This is the third part of a series examining the Many Worlds Interpretation of Quantum Mechanics (the MWI of QM). The popularity of the MWI in books, blogs, and science videos, especially among the science-minded, tends to keep in present in some corner of my mind. Blog posts are a way to shoo it out.
The first part introduced the topic and talked about cats. The second part discussed the Schrödinger equation, wavefunctions, decoherence, and the question of how multiple instances of matter can coincide. That question, to me, is a central issue I have with MWI.
This time I dig into quantum superposition and touch on a few other topics.
I think understanding quantum superposition is one key to unlocking quantum mechanics. Others are entanglement, decoherence, and interference. (The last two are relevant here and discussed, but I’ll leave entanglement for other posts.)
What does it mean for a (quantum) system to be in superposition? I’ve shown the usual bra-ket formula many times:
Where the coefficients, c, are complex numbers, and |0〉 and |1〉 are two quantum states superposed to create quantum state Ψ (psi). Mathematically, we treat the coefficients as probability amplitudes for finding the system in the respective state should we measure it on the {|0〉,|1〉} basis — a measurement that always results in either |0〉 or |1〉.
I mentioned last time that experimenters have placed larger and larger physical systems into superposition. It’s often done with beams of atoms or molecules sent through fine gratings in experiments similar to the two-slit one with light or electrons. In fact the progression from photons to electrons to atoms to molecules to viruses demonstrates the wave-like nature of physical objects (which, of course, photons always were).
Experimental quantum physicist Aaron O’Connell and his co-workers put a physical micro-beam (“one micron thick and 40 microns long” — trillions of atoms) into superposition. The beam acted like a tiny tuning fork; it would vibrate at a resonant frequency if voltage was applied. They first demonstrated a “quanta” of vibration (a phonon) and that the resonator could also be in a non-vibrating state. Then they created a superposition of the non-vibrating and single-phonon vibration states.
Pretty impressive. (See this Scientific American article or this link to the paper.)
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The incredibly difficult to achieve conditions for superposing large objects supports the idea that the quantum domain is different from the classical domain. Why and how are open questions, but we see over and over the need for environmental isolation, extremely low temperatures, and a vacuum, to get quantum effects.
This supports my sense that wavefunctions aren’t meaningful for classical objects. They may well exist in the abstract sense, but as discussed previously I question how meaningful they can be.
Regardless, it clearly demonstrates the challenge of superposing large objects. Specifically it seems to say superposition is a quantum effect. And yet MWI requires that entire universes be in superposition. Or at the very least, boxes with cats in them. This is part of what drives the MWI to insist everything is quantum — superposition doesn’t apply to classical objects.
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Which is not to say there aren’t forms of classical superposition. The same note played on a guitar or piano or saxophone sounds different because of superposed harmonics (overtones) to the base note. These depend on the physical structure of the instrument, so the notes, despite the same base pitch, sound very different.
(They also have different loudness dynamics, but even if that could be ignored the notes would be clearly identifiable.)
The complex wave surface of any large body of water is a superposition of all the waves sources that contribute.
In fact, note that, generally speaking, classical superposition always involves wave mechanics of some kind. (At least any example I can think of does.) Given the wave-like nature of quantum mechanics, superposition is a nature feature.
There is perhaps a slight difference in that classical superpositions are direct sums of the values of contributing parts. In a quantum superposition the position of the wavefunction vector reflects the contributions. We use Fourier analysis to tease out classical contributors and inner products with eigenvectors to tease out quantum sub-states.
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In any event, we have, on the one hand, the superposition of the Schrödinger equation, which really amounts to saying: either this or that state with this or that probability. The mathematical superposition here isn’t mysterious.
Physical superposition seems to come in clear wave-like forms, but might have more mysterious instances (such as vibrating beams). The wave-like form doesn’t seem that mysterious other than matter acting wave-like. (With individual particles that seems almost normal to me.) Vibrating beams might turn out to be based on wave behavior, too.
Superposition seems a natural feature of any system governed by wave mechanics, and its presence in quantum mechanics may supervene entirely on the wave-like nature of QM.
My bottom line, superposition as we know it doesn’t seem up to the task of supporting superposed cats (let alone universes).
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Consider the paradox in the Wigner’s Friend scenario. It comes from Wigner’s belief he can model his friend’s lab as a superposition of his friend having measured |0〉 or |1〉. If we deny the wavefunction is meaningful for the friend or the lab, then the paradox vanishes, because Wigner has an incorrect belief.
Thinking about it from the friend’s point of view, aren’t we all in a supposed superposition of states from the point of view of distant friends? I have a sister in California. If I take Wigner on faith, from her point of view, I’m in a superposition of all the possible states I could be in (including being abducted by aliens).
Obviously from my point of view, my state is collapsed into whatever I’m actually doing, but under the MWI my sister’s point of view would be correct because all those versions of me actually exist. She just doesn’t know which branch of reality she’s in.
Or (and this is my vote), wavefunctions aren’t meaningful for classical objects. Cats, let alone scientists or friends (let alone anything bigger), because they are constantly observed by self and environment, are never in superposition.
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The idea behind MWI is that observing a quantum system that’s in superposition causes a superposition of the observing system. (Expanding that to Wigner, his knowledge an experiment is being performed in the lab supposedly puts the whole lab into superposition according to Wigner.)
