# What is causing destructive interference in double slit experiment?

• B
TL;DR Summary
Shoot a single electron at a double slit and certain points will never be reached due to "destructive interference".

We shot 1 electron. So we have a single wave.
Therefore it makes no sense talking about destructive interference since that would require atleast 2 waves.
When you do the double slit experiment with photons or electrons you get a wave pattern.
At certain points no electrons are detected.

This is said to be caused by destructive interference.
Destructive interference of what? If we shoot single electrons, one at a time, from where is this interference coming from?
Is the electron splitting up into two waves when it "hits" the slits?
If its not two waves then it makes no sense talking about destructive interference.

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And what --- exactly ---- is a single wave in this scenario?

• Dale
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It's due to quantum mechanics. The motion of even a single electron, is wave motion given by a solution of the Schrödinger equation. The probability of where the electron hits the screen depends on the wave motion.
If the solution of the Schroeder equation shows zero wave function at a point, then even a single electron cannot reach that point.

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This is sort-of a layman's explanation. Before it "hits" the double slit, there is a single wave. The slits create 2 separate waves, which interfere with each other. Since electrons can behave like waves, we observe interference patterns in electrons as well.

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The electron interferes with itself, through probability amplitides. The wave model is more of a semi-classical version of QM, as in the de Broglie matter wave hypothesis.

And what --- exactly ---- is a single wave in this scenario?
A wave is described as a sinus shaped wave, the √ of the probability function. It's not described as two separate wave functions interacting with eachother.

Hypothetically, what happens if after the slit I separate the two areas with a sheet of paper. Now these "two waves" are forever separated and I should end up with two particles on the otherside. It's ludicrious! Homework Helper
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It's ludicrious! Are you talking about QM being ludicrous or your ignorance of it?

• Are you talking about QM being ludicrous or your ignorance of it?
To say that the beam "split up" yet demand that it results in a single beam. What exactly is happening is what Im asking. Is it actually two separate rays of light? Could an electron split in two? If not then shouldn't it always be able to be defined by a single wave function and not have to be the result of two interfering waves?

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To say that the beam "split up" yet demand that it results in a single beam. What exactly is happening is what Im asking. Is it actually two separate rays of light? Could an electron split in two? If not then shouldn't it always be able to be defined by a single wave function and not have to be the result of two interfering waves?
The formalism of quantum mechanics is a calculational recipe, designed to predict the probabilities of various directly observed macroscopic outcomes. Quantum probability is not the probability of where the electron is. It’s the objective probability of where you (or anyone) will find it when doing certain experiments. The formalism resists pictorial representations.

• DennisN
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A wave is described as a sinus shaped wave, the √ of the probability function. It's not described as two separate wave functions interacting with eachother.

Hypothetically, what happens if after the slit I separate the two areas with a sheet of paper. Now these "two waves" are forever separated and I should end up with two particles on the otherside. It's ludicrious! I can recommend reading the Feynman lectures.
There is a series of Feynman himself delivering quite accessible lectures at Auckland.
Patience and an open mind are helpful ##\ ##

• PeroK
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This is sort-of a layman's explanation. Before it "hits" the double slit, there is a single wave. The slits create 2 separate waves, which interfere with each other. Since electrons can behave like waves, we observe interference patterns in electrons as well.
I don't know, what you mean by "single wave". In non-relativistic quantum theory there's a single-particle wave function, obeying the Schrödinger equation. The solution describing a particle (e.g., an electron) with pretty well determined momentum moving to through a double slit is given (approximately) by Huygens's principle, and that's how interference and diffraction is described. It's pretty much the same as in classical electrodynamics.

The difference is the meaning of the wave function, i.e., in quantum theory ##|\psi(t,\vec{x})|^2## is the probability-density distribution for the position of the particle, i.e., each single electron leaves one spot on the screen with a probability given by the solution of the Schrödinger equation described above. If you repeat the experiment with equally prepared electrons very often, you'll see the expected diffraction pattern to be built up according to this probability distribution:

https://physicsworld.com/a/the-double-slit-experiment/

• PeroK
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I admit it was not my best attempt at an analogy @vanhees71

My thinking was a wavefront, like from a single antenna source.

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OP has quite a different problem ...

