QED and photon path experiments

[LightPhoton]

I was reading Optics by Hecht where he states that the law of reflection is only valid statistically and some photons might reach the observation point (P in image, S being the source) by following different paths, that is, the paths for which the angle of reflection is not equal to the angle of reflection. Have there been such experiments performed where the experiments deduced the path followed by photon and showing that sometimes the law fails?

 

[pines-demon]

I was reading Optics by Hecht where he states that the law of reflection is only valid statistically and some photons might reach the observation point (P in image, S being the source) by following different paths, that is, the paths for which the angle of reflection is not equal to the angle of reflection. Have there been such experiments performed where the experiments deduced the path followed by photon and showing that sometimes the law fails?
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Does the Hecht specifically states "photons" or something else? What kind of source are we talking about? the source S as presented in the image could be illuminating all the points A to Q, yet only the light rays with the right angle and that hit the right spot will reach P.

 

[PeterDonis]

the source S as presented in the image could be illuminating all the points A to Q, yet only the light rays with the right angle and that hit the right spot will reach P.

You're using classical optics here, but this thread is in the QM forum and so we are talking about QED. There are no "light rays" in QED.

 

[LightPhoton]

Does the Hecht specifically states "photons" or something else? What kind of source are we talking about? the source S as presented in the image could be illuminating all the points A to Q, yet only the light rays with the right angle and that hit the right spot will reach P.

We can appreciate how all of this comes together by treating the reflection pictured in Fig. 4.79; a point source S illuminates a mirror, and light is subsequently scattered upward in every direction from every point on the mirror. We wish to determine the probability of a detector at P, recording the arrival of a photon. Here the classical perspective, with its familiar wavelet model, can be used as an analogue to provide guidance (and perhaps a little intellectual comfort, if you still believe in classical EM waves).

 

[PeterDonis]

I was reading Optics by Hecht

I don't have this textbook, but from what I can gather it appears to be a textbook mainly on classical optics. However, the statement you refer to is a statement about quantum optics, i.e., based on quantum electrodynamics, QED. And, as I commented in post #3 just now, this thread is in the QM forum, so presumably QED is to be the basis for discussion.

For a good layman's discussion of how QED treats this case, including discussion of experiments in which QED's predictions about things like this are confirmed, you might try Feynman's book QED: The Strange Theory of Light and Matter.

With all that said:

the law of reflection is only valid statistically

It depends on what you mean by "the law of reflection". See below.

some photons might reach the observation point (P in image, S being the source) by following different paths, that is, the paths for which the angle of reflection incidence is not equal to the angle of reflection.

Some photons might--at least if we are using the path integral formulation of QED (which is what Feynman uses in the book I referred to above) and being somewhat hand-waving in our description.

A more accurate description is that the probability of a photon going from S to P by bouncing off the mirror in between depends on the specific point on the mirror at which the photon bounces. The highest probability is for the classical path, the one where the angle of incidence (note my correction in the quote above) equals the angle of reflection. As you move away from that point on the mirror, the probability decreases, but it is nonzero for a fairly wide range of points on the mirror, so the total probability for a photon to go from S to P by bouncing off the mirror will include a fairly wide range of points on the mirror; it cannot be accounted for solely by photons traveling on the classical path.

I should also correct a common misconception: in the above, when I talk about photons following different paths, I am not talking about different photons--i.e., I am not saying that some photons follow one path and some another, and adding all the photons together gives the observed intensity of light going from S to P by reflecting off the mirror in between. QED's model does not say that. What QED's model says, in the path integral formulation, is that every single photon travels on all possible paths, and each path has a probability amplitude associated with it, and the final probability for a single photon to go from S to P by bouncing off the mirror in between is obtained by adding together all the amplitudes.

I don't think "the law of reflection is only valid statistically and sometimes fails" is a good way to describe the above. Again, I don't have Hecht's textbook so I don't know the context in which the statement you refer to was made. (I also don't know how much your paraphrase of the statement distorts Hecht's intended meaning.)

Have there been such experiments performed where the experiments deduced the path followed by photon and showing that sometimes the law fails?

No, because, as above, a photon does not have just one path, and "sometimes the law fails" is not a good description of what QED actually says about this scenario. But experiments have certainly confirmed the predictions of QED in this regime many, many times.

 

[PeterDonis]

Here the classical perspective, with its familiar wavelet model, can be used as an analogue to provide guidance (and perhaps a little intellectual comfort, if you still believe in classical EM waves).

This does not seem like a rigorous statement of what an actual physical model, QED, says. It seems like a heuristic, hand-waving statement that is not even meant to be an accurate description of the actual physics.

I also note that what you quote does not say that the law of reflection is only valid statistically, or that it sometimes fails.

 

[pines-demon]

You're using classical optics here, but this thread is in the QM forum and so we are talking about QED. There are no "light rays" in QED.

The book OP cites is not a QED book as you already noticed and could be using the "photonic" language a bit informally. That's why I ask for more precision.

Edit: this also concerned the image, under classical light rays the image is false, so one must explain what is being illustrated here.

 

[PeterDonis]

The book he cites is not a QED book

If so, then the OP should not be using it as a source for statements about what QED says.

