The quantum double-slit experiment, in which objects are sent toward a wall with two slits and then recorded on a screen behind the wall, creates an interference pattern that builds up gradually, object by object. And yet, it’s crucial that the path of each object on its way to the screen remain unknown. If one measures which of the slits each object passes through, the interference pattern never appears.
Strange things are said about this. There are vague, weird slogans: “measurement causes the wave function to collapse“; “the particle interferes with itself“; “electrons are both particles and waves“; etc. One reads that the objects are particles when they reach the screen, but they are waves when they go through the slits, causing the interference — unless their passage through the slits is measured, in which case they remain particles.
But in fact the equations of 1920s quantum physics say something different and not vague in the slightest — though perhaps equally weird. As we’ll see today, the elimination of interference by measurement is no mystery at all, once you understand both measurement and interference. Those of you who’ve followed my recent posts on these two topics will find this surprisingly straightforward; I guarantee you’ll say, “Oh, is that all?” Other readers will probably want to read
- this post on measurement
- (and perhaps this one too about how to make a measurement permanent)
- these posts on interference for one particle and for two particles
The Interference Criterion
When do we expect quantum interference? As I’ll review in a moment, there’s a simple criterion:
- a system of objects (not the objects themselves!) will exhibit quantum interference if the system, initially in a superposition of possibilities, reaches a single possibility via two or more pathways.
To remind you what that means, let’s compare two contrasting cases (covered carefully in this post.) Figs. 1a and 1b show pre-quantum animations of different quantum systems, in which two balls (drawn blue and orange) are in a superposition of moving left OR moving right. I’ve chosen to stop each animation right at the moment when the blue ball in the top half of the superposition is at the same location as the blue ball in the bottom half, because if the orange ball weren’t there, this is when we’d expect it to see quantum interference.
But for interference to occur, the orange ball, too, must at that same moment be in the same place in both parts of the superposition. That does happen for the system in Fig. 1a — the top and bottom parts of the figure line up exactly, and so interference will occur. But the system in Fig. 1b, whose top and bottom parts never look the same, will not show quantum interference.
In other words, quantum interference requires that the two possibilities in the superposition become identical at some moment in time. Partial resemblance is not enough.
The Measurement
A measurement always involves an interaction of some sort between the object we want to measure and the device doing the measurement. We will typically
- use a small object to carry out the basic initial measurement, and then
- amplify the result so that it can be made permanent.
For today’s purposes, the details of the second step won’t matter, so I’ll focus on the first step.
Setting Up
We’ll call the object going through the slits a “particle”, and we’ll call the measurement device a “measuring ball” (or just “ball” for short.) The setup is depicted in Fig. 2, where the particle is approaching the slits and the measuring ball lies in wait.
If No Measurement is Made at the Slits
Suppose we allow the particle to proceed and we make no measurement of its location as it passes through the slits. Then we can leave the ball where it is, at the position I’ve marked M in Fig. 3. If the particle makes it through the wall, it must pass through one slit or the other, leaving the system in a superposition of the form
- the particle is near the left slit [and the ball is at position M]
OR - the particle is near the right slit [and the ball is at position M]
as shown at the top of Fig. 3. (Note: because the ball and particle are independent [unentangled] in this superposition, it can be written in factored form as in Fig. 12 of this post.)
From here, the particle (whose motion is now quite uncertain as a result of passing through a narrow slit) can proceed unencumbered to the screen. Let’s say it arrives at the point marked P, as at the bottom of Fig. 3.
Crucially, both halves of the superposition now describe the same situation: particle at P, ball at M. The system has arrived here via two paths:
- The particle went through the left slit and arrived at the point P (with the ball always at M),
OR - The particle went through the right slit and arrived at the point P (with the ball always at M).
Therefore, since the system has reached a single possibility via two different routes, quantum interference may be observed.
Specifically, the system’s wave function, which gives the probability for the particle to arrive at any point on the screen, will display an interference pattern. We saw numerous similar examples in this post, this post and this post.
If the Measurement is Made at the Slits
But now let’s make the measurement. We’ll do it by throwing the ball rapidly toward the particle, timed carefully so that, as shown in Fig. 4, either
- the particle is at the left slit, in which case the ball passes behind it and travels onward,
OR - the particle is at the right slit, in which case the ball hits it and bounces back.
(Recall that I assumed the measuring ball is lightweight, so the collision doesn’t much affect the particle; for instance, the particle might be an heavy atom, while the measuring ball is a light atom.)
