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.
28 Responses
Hi Matt, I left a comment on twitter, but your website allows for more verbosity, so I’ll chat here.
I am confused by the language you use. Your language seems to only make sense within the pilot-wave interpretation, but I found a comment of yours from six months ago where you say you “don’t see the point in the pilot wave approach”.
Above Fig. 3, you say “it must pass through one slit or the other” and say this is a superposition. You bold the “or”. I am surprised that you don’t use “and”. In Fig. 4, the message that comes across is that the particle is taking a path and the measurement reveals what is already there. You even say “The measurement process … segregates left-slit cases from right-slit cases”.
If not pilot-wave, could you tell me what your interpretational framework is or is similar to? It will also help if you named a few interpretations that most definitely do not describe your view.
I myself am coming around to the view that there is indeed something in my language that is confusing. You’re the second person to raise it — and I’m working out how to address it.
So in the spirit of thinking out loud, here is my latest view. Comments welcome.
First, in my view, people are way too quick to try to interpret quantum physics, and spend far too little time staring at the math and what it actually does. The goal of these posts is to explain the *math* that agrees with the experiments and look carefully at how it works. In my experience, far too few people actually understand what the math does and says. We can worry later how to interpret it; that is obviously difficult, since we’ve collectively spent a century on it.
Second, the idea that one should use “AND” is clearly antithetical to the math. In QM (not in QFT! that’s another story altogether), math does not permit the particle to have two positions at once. This is clear from the fact that the configuration space — the same configuration space as in Newtonian physics — does not grant the option of measuring the particle’s position to be double-valued. Any measurement of the electron’s position is always single-valued — said another way, no extended object can interact with the particle in two places at once, which would be expected if AND were appropriate. When you write a wave function of the form A x B + C x D, it is clear, just as in classical logic and in algebra, that x represents AND and + represents OR. This is also clear in Hamilton-Jacobi theory, to which the Schroedinger equation reduces in the WKB approximation. There it is clear that if the HJ wave can take two paths around an obstacle, this is a classical bifurcation point; the wave goes both directions, but the
objectsystem described by the wave goes one OR the other. This is not pilot wave interpretation; this is just how Hamilton-Jacobi math works.Third — and this is the key point — the math does not imply that the OR in “A+B = A OR B” means that “either A is happening or B is happening”, or that “either A(t) will happen or B(t) will happen”. It simply doesn’t follow. It would follow in classical probability; a probability distribution would indicate only a lack of knowledge of whether A happens or B happens. But clearly, from the fact that the math matches experiment, quantum physics doesn’t work that way — we can see that in the math. And we discover this is true from examples of quantum interference: if a system starts from A + B (possibility A or possibility B) and evolves to possibility C, observable (though often subtly hidden) quantum interference results. Again, that’s just what the math says.
Multi-particle systems make this all much clearer than one-particle systems, which is why I spend so much time on two-particle systems and very little on one-particle systems. In one-particle systems it is far too easy to conflate different issues, which causes many people to make mistakes.
Now, there are natural questions you may well ask. What does the math mean for our understanding of reality, i.e., how should we interpret this behavior in terms of a system of objects, the objects themselves, their interactions, measurements, and space and time? I don’t know, and I make no claim. But I do know that if you envision the math incorrectly, you will never correctly answer this question.
More specific to your comment is this: how should we state these facts about the math using language that itself cannot be misinterpreted? It’s clearly not easy, because English is not designed for it. It’s easy to conflate statements about the math as statements about the physics reality that the math is trying to describe. It’s also easy to interpret “A OR B” as a statement about reality instead of a statement about the mathematical quantum state being used to predict how reality behaves.
I clearly have not addressed this to my satisfaction, because, as you note, the use of OR is ambiguous. How can I say, in a simple way that cannot be misinterpreted, that using “A OR B” to correctly describe a quantum state at time t [in that it correctly captures that if I do a measurement right now I will find the result A OR B] does not imply that “either the time evolution A(t) OR B(t) — one or the other — must therefore subsequently happen” [as it would in classical HJ theory].
Said one last way: to say “A(t) OR B(t)” is not to say that “A(t) happened OR B(t) happened”, but instead that “the system was at all times t in a state [A(t) OR B(t)]”. It would be incorrect to say that “A(t) happened AND B(t) happened”, because no measurement ever shows this. And it is also incorrect to say “A(t) definitely happened OR B(t) definitely happened”, because no measurement shows this either (and because it if were true, there’d be no interference.) What quantum physics seems to do, at the level of the math anyway, is introduce an intermediate possibility. The system is always in an OR state, and if two parts of the OR state overlap, then quantum interference may occur.
The fact that it has taken me this long to answer your simple question is an indication that language is failing me… and your linguistic concerns are valid. If you see an alternative which correctly describes the math (and does not simply replace “OR” with “AND”, which does not help one bit), I’m open to suggestions.
