I disagree with your analysis and do not see it as consistent with QM. — Kenosha Kid

This assessment, that my objection to your theory is not consistent with QM, is simply a product of your misinterpretation of QM. Clearly, wavefunctions represent waves, not particles as you insist from your interpretation. I suggest that you are interpreting QM from the perspective of quantum field theory and this way of approaching QM inclines you to apprehend these waves as being particles. But there is nothing inherent within quantum mechanics itself which would incline one to believe that a quantum of energy exists as a particle rather than as waves. Clearly the wavefunction does represents waves. So to interpret it as representing particles is a misinterpretation. This is made more evident from the fact that the relation between the wavefunction and the particle is one of probability.

So here's an example to elucidate this point. Let's say that I employ some fancy mathematics to determine the probability of you replying to this post. I cannot truthfully claim that this mathematics represents your reply (which doesn't even exist right now), because it represents the probability of your reply. You ought to consider a similar relation of probability between the wavefunction and the particle.

In how many different ways does the notion of "waves" appear in quantum theory?

Clearly, wavefunctions represent waves, not particles as you insist from your interpretation. — Metaphysician Undercover

You clearly don't know the first thing about it. I hold a PhD in it. Thanks but honestly I'm not looking for help from ignorant blowhards with intellectual pretensions. Whatever this idea of QM you have is, it isn't QM and, fascinating as it might be to you, it's not relevant to this thread, never has been, never will be.

Told!

By the way, why do you present this stuff on a philosophy forum when you are completely uninterested in philosophical discussion of it? Why leave your peers? Have you been rejected?

By the way, why do you present this stuff on a philosophy forum when you are completely uninterested in philosophical discussion of it? Why leave your peers? Have you been rejected? — Metaphysician Undercover

It's posted in Philosophy of Science to examine the philosophical ramifications of QM on determinism. This thread isn't meant as an advertisement for QM. However QM is the scope of this particular question about determinism, reason being that people use QM a lot as if to prove that determinism is dead. It's not. There are deterministic and non-deterministic interpretations. My point here is that even the seemingly non-deterministic ones don't have anything to say about determinism.

Look, I resisted playing the PhD card for four pages and really didn't want to do it, opting to leave little hints here an there that I guess you didn't see. I don't feel good about it, but if you were as interested in the subject as much as you're interested in appearing like an authority on it, this wouldn't be an issue. Anyway, I'm sorry I lost my temper too.

For instance: is the electron wavefunction the only quantity that affects where the electron can be found? — Kenosha Kid

I thought the electron couldn't be 'found' anywhere until it is measured? It is not a discrete entity that exists in some unknown location until such time as it is registered. In fact there really is no such thing as 'an electron' until it is measured, when it manifests as a registration on a plate - which is the basis of 'the measurement problem'. It doesn't exist somewhere, lurking about undiscovered - all you can point to is the distribution of probabilities. There is no 'it', per se, until it's measured.

But your explanation presumes that there is an electron as a discrete existing particle that exists independently of being measured. Whereas, if you are to question the 'Copenhagen Interpretation', isn't that precisely the point at issue?

Incidentally, 'the copenhagen interpretation' was a phrase coined by Heisenberg in 1955 when he wrote Philosophy and Physics. It referred only to the general ideas of himself and Bohr with respect to what could and could not be stated on the basis of quantum physics. So I hardly think it's 'simplistic'. The reason that it's objected to, is because of the challenge it poses to scientific realism, which is the idea that there are indeed discrete, mind-independent sub-atomic entities called 'particles'. That is certainly the main reason Einstein objected to it.

'According to the Copenhagen interpretation sub-atomic particles generally do not have definite properties prior to being measured, and quantum physics can only predict the probability distribution of a given measurement's possible results. The act of measurement affects the system, causing the set of probabilities to reduce to only one of the possible values immediately after the measurement. This feature is known as wave function collapse.' (Wiki).

