Exploring the Dimensions of a Photon: Understanding its Size and Structure

[billy_boy_999]

how big is a photon? what are its dimensions?

if this is a meaningless question, please tell me why...

 

[Imparcticle]

http://ethel.as.arizona.edu/~collins/astro/subjects/electromag6.html

I'm not sure if this is any good...http://www.fervor.demon.co.uk/photons.htm

 

[slyboy]

Interestingly, I was asked this exact same question in my defense of my undergrad experimental project. At the time, I said it was a point particle.

It actually depends a bit on what you mean by "how big". An excitation of the electromagnetic field can extend arbitrarily far across space. However, we only ever detect them at points.

 

[billy_boy_999]

hmm...(thanks guys)...the article says the size of a photon is inversely proportional to it's wavelength...or is it a point?

is there any way that we can say all photons - no matter their wavelength - have the same dimensions? of course, if we take them as points we can...though is a point a dimension, per se?

i'm having trouble digesting the idea that the size of a photon depends on its wavelength...if photons really are the quanta, the bare constituency of light, then surely they should have a fixed size...isn't part of the wave-particle duality the idea that light always arrives in lumps - as feynman says - and that they always have the same amount of energy? since they are always traveling at the same speed and are massless, doesn't all their energy come from their speed/momentum/velocity/whatever? so shouldn't their size also be a constant?

 

[Silverlancer]

According to Quantum Mechanics, a photon, like any other point particle, has no size at all. It is a point, if treated as a particle. If it is treated as a wave, it has wavelength and amplitude instead, amplitude being the "size".

 

[billy_boy_999]

The characteristic size of a photon is inversely related to its frequency: (c/f)

that is what the people at arizona.edu have to say...is this not a statement consistent with QM? is the point treatment reckoned to be a description of a physical particle? hardly, how can a point be a physical anything? is quantum mechanics the right theory to address the question of a photon's size?

 

[arivero]

Now, what about a massive boson? It has a momentum p, thus a characteristic length h/p, but it also has an energy $$E=\sqrt{m^2 c^4 + p^2 c^2}$$, thus a characteristic frequency E/h, thus another length hc/E. For the photon, m=0 and both sizes coincide.

 

[tavi_boada]

Aren't monochromatic waves infinite? I don't understand the syntagm "characteristic size of a photon". Can you explain??

 

[arivero]

Tavi, he means, for sure, its wavelength.

 

[russ_watters]

that is what the people at arizona.edu have to say...is this not a statement consistent with QM?

It seems sloppily worded. Do you have a link so I can see the context?

It should be clear enough though, that since a photon can be a wave or particle depending on how you observe it, "how big is a photon?" is, if not meaningless, an incomplete question.

But, when viewing it strictly as a particle, it would have to be a point particle as stated.

 

[techwonder]

Point particles have a nasty habit of having infinite energy densities , but it is true that QM assumes particles to be point like. Super String Theory assumes all particles to be small strings with a length of just about the Planck length and no width, i.e. one dimensional . In that case a photon is 10e-44 meters

 

[billy_boy_999]

and i was waiting for someone to mention Planck length somewhere...the boson length is interesting, I'm going to have to read up on that...the sloppily worded quote comes from the first link that Imparcticle had posted...

to me it feels like there's something missing from QM's point particle treatment, it feels a deferment to the abstract...maybe that's just my bias...

 

[reilly]

Turns out that issues of photon size are very difficult -- in no small measure because photons, unlike massive particles, do not have a position operator - this was proved by Newton and Wigner in 1949. Nonetheless, it is possible to develop a probability density that tells where a photon is within a volume that is big compared to the photon's wavelength -- that is the probability of the photon triggering a photoelectric detector. Among the peculiarities of photons and QM, is the fact that the distribution of the photon's energy is spread out to regions where the probability of finding the photon is zero.

The bible on photon physics is Optical Coherence and Quantum Optics by Mandel and Wolf. It discusses, in great detail what I mentioned above. It assumes a sophisticated grasp of QM and statistics -- but it starts from ground zero, and does the basics -- state vectors, coherent fields, correlations,...-- albeit quickly. it is a great book, and it is worth the fight to read it.