In the classical beam-splitter, the device supposedly enters a superposition in which both detectors trigger. If the device has, say, red and green lights to signal which detector fired, there is a superposition of both lighting up. That leads to a superposition of the lab and scientist seeing green photons from the green light or red ones from the red one. Some believe the superposition expands limited to the speed of light, others believe an entire universe effectively springs into being. Or, per the discussion of cats, there were two identical universes all along, and they diverged into one where red lights and one where green lights.
Or,… MWI is false, and none of this is true. As appears to our senses and instruments, the particle is detected in only one place and the wavefunction collapses (as mysterious as that might currently be). To paraphrase Picard, there is only one light.
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One issue here is what’s known as the preferred basis problem. The usual version of it asks why reality is observed to have definite position when there is also an observation basis for momentum in which position would be indefinite. What chooses the position basis for our perception of reality?
It’s gotten me to wondering why we perceive “particles” — which represent both observation and wavefunction collapse. Any detected particle represents a position measurement, another instance of reality apparently picking a basis.
[FWIW, I think of “particles” as fundamentally wave-like but with localized point-like interactions with other “particles” — the photoelectric effect is a good example. Photons are absorbed by electrons.]
Proponents of MWI use decoherence (that magic word again) to resolve the preferred basis problem, but their efforts seem open to dispute.
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There is another issue I think of as somewhat related. A wavefunction describes everything about a given system, and can provide a probability of any possible measurement of that system at any point in the future. For an isolated quantum system, this is doable and meaningful.
So, as I’ve pointed out before, a wavefunction for the cat experiment and lab needs to include all possible measurements, including blown fuses, power fails, car crashes, weather events, asteroids, and so on. The only way that’s possible is to have a wavefunction for all of reality — or at least everything within the lab’s past light cone. Since various light cones intersect, this implies only a universal wavefunction is up to the task of describing the lab.
The bonus is it also describes everything Wigner and everything else.
But how meaningful is a universal wavefunction that needs to describe the position and energy potentials for every particle in the universe? Remember that a wavefunction reduces all of that to a single vector, a single arrow moving around a Hilbert space with infinite dimensions. How meaningful can that single arrow be?
Now step back. In MWI that arrow not only has contributions from every particle in the universe, but from every particle in every universe. If a universal wavefunction isn’t meaningful, how much worse is a reality wavefunction with bazillions of universes?
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I haven’t touched on probability in this series. I explored it in a post I wrote year, so I won’t say much about it here. As with the preferred basis problem, probability is generally acknowledged as a challenge for MWI. Some believe it’s as big an issue as the preferred basis problem. (Yet everyone seems fine with physical matter coinciding. I don’t see that discussed much.)
At the very least, MWI confounds our usual notion of probability — that improbable events only happen rarely. In the MWI, improbable events always happen; what’s rare is find oneself in an improbable branch (or superposition).
Supposedly the math works out either way (I try to avoid statistics and probability math), but one has to wonder about the astonishment of those in branches of reality where 64-bit random number generators turn out all-zeros or other highly structured (and thus highly improbable) pattern. Of course an RNG can do that, but the odds against are so high it’s like entropy running backwards.
Or, one can just deny that MWI makes sense.
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One thing I’ve wondered is how (and if) two-slit experiments apply to MWI. Physicist David Deutsch believes they demonstrate MWI, but this is disputed.
I don’t see that the two-slit behavior has anything to do with MWI. To me, it’s a real world example of superposition and/or wave-like behavior. The interference seems fully explained by QM (in some cases even by classical mechanics). I do not see how or why the particle needs different worlds to reach the screen. (On my TODO list is his book, The Fabric of Reality. I’d like to know what he says.)
Where I can see MWI applying is in where the particle ends up on the screen. That seems observationally a random quantum event, an apparent wavefunction collapse. One implication is that a branch exists for every possible location in the screen that could have received the particle.
Note that, if we just look at the final pattern, there might be no branching since individual particle locations don’t matter, only the final pattern does. But we could amplify the screen, recording it with each particle as in the Merli-Missiroli-Pozzi experiment. If MWI is true, that would seem to require branching.
But I don’t see how MWI applies to the interference itself.
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Another reason I want to read Deutsch’s book is his claim that MWI explains the power of quantum computing. I don’t see that, either.
To me the power of QC comes simply from the power of qubits, which have two analog degrees of freedom compared to the single binary degree of ordinary bits. That expands the power of qubits exponentially both in having multiple degrees and in those degrees being analog. That creates a value field in comparison to the on-off of a bit.
I find the power of QC no more mysterious (outside the mysteries of QM) than I do that, per the above, guitars, pianos, and saxophones, all sound different. Very roughly speaking, the same sort of computation is occurring in both cases. Instruments “compute” how they sound by combining harmonics. Quantum computers compute through entanglement and state-changing operations.
No need for MWI that I can see.
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It’s sometimes claimed MWI doesn’t have wavefunction collapse, but I’m not sure that’s entirely true. Consider a simple spin measurement using a Stern-Gerlach device. MWI claims two versions of reality exist, one spin-up, one spin-down.
Okay, let’s accept that premise. The particle’s wavefunction before measuring was a superposition of any possible spin measurement we could make. That is, it can be expressed as a superposition of spins in any basis.
But after the measurement both realities see a collapsed wavefunction. In one branch, it’s collapsed to spin-up, in the other to spin-down. Both branches can characterize the new state as a superposition of states in some other basis, but they would express it with opposite phases because certain operations on the superposition need to recover the known eigenstate.
