How can you be in two places at once
When you’re not anywhere at all
— Firesign Theater
[Note: this is NOT original research. I just read the right book]
The famous double slit experiment is an unfathomably deep mystery, any number of people will tell you. People who should know. Experts.
Briefly, you shoot a beam of particles at a screen with vertical slits in it (maybe only two 
slits) and when they hit a detector screen on the other side you get a diffraction pattern. As if the beam were waves instead of particles. Even when you send one particle at a time.
Mysterious … as Feynman says
“I will take just this one experiment, which has been designed to contain all of the mystery of quantum mechanics, to put you up against the paradoxes and mysteries and peculiarities of nature one hundred per cent. Any other situation in quantum mechanics, it turns out, can always be explained by saying, ‘You remember the case of the experiment with the two holes? It’s the same thing’.”
The experiment has been in the news again. Recently, the Scientific American reported that
Now, in a paper published Sept. 23 in the journal Nature Physics, an international team of researchers has caused a molecule made up of up to 2,000 atoms to occupy two places at the same time.
What actually happened was that a team managed to successfully carry out the slit experiment with a beam of these huge molecules. Despite their size, a diffraction pattern showed up (I don’t doubt the experiment).
What many don’t realize is that the double slit experiment (with particles), proposed by Feynman in 1963, was for decades only a thought experiment. Finally, in 2013, it was successfully performed with electrons. It’s easy to see why it took so long: the slits were 62 billionths of a meter apart.
Like everyone else I was absolutely baffled by this phenomenon. But I never bought the so-called explanations. I didn’t believe that particles are at the same time waves, or that particles are accompanied by waves, or that the particles clone themselves and are in two places at once to interfere with themselves. And I certainly didn’t believe the more outlandish ones, e.g. that the universe splits in two etc.
Alfred Lande (1888-1976), German-US theoretical physicist.
Anyway, one day I’m browsing in the physics shelves of Warwick University library and this book New Foundations of Quantum Mechanics caught my eye. The author is Alfred Landé, one of the pioneers of quantum mechanics.
What a revelation! Landé argues that waves are waves and particles, in particular electrons, are particles. The fact that waves sometimes behave like particles, and particles like waves, is remarkable and important but does not change this basic fact. He rejects “dualism” – the wave/particle duality approach that says that electrons are both waves and particles at the same time. Whatever that would mean.
What about the two slit experiment? It turns out that there is a simple explanation using a well established but usually overlooked rule of quantum mechanics, namely Duane’s Law (I don’t know why Wikipedia calls it a “hypothesis”).
To understand the law, consider the slit experiment. An electron heads for the slitted screen and emerges on the other side – usually, not heading in the same direction. The electron’s momentum has changed – it has interacted with the screen and exchanged momentum with it. In particular is has exchanged momentum in the direction parallel to the screen and perpendicular to the slits.
Classically, any amount of momentum is possible meaning the electron could head in any direction with straight ahead being most probable. But Duane’s Law says this is not what happens.
Duane’s Law says that if a body is periodic in space in a given direction then momentum exchanges in that direction are quantized. That means that the emerging electron is more likely to go in certain directions than in others, depending on how many quanta of sideways momentum are exchanged. Guess what? When a stream of electrons is sent through, a ‘diffraction’ pattern results.
Duane and Landé, and others after them, have worked out the details and the pattern is quantitatively exactly what you get from a wave model. Duane and Landé have explained the slit experiment without resort to guide waves, wave particle duality, or multiple universes. Or to bodies being in two places at once.
In fact, I regard the slit experiments as experimental confirmation of Duane’s law.
Admittedly there’s still a bit of mystery left. How does periodicity in space quantize momentum (I think if it as a sort of resonance phenomenon). But it’s hardly an impenetrable, soul searing mystery that makes you question reality itself.
So how come hardly anybody knows about this? Landé himself asked this question. He called it a “closely guarded secret” and said he’s searched through the works of Bohr, Dirac, Pauli, and many others and found not a trace. It is inconceivable that Feynman didn’t know about Duane.
Duane’s become a nonperson. Possibly, Landé is wrong about something and everybody knows. But I’ve never seen a rebuttal; just silence. Recently Anil Ananthaswamy published a whole book, Through Two Doors at Once, about the two slit experiment, the experiment that “captures the enigma of our quantum reality”. Neither Duane nor Landê are mentioned; their names are not in the index.
One can only speculate why Duane’s explanation is such a secret … but it has two consequences. (1) it makes scientists seem superhuman, able to work with contradictory models and somehow know which to choose in a particular situation; and (2) it sends the message that ordinary people with ordinary, finite, rational brains, can’t grasp science any more. So don’t even try.
I can see that this narrative suits certain elite sectors of the population. Widespread knowledge of the Duane/Landé explanation would let the air out of quite a few tires. So it ain’t gonna happen (despite this post).
