Perhaps a way to distinguish it is that there is an *unrecoverable* form of collapse when we localize the wave, an action that involves *transferring* some or all of that wave to another wave. Keep in mind that, physically, this usually involves absorbing the particle. Photons disappear (it’s more complicated with electrons).

But the same way the two-slit experiment demonstrates the reality of interference, these filter experiments demonstrate the reality of wavefunction change. In many regards they’re the same thing. The two parts interfere or reenforce. What’s going on there is as real as what’s going on two-slit experiments.

đŸ˜€ As I’ve said, I’ve come to see *superposition*, *interference*, and *entanglement*, as the key mysteries. My guess is that solving those solves the package. (Note what’s not on that list: *decoherence* and *measurement*. We’re making progress on the former, and I think the latter depends on the big three.)

Right. For me, the key thing here is that since the particle wave packet can be recombined afterward, it seems like the sorting inside the boxes, by themselves, don’t cause collapse. It’s what happens afterward. It’s only when information about the property being measured gets out, when its causal effects propagate into the environment, that we get the irreversible collapse, or at least the phenomenology of collapse. (Which fits with most of what I’ve read.)

]]>I should maybe add that, if we fed *Black* electrons into the **Hardness** box, the two paths would have the |*White*⟩ state as out of phase and canceling and the |*Black*⟩ state as in phase and reenforcing.

I couldn’t resist one more. I meant to explore that Allan Adams experiment in terms of wavefunction interaction. I’ve done so below.

]]>Starting with *Figure 9* and *Figure 10* on page 7, note similar experiments but different input preparations. The first case uses *Hard* electrons, the second uses *White* ones. We obtain these starting conditions through off-stage boxes, **Hardness** and **Color** ones, respectively. Prior to that, the electrons are in an unknown “random” state (for all we know, truly random). We describe that as:

Unknown electrons are a (50/50) superposition of any orthogonal basis we like. Here we have two:

An important point: Each basis is orthogonal; its components are mutually exclusive. However, the two bases *are orthogonal to each other*. A measurement is either *Hard* **or** *Soft* (or *White* **or** *Black*) but measuring one or the other is also orthogonal. A key thing the experiment demonstrates is that orthogonality.

So the superposition above could be in terms of either of those. In *Figure 9*, the off-stage box is a **Hardness** box, and the experiment uses only the ones that emerge from the *Hard* port. So, we update the wavefunction:

It’s important to understand that, although the wavefunction has “collapsed” to *Hard*, it’s still also a superposition of *White* and *Black*. Likewise, in *Figure 10*, we have:

And that superposition is important to understanding what happens in the experiment.

In both cases, the first stage is a **Hardness** box. In the first case, *if we measured the electron*, we’d find only *Hard* ones, no *Soft* ones. That’s because the wavefunction is already collapsed to *Hard*. In the second case, *if we measured*, we’d find a 50/50 mix of *Hard*/*Soft*, because the input state there was a superposition of those states.

When we combine the output of the first stage (the **Hardness** box), we regain the input state. The **Color** box is presented with, in the first case, *Hard* electrons, and in the second case, *White* electrons. The results are exactly what we’d expect.

The kicker comes from blocking a path before the **Combine** stage in the *Figure 10* experiment (as shown in *Figure 11* on page 8). But it’s simple to understand because after the first **Hardness** box we have:

The *path1* and *path2* superpositions mathematically combine to result in a |*White*⟩ state vector (that has to be renormalized). But if either are blocked, we’re left with a superposition that the **Color** box splits into 50/50. Note that it’s the phase difference between the two |*Black*⟩ states that cancels them out. The two |*White*⟩ states have the same phase and reenforce (hence the need to renormalize the vector).

Bottom line, the experiment results are easily understood in terms of what the wavefunction is doing — how it evolves as the result of interacting with the boxes.

]]>I’ll leave off on further elaboration below. I took it up through the three-stage experiment that can be replicated at home with three polarizing filters. It’s a cool demonstration that shows we can experience quantum effects in our classical world.

More importantly, to wrap this up, hopefully you see what I mean by “interaction” — an umbrella term for many kinds of wavefunction changes (“collapses” or “non-linear updates”). That part is all QM 101. The speculation on my part is that what you term “dynamic collapse” — the kind involving localizing the “particle” — isn’t *that* much different from the shifts due to magnetic or polarizing interactions. Both involve non-linear wavefunction updates, but it’s only when we localize or “measure” the “particle” the wavefunction represents that things get “spooky.”

I further speculate that vibrations in the quantum field — Bohm’s guiding waves — are the thing. They don’t guide a particle, they *are* the “particle” — its energy is spread out in that wave. That much is what QFT basically says. The speculative part is the non-local way the energy of that spread-out wave instantly transfers to a spread-out wave in a different quantum field. The vibration in the EMF field that’s the “photon” suddenly, at a certain point, becomes a vibration in the electron field that’s the “electron.” That’s definitely spooky and I have no explanation at this time.

*But!* đŸ™‚ It does solve the measurement problem.

Ha! I was actually in teaching (or mansplaining) mode. This stuff is freshman QM and doesn’t take much thinking. It’s just a detailed explanation of these experiments. The impromptu sense, I’m sure, comes from writing it off the top of my head, as if we were hanging out in a bar. đŸ™‚

I’m sure you’d find it not over your head at all, but it does take the interest and desire to get down into the weeds. Much of what’s here channels that first lecture Adams gives. These are like the two-slit interference experiments in showing us something important about the QM world.

]]>I actually had missed it. Looks like you’re thinking on the page. Which I do myself at times, so I totally understand the impetus. But I’m afraid it’s too far over my head for me to provide any intelligent input.

