I think my model suggests that the particle passing through both slits to interfere with itself in only the third dimension is an illusion. If this is accurate, woohoo! The experiment still suggests a wave function, but a single wave propagates both backwards and forwards in time, intermittently collapsing itself in some sense. This model may only apply to a very specific kind of process and context, with wavicles in nature propagating in many more orientations than temporally forward and backward, hence the complexity of our holographic universe. But the form of this holography is partially an outcome of perception's nature, thus the observer-dependence of experimental observations enigmatically brought into sharp relief by the supraintuitional oddities of quantum physics.

Ah, I see what you're saying. Yes, in a sense the overlap between retarded and advanced waves that 'realise' the particle trajectory is a kind of interference. However it needn't and apparently doesn't collapse which slit the particle travelled through (which would destroy the interference pattern).

I'm not sure where holography comes into it though.

I'm not sure where holography comes into it though. — Kenosha Kid

A wave function collapsing itself in the double-slit experiment is relatively simple compared to most of what happens in nature, an extremely parameterized holography even in the context of three dimensions, basically like a lightning bolt. In environments outside the lab, the holograph (as viewed in lower dimensions) and its background is usually much greater in complexity, more like a supradimensional tapestry with standing waves and intricate flow at morphing rates. Maybe a particle is merely a standing wave?

Maybe a particle is merely a standing wave? — Enrique

Spot on, but in 4D instead of 3D. A good analogy is Bloch waves: these are steady-state waves in periodic structures such as crystals. Stationary Bloch states have no momenta either because a) they consist principally of zero-momentum terms, or b) they consist of non-zero momenta terms in equal and opposite degrees. The latter can be seen as a superposition of e.g. particles moving forward through the crystal and particles moving backward. In fact, statistically we cannot differentiate between two particles in these stationary states and two that are moving with equal speed in opposite directions: the many-body wavefunction is the same for each.

The idea expressed in the OP, and expressed by yourself above, is a 4D generalisation of this. Each particle is a 4D standing wave that can be decomposed into parts moving forward in time (retarded wavefunction) and parts going backward in time (advanced wavefunction). They're not exactly analogous: in Bloch waves the operation is additive, in these they are multiplicative, but they are very similar.

The idea expressed in the OP, and expressed by yourself above, is a 4D generalisation of this. Each particle is a 4D standing wave that can be decomposed into parts moving forward in time (retarded wavefunction) and parts going backward in time (advanced wavefunction). They're not exactly analogous: in Bloch waves the operation is additive, in these they are multiplicative, but they are very similar. — Kenosha Kid

This is my impression of the ideas so far (solely for educational learnings, don't come down on me too hard). Curious to see the extent that your knowledge corroborates it.

In the double-slit experiment a wave packet or "wavicle" travels through one or the other slits, but either option is equally probable across many trials, though fundamentally deterministic (thus far immeasurably so) in relation to a single wavicle. An apparent "interference pattern" is not generated by diffraction through the slits but rather produced by peaks of charge distribution along the absorber's surface rendered symmetrical by the slits, which initiate the various trajectories of wave packets in coordination with the emitter charge and determine the statistical range of possibility for endpoints.

This is near one pole of the wavicle spectrum as it exists in Earth environments, a case that can be modeled somewhat simplistically as an almost ideal duality of retarded and advanced wave related in a precisely multiplicative way during propagation of the wavicle's path, the total wavicle smeared out in an especially linear four dimensionality as it moves.

A crystal is near the opposite pole of the Earthbound wavicle spectrum, modelable as retarded and advanced waves which are instead a nearly ideal additive duality, amounting to such equilibrated, counterbalanced motion that the wavicle appears stationary even upon very large magnification, an especially polygonal four dimensionality.

Most conventionally multiwavicle matter exists somewhere in between, with waves of many varying and fluctuating rates interfering in complex patterns that may deviate greatly from four dimensionality as it applies to the poles of the retarded/advanced wave model, creating a huge range of relatively local entanglement phenomena.

