“At root for me seems the notion that QM measurements alter the thing measured (“collapse” the wave-function), while CM measurements don’t (because there isn’t a meaningful wave-function).” Right, but a “state” (a better, more general name than the wave-function, IMO) tells us the results of measurements only relative to a particular choice of operators to describe those measurements. Thus, ρ₁(M₁₁), ρ₁(M₁₂), ρ₁(M₁₃), … can give the same results as ρ₂(M₂₁), ρ₂(M₂₂), ρ₂(M₂₃), …, even though ρ₁ and ρ₂ are different and the measurement operators are different as well. The classic example is of the Schrödinger and Heisenberg “pictures” of the unitary dynamical evolution, the first of which changes the state over time while the measurement operator stay the same, the second of which changes the measurement operators over time while the state stays the same.

A *collapse picture* of measurement dynamics changes the state every time a measurement happens, but leaves the measurement operators unchanged, whereas a *no-collapse picture* has a single unchanged state but chooses different, mutually commuting measurement operators to represent the same measurements. [This is a new enough realization for me that I’m struggling to give a clear discussion of how the mathematics works; furthermore, it’s not something in the literature as far as I know, except vaguely in a paper by Belavkin from 1994, so I can’t tell you which book to look at. That aside, …] To say the above slightly differently, the mathematics of “collapse” of a state is exactly what is needed for us to be able to construct **joint probabilities**, but joint probabilities are exactly what we need for us to be able to give a classical description, using a collection of mutually commuting measurement operators.

Suppose we throw two dice and we always get a double: we would say that those results are 100% correlated. We don’t know how it’s done, but we do know how to describe that circumstance. We have a probability distribution p(x,y)=1/6 if x=y, otherwise zero.

Now we throw the same two dice, but we only look at one of them. We have a choice for how we model this experiment: if we see a 5 for the one die, we can “collapse” the probability distribution for the other die to say p(5)=1, otherwise zero; or we can work with the probability distribution for the two dice unchanged, and just note that the result of the first dice is 5. These are, I think, different pictures of the same situations, which can be more or less useful in different experiments. It’s not clear that one is right and the other wrong, but I think the empirical content of the different approaches can be made to come out the same when we perform thousands of experiments, which is arguably what matters in physics. Different ideas of what probability is “really” about might prefer one or the other picture, and might have different consequences for what future experiments we think it would be interesting to perform, however I don’t see a way to justify one or the other picture from experimental results alone.

If for a given preparation for an experiment we repeatedly measure what we call spin up-or-down followed by spin right-or-left, followed by spin up-or-down, we will obtain a given set of correlations and other statistics for that set of three measurements. We can write down a classical state that generates the statistics of those three joint measurement results. We can also write down a different state that changes systematically after the first measurement and again after the second measurement, which gives the same joint statistics. They’re very different theoretical pictures of the same world. There’s a lot to be said in favor of the “the state changes” approach at one level, but when we look at details of the measurement device, in which signal analysis looks at the output of every device picosecond by picosecond and it’s not just about a 0/1 result, I think it can also be helpful to work with a state that models correlations in a relatively simple way instead of with a state that changes.

Does that seem helpful? Thanks for pushing me to think more about spin measurements, in any case!

]]>Totally agree! Tracing back, this sub-thread seems to have started when I distinguished spin measurements from position/momentum measurements, and that came from talking about noncommutative measurements. Which came from how such are an oft stated supposed difference between QM and CM.

At root for me seems the notion that QM measurements alter the thing measured (“collapse” the wave-function), while CM measurements don’t (because there isn’t a meaningful wave-function to collapse). Spin measurement experiments seem to demonstrate this nicely in allowing multiple measurements on a quantum system. (Beam-splitter experiments usually measure just once.)

[For me there is also the question of the ontology behind multi-stage measurements. Is there something like an actual spinning string? Or a non-spinning string with a wave running along it for spin? Does the spin measurement — however it’s done — change some physical aspect of the (in this case) silver atom? The math matches experiment, but what is it describing?]

Returning to the present, as you go on to say, reality has a way of humbling our best ideas. I very much agree science is a contingent process that seeks to converge on an understanding of the patterns we observe. I think we both see QM as not quite ready to come out of the oven.

