What is causing destructive interference in double slit experiment?

[Addez123]

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.

 

[BvU]

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

 

[Meir Achuz]

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.

 

[scottdave]

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.

 

[PeroK]

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.

 

[Addez123]

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!

 

[PeroK]

It's ludicrious!

Are you talking about QM being ludicrous or your ignorance of it?

 

[Addez123]

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?

 

[Lord Jestocost]

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.

 

[BvU]

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

$\$

 

[vanhees71]

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/

 

[scottdave]

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

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

 

[BvU]

OP has quite a different problem ...

 

[phyzguy]

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.”

 

[vanhees71]

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]

@Addez123 how can PF help you ?

 

[malawi_glenn]

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?

 

[DrChinese]

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.

 

[Vanadium 50]

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?

 

[PeterDonis]

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.

 

[Chas Tennis]

You are asking a question that Quantum Mechanics never explains. What is going on?

I liked the way this situation was described in the Introduction of

Jean-Pierre Vigier and the Stochastic Interpretation of Quantum Mechanics 1st Edition
by Jean-Pierre Vigier (Author), Stanley Jeffers (Editor), Bo Lehnert (Editor), Nils Abramson (Editor), & 1 more

In other words, the math works but nobody knows why in 2023.

Some videos of Feynman lectures are good for this situation.

 

[Morbert]

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?

Let me give you a related scenario. I roll a die, and the chances of any die landing on "1" is 1/6. But if I roll two dice, the chances of any die landing on "1" increases to almost 1/3. We do not need to postulate some constructively interfering substance to explain this increase. We only need to note the change in preparation of our experiment (two dice instead of one) to understand how the dynamics will give rise to a change in probability.

The instrumentalist interpretation of QM says something similar: We do not need to postulate some destructively interfering substance to explain the decrease in probability. We only need to note the change in preparation (opening two slits instead of one).

 

[DaveE]

If we shoot single electrons, one at a time, from where is this interference coming from?

Why questions like this often don't have a satisfactory answer. That's just how the universe is. That is what we observe.

I think this Feynman lecture on YouTube would help you, he addresses your question precisely. Few people can explain this stuff better to laymen like us.

 

[lodbrok]

"Destructive interference" is just a heuristic explanation. Push it too far, and you get in trouble. Questions like the OP often lead to little clarity because they are questions about ontology, while Quantum Mechanics is not based on a single clear ontology.

When we do the calculations, we find that the terms cancel each other at some positions on the detector, which we call "destructive interference" at other positions; the terms add up ("constructive interference"). We do the measurements and find the final observed values match the results of our calculations. Still, there is no evidence from the experiments to suggest that individual steps in our calculations, including all those terms correspond to anything in the real world. All we know is that the final results match.

Different interpretations may ascribe different realities to the intermediate terms/steps and provide different answers that won't agree. They are all conjectures, not backed by experimental evidence. It would make more sense to ask what causes destructive interference according to a particular interpretation of QM. Ultimately, the question is really about what is the ontology of QM. To which the answer is there is no single universally accepted ontology. This does not stop us from using QM to reliably predict the outcomes of measurements.

 

[FallenStarFeatures]

In quantum mechanics, subatomic particle motion is described by the quantum wave function of the system under observation. This wave function is a collective superposition of all potential paths of all particles in the system. It is a complex-valued function defined not in 3D physical space, but instead in Configuration Space [1], an underlying domain of potentially limitless numbers of dimensions. The quantum wave function evolves over time according to Schrodinger's equation, which determines the weightings of the probability amplitudes in each particle's set of superpositions.

To determine the likelihood of observing a particular particle at a particular location, Born's Rule [2] is used to calculate the conjugate square of the components in each superposition at that particular location. Since these components are complex-valued, both positive and negative probability components can be produced during the application of Born's Rule. Where such bipolar components arise, they will mutually cancel out, producing destructive interference patterns in the particle's probability density map. The Double-Slit Experiment is an example of how these quantum interference patterns can be produced by physical obstacles in a particle's range of potential motion paths.

[1] https://link.springer.com/article/10.1007/s11229-015-0826-x
[2] https://philarchive.org/rec/DIKASP

 

[sillyputty]

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.”

Maybe he said that because he didn't want anyone else to figure it out. I mean, somebody is going to de-riddle this thing. Unfortunate that they won't be able to prove it by saying "And accordingly, I predict that the pattern will be terminated if you detect which slit a particle goes through". Unfortunate that they also won't be able to serve up the math which was informed/produced by their concept as to what is going on. Both those things are already established. Which brings me to ask: How could someone prove their theory true as to what is going on?

 

[phyzguy]

Maybe he said that because he didn't want anyone else to figure it out. I mean, somebody is going to de-riddle this thing. Unfortunate that they won't be able to prove it by saying "And accordingly, I predict that the pattern will be terminated if you detect which slit a particle goes through". Unfortunate that they also won't be able to serve up the math which was informed/produced by their concept as to what is going on (as in GR). Both those things are already established. Which brings me to ask: How could someone prove their theory true as to what is going on?

I think what you are searching for is a "hidden variable theory", which explains the mechanism of "what is going on" But it has been proven that this is not possible. We strongly suspect that it is not possible to "deriddle this thing" any more than what we already know. The universe behaves how it behaves, not how you think it should behave.

 

[sillyputty]

Coming up with a theory as to what is going on, does not mean that you are stating how nature should behave. That's not physics. Coming up with a theory as to what is going on, means proposing what is going on, whether you think it should be going on or not. On what is your suspicion based that it is not possible to come up with such a theory?

 

[phyzguy]

Well, try it. What exactly do you mean by "a theory as to what is going on"? Try to come up with an outline of what such a theory might look like. I think you will quickly find that it requires a version of local realism, which has been ruled out by experiment. But don't let me stop you. There is certainly a Nobel prize waiting for you if you succeed.

 

[sillyputty]

So you do not know what it means, yet you do feel that nobody could do it (do the thing you don't know what it means). You have not been making much sense here. And worth noting: any of the theoretical physicists who do try to understand nature will not be stopped by you. Not sure why you thought you could stop anyone.

 

[berkeman]

Lordy. Thread closed temporarily for Moderation...

 

[Nugatory]

Which brings me to ask: How could someone prove their theory true as to what is going on?

You don’t. Physics is an empirical science, and empirical sciences don’t prove that theories are true - it can’t be done. All that we can do is show that our theory is consistent with all experimental evidence so far, and it is helpful if our theory also makes predictions that are different from those of other proposed theories - then we can test the predictions to reject one or the other.

So any proposed theory of what is going in on (the technical term for such theories is, as @phyzguy says above, “hidden variable theories”) must be consistent with all available observational and experimental evidence so far. In particular, it must be consistent with the observed violations of Bell’s inequalities - and I strongly encourage you to read up on that, Googling for “Bell’s Theorem” would be a good start.

 

[berkeman]

Thread will remain closed. Thanks all.