this thread.  In general, I find your explanations reasonably easy to follow, as long as you don't wax too technical, so if you are going to say a bit more about the idea of "classical photons" I'll follow with interest.

Regarding the term I coined, i.e. “classical photon.” There is nothing special or new about this concept. In the physics literature you’ll find two kinds of “particles” spoken of. One type of particle has its position and momentum simultaneously determined and moves on a classical trajectory. Such particles are called “classical particles.” The other kind of particle has its position and momentum constrained by the Heisenberg uncertainty relation. Such particles are called "quantum particles."

A classical particle whose energy E and momentum p is related by E = pc and whose nature is electromagnetic in origin (i.e. can scatter off a classical charged particle such as a classical electron) is what I had in mind when I referred to a “classical photon”.

Pete

[JP]

Thanks, Bill.  It's good to know my explanations (sometimes) make sense. 

I think this debate has been over two things: whether you can accurately model light with classical particles traveling at the speed of light and whether, if you can, you should call them "classical photons."

To answer the first question, you can in some cases.  Whether you use Maxwell's equations (which are accurate, but don't include quantum effects) or quantum optics (in which light is treated more rigorously as individual quantum mechanical photons), you're dealing with waves.  Either the light itself is a continuous wave (Maxwell) or the photons are waves (quantum optics).  In certain cases, you can approximate waves over space and time by classical trajectories through space and time.  This is an approximation whose validity depends on how rapidly the waves are oscillating over space and time (faster oscillation makes this approximation more accurate).

In the case of Maxwell's equations, these trajectories are rays which carry energy at some rate.  You could divide this energy up into packets, each moving at the speed of light, and you'd have something like a "classical photon."  Alternatively, if you use the Feynman path integral formulation of quantum mechanics, you can compute the effect of the emission and absorption of a photon by accounting for all possible paths the photon can take between emission and absorption.  The analogous trick to finding rays should be to find the most probable path for the photon to take.  I believe you could call this the "classical photon" trajectory.  Its important to remember that these are approximations to more rigorous models, but they should be accurate enough in many cases.

As for whether "classical photon" is a good term for these approximations--It probably isn't, as is evident from the confusion here.  However, it is clear that what Pmb means is a model for light as particles moving along a definite trajectory at the speed of light, and as I noted above, that model is an approximation, but can be accurate in some cases.

[Pmb]

JP - When the wave nature of light is important I can't see how photons can be used. In fact that's what led to the wave-particle duality. When the wave aspect is important I'd say forget all about particles moving on worldlines. At that point you're stuck with waves in spacetime. When you use Maxwell's Theory instread of quantum field theory is another conversation in itself.

[JP]

Yes, Pmb, you need to go a bit beyond the idea of a classical "little bullet" of energy to describe light when wave effects are important.  There are many ways to do so, but none of these "modified bullets" has all the properties of a classical particle unless wave effects are negligible. 

I'll spare you the details, but the Wigner distribution function is one way of thinking of a wave as particles moving along classical trajectories.  If you read through that, you'll find that the particles in non-classical states (those where wave effects are important)  have some odd properties such as appearing to carry negative energy or probability, which ends up being required for particles to model waves: http://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution

[Pmb]

It does not happen.

In this forum we've beat that horse dead many times over. In the end whether "mass" = m, depends on speed ultimately depends on how one defines the term. And there are two well-known, but different definitions used in relativity today. One were m is a scalar. It's then given the full name with the qualifier "proper" to end up with "proper mass". When one starts with the laws of physics where in the 3+1 viewpoint F = dp/dt and m is defined as the m in p = mv where p = 3-momentum (linear mechanical) and t = coordinate time. It's then given the full name with the qualifier "inertial" to end up with "inertial mass"

So mass can and does mean either (1) inertial mass or (2) proper mass. While you seem to have used it as a conceptual crutch I know that I haven't. That's not why I prefer it when appropriate.

[lightarrow]

JP - When the wave nature of light is important I can't see how photons can be used. In fact that's what led to the wave-particle duality.

I hope not to offend you, but this sentence means you haven't understood a lot of QM, or about photons, at least.
1. A photon, as well as any other elementary particle, it's not a corpuscle; when in QM we talk of a "particle" we intend an entity which is described with a wave equation and which is detected as a corpuscle, so it has *both* a corpuscolar and a wave behaviour *by definition* (I'm referring to the QM postulates).
2. You want to see light waves and light corpuscles in a single experiment? Send individual photons trough a doble slit and detect them in a screen. You will see individual flashes on the screen (light corpuscles) distributed according to a diffraction pattern (light waves).
3. In particle/particle collision experiments in a collider, you have individual particles colliding and the result of that (particles, energies, ecc.) is something  that you can compute *only* using the wave nature of them (= wavefunctions = quantum mechanics).