*“If our minds can concentrate on perhaps half a dozen things at a time, however, I think it’s good to focus on having those half dozen things be at multiple scales.”*

Totally agree again! People can walk and chew gum at the same time. (While texting!) And, as you go on to say, the more context and background one has, the richer the experience.

*“100% correlation is just a statistic that can happen, so we have to be able to model it when it does happen, which we can; when it happens in the results of an experiment, then it is notable.”*

I think I’ve lost the thread here or just aren’t keeping up. We’d wandered into the MWI, and perhaps it isn’t particularly relevant here.

The thing that impresses me about spin or polarization experiments is the physicality. It isn’t (such as they do at CERN, for instance) a matter of picking out statistical patterns from a very noisy background. One can see non-classical behavior with just three pieces of polarizing filter. (In fact, I think that’s an under-appreciated experiment. To me it’s as mind-blowing as two-slit experiments.)

It’s interesting what you go to say about computer hardware. Indeed. Circuits are designed so transistors are run in saturated mode, either all on or all off. Capacitors dampen voltage fluctuations. At small scale and fast cycle rates, RF coupling is a problem, and at really small size scales, quantum issues arise.

It helps highlight something I’m vaguely trying to get into focus… Computers can be built on large more physical scales that effectively banish noise simply due to scale. A mechanical calculator, for instance, is almost physically incapable of accidental error. Per Church-Turing, such machines would be equivalent, in principle, to noisier machines.

With computers it’s the information patterns that matter; that’s what underlies C-T, the information patterns. Now there’s a whole thing about dualism with digital computing, and the real world is different (noise and all), but what I’m fumbling for is the idea that the patterns in our measurement data are telling us (I believe real) things about the physical world.

Our conceptions of reality may be only a kind of wireframe model, but I do think that model reflects something real. The correlations in the data are telling us something.

Great conversation! A lot to think about!

]]>I have comment indent level set to three, so WordPress doesn’t offer a Reply link on third-level comments. (A deeper comment level just means things get really narrow.) One trick is to just start a new thread at the bottom, which is what I’ll do here. That way I can merge what’s branched into two sub-threads.

Some start a new comment thread every time they reply. That works fine, especially in cases like this where it’s just us two chickens.

]]>“What’s vexing is that it seems the wave-function can work that way.” I think the point is that there is noise —something *is* unaccounted for in a statistical model— but there can nonetheless be *some* measurement results that are 100% correlated. 100% correlation is just a statistic that *can* happen, so we have to be able to model it when it does happen, which we can; when it happens in the results of an experiment, then it is **notable**.

Even more, a particular 100% correlation may only happen if we apply very complicated algorithms to what we might call the raw data of an experiment. I think that as soon as we notice an algorithm that consistently gives us 100% correlations, we look for a hardware way to apply that algorithm —because that’s an important algorithm!— then that new hardware produces what looks like a qualitatively different kind of raw data, because of that 100% correlation.

That hardware, however, conceals a complete morass of noise. A modern computer achieves a very small level of error by applying error correction at all scales, concealing that noise played a large part in the computer operating at all. It doesn’t achieve 100% correlations for what goes into memory and what comes out, but it gets very close. The engineering needed is remarkable.

From a computing point of view, I suppose a Hilbert space operator just takes an input Turing machine tape, a vector, and produces an output Turing machine tape, in one step. I suppose that any algorithm that can be guaranteed to terminate, software or hardware, can be presented by that. Some of those vectors represent 100% correlations of some measurements with others, but there are other measurements that would be barely correlated at all if we performed them. And thus, I think, the game of measurement and modeling evolves.

Commenting at this lowest level is getting slightly awkward. I have to scroll up a long way to the comment that has a “Reply” button. What to do? Just shutting up for now is an option!

]]>I think the point is that Hilbert spaces of high enough dimension and operator algebras that act upon them are general enough to model *whatever* statistics we could possibly calculate for any actually recorded experimental results. Restricting to only probability densities that admit joint probability densities is an unhelpful restriction that prevents us from modeling some kinds of statistical analysis. What nature does is amazing and amazingly complicated, so we have to do whatever is necessary to model it and our relationships with it in useful ways. I suppose. Some of what we do might make us think we really understand some aspect of nature, but I find myself that a few days or years later I start to see that something or a lot is missing and humility comes in with a bang.