The ball’s late-time behavior reveals — and thus measures — the particle’s behavior as it passed through the wall:
- the ball moving to the left means the particle went through the left slit;
- the ball moving to the right means the particle went through the right slit.
[Said another way, the ball and particle, which were originally independent before the measurement, have been entangled by the measurement process. Because of the entanglement, knowledge concerning the ball tells us something about the particle too.]
To make this measurement complete and permanent requires a longer story with more details; for instance, we might choose to amplify the result with a Geiger counter. But the details don’t matter, and besides, that takes place later. Let’s keep our focus on what happens next.
The Effect of the Measurement
What happens next is that the particle reaches the point P on the screen. It can do this whether it traveled via the left slit or via the right slit, just as before, and so you might think there should still be an interference pattern. However, remembering Figs. 1a and 1b and the criterion for interference, take a look at Fig. 5.
Even though the particle by itself could have taken two paths to the point P, the system as a whole is still in a superposition of two different possibilities, not one — more like Fig. 1b than like Fig. 1a. Specifically,
- the particle is at position P and the ball is at location ML (which happens if, in Fig. 4, the particle was near the left slit and the ball continued to the left);
OR - the particle is at position P and the ball is at location MR (which happens if, in Fig. 4, the particle was near the right slit and the ball bounced back to the right).
The measurement process — by the very definition of “measurement” as a procedure that segregates left-slit cases from right-slit cases — has resulted in the two parts of the superposition being different even when they both have the particle reaching the same point P. Therefore, in contrast to Fig. 3, quantum interference between the two parts of the superposition cannot occur.
And that’s it. That’s all there is to it.
Looking Ahead.
The double-slit experiment is hard to understand if one relies on vague slogans. But if one relies on the math, one sees that many of the seemingly mysterious features of the experiment are in fact straightforward.
I’ll say more about this in future posts. In particular, to convince you today’s argument is really correct, I’ll look more closely at the quantum wave function corresponding to Figs. 3-5, and will reproduce the same phenomenon in simpler examples. Then we’ll apply the resulting insights to other cases, including
- measurements that do not destroy interference,
- measurements that only partly destroy interference,
- destruction of interference without measurement, and
- double-slit experiments whose interference can’t be located in physical space,
- etc.
14 Responses
I wish I had heard your explanation first. It is completely consistent with Heisenberg in that is clearly shows how the act of measurement changes the result so breaks up any interference versus the collapse of the wave function I have heard in past explanations. However, it seems the particle going through the right hand slit is seriously going to be deflected left even in QM.
It’s much clearer and simpler, isn’t it? I don’t know why we continue to talk about collapses that violate the Schroedinger equation, and make easy things hard to understand.
But your statement about deflection isn’t true. The amount of deflection depends on the amount of momentum transferred to the particle relative to the amount of momentum already carried by the ball. Let’s say the “particle” has mass M and typical momentum MV toward the screen. Let’s say the “ball” has mass m and velocity v toward the particle. Then the angle by which the particle is deflected (if the collision is elastic) satisfies sin(theta)= 2mv/MV. If m is much less than M, then even if v is substantially larger than V, the angle will have theta ~ sin(theta) ~ 2(m/M)(v/V) << 1 in radians. This can easily be the case if, say, the particle is an silver atom while the ball is a proton or even an electron; then m/M can be 1/50 or even 1/10000. Even if the angle is deflection bigger, let's say Pi/6 ~ 0.5 ~ 30 degrees, it doesn't change anything else about the argument. The particle can still reach the point P from either the right slit or the left slit, but no interference effect will be observed. A point that this raises is that measurements can leave the measured object largely unchanged or change it dramatically, depending on the experimental design. In a particle physics experiment at the Large Hadron Collider, the tracker is in the first category while the calorimeter [the energy-collector] is in the second. No measurement leaves a particle absolutely unchanged. However, as we will see, measurements that don't destroy interference may affect the interference pattern only slightly if the experiment is appropriately designed. What's nice about these one-dimensional examples that I rely on is that we can explore that kind of thing in considerable detail, once I write and test the code.
Was the whole idea of a wave function a slightly poor one that has led many students and others astray.
Rather understanding every quantum phenomena as the sum over possible paths makes things a lot easier to understand and might well be closer to what is really going on.
I’m not sure it actually helps at all. The “sum over possible paths” is not individual particles taking all possible paths through physical space; it is the system of particles taking all possible paths through the space of possibilities. You’re just taking the Schrodinger equation and rewriting it in another language, so you’re moving sideways, not forward.