However, the 'collapse' of the wave function is actually a metaphor, as there never is an actual wave per se (any more than there is an actual particle). The 'wave function' is a distribution of probabilities that appears as a wave, but it's not an actual wave. Hence the fundamental ambiguity at the heart of quantum physics.

I thought the electron couldn't be 'found' anywhere until it is measured? It is not a discrete entity that exists in some unknown location until such time as it is registered. In fact there really is no such thing as 'an electron' until it is measured, when it manifests as a registration on a plate - which is the basis of 'the measurement problem'. — Wayfarer

The measurement problem is that the wavefunction that describes the electron can be in a superposition of observables, but when we measure it it's always in one. It is always a wave. Even if we managed to measure its position to arbitrary accuracy, it would be a wave in momentum space still. (Likewise if we measure it's momentum exactly it's a wave in space. This is the uncertainty principle.)

So it's a question of how the electron transforms from one wave to another. The double slit example is of it reducing to the kind of wave that grows out from the slits to the kind of wave with a fairly precise position (exact, or some kind of wave-packet which is more realistic).

But your explanation presumes that there is an electron as a discrete existing particle that exists independently of being measured. Whereas, if you are to question the 'Copenhagen Interpretation', isn't that precisely the point at issue? — Wayfarer

No, Copenhagen is just the above with that transformation being probabilistic according to the Born rule. The question of the epistemology of the wave is related but separable.

It referred only to the general ideas of himself and Bohr with respect to what could and could not be stated on the basis of quantum physics. So I hardly think it's 'simplistic'. — Wayfarer

In truth, it's less the interpretation and how it's applied. In the double slit experiment, the back screen is treated as ideal. This means the only thing that affects where the electron can be measured is the electron wavefunction, which is ambiguous, hence the measurement problem.

The insight drawn from this is that the wavefunction evolves into this ambiguous state and can collapse to any position on the ideal screen. But this holds only for ideal screens.

We'd get a different answer if we could calculate the time-dependent many-body wavefunction of the entire apparatus, but we can't. So the ideal calculation becomes the only thing we have to go on. My point is that it's unwise to take artefacts of that idealisation seriously just because we lack the computing power to do it properly.

However, the 'collapse' of the wave function is actually a metaphor, as there never is an actual wave per se (any more than there is an actual particle). — Wayfarer

As per my many responses to MU, this may well be true, but it's not QM.

and as MU observed, this is a philosophy forum, not a physics forum. I do ask questions on that forum also, but they give pretty short shrift to philosophy over there.

and as MU observed, this is a philosophy forum, not a physics forum. I do ask questions on that forum also, but they give pretty short shrift to philosophy over there. — Wayfarer

This is a thread about the implications of QM for determinism on a philosophy of science channel of said philosophy forum. If I'm out of line in my OP, can you be a bit more explicit?

If I'm out of line in my OP, can you be a bit more explicit? — Kenosha Kid

I don't think you're out of line - but I also don't think you're fully grasping the philosophical implications of the issue.

I'm not trained in physics beyond high-school but I have studied units in philosophy of science, and have read a few of the serious popular-level books on the subject, like Manjit Kumar's Quantum - sub-titled Einstein, Bohr, and the Great Debate About the Nature of Reality. Why do so many of the books about the subject refer to the 'nature of reality'? I also recently read Adam Becker's 'What is Real?' and David Lindley's Uncertainty: Heisenberg, Einstein, Bohr, and Heisenberg, and the struggle for the Soul of Science. All of them are basically dealing with the philosophical implications of physics. I've been listening to Philip Ball's lectures, and talks by Jim Baggott, both of whom are well-regarded and by no means crackpots or cranks (and there are some in this subject). They all acknowledge that there is a deep philosophical problem sorrounding the ontological status of the wave function - whether it's real, or simply a mathematical device, or an artefact of the understanding. None of that is resolved.

