What is wave of photon? oscillation of something in space?

[Nugatory]

How would existence of rest frame be related to the existence of position. We know that in classical context the photon does have a position and its time dependence comes from the formula x(t)=x(0) + \frac{p}{\|p\|}ct.

In classical context there are no photons, just electromagnetic waves described by solutions of Maxwell's equations. The waves don't have a clearly defined position.

When we move from classical to quantum physics, we add this notion of photons to describe the experimentally observed phenomenon that light, regardless of its intensity, transfers energy in discrete chunks. Why should we expect classical mechanics to apply to something that was developed to explain a quantum phenomenon that has no classical counterpart?

There is one heuristic that we use often and with great success: in the limit where quantum mechanical effects become insignificant, QM must make the same predictions as classical mechanics. But this heuristic argues against assigning definite positions to photons, because in the classical limit light is a wave and a wave has no definite position.

 

[bhobba]

How would existence of rest frame be related to the existence of position. We know that in classical context the photon does have a position and its time dependence comes from the formula x(t)=x(0) + \frac{p}{\|p\|}ct. The lack of rest frame has no effect on this.

Does it? Operationally how do you measure velocity classically? And exactly how would you apply that to a photon? I think you will find that any observation with a photon that happens at a position destroys it making that determination rather difficult - but I am all ears.

Could it be that you first decided that the position operator must no exist, and then attempted to find justification for it?

For me it was the other way around.

I originally thought it was an observable but recently was corrected (see my post 13 where I finally saw the light - pun intended ):
https://www.physicsforums.com/showthread.php?t=760945

Its like that around here - you often get erroneous views corrected - I have been through that frequently in my time here - and expect to continue in the future.

If you read the link I gave in my previous post some think the idea of having no rest frame is even not quite on the mark - that's another thing you find around here - sometimes things are a bit deeper than you may think.

Thanks
Bill

 

[Geometry_dude]

Well, I think jostpuur is criticizing the lack of realism in QM and QFT, something which is, IMHO justified, but one gets very quickly into interpretations of quantum theory when doing this and we all know how deep that hole is. Add to that the naive attempts of some textbook authors to reintroduce this realism by talking about single photons and electrons and you got your mess.

On an elementary level, one can say that QFT is a statistical theory that is experimentally well-established and does not talk about single particles like ordinary QM does in terms of wave functions. The reason for this goes back to the beginning of QFT with the relativistic analogue of the Schrödinger equation, i.e. the Klein-Gordon equation. The precise reason is that the Klein-Gordon "wave function" does not admit an interpretation in terms of a probability density and "thus" (beware: ad-hoc step) has to be reinterpreted in terms of a field that needs to be second-quantized to get back to the probability amplitude formalism.

jostpuur, if you expect quantum physics to be as nice and well-defined as "Classical physics", you will have a hard time as it evolved out of playing around with the math in an ad-hoc manner and cross-checking with experiment.

I wish I could give you a more satisfying answer, but I don't have one. Personally, I have aquainted myself with the idea that QM and QFT are phenomenological theories that are not well-understood on a conceptual level.
Of course, that doesn't mean that one shouldn't try to understand them. :)

I agree with Bhobba when he says that localizing photons is inherently problematic in the special relativistic picture due to the fact that they are assumed to "move" at c.

 

[bhobba]

The precise reason is that the Klein-Gordon "wave function" does not admit an interpretation in terms of a probability density and "thus" (beware: ad-hoc step) has to be reinterpreted in terms of a field that needs to be second-quantized to get back to the probability amplitude formalism.

That's true - but it runs deeper than that IMHO.

In ordinary QM time is a parameter and position an operator. But that conflicts with relativity which treats time and space on equal footing.

QFT's solution is for both position and time to be a parameter ie everything is a field.

Thanks
Bill

 

[bhobba]

Personally, I have aquainted myself with the idea that QM and QFT are phenomenological theories that are not well-understood on a conceptual level.

On that front you may find the following interesting:
http://arxiv.org/pdf/quantph/0101012.pdf

And also the modern version of Gleason's beautiful theorem (see post 137):
https://www.physicsforums.com/showthread.php?t=763139&page=8

QM basically from one axiom? Thought provoking isn't it?

Thanks
Bill

 

[Geometry_dude]

I hate to tell you that I'm not an instrumentalist and thus I have trouble with accepting these principles as fundamental principles of nature. It is quite interesting though.
Apart from those philosophical issues, those principles are not enough to specify the time evolution of a quantum system, which requires a description of a classical Newtonian or special-relativistic system and a quantization step to get to the corresponding quantum description. Getting rid of that is the true art.

 

[jostpuur]

Everytime I have attempted to discuss the wave functions of relativistic particles, the physicists change the topic to the creation and annihilation of particles and the particle collisions.

Operationally how do you measure velocity classically? And exactly how would you apply that to a photon? I think you will find that any observation with a photon that happens at a position destroys it making that determination rather difficult

So the topic was changed to the particle annihilation. How surprising.

 

[rubi]

Your problem seems to be that you insist on the existence of well-defined quantum theories of relativistic particles. That might be mathematically desirable, but it's not physically relevant, because our best theories just aren't particle theories. Instead, they are field theories. Of course you could ask, what the quantum analog of a hypothetical classical relativistic massless particle was. But such an object is just not physically realized, so the question is purely academic. The relevant classical theory that we need to consider is classical electrodynamics. It is a field theory and it's quantum analog is quantum electrodynamics, which is a field theory as well. That means that the observables of the theory aren't position $x$ and momentum $p$, but rather the field $A_\mu(x)$ and it's conjugate $\pi_\mu(x)$. Position $x$ isn't an observable in classical electrodynamics either, so there's no reason to believe that such a concept needs to appear in the corresponding quantum theory. The notion of photons doesn't refer to particles. Instead, we have a bosonic Fock space built from the Hilbert space of an irreducible massless helicity=1 representation of the Poincare group and a photon is just a vector in such a Hilbert space. It's a well-defined mathematical concept, but it doesn't refer to a particle, although many poor textbooks want you to think of it that way and the "-on" suffix just encourages you to do so.

 

[bhobba]

Apart from those philosophical issues, those principles are not enough to specify the time evolution of a quantum system, which requires a description of a classical Newtonian or special-relativistic system and a quantization step to get to the corresponding quantum description. Getting rid of that is the true art.

You should read chapter 3 of Ballentine - QM - A Modern Development:
https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20

It actually follows from the POR ie symmetry - specifically the probabilities are frame independent.

Thanks
Bill

 

[Geometry_dude]

That is indeed very nice, I wish my quantum theory course would have been like that. Thank you for the recommendation.