Why does classical physics not predict particles in the double-slit experiment to land in just two different locations?

Question

I stopped being able to understand the double-slit experiment way before any of the interference and associated "quantum weirdness" came into play. I get that one needs to approach this field with an open mind. I get it. And yet, every single video I watch on the topic doesn't even bother to explain why the particles get scattered at all. That is, why does the set of geometric points where the particles land contain more than 2 elements?

I will illustrate with screenshots from this video:

I tried to really figure this one out by resorting to an actual physics textbook, not just videos. There I could read in great detail about polarized light, the Huygens principle, light diffraction, wavelength and slit size... But this is not about light. Right from the video we learn that the entire experiment can be performed with molecules of buckminsterfullerene. We might as well be throwing wheelbarrows through a pair of windows.

Perhaps the scattering is caused by the fact that it is physically impossible to create slits with exactly the same diameter as the diameter of the particle. It could be the Van der Waals force between the particle and the edges of the slit. Or perhaps it is just hard to "shoot straight". It could be our trembling, clumsy hands foolishly trying to cut precise slits before we had our first drink of the day. But all these things are nuisances that we are trying to eliminate as much as possible for the sake of the experiment, right? Getting the particles only to go one of two exact ways is the point of making the slits in the first place, or not? Surely the experiment itself does not rely on these imperfections that someone with a bigger budget and unburdened by alcoholism would strive to eliminate, right?

My guess would be something to do with the slits being elongated in the vertical (but possibly arbitrary) direction. In any case, it seems that all the virtuous free content creators (absolutely no sarcasm is intended, I am truly blessed to get all this knowledge for free) who teach about the experiment share some insider knowledge that is too trivial even to mention.

EDIT: Thanks to Vincent for his comment which made me change the title to clarify what and why I am asking. I am not trying to advance any new theories, debunk any existing or contribute anything to the existing scientific corpus. I just want to understand the experiment for my own satisfaction.

The narrative, as I understand it, is that the hero, ignorant of quantum physics, sees the interference patterns, is profoundly shaken by their appearance, and, with his beliefs and theories shattered, is only then ready to embark on the great quantum physics adventure. I want to know why the hero expects to see presumably a cloud of points without interference patterns as opposed to two points.

Answer 1

You need to look first at the case with only one slit. There you will find that not just one spot is illuminated (straight behind the slit) but that you get diffraction [Fraunhofer diffraction equation] into a much broader pattern.

As you rightfully mention, this is indeed logically speaking an essential first step before starting to analyze the double slit system. But it also is of importance for the precise shape of the double slit diffraction pattern. The pattern for each of the single slits is still visible in there (see explanation in [answer 813136] about the extra $\sin$ factor due to the finite slit width).

Answer 2

It is often said that particles are sometimes particles and sometimes waves. This is one source of confusion. They are sort of like particles and sort of like waves. They are really like nothing classical, nothing familiar. But you can get some understanding from comparing them to familiar objects. This explains a bit more - How can a red light photon be different from a blue light photon?.

You can also be misled by thinking of waves and particles. You know how particles behave. They go through one slit or the other. Small things are different. They go through both like a wave. You know how waves behave, When they hit a screen, they hit everywhere. Small things are different. After going through both slits like a wave, they can hit one atom in a screen and not disturb the others.

This is a second source of confusion. It makes no sense if you try to explain the behavior with either particles or waves. Trying to apply cause and effect to explain how the spread out "wave" chooses which atom to hit doesn't work. So what are they like? All you can say is that small things are different from particles and waves and common sense. This post explains a bit about how electrons behave. Does the collapse of the wave function happen immediately everywhere?

Another common saying is that if you think you understand quantum mechanics, you don't. To a degree, this is true. But there are rules that explain how the quantum mechanical world behaves. They are very different from what you are used to. But they can be learned. You can get used to them. It gets less strange and more familiar with practice.

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Classical mechanics can be used to explain things at everyday sizes. It doesn't work for the very small. Quantum mechanics must be used there. Quantum mechanics is a more complete and correct description of nature. It can be used to explain how everyday sized objects behave too.