(Lately I've discovered, through this forum, a French philosopher of science called Michel Bitbol, whom I think has the best take on the philosophical issues.[/url] He's done some really interesting papers on the philosophy of physcis of Schrodinger and Heisenberg, amongst other subjects (which can be found here). Distinctly Continental, I suppose you might say, but in this area I think the Continentals are streets ahead of the Anglo's!)

In the double slit experiment, the back screen is treated as ideal. This means the only thing that affects where the electron can be measured is the electron wavefunction, which is ambiguous, hence the measurement problem.

The insight drawn from this is that the wavefunction evolves into this ambiguous state and can collapse to any position on the ideal screen. But this holds only for ideal screens. — Kenosha Kid

The back screen is physical, it's not 'ideal'. When you run the experiment, the results are recorded on a physical screen.

The measurement problem is that the wavefunction that describes the electron can be in a superposition of observables, but when we measure it it's always in one. It is always a wave. — Kenosha Kid

But again, the Schrodinger equation is wave-like, but it is an actual wave? I posted a question about this experiment , which you can see here on Physics Forum and here on Physics Stack Exchange if you're interested.

The gist of the question:

With the double-slit experiment, you can considerably vary the rate at which particles are fired without effecting the resulting interference pattern. That is, roughly speaking, 24 hours at 1 particle fired per second would give the same pattern as 86,400 particles fired in 1 second (all else being equal).

I know this is one of the strange things about the experiment, and as I understand it, this is the origin of the idea that the particles fired one-at-a-time 'interfere with themselves', which I think seems a very lame idea (but as I said, I'm not a physicist).

However the point which struck me is that if the inteference pattern is not rate-dependent, then it means that time is not a factor in the generation of the interference pattern i.e. if the same pattern can be generated in 1 second as in 24 hours, then 'time' is not a variable (as 'rate' is a function of 'time'). And that struck me as being at least philosophically significant.

One comment is that 'the boundary conditions of the experiment are not time-dependent'. So I was trying to argue that the wavefunction itself is therefore transcendent with respect to time (and so also space, as in relativistic physics time and space are aspects of the same reality). A timeless wave, if you like. But that got smacked down with: don't be stupid, the particle interferes with itself! (per Dirac).

The measurement problem is that the wavefunction that describes the electron can be in a superposition of observables, but when we measure it it's always in one. It is always a wave. Even if we managed to measure its position to arbitrary accuracy, it would be a wave in momentum space still. (Likewise if we measure it's momentum exactly it's a wave in space. This is the uncertainty principle.) — Kenosha Kid

Do you recognize the difference between a mathematical statement of probability, and a description? If so, let's move away from the idea that the wavefunction describes anything. Furthermore, when we make predictions (and a prediction is not a description) concerning events, using probabilities, we refer to the possibility of those events either occurring or not occurring. When an event may or may not occur, as is the case with a prediction, it is apprehended as not determined. Since the wavefunction is a statement of probability concerning a future event, the probability of detecting a particle, it refers to something which is not determined. With what part of this do you disagree?

But your explanation presumes that there is an electron as a discrete existing particle that exists independently of being measured. — Wayfarer

Kenosha Kid likes to waffle. When it suits Kenosha's purpose, the electron is a particle. When it suits Kenosha's purpose, the electron is a wave. But Kenosha adheres to no concrete principles to distinguish between when the electron is observable as a particle, and when it is observable as a wave. Kenosha Kid will call it a particle, or a wave, depending on what is required at that point in the discussion.

Kenosha Kid likes to waffle. — Metaphysician Undercover

I generaly find Kenosha's posts a model of clarity. I often don't agree with them but not because I think they're 'waffle'.

