Why do we get an interference pattern in a double slit experiment?

[Fiziqs]

This is another one of those things that I had always assumed to have a very simple explanation. After all, I've seen so many simulations of waves interfering with each other and forming the distinctive interference pattern, and even watched the patterns emerge in actual water waves. The pattern was so familiar that I didn't even bother to give it any thought when I was told that the pattern produced by a double slit experiment is caused by interference. The pattern is there, it looks just like an interference pattern, so logically it's caused by interference.

But then in one of those moments of either enlightenment or confusion, I'm not sure which, the whole idea of an interference pattern in the double slit experiment seemed to make no logical sense at all, and here's why. When you watch a simulation of the double slit experiment, they will invariably show a series of waves being produced by the double slits, but if you're sending particles through one at a time, why are you getting a series of waves? Shouldn't you be getting just one wave from each slit? And one wave propagating from each of two slits isn't going to produce the familiar interference pattern is it? So where does the interference pattern come from? Or alternatively, where does the series of waves come from?

Obviously there's something that I'm missing, but I have no idea what it is. If someone could explain the flaw in my reasoning I would appreciate it.

Thanks

 

[DrChinese]

When you watch a simulation of the double slit experiment, they will invariably show a series of waves being produced by the double slits, but if you're sending particles through one at a time, why are you getting a series of waves? Shouldn't you be getting just one wave from each slit? And one wave propagating from each of two slits isn't going to produce the familiar interference pattern is it?

One "wave" propagating from each slit does not yield the familiar pattern because there will only be one blip on the screen. A series of waves - they can be as far apart in time as you like - will build up to the pattern. That is because the probability of hitting somewhere does follow the pattern, even for one particle.

But just as with a pair of dice, you cannot see that 7 is the most likely value from 1 roll - you cannot see the familiar interference pattern from a single iteration.

 

[dauto]

but if you're sending particles through one at a time, why are you getting a series of waves?
Thanks

The wave passes through both holes even if there is only one particle. That's QM.

 

[Fiziqs]

One "wave" propagating from each slit does not yield the familiar pattern because there will only be one blip on the screen. A series of waves - they can be as far apart in time as you like - will build up to the pattern. That is because the probability of hitting somewhere does follow the pattern, even for one particle.

Thanks for the answer DrChinese, but it didn't really address the question. Which means that I probably did a poor job of expressing it. I was indeed aware that the pattern needs to build up over time, but the real question is, why does the "cumulative" result show an interference pattern, if each individual particle doesn't interfere with anything, not even itself. Thus where does the cumulative interference pattern come from?

The accepted answer is that the particle passes through both slits and interferes with itself, but how can this happen if it requires a series of waves to create an interference pattern, and since each particle is passing through the apparatus as one discrete "set" of waves, then there is no "series" of waves for it to interfere with.

Like I said this is something that I had never even considered before. I had always just accepted the standard explanation, it's an interference pattern, but an interference with what, if it can't be interfering with itself?

Two single discrete waves, propagating one from each slit, should be incapable of interfering with each other in the manner necessary to produce the cumulative interference pattern that is commonly observed.

I'm still not sure that I have expressed this question clearly enough, but hopefully someone will see what I'm trying to get at and provide me with a logical explanation.

The wave passes through both holes even if there is only one particle. That's QM.

Yes, but even if it travels through both holes, unless there is a series of waves you can't produce an interference pattern. Two discrete waves propagating one from each slit won't interfere with each other in the manner that the cumulative pattern displays.

I do realize that the cumulative result is an interference pattern. But my question is why?

 

[TheFerruccio]

Think of it in terms of Heisenberg Uncertainty Principle. If you fire a localized wave along a string, there is very little that you can say about its wavelength. If you fire a single photon out of a beam emitter, and you *know* precisely when that photon was launched, then there is nothing you can say about that photon's energy. In fact, if you could make such a gun that precisely fired photons in an absolutely deterministic way, I would surmise that you wouldn't get an interference pattern.

The interference pattern arises from the nondeterministic properties of the light being shone upon the double slits. For instance, for a green laser shining at 435nm, with the power pumped into the laser turned waaaaay down, it can be precisely known what a photon's energy is, but there is little that can be said about when that photon will be spontaneously emitted from the laser. Nothing can be said about where a photon is between the laser and the wall the photon will inevitably hit. This allows the energy of different photons to be known with accuracy, and you will see the resulting interference pattern, even with one or two photons.

I suppose, like any attempt to explain a quantum phenomenon through classical analogy, the "interferes with itself" phrase falls short and is misleading. You can't say anything about what that photon is doing until it hits the wall. Before that point, there is a wide variety of possibilities for what that photon is doing, and each possibility has a different associated probability.