This means that rocks and such are something like particles and something like waves. You don't see this. Bigger objects have smaller wavelengths. The waves that describe the objects have more abrupt edges. The interference effects that generate quantum behavior occur over such short distances that all you see is an average. The quantum description becomes indistinguishable from the classical description. But in theory, the difference is there.

Electrons are small enough that you have to use quantum mechanics to describe how the behave in an atom. The size of the quantum fuzziness determines the size of atoms.

A proton is 1800 times heavier. It is usually treated as a point particle when describing atoms. Bigger atoms are even more particle like.

But experiments have been done that show the wavelike properties of atoms. The slits have to be very small indeed. The spaces between atoms in a crystal has been made to work. I don't know the details for Buckyballs, but it wasn't easy to set up a situation where the wave nature was apparent.

Answer 3

Why does classical physics not predict particles in the double-slit experiment to land in just two different locations?

It does. If it’s a particle.

Classical physics predicts that if you are firing photons, or wheelbarrows, towards the slits the vast majority will not pass through, but that those that do will make two vertical lines on the line between the wheelbarrow gun, the slit, and the screen. Think of firing a real machine gun at a concrete building with two narrow vertical windows: most of the bullets hit the concrete walls, those that pass through the windows will hit the far wall in line with the gun and the window.

Now, if instead of a machine gun, we had a sonic cannon firing monotone sound waves at the building, classical physics predicts that we will see an interference pattern. Most of the wave will hit the concrete and reflect but the part of the wave that hits the windows will, unlike the particle-like bullets, spread out into the room through diffraction and because there are two slits, constructively and destructively interfere with itself. Because the screen (or inferior wall) is flat, the off-centre lines are fainter because of the waves travel further and drops off as the square of the distance.

A wave can go through both slits, but a particle can only go through one.

So, if light is a particle, classical physics expects two lines, if it’s a wave it expects a multiple-line interference pattern. When we do the experiment, we see interference, so it’s a wave, right? But that contradicts other experiments, like the photoelectric effect that shows that it’s a particle. So which one is right?

Well, it can be that the individual particles collectively behave like a wave. That is, as a particle passes through a slit, it coordinates itself with other particles so that the wave-like interference pattern appears. That can happen, right? I mean, a sound wave is just the coordination of movement of particles in the medium, right?

So, Thomas Young has an idea. He turns down the intensity of his light source so low that he knows there is only one photon in the air at a time. That is, when the source emits a photon, that photon must have (or as we now know, with a very high probability) hit the screen before the next phonon is emitted. Now, we’ve replaced the machine gun with a rifle and we wait long enough between each shot so that there is only ever one bullet in flight.

Now the particles can’t coordinate because only one is in existence at any one time. It’s clearly impossible for particles to coordinate with particles from the past or the future, right?

However, when Young, or I (because I have done it myself), or anyone else does the experiment, a weird and wonderful thing happens: the interference pattern appears right before your eyes as, one-by-one these totally time-isolated particles from an interference pattern right before your eyes. Or, at least before the “eyes” or your CCDs.

So either, these particles can communicate with the future or, the more common interpretation—they pass through both slits at the same time. So, you fire your wheelbarrow at the windows and part of it goes through one window and part of it goes through the other and it interferes with itself.

Except it doesn’t work with wheelbarrows—the quantum effects average out and we get boring classical results. Basically, the bigger the object (or rather the greater its momentum which is proportional to mass), the smaller its wavelength. So, to see wheelbarrows interfere you need very, very small slits—considerably smaller than, say, a wheelbarrow, so wheelbarrows can’t fit through. That’s why we don’t see this at macroscopic scales.

So this tells us that the classical physics division between waves and particles is wrong. Matter is wavelike and particle-like at the same time.

Answer 4

This is indeed one of the experiments that led to the development of quantum mechanics. The depiction of the video is misleading as electrons simply cannot be pictured as point particles "moving" as the classical concepts of motion and trajectories do not really exist in quantum mechanics.

The point is that classical intuition simply cannot be used when it comes to quantum mechanics as it is a non-classical theory. Quantum mechanics itself is a well-defined theory whose predictions agree with experiment to a large degree of accuracy. This theory was developed because of experiments whose outcomes couldn't be predicted by classical predictions. It's an entirely different set of rules from classical physics so there is no reason for any preexisting intuition to carry over. To insist on using an intuition that completely disagrees with experiment means to be wrong. In such cases, the sensible thing to do is not to insist but rather rebuild our intuition based on what actually happens. Physics cannot really fundamentally explain "why" the universe is the way it is. It devises theories to model the universe in various regimes and checks their predictions against experiments and observations.