The point is that both branches see the same “collapsed” wavefunction as in a standard interpretation. In either case, the wavefunction suddenly changes to a known eigenstate.
I’ve seen MWI proponents claim it’s due to interactions with the device and environment, but doesn’t that same logic apply to the standard interpretation? Interactions cause the wavefunction to change. Of course they do.
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Bottom line, on the one hand an extravagant theory with a reality wavefunction with infinite universes superposed, physically coinciding, but not interacting because “decoherence,” and little clarity on probability, how branches happen, or why reality has a basis for appearing as it does.
On the other hand an incomplete theory with a mysterious divide between quantum and classical (but we’re working on it and making progress, and I think it’s kind of a matter of time until we resolve it) and some big questions to answer about measurement.
Even on the premise that everything is quantum, MWI still fails for me because the classical world is singular. Quantum objects might superpose, but classical ones don’t.
Reality is what has been observed, and the universe is always observing itself. The cat observes itself; the detector observes itself; the radioactive sample observes itself. We are obviously not in superposition to distant friends because we observe ourselves. So does the universe. It’s always peeking in.
Stay singular, my friends! Go forth and spread beauty and light.
∇
Logos con carne 
July 9th, 2021 at 9:17 am
This probably the last of the series, although I had intended to explore actual experiments in more detail. Another time, perhaps!
(I’ll be dog-sitting my pal, Bentley, this weekend, so might not be online as much as usual.)
July 9th, 2021 at 9:38 am
A very rich discussion. I wrote a long comment on your first MWI post but deleted it partly because I wanted to see the second and this third before I said anything. I think you’ve now touched on a lot of what I had to say, but hopefully you’ll find the following worthwhile.
That earlier comment centered on the question of whether the world “branches” in the details of the math of QM, if we assert that there is only unitary evolution (which is the starting point for Everett’s Relative State Interpretation, MWI, and other interpretations). I think there are no branches in the math, in which case RSI and MWI become apparently indistinguishable from a many worlds interpretation of classical probability (in which every possible world really exists but it’s completely inaccessible to any other possible world and each is at all times slightly different from all the others; that’s just one of several competing interpretations of probability in the philosophy literature.)
The RSI seems particularly clear that there is —for me, now— a definite history of recorded experimental results, which is not different from a definite classical history. For the future, saying that (1) knowing only the quantum state only tells us probabilities for what a future result will be is not different from saying (2) that knowing less than every detail of a classical state only tells us probabilities for what a future result will be (and, per our previous to-and-fro, knowing every detail, and being certain we’ve missed no details whatsoever, is tricky if there’s noise at every scale). I think it may be this closeness to a classical model that makes RSI (and MWI, when it follows the mathematics, not the bombast of branching worlds) so attractive to people.
One thing that I’ve found it useful to focus on, which I think you don’t as much, is the extent to which a quantum state is known or hypothesized. If a quantum state is confirmed by experiment to be a superposition and not a mixture then in that sense we can we say “here’s a superposition” differently. To make that confirmation requires us to perform incompatible measurements (that is, on the idea of “incompatibility” in the quantum probability literature, measured probability distributions that do not admit a joint probability distribution), but I think that’s only possible in practice if we perform incompatible measurements on different subensembles, which enters into a whole array of issues.
July 9th, 2021 at 10:47 am
“I think there are no branches in the math,…”
This is a huge question I have about MWI. I explored it a bit in the first post, and I’d really like to see a Schrödinger solution for a beam-splitter. In lectures I’ve seen animations of the wavefunction for a particle tunneling through (or scattering off) a barrier. The description of position has a single particle approaching the barrier, but then it describes two, one that scatters, one that tunnels.
So in this sense the math appears to “branch” but was that math always a superposition of two particles, or is the appearance of the second one created at the barrier? My math isn’t yet up to the task of being able to figure that out.
“…that knowing less than every detail of a classical state only tells us probabilities for what a future result will be…”
Could be. The probabilities in QM come from inner products of vectors. Would a classical approach give the same results?
“One thing that I’ve found it useful to focus on, which I think you don’t as much, is the extent to which a quantum state is known or hypothesized.”
I’m not sure I followed this. Can you give me a concrete “for instance”?
July 9th, 2021 at 11:24 am
About your first: I think I haven’t included links here to the three posts I wrote last year on a website called The Quantum Daily, after AlgKoopman was published:
(1) https://thequantumdaily.com/2020/02/16/unifying-classical-physics-and-quantum-physics/
(2) https://thequantumdaily.com/2020/02/23/unifying-collapse-and-no-collapse-approaches-to-quantum-physics/
(3) https://thequantumdaily.com/2020/03/08/breaking-the-hold-of-bell-inequalities/.
In the second, I say this, about the branching or not:
“If there are no collapses, however, then there is another important property of measurement, both for classical mechanics and for quantum mechanics: when we repeat a measurement, we always get exactly the same measurement result. This has many consequences, but perhaps the most significant is for the many-worlds interpretation of quantum mechanics: there can be many worlds, but there cannot be any branching.
Here’s why: suppose that two worlds are different but they are both branches from the same, earlier world. If they are different, then there is at least one measurement that will give different measurement results. But that’s impossible, because we could have performed the same measurement before the branching, in which case whatever measurement result would have been obtained then would have to be same as two different values.
Nonetheless, thinking classically —which, if we’re alive to subtleties, we can now allow ourselves to do—, there can be an appearance of branching if the dynamics is chaotic. We might notice no difference between two worlds until the chaotic dynamics makes the difference suddenly conspicuous.”