I like this quote from Feynman,
"Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that? ' because you will get 'down the drain', into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”

• DennisN
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OP has quite a different problem ...
Which is? I had the impression that he has some misconception about the wavefunction and its meaning. It should be clear that there is a wave function and that's it. It's not a "single wave" or something that "requires two waves".

For the intuitive picture just think in terms of wave fields, and here you can think in terms of Huygen's principle (which is just the intuitive result for a retarded Green's function of the Helmholtz equation in 3D space).

Then you have to think about the interpretation of the wave function, which is probabilistic referring to the probability density of the particle to be found at ##\vec{x}## when measured at time ##t## to be ##|\psi(t,\vec{x})|^2##.

That's also the escape of this unfortunate quote from Feynman. He is right in saying that thinking about something "behind the probabilistic interpretation" is a blind alley. According to all we know after 98 years of modern quantum theory there's nothing else behind than the probabilities. Nature on the fundamental level behaves randomly in the exact sense QT tells us it does. That it's strange to our intuition, which is trained from the experience with macroscopic bodies, which behave (according to quantum statistical physics!) classically, is no surprise!

• BvU
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• Homework Helper
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A wave is described as a sinus shaped wave, the √ of the probability function. It's not described as two separate wave functions interacting with eachother.

Hypothetically, what happens if after the slit I separate the two areas with a sheet of paper. Now these "two waves" are forever separated and I should end up with two particles on the otherside. It's ludicrious! Which two areas? Can you draw a picture?

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To say that the beam "split up" yet demand that it results in a single beam. What exactly is happening is what Im asking. Is it actually two separate rays of light? Could an electron split in two? If not then shouldn't it always be able to be defined by a single wave function and not have to be the result of two interfering waves?
If you place a barrier between the 2 halves, then you will NOT get interference. And you get 1 dot (detection), never 2 associated with a single particle entering the apparatus. This is a specific prediction of QM.

Considering specifically the case of a single photon: interference tends to highlight the so-called wave nature of light (or of any quantum particle or system actually). The different potential "paths" can produce interference effects. But the particle nature is still present, and there is conservation rules still in effect. If you know 1 particle goes in, then only 1 particle is ever detected... as the following experiment demonstrates:

http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf
Abstract: While the classical, wavelike behavior of light ~interference and diffraction! has been easily observed in undergraduate laboratories for many years, explicit observation of the quantum nature of light ~i.e., photons! is much more difficult. For example, while well-known phenomena such as the photoelectric effect and Compton scattering strongly suggest the existence of photons, they are not definitive proof of their existence. Here we present an experiment, suitable for an undergraduate laboratory, that unequivocally demonstrates the quantum nature of light. Spontaneously downconverted light is incident on a beamsplitter and the outputs are monitored with single-photon counting detectors. We observe a near absence of coincidence counts between the two detectors—a result inconsistent with a classical wave model of light, but consistent with a quantum description in which individual photons are incident on the beamsplitter.

In other words: one particle, one detection, regardless of whether interference is present or not. Yes, it is difficult to draw a mental picture of what is occurring. But as has been pointed out several times above, the math says it all.

• Lord Jestocost and vanhees71
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I despair of helping the OP - what he has written so far suggests that all he knows of QM is that he doesn't like it. However, assuming we can get past this...

OP, do you have a problem with the double-slit experiment for light? If so, we should back up and address that first. If not, in what way is repeating this with other experiments different?

• DennisN, vanhees71 and PeroK
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Destructive interference of what?
Probability amplitudes. That's always where interference comes from in QM.

If we shoot single electrons, one at a time, from where is this interference coming from?
The probability amplitudes for the electron reaching a particular point on the detector screen through each of the two slits.

Is the electron splitting up into two waves when it "hits" the slits?
This is a common heuristic description, but it can be misleading. The electron wave function is a single function, but in the region of space behind the slits this single function is a sum of two terms, giving the amplitude for the electron to reach a given point in space through each of the two slits. If the two terms sum to zero at a particular point, we say that destructive interference prevents the electron from being detected at that point.

If its not two waves then it makes no sense talking about destructive interference.
This is much too simplistic. See above.

• • berkeman, vanhees71 and PeroK