 

[Fiziqs]

The interference pattern arises from the nondeterministic properties of the light being shone upon the double slits. For instance, for a green laser shining at 435nm, with the power pumped into the laser turned waaaaay down, it can be precisely known what a photon's energy is, but there is little that can be said about when that photon will be spontaneously emitted from the laser. Nothing can be said about where a photon is between the laser and the wall the photon will inevitably hit. This allows the energy of different photons to be known with accuracy, and you will see the resulting interference pattern, even with one or two photons

Thanks TheFerruccio, that solves the problem completely. I hadn't considered the indeterminacy of the when. The indeterminacy of the when, leads to an indeterminacy of the where, which leads to the wave being able to be at various locations along its path. Pretty simple now that you point it out.

I knew that I was overlooking something, but heck if I could figure it out myself. Thank you for understanding the question, and providing a clear and simple answer.

 

[San K]

Like I said this is something that I had never even considered before. I had always just accepted the standard explanation, it's an interference pattern, but an interference with what, if it can't be interfering with itself?

Two single discrete waves, propagating one from each slit, should be incapable of interfering with each other in the manner necessary to produce the cumulative interference pattern that is commonly observed.

I'm still not sure that I have expressed this question clearly enough, but hopefully someone will see what I'm trying to get at and provide me with a logical explanation.

Yes, but even if it travels through both holes, unless there is a series of waves you can't produce an interference pattern. Two discrete waves propagating one from each slit won't interfere with each other in the manner that the cumulative pattern displays.

I do realize that the cumulative result is an interference pattern. But my question is why?

Do you mean a bunch/couple of waves from each slit (at the same time)?

...instead of one single wave from each slit?

and those waves then interfering with each other?Maybe this will help: There is interference even in a single slit, single photon experiment...at the edges

As Feynman put it - assume light (photon) travels all possible paths...at the least...for calculation purposes.

 

[zonde]

The wave passes through both holes even if there is only one particle. That's QM.

That's Pilot wave interpretation.
QM says wavefunction passes through both slits and if wavefunction describes single particle then single particle passes through both slits (basically oximoron).

 

[zonde]

Thanks TheFerruccio, that solves the problem completely. I hadn't considered the indeterminacy of the when. The indeterminacy of the when, leads to an indeterminacy of the where, which leads to the wave being able to be at various locations along its path. Pretty simple now that you point it out.

Would you care to tell how it solved the problem for you?
Do you mean that particle interferes with other particles passing through the other slit even so they are not detected at the same time? Or some different way?

 

[Rena Cray]

I think to myself "if these folks would stop thinking of the "photon" did this, or the "electron" did that, you quantum philosophers would get somewhere.

 

[San K]

But just as with a pair of dice, you cannot see that 7 is the most likely value from 1 roll - you cannot see the familiar interference pattern from a single iteration.

I got 3.5, how did you get 7?...:)

 

[bhobba]

but the real question is, why does the "cumulative" result show an interference pattern, if each individual particle doesn't interfere with anything, not even itself. Thus where does the cumulative interference pattern come from?

The accepted answer is that the particle passes through both slits and interferes with itself, but how can this happen if it requires a series of waves to create an interference pattern, and since each particle is passing through the apparatus as one discrete "set" of waves, then there is no "series" of waves for it to interfere with.

Actually that's not the accepted answer, but its easy to get confused, as, hopefully, what I say below will explain.

The issue here is the double slit experiment is used to motivate the formalism of QM via handwavy arguments such as the wave particle duality and particles go through both slits etc. This is the beginning stages QM and unfortunately it's not strictly true in view of the correct theory once that theory is developed.

For example see the FAQ section about the so called wave-particle duality of light:
https://www.physicsforums.com/showthread.php?t=511178

Authors generally do not go back and analyse the double slit experiment from the basic principles of QM once they have been fully fleshed out - they should - but don't.

IMHO its not the best approach for UNDERSTANDING QM because it doesn't get at the conceptual core and leaves exactly what's going on with things like the double slit experiment with issues. It's fine for developing intuition to solve problems - which actually is what most physicists/applied mathematicians are interested in - but understanding is another matter.

To correct that I suggest approaching QM from its conceptual basis from the start:
http://www.scottaaronson.com/democritus/lec9.html

Once that is done you can see a correct quantum analysis of the double slit experiment that should resolve your issues:
http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Thanks
Bill

 

[jtbell]

But just as with a pair of dice, you cannot see that 7 is the most likely value from 1 roll - you cannot see the familiar interference pattern from a single iteration.

I got 3.5, how did you get 7?

Note the word that I put in boldface in the quote from DrChinese.

 

[Aphysicsuser]

hello every one I am new here and this is my first comment :)

here it is what i think

Hint(be careful):if we do speak about photons there is a difference between the collective behavior and the single photon behavior from point of motion ,waves ,interference,...etc

now back to ur Q i guess that :

any particle say electron as u know has its own associated wave this wave when hits a slit is diffracted into linear sets of waves which then interferes with each other and produce the pattern hope I am right :)

 

[bhobba]

any particle say electron as u know has its own associated wave this wave when hits a slit is diffracted into linear sets of waves which then interferes with each other and produce the pattern hope I am right :)

Welcome Aphysicsuser. Hope you enjoy discussing things here.