There’s math to back this up, because we can compute the correlation coefficient for the results of doing the same measurement twice: it’s 100%. This result holds without having to introduce collapse of the wave function at all, but it does require the measurement to have discrete results (which in practice all measurements do, as we discussed earlier). There are mathematical niceties enough involved for me to worry about making huge claims for this construction, however AFAIK that hurts both ways: MWI proponents have to worry about the same niceties.
About your second: if we work in Koopman’s Hilbert space formalism for classical mechanics, then probabilities come from an inner product of vectors (or, as for QM, from a trace, for mixed states). it’s that parallelism that makes Koopman a worthwhile testing ground for ideas about the similarities and differences between classical and quantum.
About your third: I think I have to go sideways to (try to) get at this. The main issue is perhaps whether we think The State (1) really exists as a thing whether we perform any measurements or not; or (2) represents what we’ve recorded about The World and what we expect to record in future. If it’s the former, then what measurements we perform make no difference to the state, so my comment is irrelevant and forget it.
If it’s the latter, then we can’t say the state is a mixture or it’s a superposition unless we perform experiments that show that it is one or the other. To show one way or another, we have to perform incompatible measurements because, putting it briefly, what most people would call “classical” measurements are always consistent with saying, “look, a mixture”.
For completeness about things published about AlgKoopman, there was also https://news.yale.edu/2020/03/02/insights-outcomes-thermodynamics-and-algebra-everything (100 words!) and Annals of Physics selected AlgKoopman as a “highlighted article”, so there was this, by a journalist, Rob Lea, https://www.journals.elsevier.com/annals-of-physics/highlighted-article/solving-the-quantum-conundrum-uniting-quantum-and-classical
I could never persuade any other journalist that AlgKoopman warranted an article in a popsci website or magazine (I did try, but I guess I’m too crazy, I’m too old, it’s still too much work-in-progress, or for whatever reason no journalist bit.)
July 9th, 2021 at 7:44 pm
I read the three Quantum Daily articles. I confess I’m a little at sea; my background may not quite be up to fully understanding. I like that the third article has concrete info on a Bell’s test. I need to read that again.
One thought I have about signal analysis is that the existence of a signal means a measurement of some kind was made to generate that signal, so any wavefunction collapse has already happened. I think that’s why I have trouble embracing a signal analysis approach, because my interests lie in what generated that signal. And why. No question signal analysis is crucial — as I understand it, CERN is huge on that — but (rightly or wrongly) it feels like a different sector of science to me. It feels somehow after-the-fact. Could that be why science journalists aren’t biting?
My question about the Schrödinger solution for beam-splitter… In lectures I’ve seen that solutions can include multiple terms. For instance the solution for a freely moving particle seems to contain terms for motion in both directions with coefficients that pick out one of them. So does a beam-splitter solution have terms for two particles (one that scatters, one that passes through), or do terms describing a single particle evolve such that the particle diverges to two probable locations? (I watched a series of MIT QM lectures and semi-sortof kept up. I’d like to watch them again now that I’ve learned a bit more. My ultimate goal is programming some of my own Schrödinger equation animations, but I’m starting to realize how long that road is. So much to learn!!)
Speaking of which, I need to understand more about “no collapse” theories. I’m still trying to completely understand how MWI is supposed to work without it (and I kind of suspect, per the post, it doesn’t). I sometimes feel “collapse,” like “decoherence,” gets used in different ways, and I can’t always keep up.
There’s collapse of the Schrödinger equation, which some point to as a glaring problem with Copenhagen. I don’t have a problem with it; I just see it as part of our not having figured out QM yet. Then there’s what seems to happen physically when a quantum system interacts with another system. A silver atom’s spin state changing due to a Stern-Gerlach device. That doesn’t seem mysterious to me, either. (On some level, of course a strong magnetic field would affect the atom!)
Ugh, I’m getting lost in all the stuff I don’t know but want to. I need to chew on this some more…
July 10th, 2021 at 7:47 am
For Gregor Weihs’s experiment, I think the slides and what I say about them in the talk I gave at IQOQI in March this year, starting at 10:14, might also be helpful, https://youtu.be/1mfGZFkOvZ0?t=614. I can’t remember linking to that here before? What comes before that segment might usefully set the scene for how I think about signal analysis, whereas what comes after tells a more mathematical story. The graphics are better, at least, and I think what I say about measurement incompatibility is clearer. I’ll e-mail the slides PDF to you as well.
I agree that signal analysis definitely has its failings, and I can see that I might be emphasizing it too much, but my feeling is that thinking in terms of particles has its problems, not all of which are fixed by thinking in terms of wave/particle duality as causes of our records of experimental results. If we back out of those approaches, one way forward is to ask more carefully how signal analysis would justify using only such approaches, or at what points it suggests alternative approaches. I’ve been thinking in terms of events and patterns of events instead of in terms of particles as causes of those patterns for over 20 years, often having to translate back and forth into particle thinking, which I always found helpful. I think I’ve been finding that thinking in terms of signal analysis is even more helpful because it allows us to embed the signals into a wider world of a noisy field theory.
