Electromagnetic waves with regard to photons

[kmm]

The electromagnetic spectrum contains wavelengths that are on the scale of macroscopic objects. What I'm not sure about then is, does this mean that photons corresponding to these "macroscopic" wavelengths are actually that size? My guess is that these photons have a corresponding electric field and magnetic field vector which simply oscillates at a rate that gives a large wavelength. This also makes me wonder then if large EM waves behave as particles also. I'm not so sure how to think about this.

 

[jfizzix]

It would not be that far off to think of the electromagnetic waves, as a wavefunction for the photons. Just like a wavefunction for electrons, they govern the probability of finding a photon here or there. Experimentally, that would be the probability of a detector going off. It would be hard otherwise to pin down a size to a photon.

In order to see the particulate nature of electromagnetic waves you need to be able to detect individual photons of that energy. There's no reason to think that there aren't radio wave photons, but we have no detectors sensitive enough to detect individual photons of energies that small. The lowest most detectors go is infra red or microwave, and then the likelihood of getting a detection gets very small.

 

[VantagePoint72]

It would not be that far off to think of the electromagnetic waves, as a wavefunction for the photons.

I think it's very far off to think of EM waves this way. An EM wave lives in physical spacetime; a wavefunction lives in Hilbert space. They're completely different objects. How would you interpret a multiphoton wavefunction which is a function of a more than one position and time?

 

[Bill_K]

I think it's very far off to think of EM waves this way. An EM wave lives in physical spacetime; a wavefunction lives in Hilbert space.

Sounds like you're confusing a state vector |ψ>, which is an element of Hilbert space, with a wavefunction <x|ψ>, which is a function of position.

 

[dextercioby]

Sounds like you're confusing a state vector |ψ>, which is an element of Hilbert space, with a wavefunction <x|ψ>, which is a function of position.

Yes, but wavefunctions are also elements of a Hilbert space.

As to the OP, there's no valid theory describing the (spatial) size of photons, or electrons or any other fundamental particles.

 

[VantagePoint72]

Sounds like you're confusing a state vector |ψ>, which is an element of Hilbert space, with a wavefunction <x|ψ>, which is a function of position.

Huh? The (position-space) wavefunction is just the state vector's components in the position basis. It uniquely defines an element of an abstract Hilbert space and so is, itself, in a Hilbert space. I'm not arguing about what it is or isn't a function of, I'm arguing that it isn't at all sensible to interpret it as a physical wave. You're just emphasizing my point: the position-space wavefunction is just one particular coordinate representation of the state vector, so there's absolutely no reason to reify it.

I ask again, how would you interpret a correlated two-photon wavefunction like $\psi(\vec{x}_1,t_1,\vec{x}_2,t_2)$ as an actual wave propagating in space-time? The "electromagnetic field as a probability density" interpretation is insensible with even this trivial extension of the problem.

 

[kmm]

As to the OP, there's no valid theory describing the (spatial) size of photons, or electrons or any other fundamental particles.

If that's the case, I suppose I will have to settle with there being no known correct way to think about this issue.

 

[WannabeNewton]

I think it's very far off to think of EM waves this way. An EM wave lives in physical spacetime; a wavefunction lives in Hilbert space. They're completely different objects. How would you interpret a multiphoton wavefunction which is a function of a more than one position and time?

I agree that it's nonsensical as stated. However there is a sense in which the amplitude of a classical electromagnetic field can be made to correspond to photon occupation probability for a given mode of the electromagnetic field by dealing with coherent states of the electromagnetic field. See for example the following: http://info.phys.unm.edu/~ideutsch/Classes/Phys566F13/Lectures/Phys566_Lect15.pdf

 

[VantagePoint72]

I agree that it's nonsensical as stated. However there is a sense in which the amplitude of a classical electromagnetic field can be made to correspond to photon occupation probability for a given mode of the electromagnetic field by dealing with coherent states of the electromagnetic field. See for example the following: http://info.phys.unm.edu/~ideutsch/Classes/Phys566F13/Lectures/Phys566_Lect15.pdf

Sure, there are limiting cases where one may be proportional to the other, but I'm not really sure what that has to do with my comment. It doesn't change the fact that they're not interchangeable things.

 

[jfizzix]

I want to be clear that it is indeed technically inaccurate to call the electromagnetic fields one gets out of classical E and M as being wavefunctions for the photon.

For classical states of light, however, the classical EM-wave equation does effectively describe the intensity distribution of light at many energies, and so the probability if detecting a photon at many energies.

To be accurate, the photon is an elementary excitation of a single mode of a quantum electromagnetic field which can be found by quantizing the Hamiltonian form of Maxwell's equations.

The size of a photon can be thought of experimentally in the sense that we can measure photons traveling through optical fibers, and that we can measure them hitting detectors of a given size. Conceptually the problem is more difficult because we can create single-photon states of the electromagnetic field of different shapes and sizes. The photon has a size only in that we know where it is when we detect it. Otherwise, I would try not to think of photons as solid particles, since quantum mechanics doesn't seem to offer such things as realistic.

