# How big is a photon?

by Thinker007
Tags: photon
P: 5,634
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....
 P: 1 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.
 P: 2 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.
P: 1,549
 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.
P: 5,634
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.
 P: 790 Size isn't something with a precise physical meaning in this context. The size of a photon depends on how you measure it.
 P: 824 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.
 Sci Advisor PF Gold P: 11,115 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.
 P: 31 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.
 Sci Advisor PF Gold P: 11,115 Sounds ever so much like a diffraction argument is creeping in, in disguise.
 P: 2 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.
 Sci Advisor PF Gold P: 11,115 . . . . . Which leads to the conclusion that 'size' is just not a relevant property for a photon. That is, if it can be regarded as both a point and of infinite extent - haha. The general picture that people seem to carry in their heads (and is how it's often drawn) is a a squiggle or short burst of oscillations, a few wavelengths long. I guess that fails in most respects.
 Mentor P: 16,292 What is the size operator? If there is no such operator then the question is poorly defined. If there is such an operator then it is just a matter of plugging it in to a single-photon Fock state to see what the result is.
PF Gold
P: 11,115
 Quote by DaleSpam What is the size operator? If there is no such operator then the question is poorly defined. If there is such an operator then it is just a matter of plugging it in to a single-photon Fock state to see what the result is.
We're into (piece of) string, perhaps?
 P: 381 It has been shown that a photon can be arbitrarily "localized" in spacetime, i.e. there is not fundamental limit from the theory that forbids the complete localization of a one-photon state. http://prl.aps.org/abstract/PRL/v79/i9/p1585_1 Edit: Localization is meant in the sense of arbitrarily small extent of its mode function as it travels with 'c', not that you localize it in a position eigenstate.
P: 5,634

 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.
That is one view of QM...one which appeals because of its analogy to classical descriptions but fails in a number of situations. One failure is that to explain entanglement it must collapse faster than light speed.....

yes:
 photons certainly have different propties depending on the source.
 I think it's worth pointing out that 'the photon' cannot be pictured as some sort of 'burst of oscillations' ... as a little bullet.
 Size isn't something with a precise physical meaning in this context. The size of a photon depends on how you measure it.
[This is analogous to what Susskind says with his 'propeller' description.

 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.
[yes to the first part, no to the second]

 'size' is just not a relevant property for a photon.
[see the following for some further clarification of this valid point.]

///////////////////////

Other descriptions:

Albert Messiah, Quantum Mechanics, pg 66:
The wave packet...
 has a center that travels analogous to a classical point particle.
From another discussion,
from Vanhees:

 This position of a registration of a photon is a well defined physical quantity that can be measured, the position of a photon in the strict sense of an observable cannot even be defined in principle! For details, see http://www.mat.univie.ac.at/~neum/ph.../position.html
unsure of this source.....
 If a photon were truly free, not interacting with any other particles, its PLANE wave would extend across the universe to the cosmological horizon.
{} my clarification:
From Wikipedia:
 To account for the particle interpretation that phenomenon [double slit experiment] is called probability distribution but behaves according to Maxwell's equations. However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does {MAY} not spread out as it propagates, nor does it divide when it encounters a beam splitter. The photon seems to be a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the point-like electron. Nevertheless, the photon is not a point-like particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory

http://en.wikipedia.org/wiki/Quantum..._and_particles

 The "second quantization" procedure that we have outlined in the previous section takes a set of single-particle quantum states as a starting point. Sometimes, it is impossible to define such single-particle states, and one must proceed directly to quantum field theory. For example, a quantum theory of the electromagnetic field must be a quantum field theory, because it is impossible (for various reasons) to define a wavefunction for a single photon.
[Zapper had posted an identical statement to the boldface portion and I found the above confirmation.]

Also, recall that VIRTUAL photons, complex numbered particles rather than the usual real numbers, are responsible for all electromagnetic interactions as described using quantum field theory. It's QFT that is used in the Standard Model of particle physics. So not only are photon characteristics 'fuzzy' in classical terms, so too they seem to be in mathematical terms.
P: 5,634
Anybody have any comments on the paper JK423 posted.....The description seems to conflict with what has been discussed in these forums...and it is not all that new.....1997....

 It has been shown that a photon can be arbitrarily "localized" in spacetime, i.e. there is not fundamental limit from the theory that forbids the complete localization of a one-photon state. http://prl.aps.org/abstract/PRL/v79/i9/p1585_1 Edit: Localization is meant in the sense of arbitrarily small extent of its mode function as it travels with 'c', not that you localize it in a position eigenstate.
 Mentor P: 28,472 I always find it interesting that this question on the "size" of a photon (or the size of anything, really) has come up repeatedly. So let's try to narrow down what we DO know from straight-forward quantum mechanics and see if people do agree on those: 1. There is a position operator in QM, and that gives you the value of the position of the particle. 2. The spread in position of the particle is not the same as the size of the particle. 3. There is no "size operator" yet well-defined in QM. Do we all not agree on those? Zz.

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