A question from reading Feynman's book on QED

[mike1000]

I am reading Feynman's book QED: The Strange Theory of Light and Matter".

What I am getting out of this is that a photon is like a tiny harmonic oscillator traveling through space. Each harmonic oscillator has frequency and phase. If two photons have the same source and start out nearly in phase (and have same frequency) and take nearly the same path(in terms of time) then they will still be nearly in phase when they reach their terminal point and they will constructively interfere.?

As I think about it, they do not have to start at the same point and do not have to be in phase when they start. All they have to do is strike the same point on the detector screen and travel paths, such that, they are in phase when they strike the detector screen.

 

[Buzz Bloom]

Hi Mike:

Did the text say somewhere that the phase changes as the photons moves?

Regard,
Buzz

 

[mike1000]

Hi Mike:

Did the text say somewhere that the phase changes as the photons moves?

Regard,
Buzz

In a round about way it does. Feynman uses a metaphor of a photon having an internal clock. When the photon is emitted from the source the clock starts to tick. The hand of the clock moves at the frequency of the photon. For instance if it is red light, the hand on the clock moves at 36,000 times per inch. When the photon reaches the detector the clock stops and the dial on the clock is pointing in some direction. For two photons that travel very similar paths( similar path length) to the detector the hands on clock will be pointing in approximately the same direction and will add constructively. So he does not say phase but I think that is what he is alluding to.

On second thought, I think that he was talking about the relative phase between two(or more) photons in that example. I just realized you asked a completely different question. You want to know if he says that the phase of a single photon changes while the photon is moving.

 

[zonde]

As I think about it, they do not have to start at the same point and do not have to be in phase when they start. All they have to do is strike the same point on the detector screen and travel paths, such that, they are in phase when they strike the detector screen.

Yes, there is diagram in the book that illustrates this idea:

 

[mike1000]

Yes, there is diagram in the book that illustrates this idea:

I am trying to figure out what was Feynman's revolutionary idea? What was it?

 

[Buzz Bloom]

Hi mike:

I have always considered that Feynman's greatest contribution to physics was Feynman diagrams.

https://en.wikipedia.org/wiki/Feynman_diagram​

I have also always felt that his greatest contribution to the general population was his ability to present extremely clear explanations for difficult to understand issues. The best example perhaps is the O-ring problem.

https://en.wikipedia.org/wiki/Rogers_Commission_Report​

Regards,
Buzz

 

[Buzz Bloom]

You want to know if he says that the phase of a single photon changes while the photon is moving.

Hi mike:

If you can't find in the text whether a photon's phase changes with its motion, are you able to make a guess about this based on what you have read? If you are, and you guess yes, then you should then be able to think more clearly about your original guess:

As I think about it, they do not have to start at the same point and do not have to be in phase when they start. All they have to do is strike the same point on the detector screen and travel paths, such that, they are in phase when they strike the detector screen.​

Regard,
Buzz

 

[Nugatory]

I am trying to figure out what was Feynman's revolutionary idea? What was it?

He had more than one. One of them is the discovery of the path integral formalism of quantum field theory, introduced in that book.

This book is a popularization, a handwavy description of the formalism that allows a layman to sort of imagine how that formalism is used. It is a good popularization - I'm not aware of any other remotely acceptable math-free explanation of the subject, and I've recommended it to beginners so often that I've considered asking for a cut of the royalties. But be warned that like all popularizations, it is not the real thing, it is not a substitute for a serious textbook on QED (Feynman wrote one of those too), and you cannot base any new insights on the superficial picture that you get from it.

 

[zonde]

This book is a popularization, a handwavy description of the formalism that allows a layman to sort of imagine how that formalism is used.

Why do you call it "handwavy"? It seems that Feynman believed he was giving exact description of the theory except that he left spin out of the picture for most part. Of course his description is FAPP useless for coming up with quantitative predictions (and they are essential no doubt), but at qualitative level everything (except for spin/polarization part) should be good.

 

[mike1000]

I just unrealized something...

If I understand Feynman's path integral method as described simply in his book "QED...", the interference pattern comes from the fact the the photon has intrinsic frequency and there is a phase relationship between two or more photons. striking a detector. The interference pattern recorded on a detector screen just shows those places where the phases of the particles were in phase or out of phase. Looked at this way, the interference pattern is not showing us locations where the photon can strike the detection screen, rather it is merely showing us the phase relationship between many different photons. The interference pattern is not a statement of where a photon is likely to be found because it takes many photon strikes at the same location to create all the parts of the interference pattern on the screen (both the light and dark spots).

As I write this I know I am wrong about something, but I am not sure what. I must be mis-interpreting what Feynman says is causing the interference pattern. It cannot just be the path difference between monochromatic photons.

I think what I am saying is that Feynman's path integral method, as I currently understand it, does not depend upon or need in any way the uncertainty in momentum caused by passing a photon through a slit. The Uncertainty Principle ends up showing us exclusion zones for where a photon can be found, whereas, Feynmans path integral method does not imply there are exclusion zones for where the photon can strike the detector screen.

 

[PeterDonis]

If I understand Feynman's path integral method as described simply in his book "QED...", the interference pattern comes from the fact the the photon has intrinsic frequency and there is a phase relationship between two or more photons. striking a detector.