I think losing the sax solo in just simple-minded fourier analysis is absolutely a problem. If our minds can concentrate on perhaps half a dozen things at a time, however, I think it’s good to focus on having those half dozen things be at multiple scales. The overall feel of the sax solo is fine as one level, but I suppose part of what makes a performance really tingle is noticing as well the fingering of a particular sequence, the expression on the soloist’s face, and something of how the rest of the audience is responding; knowing that the wider world is raving about the previous night and knowing something about Jazz as a whole can step beyond the single event. Reducing a forest to just its component trees is not a completely successful strategy, but never taking a more detailed look at the forest leaves us with no appreciation of the trees. “Multi-scale analysis” is about trying to get at different aspects of huge and large and small and tiny.

]]>I may still be missing the point; I quite agree we can use EM to measure spin. (I think even a Stern-Gerlach device would qualify as such?) What impresses me is what happens when we do multi-stage measurements. Even performing the experiment on a single particle, the third measurement has a 50% chance of being different from the first (identical) measurement.

A question I have about a signal analysis approach to test data is forest and trees. For example, it would be possible to analyze the signal characteristics of an RF signal in myriad ways, none of which need include that the signal *content* is a sweet jazz sax solo. My dim conception here is of treating test data as signal to be analyzed. Is the sax solo lost at all in this analysis?

A quick clarification: by identical cats I mean their histories (down to the particle) are identical up to the point mechanism kills one of them. The worlds the cats inhabit have nearly identical starting conditions, but some slightest of slight differences causes the radioactive sample to decay in one but not the other. I think that’s the more sensible reading of MWI than the one promoted by Sean Carroll where one cat branches into two. (Or Carroll himself splits when he uses quantum coin app to tell him whether to jump left or right during his evangelistic talks about MWI.)

What’s vexing is that it seems the wave-function can work that way. (One reason I’m trying to learn the math of QM is to better understand this situation.) In lectures I’ve seen visualizations of a particle tunneling through a barrier. In those, the wave-function, after tunneling, “branches” into descriptions of two probable locations for the particle, one that tunneled, one that bounced.

When a photon’s location is split by a half-silver mirror, is the proper wave-function description of one photon that branches to having two probable locations? Or is it a superposition that describes two paths for the photon from beginning to end and those paths are the same until they diverge at the mirror? Or are those just two options at describing the situation?

Everett’s description, to me, seems to suggest a superposed quantum system interacts with a measuring device causing a superposition of possible measurements, and this spreads to the scientist and Wigner and the world. One cat becomes two. But calling it the “universal wave function” makes me wonder if I’m misreading that.

Thinking about the dual description and the idea that some initial starting condition must differ to create the divergence, I’m not sure, under MWI, that *completely* identical worlds can’t diverge given the probabilistic nature of QM. (And perhaps CM!) Couldn’t completely identical worlds diverge by collapsing differently? A photon with a 50% chance of passing through a filter does in one (set of) world(s) and not in other set(s)?

“the way each measurement seems to affect — “collapse” — the wave-function”. Since “The collapse of the quantum state as a signal analytic sleight of hand” is not published, it’s only on arXiv, it doesn’t have the same status as AlgKoopman. But if I make a grand claim for it anyway, what it says is that collapse is an artifact of a particular way of modeling an experiment. That’s fine, it works, but there’s another picture in which there’s a different state and different measurements and there are no collapses. I’ve been claiming that this is not unlike the difference between the Heisenberg and Schrödinger pictures, which apply an evolution to the measurements in the first case and to the state in the second case. That’s just mathematics, so I think we can’t easily just dismiss it, but of course we can suggest perhaps quite divergent ways to think about and to use that mathematics. Strangely, I think that mathematics is vaguely implicit in Bohr’s thinking, but it’s also explicitly enough like some mathematics done by Belavkin in 1994 that Richard Gill pointed me to it.