Thanks for taking the time to answer. I didn’t expect so much on OR vs. AND. One thing that particularly interests me is how people visualize the unitary picture without collapse, so I was looking for your interpretational framework so that I may read you properly.
Here are some thoughts as I read your response.
In the paragraph that starts with “Second, the idea…”, I am almost immediately at a loss to see exactly how you picture things. Could you answer/comment on the following two points?:
1) In your view, is a particle a tiny little ball? A geometric point? A click in a detector?
2) You mention measurements to invoke the location of a particle. Does a particle exist between measurements? Does it follow a continuous path at all times?
You say: “Any measurement of the electron’s position is always single-valued…” I disagree with this because it assumes perfect measurements. In reality, position measurements come with error bars.
In the paragraphs on reality, you say you make no claim about reality. But I must tell you that, unless I missed you giving a caveat, most every reader thinks you are trying to describe reality. Many would ask what’s the point of the figures if they aren’t usefully illustrating reality for the reader.
In the last paragraph, you give an invitation for an alternative explanation of the math. The problem is that I don’t see our formalism as giving a complete unitary picture, so I can’t follow your path. Additionally, I think you’ve constrained what you can say by drawing tiny little balls. Instead, what I would describe to laypeople (and have described elsewhere) is that the three-dimensional matter density (as described by density-functional theory) goes through both slits. And later, downstream of the slits, somehow that matter density gets localized in the pixel of a detector. Some would say the wave function spontaneously collapses into the pixel.
As I emphasized, I’m minimizing the interpretational framework, and focusing on the math as a means for prediction. Most of my definitions are therefore operational.
On the two points:
1) I have no idea what a particle is; I only know that I can match experiment [specifically those for which 1920s quantum physics applies, leaving aside those for which I need quantum field theory] by developing a concept of an object to which we can attribute specific measurable properties, namely position and momentum (and possibly others such as spin, charge, etc.) which itself requires other concepts, such as space and time, and interactions among these objects for which we have concepts. I don’t want to give a whole lecture on this, but obviously I have thought carefully about what we actually learn from experiment and the math we have found to predict its results. My goal in these blog posts is not to get bogged down in this kind of question, but rather to explain how the wave function behaves, and point out ways to view it that are inconsistent with the math and with its mapping to experiment. For example, to view an electron as a “geometric point” described by 1920s quantum physics is inconsistent with combining 1920s quantum physics with special relativity, so we can rule that out. But that only tells us what an electron in our universe is not. Trying to say what it is, “in truth”, is inevitably metaphysics, as it is not testable; and that is true just as much in Newtonian physics as in quantum physics.
2) Again, we only know (a) what experiments [defined generally, to include all sensory observations] tell us, and (b) what the math that we use to make predictions actually says. The math that we use to make predictions makes it clear that a definite continuous path is not consistent with quantum interference. As for existence, that’s not decideable, but since the entire universe forms a single interacting system and since quantum physics should (apparently) be applied to all of it, it is conceptually inconvenient to suggest that parts of the universe (or the universe as a whole) flash in and out of existence between interactions [there being no sharp divide between general interactions and definite measurements.] I therefore prefer to take the math at face value and say that it describes possible results of measurements that I could have made as well as ones I arranged to make, which implies that the universe exists between measurements that are actually made. But I’m not going to argue with someone who takes a different view on this undecideable point.
You disagreed with my statement that any measurement of the electron’s position is always single-valued “because it assumes perfect measurements.” Please, let’s not waste time on silliness; you’re talking to a professional physicist with 35 years of experience doing data analysis with error bars. Double-valued obviously means: “returns two values that are much further apart than the uncertainty on the measurement”. Obviously there is no relation between double-valuedness and uncertain single-valuedness. In 1920s quantum physics, use of “AND” would imply that an electron can both be measured to be in NYC and Boston at the same time; and if a position measurement has an error bar so large that Boston AND New York cannot be said to be double-valued, then perhaps a better techique should be used. I encourage you to reconsider your objection, which is clearly spurious.
“Many would ask what’s the point of the figures if they aren’t usefully illustrating reality for the reader.” The risk is real. The question of which caveats to place, where to place them, and how often to place them is a challenge that I face in every post that I write. I can’t reproduce every caveat in every blog post everywhere it could be needed; and no matter what I do, many readers will miss the caveats or fail to appreciate their importance. I have warned readers many times that I am describing the workings of 1920s quantum mechanics, and that this is in disagreement with reality, since (a) special relativity works well, so we know we need quantum field theory, and (b) assumed-elementary “particles” such as electrons are completely different beasts in QFT than in quantum mechanics, with completely different properties. Clearly, that means my current set of blog posts are not about fundamental reality, since we’re not doing quantum field theory, which is the only math that matches all experiments. But not every reader is going to read the post that makes that clear. There’s only so much I can do, though I can try to do better, and I can answer comments/questions carefully.