Conclusion: if you use the word "photon" you are talking of quantum mechanical description by definition.

[Pmb]

Conclusion: if you use the word "photon" you are talking of quantum mechanical description by definition.

I disagree.

First off JP knows his QM quite well so one would be quite off the mark and misleading themselves to think that he doesn’t understand QM a great deal.

The term photon is often used in areas of physics where it’s treated like a classical particle. The same holds for any other particle that we know since what you can say about a photon regarding its properties as a particle you can say about any elementary particles in nature. That’s why we quit often use the term photon in relativity,

What you spoke about above also holds true for electrons and when you use the term “electron” it doesn’t mean that you’re talking about a quantum mechanical description. We use the term “electron” in classical electrodynamics which by definition is a classical, not a quantum, branch of physics. .

[lightarrow]

What you spoke about above also holds true for electrons and when you use the term “electron” it doesn’t mean that you’re talking about a quantum mechanical description. We use the term “electron” in classical electrodynamics which by definition is a classical, not a quantum, branch of physics.

But in those cases you neglet the wave aspect of the particle. Instead you intended to discuss exactly the case of the wave aspect of particles, infact you wrote:
"When the wave nature of light is important I can't see how photons can be used".

[Pmb]

But in those cases you neglet the wave aspect of the particle.

Of course. That’s entirely the point. Maybe that’s what has you confused. You must have thought that somewhere someone was making the claim that under all conceivable scenarios the photon can always be treated as a classical particle.  Not true. If you thought that someone made such an assertion then you were mistaken.

When one is considering only those experiments in which the limits of the experiments/observations are such that one can describe the motion of a photon using a classical trajectory and thus a worldline in spacetime (null worldline to be exact).

Not all experiments and observations pertain to the wave aspects of photons. Those experiments and/or observations which treat the photon as a particle and for which the limits of accuracy of the experiment are such that one can ignore the limitations imposed by the uncertainty principle can one treat the photon as a classical particle.

When one is, say, analyzing photons in Young's double slit experiment then one is going outside the scope of classical relativity since a classical trajectory cannot be used to describe the motion of the photon.

However in other circumstances, say, when one is tracing a photon as a particle bouncing off mirrors which are moving in a vacuum or are being emitted and detected by photon emitters and detectors then one can use classical relativity and classical trajectories. If you want a good example of a photon being treated as a classical particle in special relativity then crack open “Gravitation” by Misner, Thorne and Wheeler. I know of a particular example of a photon being treated as a classical particle in that text. If you have the text and want to read it then I’ll try to find if for you.

Another treatment of a photon as a classical particle (in fact in a derivation where a photon is used in a center of mass calculation) see the article Inertia of energy and the liberated photon, Adel F. Antippa, Am. J. Phys. 44(9), September 1976. I have this article and if you’d like to read it I can make it available on my website for you to download and read.

The new version “Exploring Black Holes – Second Ed.” has examples where photons are treated as classical particles. This version of the book should be out later this year.

[lightarrow]

But in those cases you neglet the wave aspect of the particle.

Of course. That’s entirely the point. Maybe that’s what has you confused. You must have thought that somewhere someone was making the claim that under all conceivable scenarios the photon can always be treated as a classical particle. 

I have never thought it. The point is that the photon can never be treated as a classicle particle  []

When at a certan point you talked of "luxons" I believed to have understood that you intended this, with "classical photon", and I accepted to end the discussion. But I see you insist   []

Not all experiments and observations pertain to the wave aspects of photons.

If you want to talk about photons in that sense, you can do it only if you talk of the interaction energy and not when you talk of "something in fly between source and detector" which was what I was discussing with (I don't remember who) because he was talking of "the centre of a two photons system".
You can talk of the centre of two heavy atoms, if they are not cooled down to low temperatures, because they are still almost classical particles, maybe in some cases you could even talk of classical electrons, but absolutely not about photons; if there is an example you can't talk of classical particles is just that...

When one is, say, analyzing photons in Young's double slit experiment then one is going outside the scope of classical relativity since a classical trajectory cannot be used to describe the motion of the photon.

However in other circumstances, say, when one is tracing a photon as a particle bouncing off mirrors which are moving in a vacuum or are being emitted and detected by photon emitters and detectors then one can use classical relativity and classical trajectories.

Yes. But then you talk of *light rays and geometrical optics or classical electromagnetism*, *not* photons, until they are detected.