I don’t go as far as Bell’s famous article “Against Measurement”, but I think it’s worth not always thinking of experiments in terms of measurements and their results. For me that’s because I don’t always want to think of a “measurement” as a “measurement of a property of a particle/wave thingamagig”, insofar as I think of any record of a signal, as an event timing or as a voltage at a particular time, or whatever, as affected by many aspects of the surroundings of the apparatus. If we get a little wild and woolly, every “measurement” is a “measurement of the universe as seen in the formal laboratory record of that signal”, which has to somehow be made to sit well enough with less wild and woolly engineering.
I skipped the beam-splitter, above. I’ll give it a try here, in quantum field theory terms: A laser conditions or modulates the state of the (quantized, noisy) electromagnetic field to be different from the vacuum state of the EM field in a particular way, changing the statistics of events in avalanche photodiodes (APDs), depending on where the APDs are placed. Now we can put different materials (and mirrors, lenses, half-wave plates, wave-guides, and all the paraphernalia of quantum optics) close to the output of the laser and see how the statistics of events in APDs in different locations change. It turns out that we can condition or modulate the noisy EM field (using what we call a beam-splitter but that we could perhaps also call a coincidence-creator), so that even though the events are still at random times (the noise), in accordance with some statistical distribution, there are nonetheless event coincidences (not all events are coincident, but many are! I think of this as “noise engineering”, amplifying and minimizing noise in different places.) Even more than that, and considerably trickier, we can put other apparatus close to the APDs that condition or modulate the EM field so that Bell-CHSH-type inequalities are violated. Section 7.2.1 in AlgKoopman, and part of that talk at IQOQI, is about how I think we can and should pick apart how such correlations and violations evolve over time under different conditions.
Most of what I currently have to say about the relationship between collapse pictures and no-collapse pictures of QM is in the SleightOfHand paper. Although some people seem to be seeing it as significant, I’ve not yet had anyone ask me focused enough questions for me to move on very much. For me, that paper gives a formally mathematical enough relationship between collapse and no-collapse pictures for us to be considerably clearer about what RSI/MWI commits us to as a picture of QM, enough that I’m now mostly OK with RSI.
July 15th, 2021 at 12:02 am
I’ve started watching your videos (in the order posted on your YT account — the IQOQI one is last but I’ll get there). You might want to consider reshooting the one with the “up the nose” camera angle. Not a flattering look. 🙂
I think I found, in your slides, a key aspect of how we see things differently:
I’m pretty firmly of the opinion we should say “yes” to both. 😉
Another difference, perhaps, is that I’m also pretty firmly realist, and I noted you acknowledged that your theory here is anti-realist. (I can see why Andrei referred to it as “instrumentalist.”)
I do agree the notion of “particles” is problematic, but my approach lies in trying to solve those problems. As I believe you point out, the key mystery is why something with a wave description and arguably very large size has point-like interactions. That said, and I think is part of what drives your approach (?), that interaction is a disturbance in the EMF field that transfers energy to the electron field of some “electron” in the material of the detector. Who can really say how actually “point-like” that interaction really is. The electron’s position isn’t localized either.
In fact, as with the mystery of which radioactive atom in a sample decays to preserve the half-life stats (which seems to require a collaboration of all the atoms in the sample), the question of which electron of which atom in the detector may well involve the entire electron field of the detector. If Frank gets cross, can it really be tied to a specific electron absorbing the photon? The realist in me wants to say “of course” but maybe it’s more complicated than that.
I suppose another difference is that I think there might be a Heisenberg Cut that divides QM from CM. My working notion is that CM emerges from QM. As with anything emergent, it’s possible to describe it in terms of the lower level, which perhaps is what your program of bringing noncommutativity to CM. (Ironically, it seems Andrei would prefer to take commutativity to QM.)
I’ll come back to this later. I just wanted to let you know I hadn’t faded out completely. It just takes me a while to get to things these days. Two last bits:
“I skipped the beam-splitter, above.”
I get how you’d see it in terms of your approach. My question in terms of MWI is more pedestrian and specific. How does the Schrödinger equation describe a beam-splitter? Or the two-slit experiment? I’m still trying to learn how to do that math. (So I’m a long way from keeping up with your paper!)
(It is interesting to know about APDs though. I’ve been meaning to look into how single photons are detected. A few Google searches I tried didn’t return helpful hits I guess because I didn’t know what to search for.)
“Most of what I currently have to say about the relationship between collapse pictures and no-collapse pictures of QM is in the SleightOfHand paper.”
What I’ve seen so far is heavily mathematical. I’m not clear on how a measurement can collapse, a phrase I think I saw on a slide. I do get that, in many of these experiments, we make many measurements on presumably similarly prepared systems and treat them as an ensemble.
In any event, I don’t have the focus on collapse (or non) that some do. (Proponents of MWI include it in their mantra, for instance.) I see it as a secondary issue to more primary concerns, such as superposition, interference, and entanglement. Those are physical mysteries I want to solve!
July 15th, 2021 at 12:14 pm
You must be something of a completist if you’re watching everything on my YouTube channel in order! I tell myself that the nose video is appropriately ego-deflationary and I’ll let it be. I’ve always thought it’s bad enough that it’s beyond so bad it’s funny. I’m definitely not someone who never changes their mind, so I will need you to cut me some slack for that.
I’m happy to grant you the yes-to-both. I often feel that “here’s a particle” is much too common in what people say about QM, so I lean into saying the opposite, but saying there are no particles or particle properties whatsoever and that it’s never helpful denies too much, so I try to gradually walk it back. It may lead to trouble if you say that the spin is a persistent property of a particle, however, so, when it is trouble, perhaps it’s preferable to think of that “spin-up” property as only momentary.