Finally, I am describing the unitary picture [i.e. the one based on the Schroedinger equation] and how it works, period. It’s a consistent formalism. Whether it is complete or not is up for discussion. If you want to say it’s not complete and invent a whole theory of how to discuss it and so forth, all power to you. If your approach has experimental consequences that we can test, I’m very interested; if not, then I’m not interested, since then it’s just opinion. As for “three-dimensional matter density” and “density functional theory”, does this generalize to quantum field theory? Since that’s what actually agrees with experiment, I’m only interested if you have made that generalization. Part of the point of my blog posts is to explain how the math of QM works, and then show how different QFT actually is and how the questions change completely.
Matt already used both the words “or” and “and” in the full description above fig 3:
“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]”
It would be even more confusing if he used the same word (“and”) for both those meanings…
I guess you just have to choose one word for each meaning, and try to use it as consistently as possible. I also think it helps that he was explicitely saying these were superpositions of possibilities (not necessarily actual paths).
Professor, this explanation seems reasonable, but what is unreasonable about it? What limitations do we receive when we apply this theory to understanding the real world? Or what contradictions do we encounter?
One issue arises with the original premise: “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.” I showed in earlier posts that this is true (or more precisely, I showed that it is true in any system described by the Schrodinger equation, and the latter agrees with experiment, so apparently it is true in nature, at least to some degree.) How can this be so? The implications of the statement that interference occurs at the level of an entire system is astounding, and confusing. I emphasized this in https://profmattstrassler.com/2025/03/31/quantum-interference-5-coming-unglued/ ; see especially the final section of that post. The whole notion of what the world consists of comes into question… and no answer has yet been given.
The second issue is that the equations do not predict what we actually observe, only what we may observe. This is discussed in detail in https://profmattstrassler.com/2025/03/10/do-quantum-wave-functions-collapse/ . The fact that people disagree as to how to think about this foundational question — that there is no agreed-upon answer — is a sign that we are still far from settling basic issues in quantum physics.
As you see, neither of these issues is about measurement-induced wave-function collapse, classical vs quantum objects, wave-particle duality, etc. Those, in my view, are distractions from the actual problems — distractions that were introduced to try to address the core problems, but fail to do so.
What is the difference or connection between quantum interference of a photon and the interference of light, as we commonly see it in a 2-slit experiment, an optical grating, or a Michelson interferometer? The latter is apparently “ordinary” interference of waves (described by non-quantum Maxwell’s equations).
I’m going to get into this carefully over time. We need to look at identical particles and at how particles arise in quantum field theory. But we can’t rush this; it has the potential to become incredibly confusing (and indeed most people are, understandably, completely confused.)
The important point to start with is that quantum interference does not take place in ordinary physical space, while ordinary interference does. Understanding how, in specific circumstances, the former can be projected into the latter requires a long discussion.
Also, so far I have been discussing quantum interference in 1920s quantum mechanics. In quantum field theory, by contrast, the whole discussion has to be reoriented, because the “particles” are wavelike and the “wave function” is much less wavelike.
So we have to get through both of these confusing steps to answer your question. I promise I will answer it in 2025.
“CMS finds unexpected excess of top quarks
Data from the
@cmsexperiment.bsky.social
at CERN’s #LHC reveals an intriguing excess of top-quark pairs, hinting at the first observation of a composite particle with unique properties”
Does this mean there could be a fifth force of nature, not counting the Higgs force?
In Figure 5, the Ball appears to have 2 possible locations, ML & MR, which suggests that it should have an interaction pattern. If that is correct, then the measurement of the Ball acts like it is “stealing” probability from the Particle. Or am I confusing the parts of a system with the System?
Ignore what I just wrote about the Ball’s interference pattern (wrongly written as “interaction”). I am coming to grips with correlation/entanglement/interaction and need more time to decide if I have a real question.
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.
Ah I see what you mean. I do like your examples and I am finding it fun to try to understand them (and not quite there yet) using the alternative sum of histories approach.
In your criterion for interference you say “initially in a superposition of possibilities”. Wouldn’t the initial state be the result of some previous measurement and so not initially in a superposition of possibilities?
Specifying initial states and how they are prepared is itself a long discussion, and I am not yet entirely happy with my ability to explain it well.
But it is easy to have a system whose initial state is in a superposition of possibilities. When the Higgs boson decays to photons, the pair of photons will always be back to back but will be in a superposition of going in all possible directions. All sorts of processes create objects in superpositions of all sorts of types.
Here, the two slits are in fact the preparation device: they provide that “previous measurement”. I set up a broad, defocused beam of electrons by making it very narrow for an instant, which causes it subsequently to spread out, thanks to the uncertainty principle. The beam is now a set of independent electrons, each one in a superposition of going in many different directions. Then I send the beam at the wall with the slits. Each electron emerges from the wall in a superposition of having passed through the left slit or the right slit. That is now my initial state. In other words, the whole and only job of the slits is to create a superposition state. We could replace the slits with many other tricks and get both superposition and interference.
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.