Hello everyone,
Electromagnetic waves are usually depicted with 2 orthogonal waves. Most drawings are usually identical.
But do the two wave have a width? How could they have no width at all?
Nic.

Hello everyone,
Electromagnetic waves are usually depicted with 2 orthogonal waves. Most drawings are usually identical.
But do the two wave have a width? How could they have no width at all?
Nic.
The vector arrows point in the directions of the electric and magnetic field. The lengths of the vector arrows are the magnitudes of electric and magnetic field and do not represent a size in space.
I think this may be quite a deep question. If you think of the famous 2 slit experiment in which photons are passed sequentially through a pair of slits and you get, dot by dot, an interference fringe pattern on the screen, does one consider the "width" of a photon to be that of the individual dots, i.e. the "particlelike" quanta that are individually detected? Or does one consider that the wavefunction must pass through both slits, in order for an interference fringe pattern to appear? Clearly the area of space explored by the latter is greater than the size of the former. So what does "width" really mean, then? It's tricky, I think.
I am not sure about the proper interpretation of the double slit experiment, but the interference pattern occurs when the photons are emitted one by one, so I imagine the photon goes through both slits and interfers with itself to produce the interference pattern.
I am not sure at all.
Exactly, that's what I'm getting at. So the wavefunction goes through both, but each quantum is detected at a particular spot. I found the following on the internet which may help a bit: it is NOT a trivial question at all : quantum mechanics  How fat is Feynman
Maybe a real physicist wil interject at this point to take things further  I shall shortly be out of my depth.
Yes, but the diagrams are not showing this. The diagrams are only showing a single line without width in the direction of propagation.
As for the "width of a photon", this has no meaning in quantum mechanics unless the width has actually been observed. It is a characteristic feature of quantum mechanics that objects do not possess definite properties unless those properties have been observed directly or indirectly. This is known as counterfactual indefiniteness.
Nevertheless, if you point a stream of photons at, or not quite accurately at, an atom capable of absorbing them, the probability of absorption must depend on how close by to the atom the photons pass, must it not? It will not be a yes/no hit or miss phenomenon, clearly, but there will be some effective, probabilistically defined, "width" will there not?
The width of the photon will essentially be the width of the photon source (plus any divergence and diffraction effects). The reason one gets interference in the doubleslit experiment is because the photon has as much freedom as it is permitted to have. It doesn't constrain itself to a single slit when it is free to pass through both. When one measures which slit the photon passed through, even if this measurement was after the photon passed through the slits, one has constrained the photon to pass through only a single slit and the doubleslit interference is destroyed.
Ok, so the electric field and the magnetic field really oscillate in space.
As for the "width of a photon", this has no meaning in quantum mechanics unless the width has actually been observed. It is a characteristic feature of quantum mechanics that objects do not possess definite properties unless those properties have been observed directly or indirectly. This is known as counterfactual indefiniteness.
But isn't the width of the photon related to the amplitude of the electric and magnetic waves? And we know these 2 amplitudes, so we should know the width of the photon? So why would we know it only once it has been observed?
The probability of finding a photon at one place is proportional to the wave function squared. On the drawing on the lower left here , the blurred circles represent the probability of finding the photon are on the x axis. Will the photon be observed exactly on the x axis or in a volume around it?
I am sorry but I am confused between the amplitude of the electric and magnetic waves and the width of the photon itself.
The photon (very much like the electron) is a pointlike particle (dimensionless). You are confusing its dimensions with its position, I have explained that to you in a prior thread, the one about fitting a photon inside a black hole of very small Schwarzschild radius. It is the position that is "smeared" probabilistically, as per QM, not its dimension. Bottom line, your question about "Width of a photon" has no answer since it has no meaning.
Could it be that the act of measuring the photon after it has passed one slit forces the photon which in fact passed through the 2 slits to rejoin, and continue as if it had passed through only one?When one measures which slit the photon passed through, even if this measurement was after the photon passed through the slits, one has constrained the photon to pass through only a single slit and the doubleslit interference is destroyed.
Otherwise it would mean that the part of the photon which passed through the other slit goes back in time back through the slit it went through and goes through the slit where the photon was measured.
I understand that it is smeared probabilistically. When I am talking about the 'width' of the photon, I am not referring to the fact that it is a pointlike particle ( I agree with that ), I am referring to the fact that it occupies a certain volume ( probabilistically ). The pointless particle is everywhere in that volume at the same time with a certain probability of being at each point of that volume.
Last edited by KJW; October 6th, 2014 at 12:52 PM. Reason: "number of photons" changed to "number density of photons"
OK Howard, but I'm now curious as well. Tell me, how can one determine how close a photon has to pass, to an atom capable of absorbing it, in order for the absorption probability to be significant? If it flies by at a distance of 0.1nm from the nucleus, for example, Id have thought the probability must be higher than if it passes 10nm away.
