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## How big is a photon?

 Quote by 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.
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).

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From the OP:

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

Here are a few from others:

Carlo Rovelli:
 “…we observe that if the mathematical deﬁnition of a particle appears somewhat problematic, its operational deﬁnition is clear: particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier…” A particle is in some sense the smallest volume/unit in which the field or action of interest can operate….Most discussions regarding particles are contaminated with classical ideas of particles and how to rescue these ideas on the quantum level. Unfortunately this is hopeless.
 .... A particle detector measures a local observable ﬁeld quantity (for instance the energy of the ﬁeld, or of a ﬁeld component, in some region). This observable quantity is represented by an operator that in general has discrete spectrum.
presented in Weinberg's "The quantum theory of fields" vol.1.....

 For realistic systems with varying numbers of particles we build the Fock space as a direct sum of products of irreducible representations spaces. Then the sole purpose of quantum fields (=certain linear combinations of particle creation and annihilation operators) is to provide "building blocks" for interacting generators of the Poincare group in the Fock space. In this logic quantum fields are no more than mathematical tools.
 .... strictly speaking there are two distinct notions of particles in QFT. Local particle states correspond to the real objects observed by finite size detectors. .... On the other hand, global particle states....can be defined only under certain conditions...... uniquely-defined particle states do not exist in general, in QFT on a curved spacetime.
and from a prior discussion in these forums:

Marcus quoting a prior post:

Marcus :

 As a general rule the world is not made of particles, it is more correct and less confusing to say that it is made of fields. Unless I'm mistaken all or most of us at the Forum realize this?
Marcus' comment:

 I don't count myself in this group. As Naty1's quote said "particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier." This means that particles (not some mysterious fields) are the objects studied by real experimental physics. If "curved spacetime" does not agree with the particle concept, so bad for the "curved spacetime".
And you will note, of course, these are not all in agreement....
 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.
 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.

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 Quote by 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.
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.

 Quote by godw2718 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.
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.

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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'

 Black Hole complementary was proposing something...radical. Depending on the state of motion an atom might remain a tiny microscopic object or it might spread out over an entire horizon of an enormous black hole....William Unruh showed that near a black hole horizon thermal and quantum jitters get mixed up in a odd way...
[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.]

 Elementary particles are usually imagined to be very small objects. Quantum Field Theory begins by postulating particles that are so small they can be regarded as mere points in space. But that picture soon breaks down....
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!!

 ...If experiments cannot tell us whether particles have outlying high-frequency, vibrating structures, then we have to appeal to out best theories....[so when you speed up the shutter] what you see is is that every piece of the string is fluctuating and vibrating so the new pictures looks more tangled and spread out....String theory and QFT share the property that things appear to change as the shutter speed increases. But in QFT, the objects do not grow....String theory is different and works more like [an airplane propeller]....as things slow down, more and more 'stringy' propellers come into view. They occupy an increasing amount of space so that the entire complex structure grows...To most [Quantum Field Theorists] the notion of growing particles with unbounded, jittering structures was extremely foreign...Ironically the only other person who had hinted at such a possibility....was Gerard't Hooft...his work also expressed a sense that things grow as they are examined with increasing time resolution.
 Size isn't something with a precise physical meaning in this context. The size of a photon depends on how you measure it.
 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. When particle physics are discussed they are usually discussed in Fourier space. One infinite plain wave of say protons interacts with another infinite plain wave of protons and they exchange an infinite plain wave of photons or other stuff. The reason why one sees the particle traces in collider experiments is that protons in colliders are a short bit of such a plain wave: a wave packet. But the main physics is captured by the plain wave description. The interaction of a photon with the other elementary particles in the beams is point like, because its interaction does not depend on the momentum of the particles that it interacts width, leading to flat line in Fourier space and thus a delta peak in real space, for particles like neutrons which have an extend the interaction changes with the momentum of the interacting partners. So in a way photons are point like (in their interaction) but in another way they can be really large, in a mathematical description as large as the universe. Sorry if this reply is very technical, but we have gone a long way since the corpuscle theory of Newton, and this is all very much wave particle duality stuff.
 Recognitions: Gold Member Science Advisor I think it's worth pointing out that 'the photon' cannot be pictured as some sort of 'burst of oscillations' passing through the aether or as a little bullet. These seem to be the most popular visualisations. Old habits die hard and, before finally biting the bullet and realising that it's much harder than that, people tend to hang on to the idea that QM is, in fact, just like the old mechanical system but with a few inconsequential tweaks. No. It's 180 degrees different and you just have to get over it. "Physical Interpretation"??? Not possible.
 Size defined as the apparture of your measuring device? Being build of the same stuff your detector is made off, it becomes complex to measure size of your own building block. It then is going to depend on how well (a part of) the wave will interact with your detector, transfering just enough energy to make a difference.
 Recognitions: Gold Member Science Advisor Sounds ever so much like a diffraction argument is creeping in, in disguise.