What about the rest of QM? There are many more phenomena that are on the face of it mysterious. I don’t have explanations for all of them but I believe they can all eventually be cleared up. I think Feynman was (ironically) correct when he said
Any other situation in quantum mechanics, it turns out, can always be explained by saying, ‘You remember the case of the experiment with the two holes? It’s the same thing’
Bill Wadge's Blog 
So why does the pattern change if I have knowledge of which slit the electron went through? Experiment suggests that simply having the knowledge – not any physical act of measuring that might disturb the electron – causes the change. Where does that fit in with this explanation?
The following experimental proof seems to show that this question is no more relevant.
Experimental evidence, satisfying the Einstein-Podolsky-Rosen criterion for physical reality, for Einstein’s Einweg point of view, by N Umakantha, Nuovo Cimento. B 124 (12), 1191-1196
For ready reference, abstract of the paper reads as follows:
A real Young’s double-slit experiment which can, without destroying the fringe pattern, establish unequivocally whether a photon passes like a wave along both the paths or passes like a particle along one or the other path only, is presented. The main feature of this experiment is that the point at which the incident wave is to be regarded as being split into two parts to go along the two paths is distinct from the point at which successive incident particles are to be regarded as having random choice to go along one or the other path. Our experimental results support Einstein’s Einweg (one-path) point of view.
If Duane was right, then wouldn’t we get the same interference pattern with a single slit?
I feel the issue of wave-particle duality stems from the root of the equations. KE vs PE. It’s literally describing an object in two different states.
I’m not sure why people are amazed by interference patterns. We are literally doing the experiment on a giant magnet that is constantly in flux, adding the giant magnet has a gravitational force providing scattering.
Slight temperature variations lead to pressure variations which in turn lead to velocity changed.
There is a reason to even get a quantum computer to work we need to protect it against all kinds of interference.
Error correction is one of the biggest issues with large scale qbit entanglements.
“I’m not sure why people are amazed by interference patterns.”
Because when they fire off one electron at a time, the interference pattern is still generated. If one is thinking of an electron as a single object that will pass through only one of the slits, then this is amazing.
That’s why. The ability to understand what other people are thinking is very useful and something anyone should to cultivate.
I don’t understand why this is so shocking to anyone. Surely the angle determines where they land.
If you place a coin on its edge does it magically choose a side?
Does an electron not oscillate? Can we control that oscillation?
Being able to think for yourself is a very useful and something anyone should cultivate.
Hey, thanks for your post. I came across it from Hacker News and I find it very interesting. To be honest, I’m not a physics expert in the slightest. But I am very interested and have seen a lot of research into quantum mechanics, yet I’ve never come across Duane’s hypothesis (just going say what wiki says)… So I find this particularly interesting. Again, not an expert, so the maths is beyond me, but I have think there may be a contradiction with Duane’s hypothesis and experimental data.
Duane’s analysis seems to rebukes the assertion that the diffraction pattern of single-shot elections arises from an apparent “interference with itself”. However, it doesn’t seem to account for the situation in which we place detector’s at the slits; no interference pattern. Maybe Duane’s hypothesis does account for it because the detector imparts some kind of energy to the electron? Perhaps, but consider the results of an experiment with a passive detector (one that does not impart energy). I can’t find the particular experiment that I’m thinking of, but the results were the same in that there was no interference pattern.
Am I missing some fundamental information here that could be explained by the maths, or is this actually a contradiction with Duane’s hypothesis?
Why does no one learn this? My guess is that Duane’s model is, like the Bohr model of the atom, fine as far as it goes, but has been superseded by modern quantum theory. It emerges as a corollary of the QM of the 1930s and so we don’t need to learn it any more.
My view of QM being mysterious is that quantum computing/information gives an intuitive way of understanding a lot of it. It is also always going to be a bit counter-intuitive since in our daily lives we experience information as being classical.
In the context of this discussion it is necessary to take note of the following experimental research paper which shows that photon is particle only. Somehow, the paper has not reached many.
Experimental evidence; satisfying the Einstein-Podolsky-Rosen criterion for physical reality, for Einstein’s Einweg point of view, by N Umakantha, Nuovo Cimento. B 124 (12), 1191-1196
For ready reference, abstract of the paper reads as follows:
A real Young’s double-slit experiment which can, without destroying the fringe pattern, establish unequivocally whether a photon passes like a wave along both the paths or passes like a particle along one or the other path only, is presented. The main feature of this experiment is that the point at which the incident wave is to be regarded as being split into two parts to go along the two paths is distinct from the point at which successive incident particles are to be regarded as having random choice to go along one or the other path. Our experimental results support Einstein’s Einweg (one-path) point of view.
Also remarkable is the following monograph, in which the same author presents a new approach to non-relativistic quantum mechanics.
Physical Principles of Quantum Mechanics (In Agreement with Einstein’s Views),
N. Umakantha, Scientific Research Publishing
https://www.scirp.org/book/DetailedInforOfABook.aspx?bookID=2496