Trying to understand electromagnetic waves in quantum theory

[Delta2]

I think the OP has a justified confusion about the probability waves that correspond to solutions of Schrodinger's equation in QM that describes the time evolution of the wave function of a particle, and the EM-waves that correspond to solutions of the classical four Maxwell's equations that describe the time evolution of the EM field.

Those two kind of waves have nothing in common, except that they might concern the same particle, that is an electron. The EM-waves generated by an accelerating electron, have nothing to do with the probability waves that correspond to the wave function of the electron, when the electron is free, electron inside a box, or electron under the coulomb potential of a nucleus (different wave functions for each case).

The EM-wave is real (as much as the EM field is considered to be real), however the probability waves are not that real (though this is a debate). Probability waves and the wave function are just a mathematical tool that makes the wonder of QM to happen. Though in a threat i had posted long ago, i seemed to get answers by some sci-advisors that probability waves may correspond to waves in the fermionic field of a particle.

 

[atyy]

Just to add a bit to Delta²'s point that there are two different concepts:
(1) the wave function from which probability can be calculated, and
(2) the electromagnetic field configuration which is a classical concept that can be taken into quantum theory.

One way to see that there are two waves is to first consider the ordinary quantum mechanics of one particle. There we have position $x$, and the wave function $\psi(x)$ allows us to calculate the probability of observing a particle at each position.

When we go to the electromagnetic field, the analogue of position is the electromagnetic field configuration $A(x)$, and the analogue of the wave function is the wave functional $\psi(A(x))$.

 

[zonde]

I agree with Delta^2 point. I had the same feeling that OP is mixing up wave of probability amplitude and EM-wave.

But certainly it's easy to mix them up if you look at photons. Probability wave and EM-wave have the same wavelength for given beam of light (that means they have synchronous phase). And they both propagate at c.

 

[atyy]

But certainly it's easy to mix them up if you look at photons. Probability wave and EM-wave have the same wavelength for given beam of light (that means they have synchronous phase). And they both propagate at c.

Technically, the wave function doesn't travel at the speed of light, because it doesn't travel any "where", as it is a wave in Hilbert space, not a wave in ordinary space.

However, for single photons, it does make approximate sense to talk about the wave function of a photon traveling at the speed of light (search for "photon wave function").

 

[thierrykauf]

oh great - i got a response - thank you so much! and ok, i can picture a wave packet. but i guess my question is why is anything' waving'? before i read quantum theory, i thought there was something physically oscillating, like an electron, that emitted a line , like a line of photons, in a wave - like water from a garden hose being moved up and down. but in quantum theory, the wave is said to be a probability wave of where the electron or photon is most likely to be. ok, but why are probability paths still shaped like a wave? what is 'oscillating' the probability?

Something is waving because if it didn;t. scattering experiments would not yield what we observe, and atom's stability would receive no explanation. The wavefunction wasnt supposed to be a wave, and it is not . Only it;s complex conjugate squared is observable. The wavefunction, exponential of the action in hbar units was arrived out after the classical action angle formalism had emerged out of the study of classical equations of motion. The understanding that a particle is a wave-packet and is thus as localized as a wave. that is not at all if its momentum or wavelength is known, and that being a wave it simultaneously ges through every possible path and interferes with itself leaving behind the contribution of all the paths which interfered constructively, which were paths of sinilar action, i.e. paths for which the action varied little, that is was extremal, explained the notion of trajectory as a classical large hbar description. The wavefunction beig complex, cannot be an ordinary wave, for waves are real, and obey a second order in time.equation, which the Schrodinger equation is not.

 

[MacroMeasurer]

hmmm...well, thank you again for your time. but let me ask this: is my garden hose and water stream wave a good analogy of how we thought em waves were being emitted from oscillating electrons BEFORE quantum theory came along? or would it have been a bad analogy even back then?

If we "leave out QM," and you were asking about radio waves versus visible light,
maybe you are asking about the classical relationship between frequency and energy?

I think it might be more helpful to use a rope in that thought experiment
(and potentially even classroom demonstration).
You can make a wave by lifting and lowering one end of a rope, right?
You can double the frequency by raising and lowering your end of the rope twice as fast.
Meanwhile, you will realize you are working twice as hard waving the rope up and down.
That's why frequency is linked to energy: high frequency waves are an embodiment of more work.

