I Does an electron have a quantum phase frequency?

[andresB]

Everyone keeps saying that, but I don't see the math. De Broglie gives E=h𝜈. Schrödinger gives an angular frequency which also reduces to E=h𝜈, except the E includes the potential energy. So those seem nearly identical to me. What equations justify your statement?

Let's say we have a wave packet representing the probability amplitude of finding an electron within some region. The evolution of the probability and of any expected value is independent of any constant you want to add to the Hamiltonian. That's what non-relativistic quantum mechanics actually says.

 

[vanhees71]

Sounds reasonable.

Also sounds reasonable but seems to be in tension with the previous statement.

It's not. It's just pointing out the usual "arbitrary choice" of the additive constant.

One could argue that the "arbitrary additive constant" is actually observable, as the maximum energy that can be extracted from a system is the energy of the system as measured from the vacuum state's energy.

The arbitary constant is not observable. All physics is invariant under the arbitrary choice of the constant.

Previously, I quoted "A Clock Directly Linking Time to a Particle's Mass", Science 1 February 2013: Vol. 339 no. 6119 pp. 554–557 doi:10.1126/science.1230767 . Among other things, they mention the Compton frequency \omega_0=mc^2/\hbar and note: "In principle, a Compton-frequency clock could be built by annihilating a particle-antiparticle pair and counting the frequencies of the generated photons." This remark suggests that there is some preferred choice of the "additive constant". Indeed, it seems natural to assign the energy of \hbar \omega to a photon.

The above is not meant to criticize anybody. It seems to me that the issue of reality of the Compton frequency is controversial.
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The frequencies of the generated photons are given by energy-momentum conservation, and thus the arbitrary additive constant simply cancels, because it's on both sides of the "balance equation".

 

[akhmeteli]

It's not. It's just pointing out the usual "arbitrary choice" of the additive constant.

So we disagree.

The arbitary constant is not observable. All physics is invariant under the arbitrary choice of the constant.

Again, one can have a different opinion, arguing that observations indicate what maximum energy one can extract.

The frequencies of the generated photons are given by energy-momentum conservation, and thus the arbitrary additive constant simply cancels, because it's on both sides of the "balance equation".

This is one way to look at this matter. However, one can argue that it would be natural to assign the same energy to each photon with the same frequency and to assign a small energy to a photon with a low frequency. However, such approach is not irrefutable either: there is always the problem of zero-point energy.

Another thing. The OP did not ask if a real electron has a definite energy, he asked if it has a definite frequency. I would say the two photons after electron-positron annihilation have definite frequencies, which seems to imply that an electron has a definite frequency too.

Again, I am not saying that your opinion is wrong, and the opposite opinion is correct, there are arguments in favor of both opinions. This is why I believe this issue is controversial.

 

[PeroK]

Again, I am not saying that your opinion is wrong, and the opposite opinion is correct, there are arguments in favor of both opinions.

Physics is about experimental results, not about arguments and opinions.

 

[akhmeteli]

Physics is about experimental results, not about arguments and opinions.

With all due respect, this sounds like an opinion without arguments.

There are always areas of physics where there is not enough clarity at the moment, so there is place for debates, opinions, and arguments. Sometimes it happens because there are not enough experimental results. For example, at the beginning of the XX century there were a lot of debates on whether atoms exist. There is a dearth of experimental results on the issue discussed in this thread (and the reason is the Compton frequencies are very high). Should we rely on the results of "A Search for the de Broglie Particle Internal Clock by Means of Electron Channeling". Foundations of Physics. 38 (7): 659–664. doi:10.1007/s10701-008-9225-1 ? I don't know.

And sometimes there is a place for debates, opinions, and arguments even when there are a lot of experimental results, as we see in the case of interpretations of quantum theory.

 

[berkeman]

With all due respect, this sounds like an opinion without arguments.

LOL. Thread is closed for Moderation...

 

[DrClaude]

This thread has veered away from the OP's original question and will remain closed.