My opinion is probably non-standard, so accept as such. IMO there is no such thing as a photon in flight. Quantization only exists at the times of emission and absorption. In between there is only the continuous development of the e/m field as described by Maxwell's equations. People will raise many objections to this and they can all be shown to be wrong.

Light, radio waves and all other forms of electromagnetic radiation  is made up of photons.  When there are very many of them it is more convenient to talk about fields.  So whether a beam or a pulse is described in terms of fields or photons is a matter of taste.  All of them therefore propagate with c.

Thank you Bo.

Are we able to measure or know the speed of an individual photon?

yes ,of course.

Photon is a quantum of perturbation of EM field. Such perturbations propagate with the speed of light, c. The space-time dependence of the photon operator \hat{A} is exp{i(kx - \omega t)} for a photon propagating in x direction. Its frequency and wave-vector absolute value are related as \omega = kc, which is one way to say (and know) that the photon speed is c. It's precisely the phase velocity of EM waves. A "beam" or "pulse" in your question probably refer to a EM wave that is a superposition of flat waves, which [superposition] has a discernible front or whatever other spatial feature that can be used for its speed measurement. At least this is my interpretation of your

> When we measure the speed of light, we measure a beam or pulse.

-- that you refer to measuring the speed of such a feature, i.e. essentially refer to measuring the group velocity. The latter is still c, as in empty space EM waves are dispersionless. With all this sophisticism -- I believe it's clear in what sense single photons "have a definite speed"; and that speed is c.

Photon is a massless particle. So according to special relativity, it must move with the speed c .

So how would we measure the speed of a single photon?  How can we know when it starts out AND when it arrives?

Please define what you mean by a single photon. How is it significantly different from a single electron for instance?

To measure the speed of propagation of some perturbation in the form of a planar monochromatic wave (that's perhaps what you are asking about -- for such you cannot "know when it starts out AND when it arrives") you use other methods, not spotting its departure and arrival (this latter method of spotting your something in several places in quantum world is not so trivial anyway).

For instance you can independently measure its frequency \nu (by noting with what frequency your detector measurements oscillate when you sit in a fixed spot in space) and wavelength \lambda (say, by some diffraction experiment, or with some detector that measures values of your oscillating quantity (electric field e.g.)  in several positions in space simultaneously). Then you know the (phase) velocity: v=\nu * \lambda = \omega/k.

Thank you Andrey

A single photon is the packet that is emitted when an electron drops in energy level.

Don't you think that if you try to detect oscillations in two positions in space, simultaneously,then one of those detectors will absorb the photon and it won't reach the other?  

it is a matter of taste to consider the photon as mass-less, because its trajectory is curved in the neighborhood of big masses (stars, planets, etc...) or is no more given free by very big masses (black holes). On the other hand I also do not see why the speed of light should be different for the single photon as for the beam of light. I do not exclude the possibility that photons can interact in a beam such that they encumber each other, but I suppose that nobody produced since now a beam of such intensity that this kind of phenomenon could be observed. [I also suppose that the energy present there would make any kind of measurement impossible...]

There is a recent article in PRL that measures just this and finds that a single photon does travel at c. Here is the link to the paper by Zhang:

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.243602

and a summary from APS (American Physical Society) for those you find Zhang's paper a bit daunting:

Zhang et al. study optical precursors, which are signals preceding the main wave packet in a light pulse with a sharply rising leading edge (as in a step function pulse). Past work has shown that even in “superluminal” media where the group velocity may be faster than light speed, the precursor is always in front of the pulse. The authors extend this work to the single-photon level with the help of cold atomic gases: a photon generated in one rubidium gas traverses a second collection of rubidium atoms. With careful use of electromagnetically induced transparency, the researchers can separate the precursor from the main pulse and confirm it travels at the speed of light. The results add to our understanding of how single-photon signals propagate but also confirm the upper bound on how fast information travels.

Hello Steve Faulkner,

Its a nice question, I know most of them would say answer is speed of light is C (They are partially right and partially wrong as well).

I will get back to you in few weeks and give you detailed answer.

Regards,

Bhushan Poojary

I'm not sure that we can actually measure the time of flight of a single photon.

What QED actually assumes is that the photon propagator diverges as 1/(E^2 - p^2c^2). This means that there is going to be a bit of a quantum wiggle room on the photon velocity implied by time of flight calculations. 

Has anyone bothered to read the paper I cited earlier? The speed of a single photon has been measured. It is an extremely important result for quantum computing.

Here it is again. Hopefully this clears up some of the misunderstanding about what quantum theory has to say about the speed of a single photon. The theory leaves it as an open question (again we are not talking about an EM wave which can travel any damn speed, even faster than c, but a single photon). It is an elegant experiment, and it shows that single photons obey causality, which makes both Einstein and those in Quantum computing and information theory very happy.

http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.106.243602

I don't have access to that paper Lawrence.

Didn't realize it wasn't freely available. I've attached a copy. Happy reading!

Thanks for bringing the result out of the walled garden, Lawrence.