[Pmb]

I have never thought it. The point is that the photon can never be treated as a classicle particle  []

Your point is wrong. And its often treated as such.

Please post a proof demonstrating that a photon can never be treated as a classical particle.

While I'm waiting for that I'll show you examples of how physicists actually do treat photons as classical particles.

Examples are under my website at
See - http://home.comcast.net/~peter.m.brown/sr/light_clock.htm
and - http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm
and - http://home.comcast.net/~peter.m.brown/sr/lorentz_contraction.htm (substitute "photon" where you see "light"
and - http://home.comcast.net/~peter.m.brown/sr/lorentz_contraction_2.htm
and - http://home.comcast.net/~peter.m.brown/sr/spacetime.htm
and - http://home.comcast.net/~peter.m.brown/sr/relativistic_optics.htm (substitute "photon" where you see "beam")

Here's an example of how one treats an electron as a classical particle
http://home.comcast.net/~peter.m.brown/sr/cyclotron.htm

In real life, strictly speaking that is, electrons are quantum particles just like in real life, strictly speaking that is, photons are quantum particles.

Those are examples of how this is actually done by physicists (including myself), contrary to your claim that it can't be done.

You have yet to post a valid reason why one can't treat photons as classical particles in certain cases. You've made assertions to that effect but statements of facts are not considered to be a proof of that fact.

When I write the expression for a null worldline, i.e. x(t) = cos(theta) ct, y(t) = sin(theta) ct. These are the parametric equations of a photon moving in the xy-plane at an angle of theta from the x-axis. That's a null worldline and this is a classical statement.
Anytime a relativist is speaking of the null geodesic that a photon is moving on then he's speaking of a classical photon.

And that, my dear lightarrow, is how its done.

[Pmb]

I'm wondering, now, if I should consider the center of the two-photons to be the center of energy; equivalent to center of mass. 

Yes. In fact please see http://en.wikipedia.org/wiki/Two-photon_physics

[lightarrow]

I have never thought it. The point is that the photon can never be treated as a classicle particle  []

Your point is wrong. And its often treated as such.
Please post a proof demonstrating that a photon can never be treated as a classical particle.

It's very simple, and I let you do it: define "photon".

[Pmb]

Lightarrow – In what follows, please do not confuse “frustration” with “irritation.” While I am frustrated by what appears to be being ignored in the examples I’ve posted or that you’ve only posted assertions without proofs, I’m not irritated in the sense that I’m angry at you. I mention this because it seems that some people in physics forums read certain emotions or intentions into posts that aren’t really there. They seem to be based on what the reader assumes about the person who’s doing the posting. Okay?

It's very simple, and I let you do it: define "photon".

I gotta tell ya, lightarrow, I'm quite baffled as to why you’ve been ignoring the examples I've posted for you. I'm not posting them for my health ya know.   They are meant as counter arguments to the assertions that you've been sticking to. If you ignore them then I see no reason to discuss the physics anymore.

You also seem to be ignoring the fact when I explained that when photons are used in classical derivations its always an approximation to real life, i.e. quantum effects or precision is either ignored or not important.. Such approximation are not unique to photons or the examples I've posted but apply to ever classical treatment in physics that there exists since all real life particles have real life uncertainties in their locations. Why you've singled out photons among other particles such as electrons and protons and why you've been ignoring the usage of classical trajectories such as those in particle physics like tacks in bubble chambers of elementary particles is something I don’t understand.

Anyway … asking for the definition of the term "photon' is not a proof that they can’t be used in the manner which you say they can’t. When photons were first discovered by Einstein and Planck there was no uncertainty principle in existence and there was no need for such even though the particle nature of photons has been used long before the term "photon" was invented. Einstein and Planck came up with the concept of "bundle of energy" long after the first thoughts of "particles of light" were first being thought of and before they knew of the exact nature of them.

In any case the definition of Photon is - a discrete bundle (aka "quantum") of electromagnetic radiation where its kinetic energy E is related to its momentum p by E = pc. Einstein called these discrete bundles "light quanta". When the term “photon” was actually first defined by Gilbert Lewis they didn't have the same properties that we now assign to them.

Here the term "bundle" does not mean that they have a finite extension in space that one might visualize when one hears the term "bundle." The term “bundle” means "finite amount," nothing more and nothing less.

Also I’ve used the term “classical photon” or referred to the use of photons in a classical setting as approximations to the more exact expressions given in quantum mechanics. In your responses its like you’re not reading the parts of my posts which clarifies this point. When the wave aspect of the photon is under consideration or more precise measurements are being considered then the classical approximation of the photon is no longer being used.