That's correct from the usual view given in high school and first year physics courses. It is however not quite what's going on from the more advanced viewpoint.

The correct analysis, as well as the actual conceptual basis on QM, is given in the links in my previous post.

Please do give them a read and post with any queries.

Thanks
Bill

 

[San K]

Note the word that I put in boldface in the quote from DrChinese.

Missed that.

Thanks jtbell...:)

 

[Fiziqs]

Once that is done you can see a correct quantum analysis of the double slit experiment that should resolve your issues:

bhobba, thanks for the links. It'll take me some time to read and understand them, but in the meantime do you have a simple way of explaining why we see an interference pattern in the double slit experiment? I realize that you and I conceptualize things differently, but I have a difficult time understanding how a particle in the double slit apparatus can experience interference, if there is only one wave being produced at each slit. It seems to me, that to end up with an interference pattern you need a series of waves capable of interfering with each other.

TheFerruccio gave me the idea that it has to do with the temporal uncertainty of the emitted particle, and I was just about ready to answer zonde's query about how this solved the problem for me, but I'll take the time to consider the links that you provided, and any further input that you may care to offer. In any case I'll respond further once I've read the linked material.

Thanks

 

[jtbell]

I have a difficult time understanding how a particle in the double slit apparatus can experience interference, if there is only one wave being produced at each slit. It seems to me, that to end up with an interference pattern you need a series of waves capable of interfering with each other.

By "one wave" do you mean a wave that is one wavelength long? If so, that is not a wave that describes one particle, except perhaps under a very unusual method of preparation. And such a wave would not have a single wavelength, but would rather have to be a superposition of waves with a wide range of wavelengths, according to Fourier analysis.

 

[WannabeNewton]

You're getting into the unfortunate trap of the (as bhobba put it in a different tone) pedagogically and conceptually disastrous notion of the "wave-particle" duality. You seem to be visualizing waves propagating through physical space from the emission point to the slits and to the detection screen, as if we were talking about e.g. water waves propagating through their natural medium. Rather, the propagation is taking place in an abstract, unphysical infinite dimensional vector space; don't confuse the production of an actual wave (the kind you usually picture e.g. a water wave) with one that is produced as a result of a countable infinity of identical statistical measurements.

 

[Fiziqs]

By "one wave" do you mean a wave that is one wavelength long?

Yes

If so, that is not a wave that describes one particle

What type of wave does describe one particle? And how can a wave describing a single photon, for example, be more than one wavelength long?

You seem to be visualizing waves propagating through physical space from the emission point to the slits and to the detection screen, as if we were talking about e.g. water waves propagating through their natural medium.

This is indeed how I visualize waves, although I am well aware that this is just a crude representation of an underlying abstract, quantum model of a wave. I am quite happy to ascribe to these waves attributes not normally present in actual physical waves such as water waves. I.E., uncertainty, commutability, and superposition. Having only a 9th grade education, visualization is my most effective tool, but I do try to understand and compensate for its limitations.

Any help in trying to fine tune my understanding, my visualization, of the waves in the double slit experiment, are considered, applied, and appreciated.

Thanks

 

[DrChinese]

This is indeed how I visualize waves, although I am well aware that this is just a crude representation of an underlying abstract, quantum model of a wave. I am quite happy to ascribe to these waves attributes not normally present in actual physical waves such as water waves. I.E., uncertainty, commutability, and superposition. Having only a 9th grade education, visualization is my most effective tool, but I do try to understand and compensate for its limitations.

The issue is that is a) the wave is more of a probability distribution as to where the particle will be detected, and b) when set up per the double slit, the left and right portions interfere with each other. In fact, every possible path interferes with every other possible path. Some of those paths net to no interference in a particular spot, some net to constructive interference, and others net to destructive interference. The total will still be 100%.

 

[bhobba]

bhobba, thanks for the links. It'll take me some time to read and understand them, but in the meantime do you have a simple way of explaining why we see an interference pattern in the double slit experiment?

The simple way is the wave particle duality, found in populist books or basic physics texts, or Feynman's little turning arrow and going via all paths in his famous QED lecture series and associated book.

However, as I think you found, when pushed too hard, those simple ways break down - and there is a reason why - strictly speaking they are not quite true.

The real reason is the math in the paper I linked to. Sorry - like many things in the more advanced areas of physics it's not amenable to simple visualisable ideas.

Feynman addressed this issue. You can try as hard as you like to convey physics in the real deal sense without the math, but in the end you will fail, doesn't matter how hard you try. Even Feynman's attempts, as excellent as they are, failed at that level.

Unfortunately with just the math of a 9th grade education at your disposal it will not take you far enough for the correct understanding.

If you like I can post some reading material that will take you to that level - but it will involve calculus, the study of which, while most certainly doable, is not a trivial undertaking.

Thanks
Bill