[RobC (OP)]

Like so many people I am fascinated by the double slit experiment. One of its most baffling features is what happens when electrons are fired one at a time. I would have thought that an interference pattern could not be produced in this situation.

[chiralSPO]

The counterintuitive part here is that an electron can interfere with itself.

[alancalverd]

Or not. It pays to be really pedantic about this.

We can model the received pattern as the interference between waves, but a single electron, photon, or any other particle, can't "partially interact" with the detector - there is no continuum of charge, mass or energy  that will allow say 10% of one incoming electron to strike the middle of the detector whilst  5% appears on either side, ad infinitum.

If you can generate and detect a single particle (and we have cascade multipliers that can) you find that each incoming particle only arrives at one point. What we record as an "interference pattern" is the sum of the probability distributions of a whole lot of particles over time. 

[stacyjones]

In de Broglie's double solution theory there are two waves. There is the wave-function wave which is statistical, non-physical and is used to determine the probabilistic results of experiments. It is a mathematical construct only. It doesn't physically exist. There is also a physical wave in a hidden "subquantic medium" which guides the particle.

John Stewart Bell
en.wikiquote.org/wiki/John_Stewart_Bell

While the founding fathers agonized over the question 'particle' or 'wave', de Broglie in 1925 proposed the obvious answer 'particle' and 'wave'. Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.

NON-LINEAR WAVE MECHANICS A CAUSAL INTERPRETATION by LOUIS DE BROGLIE

Since 1954, when this passage was written, I have come to support wholeheartedly an hypothesis proposed by Bohm and Vigier. According to this hypothesis, the random perturbations to which the particle would be constantly subjected, and which would have the probability of presence in terms of [the wave-function wave], arise from the interaction of the particle with a “subquantic medium” which escapes our observation and is entirely chaotic, and which is everywhere present in what we call “empty space”.

"The interaction of the particle with a “subquantic medium”" is another way of describing a strongly interacting dark matter.

Dark matter is not a clump of weakly interacting stuff that travels with the matter. Dark matter fills the space unoccupied by particles of matter and is displaced by the particles of matter that exist in it and move through it.

'Interpretation of quantum mechanics by the double solution theory - Louis de BROGLIE'
aflb.ensmp.fr/AFLB-classiques/aflb124p001.pdf

When in 1923-1924 I had my first ideas about Wave Mechanics I was looking for a truly concrete physical image, valid for all particles, of the wave and particle coexistence discovered by Albert Einstein in his "Theory of light quanta". I had no doubt whatsoever about the physical reality of waves and particles.

any particle, even isolated, has to be imagined as in continuous “energetic contact” with a hidden medium

The hidden medium of de Broglie wave mechanics is the strongly interacting dark matter.

For me, the particle, precisely located in space at every instant, forms on the v wave a small region of high energy concentration, which may be likened in a first approximation, to a moving singularity.

A particle may be likened in a first approximation to a moving singularity which has an associated wave in the strongly interacting dark matter.

the particle is defined as a very small region of the wave

The particle occupies a very small region of the associated wave in the dark matter.

Wave-particle duality is a moving particle and it's associated wave in the strongly interacting dark matter.

In a double slit experiment the particle travels through a single slit. It is the associated wave in the strongly interacting dark matter which passes through both. As the wave exits the slits it creates wave interference. As the particle exits a single slit the direction it travels is altered by the wave interference. This is the wave guiding the particle. Strongly detecting the particle causes a loss of cohesion between the particle and its associated wave, the particle continues on the trajectory it was traveling and it does not form an interference pattern.

The wave of wave-particle duality is a wave in the strongly interacting dark matter which fills 'empty' space.

[alancalverd]

Strongly detecting the particle causes a loss of cohesion between the particle and its associated wave, the particle continues on the trajectory it was traveling and it does not form an interference pattern.

And yet, when we "strongly interact" by putting a fluorescent plate or photographic film behind the slits, we see what looks like an interference pattern. How sad that the experiment does not support the theory.

[stacyjones]

And yet, when we "strongly interact" by putting a fluorescent plate or photographic film behind the slits, we see what looks like an interference pattern.

If you "strongly interact" with the particle prior to it arriving at the detection screen you destroy the particles cohesion with its associated wave in the strongly interacting dark matter and the particle no longer creates and interference pattern. For example, if you detect the particle as it exits the slit you destroy its cohesion with its associated wave exiting both slits and the particle will not create an interference pattern. If you are detecting the particle after it has been guided by its associated wave exiting both slits then the particle will build up to form an interference pattern over time.

en.wikipedia.org/wiki/File:Double-slit_experiment_results_Tanamura_2.jpg

I recommend you watch all of the following video. The double slit experiment is at the 2:43 mark.

youtube.com/watch?v=W9yWv5dqSKk

[evan_au]

"The interaction of the particle with a “subquantic medium”" is another way of describing a strongly interacting dark matter.
Dark matter is not a clump of weakly interacting stuff that travels with the matter. Dark matter fills the space unoccupied by particles of matter and is displaced by the particles of matter that exist in it and move through it.