Regards,
Reilly Atkinson

 

[jtolliver]

If the concept of photon size is meaningful and the size is the same for all photons then it is zero or infinite because (in the absence of charged particles at least) the field equations for the electromagnetic field are scale invariant(this is a consequence of the masslessness of the photon)

 

[Redfox]

It is essentialy an empty space. Current understanding is that in any case it is a complex multidimentional combination of EM field of various intensity spread within an unprecisely defined space, a worm that has very "blurry" head and tail and consists of EM field variations... Again orientation of this worm will depend on the relative movement...HUH.

 

[Revelationz]

Question rephrased

OK, the QM world is admittedly unintuitive to macro-particles like me So can I try a re-phrase of the question?

I think, but am not sure, this statement is true: The more you try and 'pin down' the location of a QM particle, the more it tends to 'spread out'. So as the resolving power of your locating instrument increases, you find that you can detect the particle less often within a given bounding box.

That means, I think, that as resolving power of the instrument increases, a point will be reached at which the particle is detected exactly 99.00% of the time within the limits of resolution of the instrument.

So if I am looking at photons streaming in from a 'perfectly' collimated laser beam source, and using the Palomar telescope to do so, I will observe the photons a very high percentage of the time. As I shrink the aperture of the telescope, at some point I will only observe the photons 99.0% of the time, not because the beam isn't perfect, but because Heisenberg says I can't know the position of the photons that accurately.

If the above is true, then the question about size becomes something like:

A) For light of a specific frequency in the range of, say, visible red, what is the 2-D size of the aperture (3-D bounding box?) in meters, that will enclose the position of the photons 99.00% of the time?


If this question makes any more sense than the original one, then:

B)Is this aperture (bounding box?) different in size than that of photons of a different frequency, say visible blue light?

And for a somewhat related question about quantities in photons:

A photon is a wave of EM energy, oscillating at a given frequency. How many oscillations does a photon consist of?

 

[Redfox]

I think you are very close to finding your own answer. Optical devices cannot be used for observation of photons because they use photons as a "bounce off" partice for imaging purposes. It we had means of control over a free moving EM frield interacting particle much smaller than any estimated size of photon then such observations would become possible. It is practically impossible to determine the length of a photon in meters, because you have to set the minimum EM field magnitude where your measurements will start and stop. Because it is believed that EM magnitude gradually increases from zero to the photon's energy range and then decreases back to zero over the length of the EM "snail" that represents photon, it is impossible to set its true length. All calculations will give only approximate results. It happens becase human brain uses different principles in processing of any information by setting definite borders to share one from another, it works in a big world like our every day world, but fails to work in the world of particles. We cannot truly realize that on a particle level we live in a world that is illusive because it is essentially nothing, i.e. something which singular example we would not normally see, but a mega multuple expample of which comrises all that we see and touch every day.

 

[CJames]

It all depends on how you think of a photon. In quantum mechanics a particle can't be thought of in the sense of a little piece of something. It's one unit of energy and other quantum values, but other than that it's more a wave. Upon measurement you could define its position within the wavelength of whatever you used to measure it. It will condense to that space when it interacts with that particle. But afterward it will again expand as a wave of possible quantum states. The same goes for whatever you used to measure the photon.

 

[Redfox]

True and not. As much as anything. We are based on the knowledge of approximate nature that is few decades old. It doesn't mean it is wrong - it is developing. We won't ever know if we will never know. As it was just said: "within" -- is all it is. More alternative approaches give us a better chance.

 

[jnorman]

NO NO NO - where did you guys get the idea that a photon is a point particle? photons are NOT particles in the sense that they have some specific size, location, or physical attributes. they do not have a size. the bottom line here is:
you cannot know ANYTHING about a photon between the time it is emitted and the time it is absorbed.

 

[Redfox]

No-one said it's a point particle. It cannot be a point particle because inbetween its emission and absorbtion points it is in motion at C. It can have a location, because any ray of light can be located. Ultimate conclusions that something "cannot be done" are limits of the accepted theory. Humans have been only progressing for about 300 years as a culture.

 

[danitaber]

I don't know if Billy boy 999 is even reading this anymore, but just in case, I will say that what Billy Boy 999 just witnessed is an example of a physicist's aversion to the phrase "I don't know" (ha!)