 

[Cthugha]

Sure, there are limiting cases where one may be proportional to the other, but I'm not really sure what that has to do with my comment. It doesn't change the fact that they're not interchangeable things.

But nobody claimed that they are interchangeable. That comment fully misses the point of the post you commented on. The claim was that em waves can roughly be considered in a similar manner as the corresponding "wave functions" you would get for the same wave. The claim was NOT made the other way round. There are details which one should keep in mind - first of all there is no meaningful concept of a wave function for photons, you have probability amplitudes for detection events instead - but the comparison is ok. IF you have a classical em wave, the probability amplitudes you will get from a quantum description will give you the same detection events. Of course it does not work the other way round.

I ask again, how would you interpret a correlated two-photon wavefunction like $\psi(\vec{x}_1,t_1,\vec{x}_2,t_2)$ as an actual wave propagating in space-time? The "electromagnetic field as a probability density" interpretation is insensible with even this trivial extension of the problem.

One would have to interpret it in terms of correlation functions, of course. But you are again reversing the logic here. For a classical wave, you will not get into a situation where you actually need a two-photon wavefunction.

If that's the case, I suppose I will have to settle with there being no known correct way to think about this issue.

The problem with the "size" of a photon is that there are many possible length scales of the light field and none of them makes more sense than the others. You could, for example, consider the typical length scale over which the detection probability decays, over which the energy density decays or over which self-interference goes away. While these may be the same, typically these length scales are completely different for general light fields.

 

[kmm]

I want to be clear that it is indeed technically inaccurate to call the electromagnetic fields one gets out of classical E and M as being wavefunctions for the photon.

For classical states of light, however, the classical EM-wave equation does effectively describe the intensity distribution of light at many energies, and so the probability if detecting a photon at many energies.

To be accurate, the photon is an elementary excitation of a single mode of a quantum electromagnetic field which can be found by quantizing the Hamiltonian form of Maxwell's equations.

The size of a photon can be thought of experimentally in the sense that we can measure photons traveling through optical fibers, and that we can measure them hitting detectors of a given size. Conceptually the problem is more difficult because we can create single-photon states of the electromagnetic field of different shapes and sizes. The photon has a size only in that we know where it is when we detect it. Otherwise, I would try not to think of photons as solid particles, since quantum mechanics doesn't seem to offer such things as realistic.

Perhaps my issue then is clashing classical thinking with quantum mechanics. Classically, we detect photons corresponding to some energy and say that that corresponds to a wave that could be large. From a quantum mechanical view, it sounds like we can't say that the photon itself actually is that size.

 

[Maui]

Perhaps my issue then is clashing classical thinking with quantum mechanics. Classically, we detect photons corresponding to some energy and say that that corresponds to a wave that could be large. From a quantum mechanical view, it sounds like we can't say that the photon itself actually is that size.

No. Your issue is with realism and the idea that the EM field has values at all times even when not measured.

I was confused about this in the past and only recently realized that matter and em fields are different aspects of the same thing. Quantum mehcanically, any time you insist that em fields, matter or whatever has properties outside the measurement context you run into conceptual prolems like the one stated above with "different length scales of size"(whatever that means) - i actually suppose what this means - one and the same thing that can act as two or more different things in different setups(em field, electrical current, bound states in atoms/matter or as a free electron state spread out in space).

"Size" is what you measure when you do the measurement. Outside of the scope of this measurement scenario, qm brings conceptual difficulties that cannot be overcome. These days however, no one seems to be insisting that there be a pre-existing quantum world with classical properties, so this issue is usually brushed away as unnecessarily philosophical.

 

[kmm]

No. Your issue is with realism and the idea that the EM field has values at all times even when not measured.

Isn't this classical thinking?

I was confused about this in the past and only recently realized that matter and em fields are different aspects of the same thing.

I don't think that's correct. "Matter" is a loose term anyway.

Quantum mehcanically, any time you insist that em fields, matter or whatever has properties outside the measurement context you run into conceptual prolems like the one stated above with "different length scales of size"(whatever that means) - i actually suppose what this means - one and the same thing that can act as two or more different things in different setups(em field, electrical current, bound states in atoms/matter or as a free electron state spread out in space).

"Size" is what you measure when you do the measurement. Outside of the scope of this measurement scenario, qm brings conceptual difficulties that cannot be overcome. These days however, no one seems to be insisting that there be a pre-existing quantum world with classical properties, so this issue is usually brushed away as unnecessarily philosophical.

This is basically what I'm suspecting I'm doing.

 

[Maui]

I don't think that's correct.

You can be certain that it is correct. Matter and EM fields are aspects of quantum fields which are all that exists as far as it is known today. There are no classical particles to make up a 'real' EM field. These issues are as old as quantum mechanics itself and they creep up everywhere. You only have to pay closer attention.

 

[kmm]

You can be certain that it is correct. Matter and EM fields are aspects of quantum fields which are all that exists as far as it is known today. There are no classical particles to make up a 'real' EM field. These issues are as old as quantum mechanics itself and they creep up everywhere. You only have to pay closer attention.

Oh right, in that sense I see what you mean. As I was saying, I think that looking at photons classically was my issue.