De Broglie managed to describe the self-interference effect of an electron as a wave aspect of the electron (and in fact, any particle).
These wavicles have a very short range for an electron, and even shorter for more massive particles like protons and lead nuclei, let alone a galaxy.

De Broglie did this well before anomalous rotation curves of galaxies or the patterns of light bending around galaxies were discovered, ie all the symptoms we associate with Dark Matter. These are all extremely long-range phenomena, spanning the visible width of a galaxy, and several times wider.

Occam's Razor suggests that if you have two hypotheses with equal predictive power, you prefer the one with fewer assumptions. De Broglie's model does not have any assumptions about Dark Matter, so clearly it is the simpler one.

However, if you have a hypothesis with no predictive power, you don't even apply Occam's Razor. We don't know the short-range properties of Dark Matter, so it can't predict electron diffraction.

Even worse, if a hypothesis predicts the wrong result, you can immediately discard it. De Broglie's  wavicles have an incredibly short range, but the effects of Dark Matter span a long distance outside a galaxy.

If Dark Matter were strongly interacting, we would have discovered it long ago. At present, we don't know what it is (although there are lots of educated guesses).

This "Dark Matter causes electron diffraction" hypothesis is incompatible with the evidence. Forget it.

[alancalverd]

then the particle will build up to form an interference pattern over time.

This is logically impossible. The particle is travelling at a considerable speed (c in the case of photons) and can't move sideways or hang around waiting to interact with itself over time. A single electron or light photon does not have sufficient energy to generate a signal by interacting with a fluorescent screen or photographic film at more than one point, yet the received pattern (generated over time) occupies space.

Wave mechanics describes and predicts the effect, but cannot be said to be the cause. 

[stacyjones]

Occam's Razor ...

Occam's razor: 'Empty' space has mass which is displaced by matter.

What ripples when galaxy clusters collide is what waves in a double slit experiment, the mass which fills 'empty' space.

Einstein's gravitational wave is de Broglie's wave of wave-particle duality, both are waves in the mass which fills 'empty' space.

The mass which fills 'empty' space displaced by matter relates general relativity and quantum mechanics.

[stacyjones]

This is logically impossible. The particle is travelling at a considerable speed (c in the case of photons) and can't move sideways or hang around waiting to interact with itself over time. A single electron or light photon does not have sufficient energy to generate a signal by interacting with a fluorescent screen or photographic film at more than one point, yet the received pattern (generated over time) occupies space.

Wave mechanics describes and predicts the effect, but cannot be said to be the cause.

then the particles will build up to form an interference pattern over time.

en.wikipedia.org/wiki/File:Double-slit_experiment_results_Tanamura_2.jpg

[PmbPhy]

The counterintuitive part here is that an electron can interfere with itself.

I know that is what most, if not all, physicists hold to be the case. However I myself would never speak of it in such terms. The reason for my position is that such a self-interference of a single particle with itself cannot be observed. It's not even clear to me what it means in practice. I know that it sounds nice and comfortable to speak of it that way but I have my reasons to disagree, and I hold that these reasons are strong. Here's my reasoning. Take a single particle and fire it at a double slit screen such as the one in Young's double slit experiment. The particle will strike the screen at one single location. In that experiment there is no evidence of a particle interfering with itself. If we have a large ensemble of identical setups there will be a pattern which emerges when we compare the results from all experiments. That does not imply that the particle interferes with itself.

So why is there a pattern? What determines the geometry of the pattern? There's a pattern because the double slit is in reality a potential well. The shape of the potential well determines what the wave function will be.

When you studied quantum mechanics and potential wells and found the wave function did it really occur to you that the wave function is the particle interfering with itself? I know that I never though of it in those terms. All the wave function does is determine the probability of where a particle will be found. The amplitudes of those functions interfere but its not a physical interference in my opinion but a mathematical one.

Frankly I can't believe that so many physicists interpret the wave function and the patterns it predicts to be a particle acting on itself. What could possibly be the mechanism behind such a thing?

Another thing that a lot of physicists believe, and I'm not talking about 3rd rate physicists but top notch ones such as Roger Penrose. In one of his books he says that an electron can be in two places at once. That is outrageously wrong. The difference in this case is that he's wrong and its not a matter of opinion. It's a terrible misinterpretation of the physical meaning of the wave function. Some physicists speak of the electrons in an atom as being smeared out in the space surrounding the nucleus of the atom and that's why they think that way. However that viewpoint is terribly wrong. The wave function only tells you what the chances are of finding a particle at a particular location. Before the particle's position is measured one can't even speak of it as being somewhere.

I spoke to several top notch physicists and they agree with my interpretation and agree with the essence of what I just said. That's not a proof at all. I mention it so that nobody gets the idea that I'm alone in this position and it's I who is wrong. I'll probably write a paper on this some day.

I'm almost certain that a lot of people are going to stomp on me for what I wrote above and I fully understand it and even encourage it. I'm always interested in hearing other peoples views. I like to keep an open mind. Who knows. Perhaps you'll convince me I'm wrong. ]

Let the stomping begin. Lol!