I generaly find Kenosha's posts a model of clarity. I often don't agree with them but not because I think they're 'waffle'. — Wayfarer

Yes, Kenosha is very clear and descriptive, as I said in my first post in the thread. Nevertheless, there is waffling back and forth as to whether KK believes that the electron is best described as a particle or as a wave. Let me show you. The following two quotes are from the op where we can see quite clearly that KK's intent is to reduce the electron to a particle with deterministic existence, and nothing more

Not according to the transactional interpretation of quantum mechanics, which holds that the actual trajectories a particle takes are not just determined by the retarded wavefunction going from time t to t', but also the advanced wavefunction going from time t' to t. (Advanced wavefunctions come up in standard QED as well, to yield the electron self-energy). In this interpretation, the complex conjugate is essentially a message from the future. The electron takes the real trajectories it does in part because it has information about where it's going or, from another viewpoint, where it's conjugate came from. — Kenosha Kid

The true boundary conditions of any particle are its birth and death: where and when it was created, and where and when it will be destroyed. These are facts of each particle. This is the full time-dependent wavefunction of the electron which is, relativistically speaking, equivalent to a static 4D wave. — Kenosha Kid

But when questioned, KK admits that the so-called particle is really a "wave-packet", or "plane waves", in what follows.

A good basis set that puts wavelike and particle-like extremes on equal footing is the stroboscopic wave-packet representation, on which I wrote my master's thesis. All of the above still holds: we simply replace Pauli exclusion of two electrons being in one kind of state (position) with that of two electrons being in another kind of state (stroboscopic wave-packet). The exclusion principle holds across all such bases (e.g. you cannot have two like-spin electron plane waves with the same momentum, which is what I had in mind for the states k, j', k" and k"', though these could be position, orbital, Bloch, Wannier or stroboscopic states or anything else you might consider, it makes no difference to the argument). — Kenosha Kid

And in the following reply to Harry H, KK is clear in the claim that electrons are waves.

If you want to know more about why individual electrons are waves, you can Google it. — Kenosha Kid

But then Kenosha goes right back to the op hypothesis that electrons are particles:

The new-ish bits are that a) one cannot draw conclusions about where a particle may be found at a given time by considering only that particle at the time, and b) that the birth and death of a particle are its true boundary conditions. Those might be considered novel or controversial. — Kenosha Kid

When a particle moves from event (r,t) to (r',t'), it still does so by every possible path (Feynman's sum over histories). If you sum up every possible r' at t' and normalise, you recover the wavefunction at t'. — Kenosha Kid

The OP holds that the complex wavefunction is an ontic description -- or fair approximation to such -- of how particles propagate through space and time as we represent them. — Kenosha Kid

In the following, you'll find Kenosha describe three different interpretations of QM, two in which the electron is waves, and one in which it is a particle:

This is evident in the various interpretations of QM. in Copenhagen, the electron is a complex wave, the field acts linearly, there is one measurement outcome and spontaneous collapse. In MWI, the electron is a complex wave, the field acts linearly, there are an infinity of outcomes and the wave evolves forward in time deterministically. In Bohm, the electron is a real, classical particle, the field is nonlinear, there is one outcome, and the particle evolves forward in time deterministically. In transactional QM without my edits, the electron is a complex wave, the field is linear, there is one outcome, the wave evolves forward and backward in time but probabilistically. — Kenosha Kid

Remember, Kenosha's thesis that the electron is deterministic, requires that it is a particle, like the Bohm interpretation above. But whenever pressured on the question of whether the electron really is a particle or a wave, Kenosha always returns with, it's a wave, as below:

The measurement problem is that the wavefunction that describes the electron can be in a superposition of observables, but when we measure it it's always in one. It is always a wave. Even if we managed to measure its position to arbitrary accuracy, it would be a wave in momentum space still. (Likewise if we measure it's momentum exactly it's a wave in space. This is the uncertainty principle.) — Kenosha Kid

So it appears to me, like Kenosha Kid is trying to make the argument that the electron is a deterministic particle, when Kenosha has actually learned from many years of study, that the electron is a wave, and is really not so deterministic.