It's more obvious that the wave in a rope comes from work you yourself are doing than with a hose,
where the water pressure seems to be doing a lot of work and you seem to just stand there.
Also, it would make for a much less messy classroom demonstration.

 

[meopemuk]

But certainly it's easy to mix them up if you look at photons. Probability wave and EM-wave have the same wavelength for given beam of light (that means they have synchronous phase). And they both propagate at c.

When you do the double-slit experiment with photons (or light waves), which one of the two waves is doing the interference? Is it the photon wavefunction, which interferes with itself on the two slits? or it is the electomagnetic wave, which does the trick? or they both do the interference simultaneously?

Eugene.

 

[bhobba]

When you do the double-slit experiment with photons (or light waves), which one of the two waves is doing the interference?

I may have posted it before, but here is the correct explanation of the double slit:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Its got nothing to do with waves.

The wave-particle duality is a myth - as explained in this forums FAQ:
https://www.physicsforums.com/threads/is-light-a-wave-or-a-particle.511178/

Thanks
Bill

 

[meopemuk]

Hi Bill,

So, your explanation says that the light interference picture is a quantum effect related to photon wavefunctions. And that light is just a flow of particles - photons - obeying the Rules of Quantum Mechanics. By the way, here I agree with you. Are you then willing to go further and say that description of light by means of classical "electromagnetic waves" is redundant and doesn't add anything to our understanding of this phenomenon?

Eugene.

 

[bhobba]

So, your explanation says that the light interference picture is a quantum effect related to photon wavefunctions. And that light is just a flow of particles - photons - obeying the Rules of Quantum Mechanics. By the way, here I agree with you. Are you then willing to go further and say that description of light by means of classical "electromagnetic waves" is redundant and doesn't add anything to our understanding of this phenomenon?

No - and obviously so. Classically it's described by EM fields as per Maxwell's equations. In QM its described by a quantum state. They are entirely different concepts.

Note: The explanation I gave of the double slit is problematical when applied to photons because the QM description of photons is itself problematical - one must go to Quantum Field Theory. When discussing the double slit best to stick to electrons.

But if you are willing to delve into that level of 'hurt' here are the details:
http://arxiv.org/pdf/1103.0100v1.pdf

At the beginning level best to stick with the link I originally gave and just accept it has issues with photons. Physics is unfortunately sometimes like that. Although often used at the start, the wave particle duality is wrong, and the first link I gave is a much better explanation - but even it isn't correct - the real answer being quite advanced and 'hard'.

Thanks
Bill

 

[zonde]

Are you then willing to go further and say that description of light by means of classical "electromagnetic waves" is redundant and doesn't add anything to our understanding of this phenomenon?

Radiowaves induce oscillations of charges in antenna. There are many low energy photons that contribute to the same overall effect. In order for QM to replace classical "electromagnetic waves" it would have to describe this overall effect too. I think QM is not very clear about such things. There is of course coherence but I haven't seen that it would be clearly stated as property of ensemble.

 

[zonde]

The explanation I gave of the double slit is problematical when applied to photons because the QM description of photons is itself problematical - one must go to Quantum Field Theory.

But luckily we have such a book as Feynman's "QED: The strange theory of light and matter."

 

[bhobba]

I think QM is not very clear about such things.

The reason is photons are problematical in standard QM because position is not an operator for them so they have no wave-function. Exactly what is going on is VERY clear in Quantum Field Theory - but it is HARD. As our own Nugatory said - 'anything you have read about QFT outside a OFT textbook is likely wrong'.

That said, I do rather like the following at the beginner level:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20

Thanks
Bill

 

[bhobba]

But luckily we have such a book as Feynman's "QED: The strange theory of light and matter."

Yes - it is VERY good - almost without peer. But even it has issues eg:
https://www.physicsforums.com/threads/do-photons-move-slower-in-a-solid-medium.511177/

Thanks
Bill

 

[Drakkith]

I apologize. I should have locked this thread a page or two ago due to several rules violations (which have only increased since then). If any members would like to start their own thread regarding this subject, feel free. In the meantime, thread locked.