All of this entanglement exists within fields or clouds of charge that are a medium for nonlocal causality. Charge is the nonlocal facet of entanglement in electromagnetic matter.

The science of atomic chemistry adequately (but perhaps not ideally) models a large portion of the entanglement spectrum.

I might go back and edit my embarrassing snapping at MU — Kenosha Kid

Generally that's not a good idea. For instance, if I edited out everything I said that was embarrassing to me, there really wouldn't be much left.

Generally that's not a good idea. For instance, if I edited out everything I said that was embarrassing to me, there really wouldn't be much left. — Metaphysician Undercover

In that case, I <REDACTED>

My next lecture will explicate quantum mechanics as the golden path to fourth dimensional world peace! Its the advanced wave of the future man! lol

By the way, this experiment has reputedly been performed with more than two slits. My model predicts that, within static total width parameters, the particle has roughly equal chance of traveling through any centered, equally sized and spaced slits. The erroneously-regarded "interference" pattern on the detector screen will then vary symmetrically in proportion to emitter position, also slit quantity, width and placement, predictable according to some kind of mathematical formula. Is this accurate?

My next lecture will explicate quantum mechanics as the golden path to fourth dimensional world peace! Its the advanced wave of the future man! lol — Enrique

:rofl:

The erroneously-regarded "interference" pattern on the detector screen will then vary symmetrically in proportion to emitter position, also slit quantity, width and placement, predictable according to some kind of mathematical formula. Is this accurate? — Enrique

It will vary depending on the distance from the cathode to the slits, the slits to the screen, the distance between the slits, the widths of the slits and the voltage of the cathode.

Is a triple-slit experiment with the same setup as the textbook double-slit an on average 33% probability, a quadruple-slit 25%, etc.?

In the textbook example, i.e. in conventional quantum mechanics, each particle goes through every slit, which is why there's an interference pattern. To determine the weighting through each, you'd have to solve the wave equation and take the integral of the absolute square across the area of each slit. It will depend on the distance between the slits.

In the textbook example, i.e. in conventional quantum mechanics, each particle goes through every slit, which is why there's an interference pattern. To determine the weighting through each, you'd have to solve the wave equation and take the integral of the absolute square across the area of each slit. It will depend on the distance between the slits. — Kenosha Kid

That interpretation doesn't make sense to me. It fails to account for why a detector at one of the double slits only registers a particle half the time, nor the apparent randomness of localized absorber contact amongst even dozens of particles. Technically its possible for an electron "lightning bolt" to divide in some proportion, travel through all slits, and then recombine on the opposite side to contact a single spot on the florescent screen, but this seems highly unlikely for particles consisting of hundreds of atoms.

I think researchers managed to radically misinterpret the experimental results because of their reificational love affair with solving the wave function. The real source of absorber pattern statistics must be relative distribution of negative charge along its surface, not particle interference.

That interpretation doesn't make sense to me. It fails to account for why a detector at one of the double slits only registers a particle half the time, nor the apparent randomness of localized absorber contact amongst even dozens of particles. — Enrique

It's easier to see it in the case of photons. The photon must travel through the undetected slit and not be destroyed or the detected one and be destroyed. There's no possibility in that case of interference.

It's easier to see it in the case of photons. The photon must travel through the undetected slit and not be destroyed or the detected one and be destroyed. There's no possibility in that case of interference. — Kenosha Kid

I'm not aware of any direct evidence that the particle travels through both slits simultaneously as a wave, then recombines into a particle. It might be the case for photons while not for much more massive particles, but what could possibly be the mechanism?

It seems more plausible to me that the detector at the slit affects overall charge distribution in the chamber such that all possible pathways are influenced to produce bright bands instead, rather than disrupting some sort of superposition or entanglement of the wavicle with itself at multiple slits. Even Schrodinger hated the collapse of the wave function concept and he invented the wave function!

