# How big is a photon?

1. Dec 6, 2012

### Thinker007

I was listening to a physics professor lecturing on QM and he raised the question "How big is a photon?" and indicated it had arisen during his PhD defense.

He than began to discuss the accurately known frequency and wavelength of a laser emitted photon (and thus accurately known momentum) in the context of the uncertainty principle. The product of the uncertainty in position and accurately measured momentum is greater than or equal to (up to a small numerical factor) Planck's constant. He then concluded that in the direction of travel, the position was unknown to within a surprisingly large distance - a meter or so. Or more accurately, that is how I interpreted it. He didn't say position is unknown, he was still talking about "size".

Without really saying it, the implication was that the answer to the question was that a photon was a meter or so long in the direction of travel (and the emitting aperture wide in the transverse direction).

Does that description of "size" make sense to those here? I would probably have said that the photon is a point particle unless we're doing string theory, and the location was just poorly known along the travel direction. If the photon was truly "big" I'd think it would take 3 nanoseconds to finish arriving at a detector assuming a foot or so per nanosecond speed of light, and that should easily be measurable. Do photons take a finite amount of time to "arrive" at a detector?

Thanks.

2. Dec 6, 2012

### dextercioby

The current theory works very well with a pointlike particle approximation of a quanta of the electromagnetic field. I don't know of a successful model (i.e. predictive and confirmed by experiments) of a finite size photon particle.

3. Dec 6, 2012

### K^2

Uncertainty and size aren't the same thing. Like dextercioby said, photons, like all elementary particles, are point-like.

Uncertainty in position of a photon produced by a finely tuned laser can, indeed, be quite macroscopic. That shouldn't be surprising. Even in classical treatment, in order to have a precise frequency, the oscillation must have significant duration. Therefore, a precisely localized photon cannot possibly have a precise frequency.

But it doesn't mean the photon is one meter long now. It means that the photon is still a point particle that's distributed over span of space of one meter.

4. Dec 6, 2012

### Redbelly98

Staff Emeritus
The size of a photon depends on its environment. If you have a cube with mirrored surfaces on the inside, then the photons that describe the electromagnetic field inside that cube are the size of the cube -- whether it is 1 micrometer or 1 kilometer.

5. Dec 6, 2012

### K^2

You are still talking about the probability distribution, not the location of a particle. If you insist on talking about EM field in terms of particles, photon is point-like.

6. Dec 6, 2012

### atyy

I think your professor is just expressing a sentiment like "the particle is part of a beam, and that beam is extracted at some time. So the particle is localized to some extent. .... To a particle the beam is the whole universe, and it is big!" http://books.google.com/books?id=CNCHDIobj0IC&dq=veltman+mysteries+facts&source=gbs_navlinks_s (p117).

Can a photon be localized? Some people think not eg. http://arxiv.org/abs/0903.3712.

Last edited: Dec 6, 2012
7. Dec 6, 2012

### K^2

Photon in a cavity might as well be considered localized. Yes, realistically, the barrier is finite, so there will be an exponentially decaying tail. But you can make skin depth thin enough and walls thick enough to make the description of localized photon be as valid as it needs to be.

But none of this still has anything to do with size of a photon.

8. Dec 7, 2012

### Thinker007

Because this was a simplified minimal mathematics lecture series for the general public I would have assumed that his "size" comment was just a fuzzy way of introducing related concepts, except that he presented it as a specific trick question he was asked during his PhD defense.

Perhaps what he was getting at is that when detected, the photon has size that interacts with the detector with pointlike properties, but while propagating before detection it has size that is described with wavelike properties distributed over the meter distance. IOW, I suppose he was trying to emphasize wave particle duality and that both are legitimate descriptions of the real world, with an equal claim to the concept of "size."

I know I tend to think of the particle as the "real" thing and the wave function as describing a probability for where that real thing is "really" located, but I know that's sort of a non-QM bias I have from growing up in a macro sized world.

9. Dec 10, 2012

### PhilDSP

It's been known since the mid 20th century that the wave trails of photons are typically some millions of cycles long (several meters). But that says nothing about a photon's possible extent in other spatial directions.

A photon may even be considered enigmatic if we ask the question: "What is a photon? Is it a particle that binds energy into a highly compressed region or is it a wave that potentially spreads into infinity as it's edges dissipate in time and space?"

10. Dec 10, 2012

### Staff: Mentor

Which parameter do you mean here?
Coherence length of most light sources is shorter than that (just a few wavelengths). You need a laser to get coherence lengths of meters with visible light.

11. Dec 10, 2012

### PhilDSP

I think we'd need to look at the experiments that produced those results. Sorry, I don't have a reference handy at the moment.

12. Feb 19, 2013

### jliu135

How about re-framing the question as follows:

If a photon travels down a direction in vacuum, how small a hole will need to be to stop it entirely.

The question might need to be asked first for visible light and then for other wavelengths should there be interesting differences (like the barrier might need to of different material).

The answer might need to be in probabilistic form, like if the photon is 450nm wavelength and if the hole is 500nm in diameter, the photon might go through 70% time.

13. Feb 19, 2013

### bahamagreen

I think you should explain this.

14. Feb 19, 2013

### Staff: Mentor

This depends on the way the light approaches the hole. A well-focused laser beam? A flashlight?
There will always be some light getting through, but for lengths smaller than the wavelength a better focus does not help any more, and the maximal (!) fraction going through begins to drop.