Is there not some probability distribution analogue of a "width" here, similar to the fuzzy but useful idea of the "size" of an atomic orbital, say?
Ok, then let's say it is moving along the x axis. What would delta py and delta pz be?Nope they are all the ERRORS (the incertitude) in measuring the momentum in the respective direction.
Ok I can imagine to some extent that there could be a momentum in the y and z direction. And the larger the energy, the larger the amplitude of the wave, so the larger the square of the wave function which gives the probability distribution, right? So the larger the momentum uncertainty will be in the y and z axis, no?
Well not exactly. After all, the Uncertainty Principle itself is a direct consequence of particles having a wavefunction. But the fact that the expectation value of the momentum in the y and z directions happens to be zero in this case doesn't prevent there being an uncertainty around that average zero value.
I suspect what we are really saying is that any question about the "width" of a photon needs to be asked in the context of a particular physical arrangement, in which the photon may interact with something (a "measurement" if you like). Perhaps it is worth a thought experiment as to what sort of arrangment would potentially interact with a photon in away that depended on its "width".
That's what I thought, the fact that the particle has a probability distribution is important here.
From what I understand, the width depends on the observer. For instance, 2 observers observing one photon with different wavelength ( depending on how the observer is moving) will not see the same probability distribution, so probably won't see the same width.I suspect what we are really saying is that any question about the "width" of a photon needs to be asked in the context of a particular physical arrangement, in which the photon may interact with something (a "measurement" if you like). Perhaps it is worth a thought experiment as to what sort of arrangment would potentially interact with a photon in away that depended on its "width".
This all depends on what you call photon. What theorists call photon is photon of single wavelenght is ideal case but impossible to create or be created as it would be infinite in time and infinite in space. What experimentators are calling photon is in fact coherent pulse that has expectation value of photon number operator 1. It has smeared probabilistic distribution in energy/ therefore its finite in time and also probabilistic distribution in kvector space therefore its finite object in space. Real photon is superposition of infinitely many planewavesinglewavelenght "idealistic" photons. The distribution functions specificaly in energy are given by broadened spectral lines (which depend on time of life of level) of atoms or objects that created the photon in first place.
The question you are asking ignores the information that Gere gave you, so perhaps it needs to be repeated, in slightly different terms.
Forget about photons for a second and just consider a sinusoidal wave. In order for that wave to consist truly of a single frequency, it must conform to sin(t) for all t. Not just for some t, but all t from the infinite past to the infinite future.
If the sine function applies only to a finite interval  as it must, since the universe has existed for a finite time  then its spectrum no longer consists of a single frequency. This result has nothing to do with QM; it comes from 18th century mathematics. And it applies to all photons, whether they were created by natural or artificial processes (whatever that's supposed to mean).
Let's be concrete... In the drawing on the upper left here , what you say means that the frequency at the start of the wave front is not the same as the frequency at the middle of the pulse. When we say that a photon has a given frequency, we are refering to the frequency in the middle of the pulse. Is that correct or did I get it completely wrong?
Thats not photon, thats wavefunction of electron probably. Frequency and position isnt really connected like this. You just have probability distribution of frequency and probability distribution of kvector/position of photon. These things are connected as tk421 tried to explain. Key word is Fourier transform.
To be honest, it seems to me neither you nor tk421 is really dealing with what seems to me to be Nic's question. All this you both describe is the wellknown linear momentum and position relations for a QM waveparticle, along the direction of propagation, in terms of a wave packet versus a monochromatic sine wave. Classic Fourier series/uncertainty principle stuff, in fact.
But, as I understand it, Nic's question is about the degree of dispersion or "width" of a photon perpendicular to the direction of propagation. That is interesting, it seems to me, in that it is not generally talked about in the textbooks. Earlier I posed the question of how far away from an atom that is able to absorb it, can a photon pass, and still have an appreciable probability of being absorbed?
The expectation value of its momentum normal to the direction of propagation is of course zero, but there will be an uncertainty around this value. Conversely the uncertainty in its position on the axes normal to the axis of travel will define the "width" of the photon. I think this is what he was trying to get at originally.
Oh, true exchemist. A bit sloppy on my part. The thing is that the distribution function (Wigners) is in fact function in whole phase space. Therefore not only is it smeared in say but also at and . This smearing (its usually 3D gaussian) through FT tels you the "size" of photon perpendicular to momentum. Such size or width is not sharp but one can "define" it to be say fullwidthathalfmaxima of distribution.
That's because I was responding narrowly only to the subpart of his question that I quoted in my reply. Sorry if I had implied that my answer applied more generally. I'm still thinking of the best way to respond to what I think is his question, because the answer depends a bit (actually, quite a bit) on the precise nature of the question (e.g., whether one is asking about absorption crosssections, say, which is the nature of your followup). His is a thoughtful question and deserves an equally thoughtful response.
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