Thanks for the summary! I see what you mean. According to the Copenhagen attitude, the electron is neither a wave nor a particle, but can present as either, depending on what experiment you do. As Heisenberg said 'We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.' 'Bohr implies that it is not possible to regard objects governed by quantum mechanics as having intrinsic properties independent of determination with a measuring device... The type of measurement determines which property is shown.' Whereas the realist attitude is that there must be something that exists independently of measurement. There's been quite a few recent articles in the science press recently about this whole conundrum e.g. https://www.livescience.com/objective-reality-not-exist-quantum-physicists.html

Told!

By the way, why do you present this stuff on a philosophy forum when you are completely uninterested in philosophical discussion of it? Why leave your peers? Have you been rejected? — Metaphysician Undercover

Disgusting, MU. Whatever happened to you that instead of a reasonable courtesy and the good sense to learn you seem invariably to default to a dogmatic whackdoodleism whose first characteristics are denial of reality and denial of fact in favour of the world as MU thinks it is. What school taught you that?

As Heisenberg said 'We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.' — Wayfarer

This is similar to Kant's phenomena/noumena distinction. Sensing the world (observing) is not a simple passive arrangement where the sentient being receives what is out there. It is an interaction with the world.

Disgusting, MU. Whatever happened to you that instead of a reasonable courtesy and the good sense to learn you seem invariably to default to a dogmatic whackdoodleism whose first characteristics are denial of reality and denial of fact in favour of the world as MU thinks it is. What school taught you that? — tim wood

Oh get real Timmy. What the fuck do you know about reality? Obviously I went to the school of MU. Ever heard of it? I approached this thread with a desire to discuss, and learn. But Kenosha Kid would not oblige me, and immediately went on the defensive, refusing to discuss the fundamentals of QM, saying that this is outside QM.

What the fuck do you know about reality? — Metaphysician Undercover

Enough to know that I ought to offer some definition of it if I'm going to do any heavy lifting (for me) about it. But you seem to know. "What the f***," then, do you know about it?

Disceptatio succumbo :sad:

They all acknowledge that there is a deep philosophical problem sorrounding the ontological status of the wave function - whether it's real, or simply a mathematical device, or an artefact of the understanding. None of that is resolved. — Wayfarer

True, and discussed in this thread in some depth. Please point out where you think I failed to understand it. The OP is fairly ambivalent about the ontology of the actual wavefunction. At one extreme, you can consider the full solution to the Schrödinger equation as ontic. At the other, only the transacted trajectories are ontic. It's not my intent to push anyone one way or another.

The back screen is physical, it's not 'ideal'. When you run the experiment, the results are recorded on a physical screen. — Wayfarer

As is clear from the preceding text:

It referred only to the general ideas of himself and Bohr with respect to what could and could not be stated on the basis of quantum physics. So I hardly think it's 'simplistic'.
— Wayfarer

In truth, it's less the interpretation and how it's applied — Kenosha Kid

this is regarding the Copenhagen interpretation. The probability of finding the electron anywhere on it is given only by the electron wavefunction, which is equivalent to treating the back screen as an ideal metal.

But again, the Schrodinger equation is wave-like, but it is an actual wave? — Wayfarer

The solutions to the Schrödinger equation are waves. The equation itself is not a wave. I think all of those books you mentioned would have told you this

But that got smacked down with: don't be stupid, the particle interferes with itself! (per Dirac). — Wayfarer

That's harsh of them. The wavefunction is time-dependent, but only in its phase. The probability of finding it at a given position is unaffected by this phase. This is not a general feature of wavefunctions.

Kenosha Kid likes to waffle. When it suits Kenosha's purpose, the electron is a particle. When it suits Kenosha's purpose, the electron is a wave. But Kenosha adheres to no concrete principles to distinguish between when the electron is observable as a particle, and when it is observable as a wave. Kenosha Kid will call it a particle, or a wave, depending on what is required at that point in the discussion. — Metaphysician Undercover

This isn't addressed to you per se, just for general clarity: the concrete principle adhered to is the expansion postulate of QM, which states that the wavefunction is always a linear admixture of one or more Eigenstates of a given operator. After measurement, this is equal to a single Eigenstate of the measurement operator.