I think a similar flow happens in my approach to realism/instrumentalism. Yes, taking signal analysis as a grounding is quite instrumental, but people have become so used to talking about particle properties, and getting into trouble because of it, that I think it’s good to take a time out. If we start from the signals out of an experiment, what can we justify from them? Events, definitely. Some aspects of particle properties, yes, but that’s definitely more hazy. I think what happens between recorded events is “real” even if we have no record of it, but we don’t have a record, so it has an epistemically slightly different status. We can interpolate and extrapolate, and I’m happy and it’s interesting/fun to do so, but also I think it’s best to acknowledge that such will be a guess and an imaginative leap amongst a plethora of possibilities. And then, we also have to say that some interpolations and extrapolations more often work well than others.
For RSI/MWI’s idea of “How does the Schrödinger equation describe a beam-splitter?”, I think decoherence as a description of how events happen in different places works well enough, if we’ve demystified “collapse” and “no-collapse”. I think RSI/MWI adopted the large numbers approach to what a detector does about as soon as the decoherence approach was invented. I take the objection to decoherence to be that it doesn’t change a state that is a superposition into a state that is a mixture, but that’s not an objection if we’re not too realist about what the state is: it’s the record of events that’s real (or the signal that we didn’t record but that we suppose we could have recorded.) That’s more-or-less the idea in SleightOfHand: we can use many different instances of a state-and-observables to model the same record of events, with or without collapse (but, significantly, in mathematical detail).
What I think I will have meant by “measurement can collapse”, or something like it, is that the collapse of a state is a result of a particular use of projection operators, bracketed around a density operator, but we can use those same projection operators bracketed around subsequent measurement operators to obtain the same result. Perhaps it’s an unfortunate turn of phrase, but I think it also somewhat agrees with what Bohr had to say about measurement.
I more think that “we create records of many events, for which we then look for a causal explanation” than that “we make many measurements on presumably similarly prepared systems”, but I’m OK with “similarly prepared systems” if by that you mean the noisy state of the electromagnetic field, not the state of a photon.
July 17th, 2021 at 1:09 pm
“You must be something of a completist…”
😀 Yeah, one might say that. 😀 It’s possible I’m somewhere on the spectrum. OCD, if not a clinical description, is definitely a metaphorical one. I’m usually able to sublimate it into my work. My code, for instance, was formatted with readability in mind (lining stuff up, for instance), and I followed the literary programming technique of ordered functions or methods in a file. Open one of my modules or classes, and you’ll know exactly where to find things.
When it comes to collections of things, yeah, definitely completist. I’ve haunted plenty of used book stores looking to complete collections, and I have all 50 state quarters plus the territories. (And then there’s this.)
“I’m happy to grant you the yes-to-both.”
I do get that from the little asides on the slides. I think we’re more or less on the same page in terms of recognizing that “particle” is a placeholder for something much more complicated and not well understood.
To be sure, I don’t intend any down grading of a program about signal analysis or one that seeks to unify CM and QM. I think those are both really great things! As I mentioned to Andrei, I’m struggling to learn the mainstream math right now, and most of my energy for basic physics goes to that end. But the signal analysis in particular does seem a rich area for development.
I wonder to what extent, or not, your work might intersect with, for instance, the part of CERN concerned with signal analysis of the massive amounts of data that come from their ATLAS, CMS, and other, big detectors. As I understand it, they necessarily throw away more data than they can keep, and that’s data known to contain collision events (let alone data during quiet periods).
I also wonder to what extent the people who built Frank, who is hugely teleological and specific, have investigated the various periods you’ve suggested. The non-event times, the dead time after one, or the power-on versus power-off differences. Seems like designers and builders would want to know those things? Is it possible they might have some of the raw data that interests you?
“We can interpolate and extrapolate […], but also I think it’s best to acknowledge that such will be a guess and an imaginative leap amongst a plethora of possibilities.”
True. My question, I think, is at what point can we allow some faith in, at least, the interpolations? Extrapolation is always tricky, but when one has a lot of closely-spaced data points, and multiple experiments with essentially identical results, is there a point we can become confident we understand what lies between those data points? (At least until something proves that wrong.)
What could we reasonably expect to find at 10-100 meters given what we know about much (much!) larger scales? (I have no idea, but it seems an interesting question.)
“For RSI/MWI’s idea of ‘How does the Schrödinger equation describe a beam-splitter?’, I think decoherence as a description of how events happen in different places works well enough, if we’ve demystified ‘collapse’ and ‘no-collapse’.”
Ah, but have we? 🙂 Before we take off on decoherence, looking at my wording, I may have given the wrong impression about my beam-splitter question. I’m not asking how MWI (or any interpretation) would account for it, but how the Schrödinger equation would express it mathematically. In particular, does it express from the beginning a superposition of two particles whose paths diverge, or does it express a single particle that takes on a superposition of likely positions. (Or does my lack of understanding make the question badly formed?)
But back on the farm, have we demystified collapse? As I’ve mentioned, I do see it as a lesser mystery, but on the other hand, it’s what led to the MWI and other interpretations, so it clearly bothers some!
Collapse is a good topic here. The previous post, part 2, goes into detail about my issues with “decoherence” as the answer to any of this. Perhaps we might discuss it there as a separate thread? (I’ll leave a comment as a seed. Feel free to ignore it.)