No. There is a phase relationship between different paths a photon can take from the source to the detector. But the different paths don't represent different photons. They represent different values of the integrand in the path integral, which tells you the amplitude for a single photon to go from the source to a particular point on the detector.

I think what I am saying is that Feynman's path integral method, as I currently understand it, does not depend upon or need in any way the uncertainty in momentum caused by passing a photon through a slit.

There are two issues here. First, "uncertainty in momentum caused by passing a photon through a slit" is the wrong way to look at it, because the momentum of the photon is not being measured. What is being measured is the position on the detector at which the photon hits.

Second, the amplitude for a given path in the path integral is affected by the interaction of the photon with the slits, so it is not correct to say that the path integral does not depend on the effect of the slits on the photon.

 

[mike1000]

No. There is a phase relationship between different paths a photon can take from the source to the detector. But the different paths don't represent different photons. They represent different values of the integrand in the path integral, which tells you the amplitude for a single photon to go from the source to a particular point on the detector.
There are two issues here. First, "uncertainty in momentum caused by passing a photon through a slit" is the wrong way to look at it, because the momentum of the photon is not being measured. What is being measured is the position on the detector at which the photon hits.

Second, the amplitude for a given path in the path integral is affected by the interaction of the photon with the slits, so it is not correct to say that the path integral does not depend on the effect of the slits on the photon.

Are you saying that Feynman's Path Integral is just a mathematical method for calculating the amplitudes for the probability distribution and says nothing about the underlying physics of what is happening?

 

[Nugatory]

the interference pattern comes from the fact the the photon has intrinsic frequency and there is a phase relationship between two or more photons.

It does not; there are no multi-photon effects interference effects involved in the calculation. We are calculating, for each individual photon (but be aware that the phrase "individual photon" is itself seriously problematic), the probability that it lands at a given point on the screen. We do this by calculating a complex number called a "probability amplitude" for every path between source and point on screen that was available to the photon, summing these probability amplitudes, and then squaring the sum to yield a real number that when properly normalized is the probability. There is no notion here that the photon actually takes anyone of these paths, or that it takes multiple paths - we're just calculating a number for each possible path and combining them in a particular way. Feynman's point in the book is just to show in layman-friendly terms that this calculation can lead to many of the familiar results of classical optics as well as the less familiar result of the single-particle double-slit experiment.

 

[Nugatory]

Are you saying that Feynman's Path Integral is just a mathematical method for calculating the amplitudes for the probability distribution and says nothing about the underlying physics of what is happening?

Yes.

It's worth noting that when you speak of "the underlying physics" you are implicitly assuming that there must be such a thing. That's a pleasing assumption in the sense that many people find the alternative to be intellectually distasteful, but it's still an assumption unsupported by any experimental evidence. Maybe the universe has an "underlying physics" that we would find aesthetically pleasing and maybe it doesn't, but without a candidate theory for "the underlying physics" that can be tested experimentally there's no science here, just idle speculation.

 

[PeterDonis]

Are you saying that Feynman's Path Integral is just a mathematical method for calculating the amplitudes for the probability distribution and says nothing about the underlying physics of what is happening?

One answer to that is the one Nugatory gave. His answer considers the possibility that QFT as we know it is not a fundamental theory, but just an approximation to something deeper (string theory? loop quantum gravity? we don't know at this point). The something deeper would be the "underlying physics", but as Nugatory says, we can't test any of it experimentally and QFT doesn't tell us anything about it.

The answer I would give, if we just take QFT as our theory and don't concern ourselves with what might lie "underneath" it, is that the path integral is the underlying physics; anything else, such as trying to interpret the individual paths in the path integral as "photon trajectories", is interpretation, and interpretation is not physics. It's just a story you can tell once you already know the physics, that describes it in terms that you find preferable.

 

[vanhees71]

I cannot see any sense in the notion of "photon trajectories", even in a very weak sense of scientific honesty calling it "interpretation". You can be sure that "interpretation" beyond of the level that is needed to make the mathematical definitions of physical theories applicable to real-world observations confuses the physical sense in general. In the particular case of "photon trajectories" there is not even a mathematical way to define what could be meant by that, because as field quanta of a massless vector field it is not possible to define a position observable for photons at all, and if there is no clear mathematical definition of position, there's no clear definition of trajectory nor does any "interpretation" of this undefined notion make the slightest sense.

In QFT the path integral is not integrating over paths but over field configurations, which solves this obvious confusion in half a sentence. Feynman's method in his popular book (it's better than most popular science books on this topic, but it's still not the true thing) has not much to do with photons. It's just a simplified way of Huygens's principle, which is an approximate solution of Maxwell's equations for diffraction in the Fraunhofer limit. The idea is that you get (an approximation) of the electromagnetic field behind obstacles like slits or gratings in thinking of any point in the opening as a source of a spherical wave. At a given point you then get the electromagnetic field (approximately) as the superposition of all these "elementary waves".

For experiments, using single photons as light source (which only in the recent years has become an easy standard in the lab by the way) the corresponding intensity on the screen has to be interpreted as detection probability for photons. The "position" is defined by the detector not by the photons. Mathematically what you measure are correlation functions of electromagnetic field operators.