Photon Velocity: Is the Real Path of Light Straight?

[TomTelford]

Good morning,

Case: You have a single photon emitter (quantum dot?) that you can control when a photon is emitted and a photon detector some distance away. You release a photon which is subsequently detected. In what cases is it reasonable to assume that the photon has indeed traveled at c in a straight line between those two points if at all?

Thanks.

Tom.

 

[ghwellsjr]

Good morning,

Case: You have a single photon emitter (quantum dot?) that you can control when a photon is emitted and a photon detector some distance away. You release a photon which is subsequently detected. In what cases is it reasonable to assume that the photon has indeed traveled at c in a straight line between those two points if at all?

Thanks.

Tom.

You have just restated Einstein's second postulate which is a valid assumption as long as everything is inertial.

 

[jtbell]

That is true in a classical context (where "classical" means non-quantum, not non-relativistic). In the context of photons as quantum objects, you have to wade into the swamps of interpretation of quantum mechanics and quantum field theory, in the Quantum Physics forum next door. Over there, four people will probably give six different answers.

 

[TomTelford]

I intend to repost over there as well but I'd like to see what the GR/SR limitations of the assumption are first for context.

Thanks,

Tom.

 

[Dale]

When you are dealing with single photons you cannot make classical approximations in general and must instead actually do QM. In QM there is no single "real path" of a photon. A photon takes all possible paths, and the probability is the sum of the probability of each possible path.

QFT is compatible with SR, but it is not compatible with assigning a single "real path" to a photon.

 

[Vanadium 50]

I intend to repost over there as well

Please don't. Multiple posting is not allowed.

 

[jfy4]

In geometric optics, if there is a light source and a lens, there are infinitely degenerate "paths of least time" from the source to the focal point through the lens. Then if you cut the intensity down, slowly, so that the source was emitting less and less light, eventually you would run into your question: I let one photon go, which of these paths does it travel? This cannot be answered classically, you need a QM approach since the realization of the situation is infinitely degenerate (temporally), and these distinct (spatially) realizations must be accounted for probabilistically. In comes quantum.

 

[bobc2]

Good morning,

Case: You have a single photon emitter (quantum dot?) that you can control when a photon is emitted and a photon detector some distance away. You release a photon which is subsequently detected. In what cases is it reasonable to assume that the photon has indeed traveled at c in a straight line between those two points if at all?

Thanks.

Tom.

A very fascinating problem, Tom. One of the problems of dealing with this is that there are different interpretations of special relativity. One of a number of different universe models could be assumed as a starting point. For example there is a model that would affirm that a single photon did travel a definite path from the emitter to the detector. Other models would not provide the basis for coming to that conclusion.

Note that (depending on your interpretation of QM--the double slit experiment for example), QM does not necessarily preclude the possiblity of a definite path. It does preclude the possibility of predicting or even measuring the path of the photon (and some claim that is equivalent to saying that there is no definite path). QM provides no way of knowing what path the photon has taken, or even if there was really just one indentifyable photon involved in the experiment. Quantum field theory suggests many possibilities about what might be going on in the field between the time of emission and detection.

But, your question is not unreasonable and motivates quite an interesting discussion. You question hints of a probing into physical reality, which is not a subject favored on this forum. And of course we really don't know what a photon is, fundamentally speaking. We know of certain properties and processes related to what we assume is (for the sake of discussions) an object of some sort.

 

[pervect]

I'll go with jtbell and Dalespam on this one.

There are many different interpetations, of which the one alluded to by DaleSpam is probably the simplest. DaleSpam's approach is based on Feynman's ideas, which you can find outlined in "QED - a strange theory of light and matter".

The problem is that Feynman doesn't tell you how to calculate anything. Apparaently the path integral approach can be made to work, but unfortunately I don't know the details of how to get usable answers out of it - and while QED is otherwise a good book, having an "answer" that doesn't actually let you calculate anything turns out to be a lot less useful than one would hope.

But Feynman and QED will proide a nicely quantified example of a simple situation where assuming that a photon follows a single path does not agree with experiment. He will, in other words, give you some good questions. And the question of most interest are the famous single and double slit experiments.

First off, if you assume that light travels in a straight line, you can't account for the diffraction phenomenon that occurs when it passes through a single slit.

WHen you have two slits, things get even worse.
If you assume that the light travels in a straight line through one slit, or the other, and add the results together (perhaps throwing in diffraction on an ad-hoc basis), you will not get what is actually observed, which is the double-slit interference pattern.

The "simplest" explanation for the interference pattern is up for some debate, Feynman's explanation is basically that the light travels through both slits, and interferes with itself.

Since multiple posts aren't allowed, you might want to move your thread if you want better answers from the quantum people. But this is pretty much the basics.

The very short version is that diffraction and intereference can't be modeled in the way you suggest. If your in an experimental realm where neither effect is important, you might get away with it.

 

[zonde]

Case: You have a single photon emitter (quantum dot?) that you can control when a photon is emitted and a photon detector some distance away. You release a photon which is subsequently detected. In what cases is it reasonable to assume that the photon has indeed traveled at c in a straight line between those two points if at all?

It is reasonable to assume straight trajectory at c if it is vacuum in between and there are no sources of gravity nearby.

 

[andrien]

see page 26.8 here,for a novel introduction of it by feynman
http://books.google.co.in/books?id=xl6871RXKxQC&pg=SA26-PA3&dq=feynman+lectures+vol.+1+fermat&hl=en&sa=X&ei=9w7wUKmfMMy6lQW-3YHQBw&ved=0CDMQuwUwAA#v=onepage&q=feynman%20lectures%20vol.%201%20fermat&f=false