I'm not aware of any direct evidence that the particle travels through both slits simultaneously as a wave, then recombines into a particle. It might be the case for photons while not for much more massive particles — Enrique

The interference pattern is the evidence. That's how they know particles are waves. The single-electron experiment was performed in 2002: https://physicsworld.com/a/the-double-slit-experiment/

what could possibly be the mechanism? — Enrique

Electrons are waves: waves diffract and interfere.

The interference pattern is the evidence. — Kenosha Kid

What is the evidence that a single emitted electron is a wave spanning multiple slits, and does this evidence obtain for molecules also? When the wavicle contacts the florescent screen, seems to me it is closer to a particle with a definite trajectory than a collapsing wave function of a large swath of the chamber, though electrons do of course evince properties in many contexts that can't be explained unless they are spatially diffuse in ways exceeding for instance a grain of sand.

What is the evidence that a single emitted electron is a wave spanning multiple slits, and does this evidence obtain for molecules also? — Enrique

I linked to an article on the paper.

I linked to an article on the paper. — Kenosha Kid

Probably involves mathematical parameters that are difficult to explain in a simple message board post. Not a physicist, but maybe I'll take a look at it.

Probably involves mathematical parameters that are difficult to explain in a simple message board post. Not a physicist, but maybe I'll take a look at it. — Enrique

Ah okay. Basically the interference pattern on the screen is determined by how the wave propagates to it. The pattern is what's called a Fourier transform of the slit setup. For a single slit, this is something like a bump. There's no dark and light bands because there's no positive and negative fields to cancel each other out. The bulk of the wave passes in a straight line between the cathode and the screen, with some spreading out as it passes through the slit.

To get the dark and light bands of the interference pattern, you have to have multiple sources that can reinforce or cancel each other out. You can't get this kind of pattern with a wave and a single slit, and you can't get this pattern with point particles and multiple slits, as these would just produce multiple copies of the same thing you'd get with a single slit.

Putting a detector behind one of the slits basically gets you back to the pattern you'd get with point particles. The wave has to get past the detector or not, so go through one slit or the other. You can't get interference this way. You can only get interference if it goes through one slit *and* the other.

To get the dark and light bands of the interference pattern, you have to have multiple sources that can reinforce or cancel each other out. You can't get this kind of pattern with a wave and a single slit, and you can't get this pattern with point particles and multiple slits, as these would just produce multiple copies of the same thing you'd get with a single slit.

Putting a detector behind one of the slits basically gets you back to the pattern you'd get with point particles. The wave has to get past the detector or not, so go through one slit or the other. You can't get interference this way. You can only get interference if it goes through one slit *and* the other. — Kenosha Kid

Sorry this nonexpert is getting so nitpicky, but I'm curious. Does observable evidence exist that the particle travels through both slits during a single trial, or is that only an assumption? I've read an "interference pattern" results from molecules with up to a thousand atoms. It seems to me these must be very much like point particles compared to an electron, so claiming they travel through both slits could be problematic. For the relatively large molecule at least, the endpoint on a florescent screen is then produced by retarded/advanced waves linking up approximately halfway along the path determined by one of the slits, not both, meaning the wavicle stretches more linearly rather than spreading horizontally, though over many trials the particle is equally likely to travel through either slit.

But it depends on the mathematical specs of distance between the slits, slit width, particle size, charge distribution, etc. Don't have the foggiest notion of exact proportions.

Failure to get the interference pattern from molecules larger than a thousand atoms could be the result of the molecule being too large to be influenced by an absorber's charge as induced in consort with the emitter like a thunderstorm, not a "collapse of the wave function" decoherence caused by entanglement properties at the slits. The sensor might somehow affect trajectory through either slit (in separate trials) even though it only records the particle at one of them, so that decoherence in this case is not a feature of the particle itself. This could imply that decoherence is not as large a constraint on particle behavior as might have originally been thought, allowing more quantum degrees of freedom to be anticipated for molecules in nature.