QM does not maintain two different types of electron: one wave-like, one particle-like, and swap between them. It is always a wave. That wave can be a position Eigenstate or not. I think I've already addressed this once before.

The particle-like behaviour evident in measurement is not that the electron ceases to be a wave at all, but that the wave somehow reduces to a single Eigenstate of the measurement operator.

Please point out where you think I failed to understand it [the interpretation of the wave function collapse] — Kenosha Kid

If you posted your OP at physicsforum.com, I'd be interested to see what other physicists say about it. I intuitively feel there's a problem with it, but of course I don't have the skills to say what, exactly. And this is a philosophy forum, where [E−V]u=12m[p−A]2u is not, as it were, lingua franca.

The probability of finding [the object] at a given position is unaffected by this phase. This is not a general feature of wavefunctions. — Kenosha Kid

Yes - and this is 'a difference that makes a difference'. The fact that time or rate is not a boundary condition is, I feel, of the utmost import, philosophically.

The particle-like behaviour evident in measurement is not that the electron ceases to be a wave at all, but that the wave somehow reduces to a single Eigenstate of the measurement operator. — Kenosha Kid

"Somehow"? So if its always a certain state, and only changes its state when interacting with a measuring device, which would also be made of waves, then what is so special about a measuring device (which is just a large group of electrons) that changes the nature of an electron? And how do you know that what you are talking about isn't the measurement, but what is actually measured, if the end result is an effect of electrons interacting with a measuring device which you dont get when the electron isn't measured?

If the voltage of the cathode is reduced such that only one electron fires out, say, per ten seconds, eventually the same pattern builds up. From this we deduce that each electron is a wave. — Kenosha Kid

Her you talk about single electrons, as if they are a particle before going through the slits.
And I don't see whet you addressed the issue where a single wave can interfere with itself after passing through double-slits, but a single electron, which you claim is a wave, cannot. What makes an electron wave different in that it cannot interfere with itself, but a wave of electrons (a wave of waves?) can interfere with itself? And if a wave can consist of smaller waves, then what does say about electron waves?

What prevents the electron waves in the beam from interfering with the electron waves that make up the board with the slits and the electron waves that make up the screen? Why does the wave only interfere with itself if all the other parts of the experiment are an assortment electron waves?

This isn't addressed to you per se, just for general clarity: the concrete principle adhered to is the expansion postulate of QM, which states that the wavefunction is always a linear admixture of one or more Eigenstates of a given operator. After measurement, this is equal to a single Eigenstate of the measurement operator.

QM does not maintain two different types of electron: one wave-like, one particle-like, and swap between them. It is always a wave. That wave can be a position Eigenstate or not. I think I've already addressed this once before.

The particle-like behaviour evident in measurement is not that the electron ceases to be a wave at all, but that the wave somehow reduces to a single Eigenstate of the measurement operator. — Kenosha Kid

Ok, I'm fine with this. Now, if the electron "is always a wave", can you explain the principles which allow you to refer to the electron as a particle with a trajectory. Here's an example of such speak from the op:

Not according to the transactional interpretation of quantum mechanics, which holds that the actual trajectories a particle takes are not just determined by the retarded wavefunction going from time t to t', but also the advanced wavefunction going from time t' to t. (Advanced wavefunctions come up in standard QED as well, to yield the electron self-energy). In this interpretation, the complex conjugate is essentially a message from the future. The electron takes the real trajectories it does in part because it has information about where it's going or, from another viewpoint, where it's conjugate came from. — Kenosha Kid

We would make such a demand of the cathode: for an electron to be emitted at point (r,t) there must be an electron at (r,t). It is only sensible that we do so for the hole the electron will occupy. (It's worth convincing yourself that this hole also has a history. For every electron that vacates position r to occupy position r', it leaves behind a hole and goes to where the hole previously was, describing an electron hole that vacates position r' to occupy position r. We do not need to consider it the same hole throughout, but there must be some conservation of hole-ness.) — Kenosha Kid