Personally, I think it's a meaningless question for the following reason:
We can't measure its "size". No one knows what "size" even is in regard to fundamental or quasi-fundamental particles. We can talk about wavelength, we can talk about points, we can talk about distributions and wave-packets, we can talk about strings, and we can talk about the loudness of a "blip" on a computer. We can't talk about "size". We have a hard time talking about "reality", even! (see many worlds thread, LOL)

We are less concerned with what it is than what it does. I'm sure I'm going to get jumped on (I'm slowly getting used to it) but there it is. OK, who's first for the danitaber-kabob? Refutations are welcome.

 

[ZapperZ]

I don't know if Billy boy 999 is even reading this anymore, but just in case, I will say that what Billy Boy 999 just witnessed is an example of a physicist's aversion to the phrase "I don't know" (ha!)

Personally, I think it's a meaningless question for the following reason:
We can't measure its "size". No one knows what "size" even is in regard to fundamental or quasi-fundamental particles. We can talk about wavelength, we can talk about points, we can talk about distributions and wave-packets, we can talk about strings, and we can talk about the loudness of a "blip" on a computer. We can't talk about "size". We have a hard time talking about "reality", even! (see many worlds thread, LOL)

We are less concerned with what it is than what it does. I'm sure I'm going to get jumped on (I'm slowly getting used to it) but there it is. OK, who's first for the danitaber-kabob? Refutations are welcome.

Danitaber kabob... YUM! I'll have seconds if it comes with couscous.

Actually, I don't find anything wrong with what you just said (or maybe I'm not in such a bad mood this morning). There is one thing I will pick on, though. "What it is" is DEFINED by "what it does". If you consider carefully, everything that we define is based on its physical properties. An electron has a set of properties that defines what it is. The same with a photon. You recognize a friend or family member based on physical characteristics that you observe, the sound of his/her voice, his/her behavior, etc. These are all physical properties and characteristics that DEFINE what it is.

A photon was NEVER defined as a "particle" with definite spatial boundaries, like a ping-pong ball. It was defined as a particle in the sense that each one of them carry a definite quantity of energy. The implication from this is very subtle but important, especially when we delve into things like "single-photon" sources.

Zz.

 

[jcsd]

kebab! kebab! kebab! or kebap to absoultely correct, or even kabab, but never kabob!

And while I'm on the subject how can you have vegtable kebabs? kebap literally means 'broiled meat'.

 

[danitaber]

There is one thing I will pick on, though. "What it is" is DEFINED by "what it does". If you consider carefully, everything that we define is based on its physical properties. An electron has a set of properties that defines what it is. The same with a photon. You recognize a friend or family member based on physical characteristics that you observe, the sound of his/her voice, his/her behavior, etc. These are all physical properties and characteristics that DEFINE what it is.

Thanks for not slaughtering and broiling me, Zapper.
OK, I'll agree with you there on a technical level; I'll stand by my original phrasing for metaphysical purposes only. (i.e., I am not the sum of red hair and stunning good looks :uhh: , etc. I am essentially something that I don't believe can be quantized.)

And I'll amend "kabob" to "kebab", but that's all the ground I'm giving.

 

[Tau_Muon_PlanetEater]

Reillly said'

Among the peculiarities of photons and QM, is the fact that the distribution of the photon's energy is spread out to regions where the probability of finding the photon is zero.


- Question, How can the probability of finding the photon be zero at the extremes of the distribution? Wouldn't they approach zero but never hit it?

 

[Fredrik]

i'm having trouble digesting the idea that the size of a photon depends on its wavelength...if photons really are the quanta, the bare constituency of light, then surely they should have a fixed size...

A photon has a perfectly well-defined wavelength only when it's in a momentum eigenstate, i.e. when it has a perfectly well-defined momentum (and energy). This never happens. A photon is always in a superposition of momentum eigenstates:

$$\lvert\alpha\rangle=\int{d^3p}\ f(\mathbf{p}) \lvert \mathbf{p}\rangle$$

The only quantity that we might want to call the "size" of the photon is the width of the Fourier transform of the momentum-space wave function, f, i.e. the uncertainty in the photon's position. This uncertainty could be anything between zero and infinity. (I'm ignoring Planck-scale effects here). Since it can be arbitrarily close to zero, it makes sense to call the photon a "point particle".

However, if we assume that the uncertainty in momentum is proportional to the magnitude of the momentum (which is the only thing we can assume if we know nothing about the state), the uncertainty in position is proportional to Planck's constant divided by p (the magnitude of the momentum). Since p is inversely proportional to the wavelength, the uncertainty in position is proportional to the wavelength.