]]>In case it’s not clear, in this representation:

The photon (*gamma*, γ) goes through (arrow) a filter (circle labeled ** a**—

Initially, we have:

Or any other eigenbasis. We don’t know anything about the initial polarization, so there’s a 50/50 chance the photon will pass a filter at any given angle. In this case, the first filter is set to an angle of 0° and now (assuming the photon passes — 50% of them will) the wavefunction is:

The last version shows the general case. The key point is that the photon is still described by a superposition. The interaction with the first filter “collapses” the state vector to the |**V**⟩ eigenvector, but it’s still a superposition of other eigenbases. (As shown previously, it’s even still a superposition of the {|**V**⟩,|**H**⟩} eigenbasis with coefficients of 1.0 and 0.0, respectively.)

So now suppose it goes through the second filter, which we’ll say is set to 45°. This gives us the third state of the photon. *If* it passes the filter — the probability is:

Note: This assumes the 45° angle is the same as the |**D**⟩ (diagonal) eigenvector. A 135° angle would match the |**A**⟩ (anti-diagonal) eigenvector.

The photon state is now:

The state vector has “collapsed” again, this time to the |** D**⟩ eigenvector. As before, it still can be described as a superposition, but that superposition is now relative to the |

A key point is that we’ve lost the previous information about the |** V**⟩ value of γ1. If we measure the vertical axis, our results are again 50/50.

Likewise, if we measure the horizontal axis. After the first filter, there was a zero chance of γ1 passing a horizontal filter. But γ2 has a different wavefunction, one oriented at the |** D**⟩ eigenvector, which is 45° from the horizontal. That means, as before, the photon (γ2) now has a 50% chance of passing a horizontal filter.

Assuming it does, we have:

Going through the second filter gives the photon a (50%) chance of passing the third filter whereas, without the second filter, it has a 0% chance. That’s a distinctly QM result, and it can be demonstrated with three polarizing filters. And note that, once again, we’ve lost information about the diagonal and other axes.

It’s actually kind of mind-blowing. đŸ™‚

]]>BTW: I don’t know if you saw (or if you did, if you care about) the more detailed discussion below. I got into it last night, got carried away, more like, so I’m not sure I’ll continue it unless there’s an interest.

]]>Ah, excellent! That MIT 8.04 course, with Allan Adams, is the first one I watched. He’s a really fun teacher. And of all the other lecture series I’ve found, I still think it’s my favorite. The MIT 8.05 course that follows, with Barton Zwiebach, is just as good. (I watched the 2013 **MIT 8.04** course Adams taught. There is also a 2016 version of MIT 8.04 taught by Zwiebach. I’ve been meaning to watch that one.)

So, you’re most excellently on the same page, dude! His *Figure 5*, on page 4, is exactly the three-stage experiment I’ve been referring to. (As well as what I was talking about in those QM-101 posts I linked to.) And all the experiments that follow are versions of where I’ve been taking my explanation about interaction and wavefunction “collapse” (and “measurement” or “observation”).

Many lectures later, when Adams returns to spin (using spin-1/2 particles; electrons), he tells his students that “hardness” and “color” were actually vertical and horizontal electron spin, and the boxes were essentially Sternâ€“Gerlach devices. Similar experiments use photons as the particle and polarizers as the interaction device. They demonstrate the same phenomenon.

What’s happening on page 7 (and onto page 8) is easy to explain in terms of wavefunction interaction. The *hardness* box is an interaction that leaves (“collapses”) the electron’s wavefunction to a known eigenbasis. Note that the *hardness* **eigenbasis** has two **eigenvectors**, *Hard* and *Soft*. If we detected the electron now, it could only be in one of those two states. But so long as we can (completely) describe the electron as a superposition of these, we preserve the original quantum state.

So, on page 7, in the first case we get 50/50 and in the second only *White* electrons. The *combine* box makes the superposed states into a single state, the input state. On page 8, blocking one path destroys half the superposition “collapsing” to a *Hard* or *Soft* **eigenvector**. Since *hardness* and *color* are orthogonal, collapsing to a *hardness* **eigenvector** means losing all information about *color*.

The multi-stage experiments I’ve been discussing (as illustrated by *Figure 5* on page 4) are extensions of this. The bottom line is that interactions “collapse” the wavefunction — update it in a non-linear way — but can still leave it coherent and in superposition of possible states. What we might call “ultimate collapse” comes when we localize or detect the particle. Depending on how it’s viewed, that seems to involve *“spooky action at a distance.”*

[A simple home experiment demonstrating quantum mechanics: Position two polarizing filters at 90° to each other so they block all the light that tries to pass through both. Note that, if positioned 0° to each other, they allow most of the light through (minus any tinting), and, if positioned 45° or other intermediate angle, they allow varying degrees of light through. Now, with two set in the 90° position and blocking all the light, insert a third filter *between* them angled at 45° — suddenly, where light was blocked, an *additional* filter allows considerable light to pass.]

Thanks for the spin links. I also dug up the class notes for that Allan Adams lecture. https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/lecture-notes/MIT8_04S13_Lec01.pdf

This goes to show how imprecise words like “measure” and “collapse” are. Notably, the intermediate sorting between different spins. His example (page 7) includes recombining the pathways, leading to the indeterminate state returning. But that only works if we haven’t done anything to find out which path the particle took before it reaches the combiner. That, to me, seems to indicate we don’t dispense with wave mechanics until the end of the experiment, when information about the spin states propagate out into the environment, which involves decoherence. (At least that’s my current conclusion. Might be different later.)

The term “non-local dynamics” refers to action at a distance. We get that with a physical collapse interpretation. We also get it with Bohmian mechanics. We don’t get it with many-worlds, RQM, or (reportedly) consistent histories. The epistemic collapse interpretations also often claim to avoid it since they’re only talking about our local measurements, if you accept that move.

]]>