While this was indeed breaking news before the invention of quantum mechanics, as of now, there isn't anything much more to say about this as the areas of interest have since advanced.

Answer 5

But this is not about light.

You can say that. But our experiments show that for certain setups we cannot ignore the wavelike behavior of small masses, exactly the same as we can't ignore the wavelike behavior of light.

Both light and massive particles are seen to diffract off edges depending on the wavelength involved (where that would be a de Broglie wavelength for massive objects).

We can use the same equations we use for how light diffracts (changes direction) at edges and see the same results.

Answer 6

The entire experiment can be performed with molecules of buckminsterfullerene.

I was also very surprised when I found out even such large molecules where presenting quantum effects and could be described using wave functions and probability density.

Every single video I watch on the topic doesn't even bother to explain why the particles get scattered at all

Because in the end we do not know. Or if I have to rephrase it, we do know how to describe the phenomenon, we don't understand its very nature. You're basically asking about the nature of light, why is it acting like a wave, but sometimes as a particle. I don't know how advanced you are in quantum mechanics, but one thing I like to say is that QM is simply mathematics and philosophy. We have the theory, the equations, the maths, we also know how to use everything (quantum dots, entanglement, etc.), but QM is also a very hot topic, debated, with its interpretation and point of view. Einstein thought there were hidden variables, Bohr thought (if I'm being correct) that what mattered was only the result and the probabilities in between were not important, etc.

To try answering your question now, I can suggest a very famous reference (at least in France): Quantum Mechanics by Claude Cohen-Tannoudji (Nobel price of physics). The first volume gives you a complete introduction about all the concepts you need to understand this experiment. I suggest you look at "state after measurement" to understand why the quanta behaves like particles once they're measured.

Why don't particles in the double-slit experiment land in just two different locations?

If you look at light diffraction experiment, you'll see the patterns aren't perfect dots, and they are also not flat, they are fringes, just like in the experiment you're asking questions about. Perfect one-dimensional doesn't exist, and the beam is not perfectly collimated.

Quantum mechanics is a tricky topic, and if you ever hear someone says they understand perfectly what they are talking about, take it with a grain of salt.

Answer 7

A very common misunderstanding of the quantum double-slit experiment is that if you arrange for each particle to go through one slit (e.g. by putting a detector at one or both slits) then you will get two stripes on the screen. In fact, you will get a pattern on the screen that is just as wide as when the particle goes through both slits. The only difference is that the narrower interference bands won't be present. "This guy" will still make it over there. See this answer for more.

If you permanently block one of the slits, you still get a wide pattern on the screen. So your question really has nothing to do with the double-slit experiment and is entirely about the single-slit experiment, as Jos Bergervoet's answer says.

I tend to agree with you that single-slit diffraction of particles is already non-classical without needing to add two-slit interference. Of course, you can imagine the particle bouncing off the side of the slit, which is more likely when the slit is small, but I don't think you can get a quantitatively correct model that way.

But even if there is no good corpuscular model of single-slit diffraction, one could go on imagining that there is one that we just haven't been clever enough to find yet. That's much harder to argue with the two-slit setup, where it seems to be necessary for each particle to interact with both slits somehow.

The other new and shocking feature of the two-slit experiment is that the interference pattern disappears if you record the particle's passage at the slits.

Answer 8

It's completely normal to be puzzled by this and to follow the heuristics behind the development can help understanding how all the concepts you mention fit together.

Let me start with the baseline two given aspects, obviously tautological: a particle behaves like a particle, ie using particle type formalism etc., and similarly, waves behave using the mathematical formalism that describe wave phenomena. It was a major conceptual leap to realize that light could actually behave both as wave and as particle. A major contribution of De Broglie was that he provided mathematical evidence that this dual description must work both ways, that is, it's not just entities known to behave as waves that should behave as particle, but also the other way round, that is, particle entities should also somehow behave as wave, when examined under the right conditions. The Davisson-Germer experiment proved exactly this hypothesis , by showing that electrons , until then known as just "particle-only" entities in the most naive sense, were actually able to diffract exactly like light! This was a significant milestone because it confirmed both that the wave-particle duality was a valid hypothesis, and that the Schrodinger equation was able to better explain things that couldn't be explained before (I deliberately don't use the words "Schrodinger equation is correct" because it had a lot of conceptual problems too, which were addressed by subsequent development of quantum mechanics).