So it makes sense to think of the wavelength as the "size" of the photon (or at least as something proportional to it). This may seem strange, but it is at least consistent with e.g. the fact that microwaves (with wavelengths of order 1 cm) won't go through a metal net with millimeter-sized holes (like the net that covers the window of your microwave oven), but they will go through a net with much larger holes.

You might wonder what the effect of the Planck scale is, since I said I ignored it. A Planck-energy photon will have a wavelength (i.e. "size") near the Planck length. This implies that the energy density of the region where the photon is located will be just large enough to form a black hole.

This is a pretty good reason to expect QED (and all other quantum field theories) to break down at the Planck scale.

 

[Fredrik]

Reillly said'

Among the peculiarities of photons and QM, is the fact that the distribution of the photon's energy is spread out to regions where the probability of finding the photon is zero.

- Question, How can the probability of finding the photon be zero at the extremes of the distribution? Wouldn't they approach zero but never hit it

You are absolutely right, but the numbers we are talking about are so ridicilously small that for all practical purposes they are zero. One meter away from the expected position, the probability is less than

$$\frac{1}{10^{10^{30}}}$$

 

[teal4two]

I have been wondering about the size of photons as well, or even what sense that question makes.

1) My microwave oven has metal mesh in the door. Can visible light photons from a bulb in the interior pass through the holes in the mesh? Can microwave photons pass through the holes in the mesh?

2) X-rays are scattered by crystals, but they are only scattered by part of the crystal. How big is this part?

 

[inha]

2) X-rays are scattered by crystals, but they are only scattered by part of the crystal. How big is this part?

uh.. where'd you get this idea from?

 

[marlon]

No-one said it's a point particle.

Well, a photon IS a point particle...BUT in energy space. A photon is defined as a chunk of energy, nothing more. Ofcourse it is NOT defined as a point particle that has finite spatial boundaries, so asking about the "magnitude" of a photons is useless because this concept is defined (in most cases ) based upon spatial coordinates.

Finally, the only photon quantity we know that is defined using spatial coordinates is the photon's wavelength. BUT, we are now talking about the wavelike properties of a photons while in paragraph one, we were using the particle like properties. Ofcourse, no problem with that thanks to the particle wave duality. We should however not forget that because we use a wavelike concept to describe a physical object (ie the photon) that we, intuitively, like to imagine as being a particle (ie a little ball ).

So, one can use this concept to talk about "a photon's magnitude" as long as we keep in our minds what the special nature of the "photon versus magnitude" discussion is.

regards
marlon

 

[teal4two]

uh.. where'd you get this idea from?

Do you know anything about x-ray crystallography?
Crystals are regular geometric arrays of atoms (molecules, ions). The electrons of the atoms scatter x-rays and by measuring the position and intensity of the scattered rays, information about the structure can be obtained.
Often the structure is not homogeneous. If there is local disruption, the scattering pattern shows the average local structure. If the differences are being larger domains, each containing the same local structure, a superposition of the two patterns is observed. The difference between local disorder and larger scale differences seems like it has to be based on photon size;i.e., how much of the crystal scatters the x-ray.
1) If the entire crystal scattered (large photons), all we would see is the scattering pattern of the averaged structure.
2) If the photon was tiny compared to atoms, we would not see the interference pattern of spots.

 

[CarlB]

Well, a photon IS a point particle...BUT in energy space. A photon is defined as a chunk of energy, nothing more. Ofcourse it is NOT defined as a point particle that has finite spatial boundaries, so asking about the "magnitude" of a photons is useless because this concept is defined (in most cases ) based upon spatial coordinates.