The true boundary conditions of any particle are its birth and death: where and when it was created, and where and when it will be destroyed. These are facts of each particle. This is the full time-dependent wavefunction of the electron which is, relativistically speaking, equivalent to a static 4D wave. Unlike in the QM of the Copenhagen interpretation, the conjugate solution (from death to birth) is also a solution when these boundary conditions are applied. This solution eliminates almost all of the trajectories possible (and expected) in Copenhagen QM. And this is just the single-particle picture. — Kenosha Kid

As we expand the picture to include more bodies in the universe, especially the rest of the electronic field, more and more remaining trajectories are removed by things like scattering and Pauli's exclusion principle. — Kenosha Kid

If not, we're left with a solution that looks like a hugely constrained version of the many-worlds interpretation. I name this the not-many-worlds interpretation of quantum mechanics. — Kenosha Kid

I understand "trajectory" as the path of a body or object moving through space, a common example is a projectile. Of course this descriptive term is inconsistent with the way that energy is known to be transmitted by waves. So the challenge to you is to explain how you manage to reduce the wave transmission of energy to a trajectory. You clearly affirm that the energy is a wave, yet you propose that the energy is projected with a trajectory rather than a wave transmission.

Please pay particular attention to your description of scattering, in which you describe an electron as existing at a particular position, and leaving a hole at that position. You know that having a determinate position, and having a determinate momentum are mutually exclusive descriptions of the electron. So how would you reconcile these two incompatible descriptions of the electron, one in which it has a momentum as a wave packet, and the other within which it has a position with the capacity to leave that position creating a hole there?

In relation to quantum trajectory theory, here's an article (I haven't had time to read completely read it yet) which might interest you, if the link works: https://doi.org/10.3390/e20050353
entropy 2018, 20(5), 353

Anyway, here's a line from the conclusion of that article:

Furthermore in the case of atoms the claim that these are “particle trajectories” has been re-examined recently by Flack and Hiley [47] who have concluded that the flow lines, as we shall now call them, are not the trajectories of single atoms but an average momentum flow, the measurements being taken over many individual particle events. In fact they have shown that they represent an average of the ensemble of actual individual stochastic Feynman paths.

And this is a philosophy forum, where [E−V]u=12m[p−A]2u is not, as it were, lingua franca. — Wayfarer

Ha! And that was the nice version. It's not written like that normally. The important thing is not the terms, but that energy and momentum are not linearly proportional: E ~ p^2. This translates as requiring two boundary conditions in space and only one in time: the initial state. It's the shape of the equation that's of interest.

Please point out where you think I failed to understand it [the interpretation of the wave function collapse]
— Kenosha Kid

If you posted your OP at physicsforum.com, I'd be interested to see what other physicists say about it. I intuitively feel there's a problem with it, but of course I don't have the skills to say what, exactly. — Wayfarer

That's a conversational dead-end then :rofl: I would expect the controversies would be different. Transactional QM, while mathematically identical to any other QM, is not as supported as Copenhagen, MWI, or SUaC (shut up and calculate). The reaction from Copenhagenists will be that it's absurd because it's not Copenhagen, just as MWI is absurd. The reaction from MWIers will be that it's wrong because it's not MWI, just as Copenhagen is wrong. That is the usual quality of debate about QM interpretations on Physics Forum.

The genuinely controversial part of the OP is the idea that, if we could solve the many-body wave equation for the whole apparatus, we would find that a given electron does not have the characteristic double-slit band pattern at a given time. I expect that most would say it would, but we cannot solve the equation to find out. I say it wouldn't, but we cannot solve the equation to find out. But my take includes more physics.

I don't think the stuff you're bringing up matters so much except maybe at extremes such as the wavefunction being a "metaphor" which is so far from conventional QM as to be also irrelevant here. As per my discussion with fdrake, I don't assume a particular ontology beyond the Born rule, which is a postulate of QM. The extent to which the wavefunction mathematically represents or encodes something about the physics -- which is valid since it makes physical predictions -- it is something that can be calculated and discussed as an object.