That's why I ask for more precision.

If the book is not a QED book, why would you expect it?

 

[pines-demon]

If so, then the OP should not be using it as a source for statements about what QED says.


If the book is not a QED book, why would you expect it?

The book seems to have a chapter about QED, see my next comment.

 

[PeterDonis]

The book seems to have a chapter about QED

Are the statements the OP refers to in that chapter? And is it a chapter on the actual model of QED, or just a chapter that describes heuristically what QED is like?

 

[PeterDonis]

under classical light rays the image is false, so one must explain what is being illustrated here.

I did that in post #5. The image is illustrating how the path integral formulation of QED models mirror reflection.

 

[pines-demon]

We can appreciate how all of this comes together by treating the reflection pictured in Fig. 4.79; a point source S illuminates a mirror, and light is subsequently scattered upward in every direction from every point on the mirror. We wish to determine the probability of a detector at P, recording the arrival of a photon. Here the classical perspective, with its familiar wavelet model, can be used as an analogue to provide guidance (and perhaps a little intellectual comfort, if you still believe in classical EM waves).

Ok. I checked the book, the title of the section is QED, fair enough. In that section the description is given in terms of Feynman path integrals as PD has said. It never explicitly states that the law of reflection is violated either.

The book says that you can think of it as a sum of classical EM waves that you have to sum together (this is only for that specific example and it is only a heuristic tool). Later it moves away from that idea.

Did you check the next section on law of reflection and photons? it seems to confirm that light does follow Snell law and the law of reflection due to quantum mechanics (with a very "simplistic" analogy, according to the author).

 

[pines-demon]

Are the statements the OP refers to in that chapter? And is it a chapter on the actual model of QED, or just a chapter that describes heuristically what QED is like?

More of the second, the book illustrates what QED is using a qualitative explanation, without doing any calculation just pictures and principles. Also none of the problems in that chapter are about QED.

 

[LightPhoton]

I don't have this textbook, but from what I can gather it appears to be a textbook mainly on classical optics. However, the statement you refer to is a statement about quantum optics, i.e., based on quantum electrodynamics, QED. And, as I commented in post #3 just now, this thread is in the QM forum, so presumably QED is to be the basis for discussion.

For a good layman's discussion of how QED treats this case, including discussion of experiments in which QED's predictions about things like this are confirmed, you might try Feynman's book QED: The Strange Theory of Light and Matter.

With all that said:


It depends on what you mean by "the law of reflection". See below.


Some photons might--at least if we are using the path integral formulation of QED (which is what Feynman uses in the book I referred to above) and being somewhat hand-waving in our description.

A more accurate description is that the probability of a photon going from S to P by bouncing off the mirror in between depends on the specific point on the mirror at which the photon bounces. The highest probability is for the classical path, the one where the angle of incidence (note my correction in the quote above) equals the angle of reflection. As you move away from that point on the mirror, the probability decreases, but it is nonzero for a fairly wide range of points on the mirror, so the total probability for a photon to go from S to P by bouncing off the mirror will include a fairly wide range of points on the mirror; it cannot be accounted for solely by photons traveling on the classical path.

I should also correct a common misconception: in the above, when I talk about photons following different paths, I am not talking about different photons--i.e., I am not saying that some photons follow one path and some another, and adding all the photons together gives the observed intensity of light going from S to P by reflecting off the mirror in between. QED's model does not say that. What QED's model says, in the path integral formulation, is that every single photon travels on all possible paths, and each path has a probability amplitude associated with it, and the final probability for a single photon to go from S to P by bouncing off the mirror in between is obtained by adding together all the amplitudes.

I don't think "the law of reflection is only valid statistically and sometimes fails" is a good way to describe the above. Again, I don't have Hecht's textbook so I don't know the context in which the statement you refer to was made. (I also don't know how much your paraphrase of the statement distorts Hecht's intended meaning.)


No, because, as above, a photon does not have just one path, and "sometimes the law fails" is not a good description of what QED actually says about this scenario. But experiments have certainly confirmed the predictions of QED in this regime many, many times.

I thought what the author meant was that the photon is in the superposition of all paths and when it reaches the detector its wavefunction would collapse, and by measuring the angle at which the photon hit we would be able to figure out its apparent direction.

 

[PeterDonis]

I thought what the author meant was that the photon is in the superposition of all paths and when it reaches the detector its wavefunction would collapse, and by measuring the angle at which the photon hit we would be able to figure out its apparent direction.

I doubt that's what the author meant since it's wrong.

 

[mfb]

I thought what the author meant was that the photon is in the superposition of all paths

Yes. If you calculate the amplitude at a given point then you get a Cornu spiral, where only paths close to the classical reflection path contribute notably to the amplitude.

If you want to detect the photon at a specific point then you can't measure its angle. An accurate angle measurement would need a very large detection area - which prevents you from telling at which point the photon was reflected.

 

[pines-demon]

Yes. If you calculate the amplitude at a given point then you get a Cornu spiral, where only paths close to the classical reflection path contribute notably to the amplitude.

The Cornu spiral appears in the same section quoted by OP.