Back in grad school, I was taught the same, but recently, there has been work on this by Margaret Hawton which says otherwise. The original was published in Phys Rev A, 59, 954 (1999):
http://prola.aps.org/abstract/PRA/v59/i2/p954_1

The latest arXiv preprint from the same author extends this:

In the standard formulation of quantum mechanics the real space wave function is the projection of the state vector onto an orthonormal basis of eigenvectors of a Hermitian position operator. However, it has been claimed since the early days of quantum mechanics that there is no position operator that defines such a basis for the photon. Here we will briefly review our recent work on the construction of a photon position operator and obtain a photon wave function by projecting onto its eigenvectors.
http://www.arxiv.org/abs/quant-ph/0609086

My explorations of QM have been in applications of geometric / Clifford algebra to density operator states, and it is very important to me that a position representation exist for the photon. Another Hawton article, that reads more closely to what I am doing because it discusses the gauge problem is:

Angular momentum and the geometrical gauge of localized photon states
Margaret Hawton, William E. Baylis, 2004
Localized photon states have non-zero angular momentum that varies with the non-unique choice of a transverse basis and is changed by gauge transformations of the geometric vector potential "a". The position operator must depend on the choice of gauge, but a complete gauge transformation of a physically distinct state has no observable effects. The potential "a" has a Dirac string singularity that is related to an optical vortex of the electric field.
http://www.arxiv.org/abs/quant-ph/0408017

Another article is:
Photon Position Operators and Localized Bases
Phys. Rev. A64, 012101 (2001)
Margaret Hawton, William E. Baylis
http://www.arxiv.org/abs/quant-ph/0101011

These articles have received very little attention. As an aside, Baylis seems to have his fingers in a remarkable number of interesting pies that intersect what I am working on:

Comments on "Dirac theory in spacetime algebra"
J. Phys. A: Math. Gen.35, 4791-4796
William E. Baylis, 2002
In contrast to formulations of the Dirac theory by Hestenes and by the current author, the formulation recently presented by W. P. Joyce [J. Phys. A: Math. Gen. 34 (2001) 1991--2005] is equivalent to the usual Dirac equation only in the case of vanishing mass. For nonzero mass, solutions to Joyce's equation can be solutions either of the Dirac equation in the Hestenes form or of the same equation with the sign of the mass reversed, and in general they are mixtures of the two possibilities. Because of this relationship, Joyce obtains twice as many linearly independent plane-wave solutions for a given momentum eigenvalue as exist in the conventional theory. A misconception about the symmetry of the Hestenes equation and the geometric significance of the algebraic spinors is also briefly discussed.
http://www.arxiv.org/abs/quant-ph/0202060

Hestenes geometrized spinors, I've been applying his techniques to the density matrix formalism. Here's a somewhat similar idea couauthored by Baylis, sort of half spinor and half "idempotent" theory:

A Geometric Basis for the Standard-Model Gauge Group
J. Phys. A. 34, 3309-3324 (2001).
Greg Trayling, William E. Baylis, 2001
http://www.arxiv.org/abs/hep-th/0103137

An introduction to the Clifford algebra / geometric algebra ideas we are using is here:
Relativity in Introductory Physics
William E. Baylis
http://www.arxiv.org/abs/physics/0406158

Carl

 

[ZapperZ]

But to what extent is the "position" of a photon has anything to do with the "size" of a photon?

Note that anytime we detect a photon, be it on a CCD or via a PMT, we have narrowed down its position. So a photon's location in space is not meaningless concept simply based on experimental observation. However, this doesn't mean that its "size" is a meaningful concept.

Zz.

 

[inha]

Do you know anything about x-ray crystallography?
Crystals are regular geometric arrays of atoms (molecules, ions). The electrons of the atoms scatter x-rays and by measuring the position and intensity of the scattered rays, information about the structure can be obtained.
Often the structure is not homogeneous. If there is local disruption, the scattering pattern shows the average local structure. If the differences are being larger domains, each containing the same local structure, a superposition of the two patterns is observed. The difference between local disorder and larger scale differences seems like it has to be based on photon size;i.e., how much of the crystal scatters the x-ray.
1) If the entire crystal scattered (large photons), all we would see is the scattering pattern of the averaged structure.
2) If the photon was tiny compared to atoms, we would not see the interference pattern of spots.

I've performed numerous XRD and SAXS experiments while working in an x-ray laboratory and taken many courses in solid state and x-ray physics so yes, I do know something about crystallography. When one derives the elastic scattering cross section, Bragg's law etc. the photons "size" does not come up in the calculation. Wavelength does but it doesn't equal size. As many others have pointed out it's meaningless to talk about a photons size. And photon-solid interactions are many body processes in the end so it's also pointless to talk about only a part of the solid being involved in the process. Unless of course one has a beam of a certain size and a sample of a certain size, but that's not what you were after.