I've already given you many examples of how and where photons are used in derivations using the conservation of center-of-mass. In particular, they are used in the article

Inertia of energy and the liberated photon by Adel F. Antippa, Am. J. Phys. 44(9), September 1976

A similar derivation is given in Special Relativity by A.P. French on pages 17 and 27.

In each version of the derivation the correct results are obtained.

I'd like to remind you that it was you who first claimed that the center of energy of a system of photons couldn’t be defined because you claimed that photons couldn’t be localized. In that response you had your mind fixed on quantum mechanics and were ignoring the sense in which that person was using the concept of photons. To be 100% accurate, nothing in the universe can be localized to a mathematical point. What you failed to mention was the fact that any particle can be localized to a finite region of space. If that weren’t true then nobody would have ever referred to anything in physics, quantum or classical, as a “particle.”  In fact even in quantum mechanics photons can be localized to an arbitrarily small region of space. One just has to give up some uncertainty in the knowledge of the photons momentum. If we were to take your response literally then you would have said that the center of mass of electrons, protons, neutrons etc. couldn’t be defined because no elementary particle can be localized in space. I’m rather baffled at where you got the notion that photons can’t be localized. No treatment of quantum mechanics would ever make such an assertion. Perhaps you made the mistake of thinking that “localized” meant “located at a mathematical point.” If so then no elementary particle can be localized. But that’s not what is meant by “localized” in quantum mechanics.

I think this point needs to be clarified more (Let’s use the double slit experiment and for purposes of illustration we’ll only look at the x-component). When one is considering experiments like Young’s double slit experiment then what is observed under low enough intensity of the light source are photons hitting the screen at finite locations. That means that if the screen were made of a huge amount of very small pixels (let’s say 0.001 mm) then only one pixel at a time is illuminated at one time. The location of that pixel is then recorded. After a large number of photons hit the array of pixel what you’ll have a bunch of numbers that denote locations where the photons were localized to a region 0.001 mm long. If you were to plot the number of photons at a particular x-location verses the x-coordinate what you’ll have is a graph which has the general shape of a bell curve. Let the width of that curve be dx. This is the dx that the uncertainty principle uses, not the size of a pixel. That is precisely what it means to localize a photon and precisely why photons are said to behave like particles in this experiment.

In case you ignore my previous posts and explanations (since you failed to explain why you’re claiming that all these physicists who use these explanations got them all wrong) I’ll have to repeat myself. I showed you how physicists are and have used photons in a classical context. You didn’t acknowledge the derivations that I’ve shown you. They are at  - http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm

Go down to below Eq. ( and you'll see how they are used in the classical sense, i.e. by using them in the center of mass theorem. This is how Antippa and French used them.

Other uses are when physicists draw spacetime diagrams and show the worldliness of photons. Such worldliness are classical approximations to what photons actually do on a small scale. When such diagrams are drawn the worldliness used as example are often of the order of a meters. The uncertainty of the photon’s location along such paths is negligible when drawing such diagrams. Thus the width of the worldline is approximated to be zero rather than the real life finite width one would get in experimental data. When one draws a classical trajectory like this for a particle then, in all cases, one is using an approximation. Just like when the path of an electron is drawn as a circle in a cyclotron. That path is also an approximation to real life.

From now on I’ll have to wait until you give a proof and a valid reason why the above approximations cannot be used. Until then I won’t respond to any other post of yours in this thread since all you’ve been doing is making a claim that they can’t be used with no acknowledgement that (1) I’ve been referring to approximations and (2) that they are indeed used by physicist and appropriated so and without error in their derivations.

One last comment before I end this post: To drive this point home let me remind you that what I’ve been, i.e. what I’ve labeled a “classical photon” which you seem to keep mistaking for a “quantum photon” which has a wavelength L related to its momentum p by p = h/L and whose position and momentum satisfy the uncertainty relationship.  Now recall what a “classical electron” is. It’s a particle with charge e = 1.60x10^(-19) C, a proper mass of 9.11x10^(-31)kg which moves on a well-defined trajectory. This is different than a “quantum electron” which has a wavelength L related to its momentum p by p = h/L and whose position and momentum satisfy the uncertainty relationship.

With this in mind recall the definition of "classical photon" a quantum of radiation whose kinetic energy is related to its momentum by E = pc which moves on a well-defined trajectory. From this definition it follows that the proper mass of a photon is zero.

Do you understand what I meant by "classical photon" now?