[jeffreyH]

Pete I generally tend to take notice of what several people say on this forum. Among these are you, Alan, Evan, Chiral and Colin. If I have missed anyone my apologies. It's a pity others don't do the same. Where else would you get scientists willing to listen to plebs like us?

[alancalverd]

then the particles will build up to form an interference pattern over time.

Exactly my point. The wave function describes the probability of a particle being in any given place, so eventually a sufficient number of particles will have appeared at the places predicted by the wave function, that it looks like an interference pattern. But a single electron can only form a single point on that pattern - it can't "interfere with itself" or spread out and appear partially in several places at once.

If you want the long form of the argument, read Pete's reply. Just for once, we are in agreement about something!

[stacyjones]

Exactly my point. The wave function describes the probability of a particle being in any given place, so eventually a sufficient number of particles will have appeared at the places predicted by the wave function, that it looks like an interference pattern. But a single electron can only form a single point on that pattern - it can't "interfere with itself" or spread out and appear partially in several places at once.

Exactly. Wave-particle duality is a moving particle and it's associated wave in the aether. The part always travels through a single slit and the associated wave in the aether passes through both.

[alancalverd]

So you keep saying, but the aether concept, and wave-particle duality,  doesn't explain anything better than quantum mechanics, which does not require this imaginary drivel, and also explains the existence of atoms, the shape of molecules, the photoelectric effect, the black body spectrum, lasers, masers, and how this computer works.

Why mess about with a useless, unnecessary, discredited and outdated fantasy? 

[stacyjones]

So you keep saying, but the aether concept, and wave-particle duality,  doesn't explain anything better than quantum mechanics, which does not require this imaginary drivel, and also explains the existence of atoms, the shape of molecules, the photoelectric effect, the black body spectrum, lasers, masers, and how this computer works.

Why mess about with a useless, unnecessary, discredited and outdated fantasy?

Because it's what waves in terms of wave-particle duality.

[agyejy]

Being the devil's advocate here you can measure quantum wavefunctions (at least square magnitudes) many different ways. The following link is about one direct method and mentions some indirect ones:

http://physics.aps.org/articles/v6/58

Beyond that delocalization can have observable physical consequences. For example:

http://physics.aps.org/articles/v9/43

Where the very shape of the water molecule is predicted to change due to the delocalization its hydrogen atoms.

Now none of this is supports the concept of an aether. However, to dismiss the quantum mechanical wavefunction as purely mathematical does a great disservice to many experimentalists who've done very clever things to prove that the opposite.

Here is some more work to support the reality of the wavefunction:

http://www.nature.com/nphys/journal/v11/n3/full/nphys3233.html

In my opinion it is best to give up on both classical wave and classical particles and accept that the waves of quantum mechanics have properties that aren't like either classical waves or classical particles. In short there isn't a wave particle duality there is just the wavefunction which has properties that we associate with classical waves and properties that we associate with classical particles. It isn't a wave under some cases and a particle under others. Nor is it somehow a wave and a particle at the same time. it is an entirely different entity that has both what we would call wave and particle properties. This is particularly surprising as it isn't the first time out classical notions have proven insufficient.

[stacyjones]

Being the devil's advocate here you can measure quantum wavefunctions (at least square magnitudes) many different ways. The following link is about one direct method and mentions some indirect ones:

http://physics.aps.org/articles/v6/58

Beyond that delocalization can have observable physical consequences. For example:

http://physics.aps.org/articles/v9/43

Where the very shape of the water molecule is predicted to change due to the delocalization its hydrogen atoms.

Now none of this is supports the concept of an aether. However, to dismiss the quantum mechanical wavefunction as purely mathematical does a great disservice to many experimentalists who've done very clever things to prove that the opposite.

Here is some more work to support the reality of the wavefunction:

http://www.nature.com/nphys/journal/v11/n3/full/nphys3233.html

In my opinion it is best to give up on both classical wave and classical particles and accept that the waves of quantum mechanics have properties that aren't like either classical waves or classical particles. In short there isn't a wave particle duality there is just the wavefunction which has properties that we associate with classical waves and properties that we associate with classical particles. It isn't a wave under some cases and a particle under others. Nor is it somehow a wave and a particle at the same time. it is an entirely different entity that has both what we would call wave and particle properties. This is particularly surprising as it isn't the first time out classical notions have proven insufficient.

In de Broglie's double solution theory there are two waves. There is the wave-function wave which is statistical non-physical and is used to determine the probabilistic results of experiments. It is a mathematical construct only. It doesn't physically exist. There is also a physical wave in a hidden subquantic medium which guides the particle. Classical notions are sufficient.

[alancalverd]

Classical notions are sufficient.

But completely unnecessary, nonpredictive, and selfcontradictory.

[stacyjones]

Classical notions are sufficient.

But completely unnecessary, nonpredictive, and selfcontradictory.

In a double slit experiment the particle always detected traveling through a single slit because it always travels through a single slit is not contradictory.