“…the collapse of a state is a result of a particular use of projection operators, bracketed around a density operator, but we can use those same projection operators bracketed around subsequent measurement operators to obtain the same result.”
That math is on the edge of what I can follow clearly, so I know what you’re referring to here. I have some difficulty, though, seeing how what appears purely a math operation connects with experiment. What does it translate to in terms of what I could, or could not, do experimentally?
This is, again, my ignorance, but it seems like the ability to do things with numbers doesn’t always have a physical meaning. Can you tie the notion of collapse of measurement to a concrete set of experimental steps?
“I more think that ‘we create records of many events, for which we then look for a causal explanation’ than that ‘we make many measurements on presumably similarly prepared systems’, but I’m OK with ‘similarly prepared systems’ if by that you mean the noisy state of the electromagnetic field, not the state of a photon.”
Oh, sure, you betcha. (I’m curious what your objection is to my wording. Don’t we record events of a specific system and do that multiple times?)
July 17th, 2021 at 2:30 pm
I’m still and may always be too much on the sidelines to get the chance to have a long conversation with experimentalists. I’ve seen people give talks at the Yale Quantum Institute that have veered towards a signal analysis perspective, but I think it’s never been the main course, which is either almost bare math or it’s the QM particles-kinda-go-from-here-to-there story. Which is largely fine, because we’re all well used to translating those stories into Hilbert spaces and operators (and a long list of fancier linear algebra of operations and transformers and POVMs and …), and we hedge everything with wave language as needed.
Part of what I like about Frank is that of course we all know it’s not a teleological story, but I think we also all have to work hard not to let it worm itself into our heads as a teleological story. I think how that goes down might make it possible to think about measurement as much less in our control — which it isn’t because Frank chooses when to get cross, we don’t choose a moment as the moment of measurement. We put Frank in the way and let him do his thing (now say all that without Frank as an intermediary).
In six months time nobody may remember Frank, but he’s showing signs of being something of a meme: I’ve seen multiple people find him curiously different from the usual ways of talking about measurement devices without me pushing him hard.
On interpolation, I think of the J/Psi particle discovery as something of a counter-example. It was only when they scanned the energy spectrum with enough precision that they were able to spot it (https://www.google.com/search?q=J%2Fpsi+peak+graph, for example). On interpolation alone, J/Psi could be as good as nonexistent. Depending on how you compute statistics and interpolate, say with different order polynomials, you can get graphs that look massively different. There can be methods that turn out to work well in many different cases, so we get used to using those instead of other methods: when we find that kind of thing we like to have a sense of why so we don’t overuse it.
I’m almost always nervous of the idea of “systems”. Quantum field theory arguably has no such thing, insofar as there are just regions of space-time and measurements associated with those regions, but QM can’t go more than a paragraph without introducing them. So somehow the idea of a system as something different from a region of space-time has been slipped in. I have a kinda workable sense of how, and yes, it becomes quite solid when systems are tables and chairs, but it doesn’t feel precise enough and my spidey-sense objects much more strongly to this than I see in what other people say about QM. If you say “systems”, I practically have to tie myself down not to object (which I can do, because people get bored with it, but it happens a lot). Bohm’s implicate and explicate order (loosely, there are connections of everything with everything), is something that I find more-or-less congenial, but that’s a dangerously crazy-vague thing to claim any affinity with (it looks to me, however, as if Bohm came to the implicate-explicate order ideas as much out of the math of QFT as out of Eastern philosophy).
July 20th, 2021 at 9:37 am
“I’m still and may always be too much on the sidelines to get the chance to have a long conversation with experimentalists.”
Are there papers published by data capture scientists at CERN (or other labs) or are their processes too proprietary? It does seem this is an area others ought to be considering. Both in terms of signal analysis and small scale observation. Humans poke into everything; one would think this as well. But then science does seem to have some weird oversights.
“Part of what I like about Frank is that of course we all know it’s not a teleological story,”
Can you expand on that? To me, Frank’s design and construction are entirely teleological. By which I mean intentional and for a purpose. Do you define teleological differently? Or are we talking about two different things?
One thing that strikes me about a signal analysis approach is that the signals, as you’ve stressed, come from the experiment but also the detector and all following electronics. An SA approach means having to factor all that into account. One ends up with a theory that includes the whole signal chain. I guess that’s been part of your point all along?
“I’m almost always nervous of the idea of ‘systems’.”
(I assume not the plural use, but the word itself.) I think I see a “system” — as you say — as a ‘region of space-time’ and associated measurements. As with “particle” I see it as a short-hand word that often needs unpacking in specific contexts.
I do think we mean a bit more than just a region, though. The physical structure of that region is significant and has to be part of the account. That’s probably what “system” is reaching for — the notion objects and relationships between them (whatever those objects might be; fields are objects).
One thing that’s becoming clear from the videos and slides is that your program is, as you’ve said, anti-realist (and, I think, strongly instrumentalist). Without in any way devaluing programs based on those notions, I have to be honest that I don’t share them. I’m strongly on the side of philosophical realism, and that extends to scientific realism. My interests lie in theories that explain the physical world.
There is also that it’s a heavily mathematical theory, and a lot of the math is way over my head, so keeping up there is hopeless for me. (The math that appears in some of my posts pretty much represents how far I’ve gotten. A lot of these posts are almost a kind of homework for me — trying to improve understanding by writing about what I’m learning.)