Thanks Lawrence Margulies,

For sharing this paper.

Regards,

Bhushan Poojary

Thanks Lawrence. I'll have a read.  I generally don't have access to journals.  I need to find myself an affiliation with an academic institution; then I would.

My opinion is probably non-standard, so accept as such. IMO there is no such thing as a photon in flight. Quantization only exists at the times of emission and absorption. In between there is only the continuous development of the e/m field as described by Maxwell's equations. People will raise many objections to this and they can all be shown to be wrong.

Steve, right, that's why I wanted you to define the terms. I talked about the concept of speed re flat wave and ways to measure that (as that seemed to me the point you wanted to make -- a wave packet (or beam or pulse) may have a front that we can spot several times and thus define its speed, whereas the flat wave is kind of the same everywhere; and "photon" is normally related to a flat wave).

Speaking about quantum world: you did not answer how electron is different from a photon (in a way that makes measuring its speed any simpler). Photons as well as electrons and other particles are described in QFT like the following. You have creation and annihilation operators for all these particles. Bases for these linear fields of operators can be chosen in infinite number of ways. One convenient and most often used way is to take basis operators such that they create/annihilate your particles in states with defined momentum and energy. Such a basis is convenient because kinetic terms have a simple form in this basis , kinetic energy density operator is diagonal. It is also this basis in which velocities are defined. Namely (talking about absolute values here), in a state with defined p and E (or k and \omega if you like) m^2=(E^2-c^2 p^2)/c^4, and v is then defined from E=mc^2/ \sqrt(1-v^2/c^2), if so found m is nonzero. For photons m^2=0 (from the above equation: for experimentally found E and p, in that state with defined E and p), and that again unequivocally means that v=c. Once you talk about photons (-- a QFT concept) that's it.

If you have your own definition of photons and don't follow this route of QFT -- then we should understand the essence of the question better. Say, about your "photon" emitted when an electron changes its state (between states with defined and different energies) -- we have to decide whether this "photon" has its momentum defined, or is in a state which is some superposition of photons with different moementa (we don't question QED basics, in part its picture of photons, do we? If we don't, one of the above possibilities in this sentence before the brackets must be true). If it's in a state in which the mometum is not defined it's trickier to talk about such a photon velocity; but anyway once we catch such a photon with a detector which measures momentum and energy we are in a good shape to talk about the velocity of what we caught -- and it will be c as is clear from the above.

I thought the question referred to the actual measurement of a velocity vector as a rate of change of position with respect to time, not to a formal definition. please clarify.

Oscar, please clarify. What's the difference? In case until someone shows otherwise the question has been answered and linked by me twice. So come one people let's stop beating this poor dead horse. There are many other much more interesting things to discuss than personal views on a question that has already been solved many time at the highest level of rigor.

Hi.

The difficulty I was addressing in asking this question is this:  A beam of light, consisting of many photons, has a velocity because you can measure the two times when a light pulse is detected passing two different positions. In detecting the pulse at these two positions you will eliminate a minimum of 2 photons from the pulse -- one for each detector at each of the two positions.  I would expect, however, that a single photon could only be detected once (at one of the positions).  

Am I wrong to think that the only things we can know about a photon is its position or its wavenumber, and even wavenumber can only be measured when the photon is part of a beam.  Furthermore, we can only know frequency if we firstly know wavenumber. And even worse, we can only calculate frequency if we assume a photon has the same speed as the beam it belongs to.

@Ray - I agree with the substance of what you're saying. The way I would put it is that interaction occurs in position space and is thus localised, while propagation occurs in momentum space and is thus delocalised, and that's the origin of "wave-particle duality".

@Oscar: in quantum mechanics you cannot really speak of "velocity vector as a rate of change of position with respect to time", only of time-of-flight measurements. And that's for "thought experiments". For real experiments you have to be a little more imaginative, as in the paper Lawrence shares in which you use a process emitting two photons, use one to determine the "time of emission" and the detection of the second photon defines the "time of flight".

Photons are massless and are indistinguishable - therefore they travel at c regardless of being in a group or single.

Did not Maxwell describe c as the rate at which the EM wave propagates by establishing mu and epsilon? I dont believe he inferred that this propagation was along a straight line. In fact, he drew out his “spinning cells” to help him (and others) visuallize a possible propagating waveform.

This being the case, the real question here then would be along which length (straight or arc) are our instruments attuned to?

Following the shortest path, an ellipse, the fastest speed of light c travels most linearly along the major axis before meeting the minor axis at h or the Big Bang and slowing (slowed or stored energy =matter) along the sharper parabolic (x-squared) curve (gravity; visible universe) and becoming orthogonally c-squared or electromagnetism, other quanta, elements, helical DNA, galaxies, a rugbyball-shaped universe (cf. Grigory Perelman's Poincaré conjecture solution), their respective entropies conically at their respective minor axis apexes, and finally respective black holes, or linear, flat space light c again, so on and so on, to which the self-same instrument of our imagination may be attuned.