So the challenge to you is to explain how you manage to reduce the wave transmission of energy to a trajectory. — Metaphysician Undercover

This is discussed in the OP here:

in relativistic quantum theories, we do not proceed by specifying an initial state, time-evolving it forward, and asking the probability of spontaneously collapsing to a particular final state. Rather, we have to specify the initial and final states first, then ask what the probability is. This is constructed as a Green's function G(r, t; r', t'). — Kenosha Kid

In perturbation theory and path integral formalisms of relativistic QM, such as quantum electrodynamics, one specifies initial and final states, as per the form of the Dirac equation which is power 2 in space and time (momentum and energy). This is what is meant by a path or trajectory.

If we do this with final position states for all positions on the back screen, we reconstruct the wavefunction defined over all of those points. The wavefunction and the Green's function are highly related.

So how would you reconcile these two incompatible descriptions of the electron, one in which it has a momentum as a wave packet, and the other within which it has a position with the capacity to leave that position creating a hole there? — Metaphysician Undercover

These descriptions aren't incompatible. Any wavefunction can be written as a superposition of Eigenstates of any measurement operator. If my electron collapses to an exact position state, for instance, and an electron in the screen is a wave-packet spread around that position, either the latter has to be scattered away from that position or the former is blocked from being found there.

In relation to quantum trajectory theory, here's an article (I haven't had time to read completely read it yet) which might interest you, if the link works: https://doi.org/10.3390/e20050353
entropy 2018, 20(5), 353 — Metaphysician Undercover

Great title! Yes, in Bohmian mechanics the electron always has definite position and momentum, and thus a well-defined trajectory.

Interestingly this popped on my radar today, describing something very similar to what the OP describes but with light waves instead of electron waves.

https://scitechdaily.com/scientists-crack-quantum-physics-puzzle/

Interestingly this popped on my radar today, describing something very similar to what the OP describes but with light waves instead of electron waves.

https://scitechdaily.com/scientists-crack-quantum-physics-puzzle/ — Kenosha Kid

Full paper here: https://www.nature.com/articles/s41467-020-18652-w

This isn't quite what I thought it was, but exhibits similar behaviour.

Anderson localisation is caused by impurities in semiconductors that cause the wave to scatter so much and so randomly that it interferes out almost completely and cannot progress.

In the OP, the scattering sites are just other electrons in the screen, which will be much less severe.

However both cases have similar outcomes insofar as paths that aren't viable in the future are never tried in the past.

The genuinely controversial part of the OP is the idea that, if we could solve the many-body wave equation for the whole apparatus, we would find that a given electron does not have the characteristic double-slit band pattern at a given time. — Kenosha Kid

Is there any 'given electron' - prior to it being measured?

Is there any 'given electron' - prior to it being measured? — Wayfarer

Yes, in quantum theory, including quantum field theory, the electron is considered to be there whether it's measured or not. For instance, it interacts with the Higgs field all the time, without which it would move at the speed of light.

Yes, in quantum theory, including quantum field theory, the electron is considered to be there whether it's measured or not. — Kenosha Kid

But that is the whole point at issue in the 'measurement problem', is it not?

What is meant by ‘position’ in the quantum realm? Nothing more or less, Heisenberg answered, than the result of a specific experiment designed to measure, say, the ‘position of the electron’ in space at a given moment, ‘otherwise this word has no meaning’. For him there simply is no electron with a well-defined position or a well-defined momentum in the absence of an experiment to measure its position or momentum. A measurement of an electron’s position creates an electron-with-a-position, while a measurement of its momentum creates an electron-with-a-momentum. The very idea of an electron with a definite ‘position’ or ‘momentum’ is meaningless prior to an experiment that measures it.

Kumar, Manjit. Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality (p. 236). Icon Books Ltd. Kindle Edition.

The bolded sentence seems to undermine the premise that the electron can be considered to be there, measured or not.