[Pmb]

... "Is there such a thing as a "classical" photon?" …

The answer is “No.” Does that mean that the concept is not useful or that it’s not being used in the physics/relativity literature? The answer to that is “No” as well. Then again there is no such thing as a “classical electron” since no particle exists that has the same properties of a “quantum electron” and also does not move on  a well-defined trajectory. Also no “classical electron” satisfies the uncertainty principle. That also doesn’t mean that the concept is not useful or that it’s not being used in the physics/relativity literature.

A classical photon is an approximation to a real photon just as a classical electron is an approximation to a real electron.

Compare this with the Earth’s gravitational field. Does a particle of mass m moving in the Earth’s (Earth mass = M) gravitational field a distance r from its center have a force on it given by F = GMm/r^2. The answer is no. This is true because the Earth is not a perfect sphere and F = GMm/r^2 only holds for a particle moving in the gravitational field of a perfectly spherical body. To say that this is not a useful approximation would be quite wrong.

[lightarrow]

... "Is there such a thing as a "classical" photon?" …

The answer is “No.” Does that mean that the concept is not useful or that it’s not being used in the physics/relativity literature? The answer to that is “No” as well. Then again there is no such thing as a “classical electron” since no particle exists that has the same properties of a “quantum electron” and also does not move on  a well-defined trajectory. Also no “classical electron” satisfies the uncertainty principle. That also doesn’t mean that the concept is not useful or that it’s not being used in the physics/relativity literature.

But there is a difference because you can treat electrons as classical particles in some cases, for example in Maxwell's electromagnetic description you can consider electrons as point charges. Furthermore, considering the electron as a classical particle, you can describe the most important features of the hydrogen atom; in which case you can do something similar with the photon?

http://en.wikipedia.org/wiki/Photon
<<A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation,>>

just the term "quantum" removes every "classical" description *by definition*. A photon is the quantum of the electromagnetic field, that is a quantum object that comes from the QED "quantum electrodynamics", it doesn't have a classical origin as the electron, it borns quantum....

[Pmb]

But there is a difference because you can treat electrons as classical particles in some cases, ...

Just as you can treat a photon as a classical particle in some cases.

Furthermore, considering the electron as a classical particle, you can describe the most important features of the hydrogen atom; in which case you can do something similar with the photon?

Already done in the examples which you continue to ignore.

http://en.wikipedia.org/wiki/Photon
<<A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation,>>

just the term "quantum" removes every "classical" description *by definition*. A photon is the quantum of the electromagnetic field, that is a quantum object that comes from the QED "quantum electrodynamics", it doesn't have a classical origin as the electron, it borns quantum....

You’re mistaken. All the term “quantum” means is discreteness. Period. That’s all. That photons first arose in the photoelectric effect in no can be interpreted that they can only be used in a quantum context. Electrons arose in a classical context but it was later shown that they can’t be used in all classical situations. And it’s quite clear that an electron can be referred to as a quantum of charge.

So I see that you once more have nothing to add other than making unfounded assertions and you keep ignoring the counter examples given to you which prove you wrong. You certainly can’t back up your position merely by repeating yourself and making statements that you can’t back up.

[JP]

If you look at the Standard Model of particle physics, photons are a quantum of the electromagnetic field, and electrons are a quantum of the electron field: this symmetry between matter and fields is a major part of the Standard Model.  We know that we can take a classical limit of the quantum description for electrons and arrive at classical electrons.  I've never seen it done explicitly, but I suspect you could do the same for photons and arrive at a classical limit for photons--i.e. the classical photons Pmb brings up.  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.

[Pmb]

If you look at the Standard Model of particle physics, photons are a quantum of the electromagnetic field, and electrons are a quantum of the electron field: this symmetry between matter and fields is a major part of the Standard Model.  We know that we can take a classical limit of the quantum description for electrons and arrive at classical electrons.  I've never seen it done explicitly, but I suspect you could do the same for photons and arrive at a classical limit for photons--i.e. the classical photons Pmb brings up.  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.

The reason I know why we can is because I see it done all the time with success. Especially when it comes to calculating the deflection of light past the sun and deriving E = mc^2 using the conservation of the center of mass of a atom-photon system. In the case of the former one generates a null worldline a particle of zero proper mass that is passing by the sun and calculates its trajectory and the correct value of deflection is obtained. In the later case one assigns a position vector to both the atom and the photon and the results yield E = mc^2. I’ve never done the former on my web site (perhaps I did it on paper) but the later  I did in two ways on my website which is at http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm

Scroll to just past Eq. ( and follow the derivation. You’ll notice that the properties of the photon are used and the result is valid