Are there proposed physical processes for superposition

[rasp]

I’m understanding that QM superposition in which, for example, a single electron acts as a wave in a double slit experiment and interferes with itself by passing through both slits simultaneously (when there are no detecting devices priorly measuring either slit) presents a result which is inconsistent with classical logic. I have also read that the actual photographic interference patterns should be considered as probability interference, but I’m not sure what that means. Yet, it seems to me that a real process has occurred, and the explanation for the electron arriving at the screen simultaneously from 2 paths might require some rethinking of physical processes, possibly space or time. My question is, “are there theories as to what is “actually” happening?”

 

[PeterDonis]

I’m understanding...

I have also read...

Where have you read these things and where are you getting your understanding from? Please give some specific references.

 

[.Scott]

I'm not sure what "probability interference" refers to either.
But as for what is "actually happening", you can't do better than to calculate the probabilities of where the photon will be detected on the screen. And, of course, after many photons have been detected, the interference pattern will emerge.

What is "really happening" is that each photon is emitted and then detected on the screen. You could attempt to model their trajectories, as if they were small baseballs, but that is not "real". Baseball's have lots of intermediate locations. Photons do not.

As you learn about more experiments, you will likely become more willing to abandon the notion of photons having absolute paths.

For example, if you work with a Mach-Zender interferometer (https://en.wikipedia.org/wiki/Mach–Zehnder_interferometer), the interference pattern can be extinguished by blocking the path of the light. So photons landing on what were the dark areas of the interference pattern are able to reach the screen because they could have been blocked - but were not. In contrast, baseballs are only effected by what actually happened during their flight.

 

[rasp]

.scott. I understand your reply, re not trying to fix a trajectory. However, my question is more nuanced. If something was here and then becomes there without a fixed trajectory, then what physical process is postulated to allow it to get from here to there without a defined path?

 

[PeterDonis]

If something was here and then becomes there without a fixed trajectory, then what physical process is postulated to allow it to get from here to there without a defined path?

There isn't one. More precisely, QM does not tell you there is one, much less tell you what it is. Various "interpretations" of QM attempt to tell you some physical process, but they all make the same predictions for all observable results, so there is no way to tell which one is "right" by experiment.

For example, here's one interpretation, loosely based on the path integral formulation of QM: the electron takes all of the possible paths, and the amplitudes for each path interfere with each other to produce the observed interference pattern at the detector. There is no way to disprove this by experiment; but there's no way to prove it either.

 

[DarMM]

.scott. I understand your reply, re not trying to fix a trajectory. However, my question is more nuanced. If something was here and then becomes there without a fixed trajectory, then what physical process is postulated to allow it to get from here to there without a defined path?

As @PeterDonis has said there are several proposed explanations of what is happening (the interpretations of QM).

In one interpretation the photon does travel along a path, being is guided by a wave (DeBroglie-Bohm interpretation).

In another (Relational Block World) there isn't really a photon. One device just loses some energy and momenta and later another device gains some, without anything being transmitted. The loss and emission simply both being "required" by the laws of physics.

So the explanations really vary and currently the only experimental differences between them apply to very extreme scenarios we can't test. We have managed to logically exclude a good deal of possible explanations though through what are known as no-go theorems.

 

[bhobba]

There sort of is - it comes from a theorem called Gleason's Theorem:
http://kiko.fysik.su.se/en/thesis/helena-master.pdf

It states average of the outcome of a observation is Trace (OS) where O is the observation, S, which is a positive operator of unit trace, that Gleason's Theorem proves exists, by definition is called the state. So called pure states are of the form |u><u| where the |u> form a vector space. Linearity - ie the principle of superposition, is a defining property of a vector space. So yes we know the why of superposition - with a caveat explained below.

Looking at the theorem it may seem watertight - but there is a subtle assumption called non-contextuality - but since this is an I level thread I will let you investigate that. It's tied up with the Kochen-Specker theorem, which while often proven independently of Gleason, is actually a simple corollary to to it (ie Gleason's Theorem):
https://plato.stanford.edu/entries/kochen-specker/

Knowing this will deepen your understanding of the foundations of QM.

Thanks
Bill

 

[rasp]

Thank you all. I will follow up on your references. I would like to end my participation in this thread by acknowledging a level of frustration. I feel that even if I become familiar with QM states( like entanglement and superposition, and the linear algebra that describes them) because I don’t actually work in the field, I won’t feel a satisfaction of knowing, because I can’t theorize the underlying physical processes. Do some of you share that feeling?

 

[dlgoff]

Thank you all. I will follow up on your references. I would like to end my participation in this thread by acknowledging a level of frustration. I feel that even if I become familiar with QM states( like entanglement and superposition, and the linear algebra that describes them) because I don’t actually work in the field, I won’t feel a satisfaction of knowing, because I can’t theorize the underlying physical processes. Do some of you share that feeling?

You should watch this video (part 6 of 7); Richard Feynman-The Character of Physical Law - Part 6
Actually you should watch all 7 parts. You'll be glad you did.

 

[DarMM]

It states average of the outcome of a observation is Trace (OS) where O is the observation, S, which is a positive operator of unit trace, that Gleason's Theorem proves exists, by definition is called the state. So called pure states are of the form |u><u| where the |u> form a vector space. Linearity - ie the principle of superposition, is a defining property of a vector space. So yes we know the why of superposition - with a caveat explained below.

Granting non-conterxtuality this does explain superpositions as just the form probability theory takes when dealing with non-commuting observables. The question then becomes what is the physical reason for the observables being non-commuting.

 

[DrChinese]

... I won’t feel a satisfaction of knowing, because I can’t theorize the underlying physical processes. Do some of you share that feeling?

You can theorize all you like, although PF isn't the spot for speculation and/or most original research.

On the other hand: If you follow the threads where the interpretations of QM are discussed, you will learn a LOT that will help you to understand the depth and complexity of the issues involved. There is a lot of original research being done on the underlying mechanisms (if there are any) of quantum phenomena. Given articles I have read on this subject over the years, I would be surprised if your ideas had not considered by others. You might benefit from having a deeper understanding of previous attempts to solve these riddles.

 

[Mentz114]

The question then becomes what is the physical reason for the observables being non-commuting.

I'm not sure what you mean. The reason seems to be geometrical. If one performs rotations with some apparatus ##\sigma_x\sigma_y|\psi\rangle## is not the same as ##\sigma_y\sigma_x|\psi\rangle##. There have been experiments using tomography that show the phase shift between those states.

 

[DarMM]

I'm not sure what you mean. The reason seems to be geometrical. If one performs rotations with some apparatus ##\sigma_x\sigma_y|\psi\rangle## is not the same as ##\sigma_y\sigma_x|\psi\rangle##. There have been experiments using tomography that show the phase shift between those states.

Do those quantities not commute in classical mechanics? It cannot be purely geometric or it would follow through in classical mechanics as well. Given the rest of QM geometric arguments imply they would not commute yes.

Also why do, for example, position and momentum not commute, is there a geometric reason there?

Even more accurately why does the observable algebra have a form that doesn't admit a common sample space.

 

[Mentz114]

Do those quantities not commute in classical mechanics? It cannot be purely geometric or it would follow through in classical mechanics as well. Given the rest of QM geometric arguments imply they would not commute yes.

Also why do, for example, position and momentum not commute, is there a geometric reason there?

Even more accurately why does the observable algebra have a form that doesn't admit a common sample space.

The case of position and momentum is more difficult. As far as I know the 'disturbance' argument (inability to measure one without changing the other) doesn't explain the last question, so that is a problem for the free particle.