Interference, meanwhile, is something we observe in experiment, so rewriting the theoretical framework from wave functions in the space of possibilities to interfering paths in the space of possibilities doesn’t change the fact that measurement makes the observed effects of interference go away, or that the interference cannot be localized in physical space.
The wave function has the advantage that you can draw it and understand it conceptually. The sum–over-all-system-paths is simple if you have a system of one particle, but it becomes very unwieldly conceptually if things are any more complicated. We’ll see that at some point later this year.
This definitely helps demystify it a bit for me. I have seen it written that “observation” causes the wave function to collapse, which makes it sound like the wave function of a particle is observer relative or that we have some occult power over particles.
But thinking of the measurement as changing the state vectors from <a,b| to <a,b,c| brings back objectivity. It is still strange to me how the particles (a and b) behave differently based on the presence of c. How does the particle that isn’t hit by the ball know about the ball? Are there any theories about this?
I am wondering if you might be confused… In figs 2-5, there is only one particle here; there is no a and b. There is just one particle at one position OR at another, along with a ball whose position may or may not be correlated with the particle’s position. Could you clarify your question?
In other words, we need to think of the Schrodinger equation as applying to the whole system and not just the particle itself and then there is no mystery? Would that be an accurate summary?
Yes, except it’s not that there is *no* mystery. But it helps you see what is and isn’t mysterious. Quantum interference is mysterious — see my previous post: https://profmattstrassler.com/2025/03/31/quantum-interference-5-coming-unglued/ . Once you understand how it works, the fact that measurement eliminates it isn’t mysterious at all. But to make sense of why it works that way — well, we physicists are still trying to figure that out.
Hi Matt, I’m just wondering whether the difference between “will” and “may” in these two sentences is significant?
“a system of objects … will exhibit quantum interference if the system, initially in a superposition of possibilities, reaches a single possibility via two or more pathways.”
“Therefore, since the system has reached a single possibility via two different routes, quantum interference may be observed.”
Thanks for noticing that; I did equivocate there. The question is whether there are any circumstances in which the wave function can behave in such a way that as the two states in the superposition merge, they line up too perfectly (in the momenta as well as the positions) in which case the interference effect might be tiny. I should really spend some time to think this through, but it would be safer, for now, for me to say “may” rather than “will.”
There are a lot of subtleties in this business, and I’m doing my best not to make incorrect statements.
In this post you have equivocated between collapse and decoherence. 1920’s QM indeed is not vague about the latter, but it is famously vague about the former. I think you understand this, which is why you only mentioned “collapse” in your second paragraph, but then for the remainder of the post focused entirely on the disappearance of interference. But this equivocation is central to many folks’ confusion on this topic, and the question of collapse (as opposed to decoherence) is the primary reason why so much ink has been spilled on this topic in the quantum interpretations literature, starting with Einstein’s early objections about locality (the instantaneous collapse of a wave function extended throughout space).
Well, I just reread the post and I don’t see any equivocation at all. At no point do I advocate for collapse, and in fact, this entire post is dedicated to showing that collapse does not occur in the Schroedinger equation, and that decoherence happens long before any classical measurement takes place. The second paragraph is a criticism of “collapse”; “collapse” is listed under “weird, vague slogans”, which is hardly an endorsement. (See also https://profmattstrassler.com/2025/03/10/do-quantum-wave-functions-collapse/ , which gives a more complete critique of vague collapse notions.)
Authors in the quantum interpretations literature needs to either embrace the Schrodinger equation or (if introducing collapse as a concept) reject it; either is honorable, but one can’t have it both ways. The only correct notion of collapse is that somewhere between the top of Fig 3 and the bottom, and somewhere between Fig 4 and Fig 5, an equation different from the Schrodinger equation is kicking in and changing the answer by eliminating the superposition… even though everything in the problem is microscopic.
I think you are misunderstanding the criticism, and misunderstanding how your viewers might be confused. If there is no wave function collapse, then you are implicitly advocating for an Everettian view. Are you? If not, then how do you propose to continue to make correct experimental predictions post-measurement?
The first thing to do is understand the wave function and the Schroedinger equation, and only later make the choices you are referring to. One does not need to choose yet between Everett and hidden variables; the Schroedinger equation and the probabilistic interpretation apply to both. (Wave function collapse is something else; that violates the equations.)
So far, no readers have yet expressed confusion. When they do, I’ll refer them to the discussion of wave function collapse presented here
https://profmattstrassler.com/2025/03/10/do-quantum-wave-functions-collapse/
which I believe is far clearer than in most books.