July 20th, 2021 at 11:19 am
As you know from software, entering into a huge body of software and hardware is extremely time-consuming without a guide. I think many people have poked deep into this, but I think it’s not very often discussed in popular science articles or textbooks about quantum theory.
I can see that I introduced a confusion by saying teleological without elaboration. Sorry. As I think I said in the IQOQI talk, Frank is complicated, even perhaps including patterned substructures that are very complicated indeed, but it (not “she/he”) is not conscious (though if Frank were to use a mouse brain as part of the chain of signal analysis, boundaries might be blurred). I think my point is that Frank doesn’t have intentions, but, as you say, the designers and builders of Frank do have intentions.
A system is to me very different from a region of space-time. Part of my problem is that I’m not sure how we should define a system in terms of regions of space-time. The only definition that is consistently used in QFT is Wigner’s definition in terms of irreducible representations of the Poincaré group, which is infinitely extended over all space-time. I think your attempt to say what it is shows clear signs of struggling, then you fall back on an essentially classical idea of objects and relationships between them that has nothing to do with regions of space-time. That’s fine, but QM takes “systems” as an obvious concept whereas QFT takes space-time regions as an obvious concept, which I think introduces a problematic leap given how much rides on it.
Fields (quantum) are not objects! At least, I think they’re objects only in a relatively much more abstract sense than an experimental apparatus. A quantum field provides us with a collection of operators. A quantum state ρ gives us a number ρ(O) for each operator O in that collection. We somehow make a pragmatic bridge between many such numbers ρ(Oᵢ) and particular statistics Sᵢ out of an experiment. Across many experiments over many decades, those bridges become engineering rules. I think of the statistics as firmly associated with objects, the experimental apparatus, and the ρ(Oᵢ) only slightly less so, but without a state to give us numbers I think the association has become too tenuous for us to say that a quantum field, as a collection of O’s, is an object without any qualification. All I’m saying, I guess, is that a quantum field is not the same kind of object as an experimental apparatus.
I started out, 30 years ago, as realist as I think anyone could want, but it eventually seemed to me that it was not good for my state of mind. I became too emotionally attached to one idea or another. So I started to reconstruct myself as an anti-realist. Over time, everything mathematical/physical has become “just” a model, or a placeholder for what there is, or whatever. In many ways, I’m now in the process of reconstructing a more realist way of thinking about the mathematics I’ve been doing. I doubt I’ll ever be as realist as someone who hasn’t so resolutely backed away from realism for so long, but if that’s the price of doing the work without falling apart, so be it, I guess.
Signal analysis is not isolated from the experimental apparatus that generates it, so I think we can fill in between what we have as formal records from our experiment, just as we can fill in from background knowledge and a subway map to get some idea of what each station might look like on the surface. Given background knowledge and an abstract quantized simple harmonic oscillator, think what an actual experimental apparatus that is modeled by that qSHO would look like? Some people, having more background knowledge, will be able to do that better than others.
I think the game I’m playing takes existing equations in the physics literature and fills in between them in mathematically unusual but correct enough ways that a physicist hopefully can recognize them. I get out of the box and then I try to come back. If I do it well enough I can get the work published in decent physics journals, which I have done, but I might not be able to do in future. I can’t make very good contact with the experimental apparatus because I don’t have enough of that experience, but perhaps I can make enough contact with physicists who have. At the same time I’m apparently interested enough in making contact with interested non-physicists to expend considerable effort replaying the mathematical ideas in different ways to see what happens next. We can stop now, if you like, or whenever.
July 22nd, 2021 at 12:52 pm
“We can stop now, if you like, or whenever.”
Your most recent comment confirmed what this implied. As I replied, totally understand, and I hope it wasn’t without value. Your story about realism not being a good fit; perhaps it means you’re a natural theorist. More than just a theorist, an explorer theorist. You’ve certainly given me some new perspectives.
I’ll leave it with this:
I keep thinking about the contrast between Frank-the-APD and Frank-the-human, who, as all of us are, is also a detector. Both are constantly detecting stuff. There is also Frank-the-rock-in-my-garden, who is also a detector (famous in discussions of pancomputationalism, Frank-the-rock-computer).
What all three Franks seem to have in common to me is that they are not quantum objects and cannot be usefully treated as such. As I’ve confessed, my possible insanity is an abiding belief in a Heisenberg Cut that divides the quantum and classical worlds. I believe CM is emergent with its own set of behaviors.
I think all three Franks are classical objects that CM describes well until we seriously zoom into one tiny part of it. The leptons that comprise the Franks are the same in all three cases, and certainly are quantum objects with quantum descriptions. The atoms have some variance — the APD has some exotic ones; the rock is mostly silicon — and the molecules are even more varied. That’s two levels of emergent behavior, each with less and less quantum behavior. The rock won’t have much differentiation (but some) whereas the other two Franks have a lot of internal structure. The human has complex compounds, then cells, then organs, all of which do really well with classical descriptions — in fact, which would be challenging to describe in terms of QM.
So Frank doesn’t seem to have a useful quantum description, but ever smaller sub-sections of him do. By “useful” I mean that no doubt there is some quantum density matrix that describes Frank, but it seems it would be of such vast size that it can only be viewed as an abstraction. Indeed, can we even talk about Frank as a quantum object without including his environment? Even more complex!
Anyway, good luck with your QFT program! Drop by any time!
October 28th, 2021 at 8:08 am
With regard to the claim that quantum computing requires multiple worlds to do it’s special computing, this rebuttal:
Yes! Exactly!