15. Feb 20, 2013

### jliu135

laser or flashlight? It shouldn't matter. The question is for one photon. The source should not matter except for a laser, all the photons would be same wavelength and the flashlight would be many.

16. Feb 20, 2013

### f95toli

No, photons certainly have different propties depending on the source. You can't strictly speaking have a single photon from a flashlight, since those photons are thermal; you can only talk about a definitite number of photons (e.g. 1) for sources that emitt photons in a number state. This is why you can't create a real single photon source by simply attenuating a normal source of light (not even a laser, sine a laser emitts coherent photons).

Moreover, and perhaps more relevant to the OP, single photons can even have different "shapes"; at least if you believe that what is being measured is actually a "real" property of a photon

see e.g.

http://arxiv.org/abs/1203.5614

The correlation plots in e.g. fig 2 represent the "shape" of a single "two-peak" photon, at least if you believe the authors (I saw a talk about this at a confence a couple of months ago)

17. Feb 20, 2013

### jliu135

Ah, a bit of clarification needed here. I meant when you get down to one photon, the source should not matter except that the source would determine the wavelength or a range of wavelengths.

From the article, I find this "Here, we demonstrate that single photons deterministically emitted from a single atom into an optical cavity...". So it seems now feasible to emit single photons at will.

18. Feb 20, 2013

### f95toli

But it DOES matter. There are lots of different single photon sources available, so we now know how to generate snlge photons at many different wavelenghs.
However, all of these sources are fundamentally "quantum mechanical" in that they are able to generate a single excitation, they are very different from a flashlight.
If you start with a thermal source you can of course attenuate it so that it looks like it on average emitts say a single photon per second when you measure the energy it outputs; but it won't be a true single photon source since a thermal field (as it is known) does not contain a fixed number of photons. The emitted radiation simply does not HAVE a property "X number of photons". A source that can generate single photons emitts radiation that is in what is known as a number (or Fock) state, and then this property exists (but the price you pay is that now the phase is undetermined).

19. Feb 20, 2013

### Naty1

From the OP:

That's a good description, I think....

Here are a few from others:

Carlo Rovelli:
presented in Weinberg's "The quantum theory of fields" vol.1.....

and from a prior discussion in these forums:

Marcus quoting a prior post:

Marcus :

Marcus' comment:

And you will note, of course, these are not all in agreement....

20. Feb 20, 2013

### cnickford

My understanding is that when we make a measurement we are really poking at the wavefunction, which holds all the measurable information about a particle within it. When the measurement is made it causes any probabilities to collapse and take on a definite value.

21. Feb 20, 2013

### godw2718

Let us assume that a photon propagate in z direction.
For the z direction size, we can make it as small as possible (at least theoretically) by superpositioning a various wavelength photon states, which becomes a delta function in position space while it's just a plane wave in momentum space. Moreover, we can also make it small in x and y direction by superpositioning standing waves, thereby make it small.
If you express a photon as a wave packet, we can see that the wavefunction does not spread as time goes on.(for a mass zero particle while for electrons which as a finite mass it spreads out)
I think, if the principle of superposition in quantum mechanics is valid in all circumstances, we can make it localized in position space.

22. Feb 20, 2013

### Cthugha

This already implies that this "duration" of the wavepacket defines some photon size. This is incorrect - besides that you do not take into account emission time uncertainties, there is no reasonable and accepted definition of photon size.

Can you? Really? So what defines your "photon size" then. You can get some superposition to get some kind of spatial localization of the real space photon wavefunction. If you then go ahead and calculate the energy density distribution of that photon, you will find that it is not locally connected to your real space wavefunction. It spreads and falls off as r^-7. Even worse you will find a non-zero detection probability away from the position where you "localized" your wavefunction. This probability also falls off as r^-7. So, which of these quantities defines size now?

For details, read the famous quantum optics bible "optical coherence and quantum optics" by Mandel and Wolf. In my edition chapter 12.11 discusses the problems of a meaningful localization of photons.

23. Feb 21, 2013

### Naty1

So while we are at it describing the 'size of a fundamental particle' and seeing there is no 'real' answer, at least no simple one, here is perhaps the craziest explanation of all. From Leonard Susskind whose work in black hole complementarity has won him widespread recognition, from THE BLACK HOLE WAR, Chapter 20:

[Susskind is relating here views of quantum field theory and string theory and while he uses 'atom' in the following description, he is could just as well have used 'particle' or 'photon'

[This refers to the fact than a hovering observer and a free falling observer will 'read' very different radiations emanating from a black hole horizon. So the observed 'size' of a particle as well as the very existence of a particle is impacted by the presence of a cosmological horizon.]

He compares such 'particles' to a rotating airplane propeller....where maybe all we can see is the hub, and maybe the inner portion of the blades....but progressively faster high speed photos would reveal additional extended structure....we can see further out on the rotating blades....see further quantum jitters!!

24. Feb 21, 2013

### Khashishi

Size isn't something with a precise physical meaning in this context. The size of a photon depends on how you measure it.

25. Feb 21, 2013

There are basically two (compatible) definitions of a photon. The usual one is that it is an eigenmode of the electromagnetic spectrum. In the strict sense an eigenmode does not change in time. Therefore in a cavity the eigenmode fills the whole cavity, and in free space a photon is an infinite plain wave (with no amplitude... but well...) Inside these eigenmodes energy is stored, and that is the real idea of a photon. The intensity of the eigenmode drops by a quantized amount a multiple of $$\hbar \omega$$ when the light field interacts with something else.