I suggest, if you cannot take my word for it, that you read the article I sent you. It's written more for non-experts.

I suggest, if you cannot take my word for it, that you read the article I sent you. It's written more for non-experts. — Kenosha Kid

Is an "interference fringe" the interference pattern on the absorber or something else?

So an electron beam interferes with itself as it travels through a crystal or when divided by a metal filament, that's pretty certain. But the interference pattern can't account for why the particle shows up as a point on the screen instead of a wave. Looks like the double-slit experiment works with molecules having as many as two thousand atoms, so the postulated "interferes with itself" mechanism has not reached its limit, but seems dubious to me nonetheless.

Aye, it's a band of the pattern formed on the back screen. The key result of the paper is that only one electron is diffracted at a time, meaning that the electron wave must be interfering with itself, meaning it must be going through both slits.

The key result of the paper is that only one electron is diffracted at a time, meaning that the electron wave must be interfering with itself, meaning it must be going through both slits. — Kenosha Kid

How can a diffuse wave interfere with itself to form a single particle on the screen? It doesn't make any sense. What is the direct evidence of diffraction at both slits simultaneously?

How can a diffuse wave interfere with itself to form a single particle on the screen? — Enrique

I'm not sure what you mean by "to form a single particle on the screen". It interferes with itself. Not to do something: that's just what it does anyway.

Unless you just mean "how does it end up as a point on the screen?" That's the measurement problem described in the OP:

How the electron got from a field to a point is called the measurement problem, and different solutions to the measurement problem have yielded different interpretations of quantum mechanics. The oldest successful interpretation was the Copenhagen interpretation which states that, upon measurement, the electron wavefunction collapses probabilistically to a single position, the probability given by the absolute square of the wavefunction (the Born rule).

This idea of the absolute square is important. It is how we get from the non-physical wavefunction to a real thing, even as abstract as probability. Why is the wavefunction non-physical? Because it has real and imaginary components: u = Re{u} + i*Im{u}, and nothing observed in nature has this feature. The absolute square of the wavefunction is real, and is obtained by multiplying the wavefunction by its complex conjugate u* = Re{u} - i*Im{u} (note the minus sign). Remembering that i*i = -1, you can see for yourself this is real. We'll come back to this.

There are other probabilistic interpretations, and also some deterministic ones, such as Bohmian mechanics, wherein the electron always has a single-valued position and momentum (hidden variables), and Many-worlds interpretation in which the wavefunction does not collapse but, thanks to the mathematical rules of entanglement, you can never have a term in the wavefunction in which the electron hit the screen at position y but you observed it at position y′≠y. — Kenosha Kid

In the absence of obvious proof that the electron is diffracting through multiple slits simultaneously, I think my alternative explanation for the measurement problem might actually be accurate:

In the double-slit experiment a wave packet or "wavicle" travels through one or the other slits, but either option is equally probable across many trials, though fundamentally deterministic (thus far immeasurably so) in relation to a single wavicle. An apparent "interference pattern" is not generated by diffraction through the slits but rather produced by peaks of charge distribution along the absorber's surface rendered symmetrical by the slits, which initiate the various trajectories of wave packets in coordination with the emitter charge and determine the statistical range of possibility for endpoints. — Enrique

Its worth noting that the experiment requires very specific molecules to work at large masses, so hidden variables must exist. It works with a bucky ball, and there's no way one of those is divided in two by the slits, transcending its chemical bonds completely, to then recombine on the opposite side and end up as a point on the screen.

I'm suggesting the primary hidden variable is charge distribution in the double-slit chamber that materializes prior to the emitted particle reaching the slits, which parameterizes statistical distribution while determining the particle's trajectory in the same retarded/advanced wave manner as a lightning bolt. Do you find this explanation at all compelling?