With respect to your specific question "why this particle there end up in that position", as far we can tell, we can't identify the behavior of a single, specific particle, but we are able to associate a density probability density, and therefore calculate what is the chance of a particle to end up there. The fundamental meaning of the so-called wave-function in the Schrodinger Equation does exactly this: it allows you to calculate the density of probability.

Finally, I'd like to conclude with a short but crucial remark: in all the discussion above, we speak of particles (as you do in the question) but really the modern point of view is no longer a particle-point of view but rather "field". That's why modern quantum physics is really about field theories, even though "particle physics" is still used for historical reasons and for practical reasons too (the expression "particle physics" reflects accurately what experimental particle physicist do at CERN etc.) . But from the current theoretical physics perspective, which took decades to develop, particles emerge as quantization of fields, and the fundamental object is then field, rather than the particle.

Answer 9

Why does classical physics not predict particles in the double-slit experiment to land in just two different locations?

It does according to the previous answers???

Answer 10

Lots of great answers but I didn't see anyone really address this aspect of your question the way I would do so -

every single video I watch on the topic doesn't even bother to explain why the particles get scattered at all.

This is because the particles aren't getting scattered. At least not in the mechanical sense I think you're thinking of.

Think of the double slit not like barriers to be squeezed through, but instead think of it as a filter. The particles that make the interference pattern don't interact with the physical structure of the slits; they don't graze it or get deflected, etc. There will always be a clear line of sight between each detection point and the particle source. Classical physics indeed predicts that this would result in two blurry lumps of particles and cannot explain the interference pattern.

Thus it's not the mechanics of the double slit that ultimately causes the pattern. They make the pattern possible but they're not sufficient. What ultimately matters is the information that the setup allows us to learn or not learn. Any setup that could even hypothetically allow us to infer a specific path for a specific particle eliminates the pattern and causes the "classical" noisy result to be seen instead. In the complete absence, in principle, of "which path" information, the two equally probable paths destructively interfere to make the infamous pattern.

Anything beyond this is interpretation and this is why educational sources don't address it unless specifically discussing quantum interpretation, for which there is no shortage of candidates but no consensus on whether or how they can even be tested let alone which is right. The only objective thing that we can say, that's not subject to interpretation, is that it's the informational state of the system - or more formally, the square of the wave function - and not some mechanical action like scattering - that determines the probability of detecting the particle at any particular position. The probabilities are what get scattered, not the particles.

Answer 11

Do a single slit experiment and get a single blurry line. Now do another single slit experiment with the second slit moved over a bit. You will get another line. Both lines will be blurred a tiny bit by diffraction. Now open both slit. You would expect both slits open would get two blurry lines. But You get an interference pattern. This implies a wave, not a particle. Now send one photon at a time. You still get an interference pattern. That means each photon is a wave and it goes through both slits at once. This violates locality of particles and upset Einstein because the particle wave in both slits at once communicated spookily at a distance faster than light.

Answer 12

The diffraction pattern that appears even when slowing the particle gun to one particle at a time is the literal manifestation of the probability distribution of the most likely position for those particles to land.

It may seem mysterious that particles shot one at a time seem to "interact" with each other to form such a pattern but what you're seeing is near identical particles being created in a near identical way, one after another.

So that each exhibits essentially the same probability pattern and therefore acts as if they were being shot out at all at once and interfering with each other.

The interference that occurs here is actually a probability distribution that is recreated each time the gun fires.

Particles aren't interfering with others that don't exist yet or that have already struck the screen, a given particle isn't somehow flowing through both slits... its overlapping near identical probability distributions writ large.

A detector that is setup to determine which slit a particle passes through, necessarily interacts with that particle to detect its passing and in doing so, collapses its probability distribution at the slit to a much smaller potential set of locations for the particle to land and hence you'll no longer see that larger diffraction image on the screen.