The account I give above for an MRI —as a purely electromagnetic way to detect the spin precession of atoms that are perturbed by a relatively large EM field and also radio frequency perturbations— seems to me in retrospect to be a moderately potent argument that we *can* talk just about EM measurement. Then we can deduce information about spin properties from those EM field measurements. Of course when I say we measure the EM field, what I *really* mean is that the EM field induces currents in an electronic circuit, which we then record in computer memory as a number (which, if it’s on a hard disc, is just aligned magnetic spins, which we can detect because of its effect on the magnetic field in the hard drive head, so there’s a lot of chicken and egg in such an account!)

I’ve never been a string theory guy. Whenever I’ve tried to read the papers and textbooks, I’ve always been repelled by how easily they leap into (difficult) mathematics without enough understanding of QM in particular.

I hope you find those 20 minutes of the IQOQI video worthwhile. I will certainly be interested in any response.

]]>The way the math works, if we can perform noncommuting measurements on different subensembles, then with enough measurements we can distinguish between mixtures and superpositions. I don’t put much weight on my discussion of cats, which is why I pass it off as whimsical, but that noncommutativity

“there were always two (infinite, actually) cats, but they were identical cats until one infinite bunch diverged from the other infinite bunch.” You modify that slightly later on, to say that different cats “have *nearly* identical starting conditions” (my emphasis).

I think that comes to be almost exactly the same as what I think my position is: essentially just a many-worlds interpretation of classical probability and Liouvillian evolution of a classical probability, so that chaos sometimes makes two worlds that are almost but not exactly identical now quite far from identical after even a short time. All worlds that are different in any way whatsoever *are* different, and it’s the leveraging of whatever that difference is that we eventually notice. As a mostly-empiricist, I don’t think classical many worlds is necessary, but if it makes some people happy then OK. Conservation of energy is OK for the Liouvillian evolution of classical probabilities.

I think superdeterminism is more-or-less coherent, but if noise and the axiom of choice enter into the game then the mathematics is a seriously wild mess.

]]>I want to chew on this one a bit more, but a couple quick responses: I do agree some specific cat can have the macro eigenstates |**dead**⟩ or |**alive**⟩ but I’m not sure they are meaningful. Per your reply, perhaps “not useful” is a better term. It just seems that all the participating terms in the wave-function would make it impossibly mixed.

Now I’m not quite sure what to make of eigenstates such as |*can-be-killed*⟩ or |*can-be-revived*⟩. There seems something of a basis problem there. The “can” could lead to so many possible measurements (can be petted, can be found, can be sold,…).

I quite agree MWI is just wrong. My reasons have evolved over time. My main objection used to be about energy. How could reality branch in light of E=mc2? Sean Carroll speaks of energy “thinning out” which I just can’t buy at all. First there is one cat, now there are two. How is that possible with cats let alone, as the theory implies, entire universes?

There seems another interpretation, that there were always two (infinite, actually) cats, but they were identical cats until one infinite bunch diverged from the other infinite bunch. Other infinite bunches missed the experiment for various reasons, and all sorts of things happened to other infinite bunches. Anyway, there’s no branching of universes, just an infinite number evolving their own wave-function, coinciding with others until they don’t.

I take your point about unitary evolution. I guess the idea is that tiny differences in earlier conditions cause the wave-function to eventually diverge in its evolution. MWI theories are implicitly deterministic and don’t include free will. The idea, as I understand it, is that each world’s wave-function has different starting conditions. The ones “closest” have nearly identical starting conditions and, presumably, evolve the same way until a certain cat either dies or doesn’t. I suspect MWI and superdeterminism theories go hand-in-hand.

Multiple cats gets around the energy issue, and other issues with worlds actually splitting, but opens entire cases of cans of worms on its own. My current question: *How does physical reality coincide?* The canonical answer seems to be “decoherence” but I don’t see how that applies.

Anyway, yeah, MWI is just wrong. (I don’t think superdeterminism is, as they say, even wrong.) 🙂

More later.

]]>Your comments about students and teaching (and quantum reconstruction in general) remind me somewhat of posts Stacy McGaugh has been writing over on Triton Station with regard to dark matter and MOND. There issue there is a view that DM must exist, it’s just a matter of finding it. That blinders many from the latest evidence and thought.

Education is slow to shift sometimes. (Yet oddly over-reactive in other ways.) I suppose a problem with both education and science is the degree to which politics and social biases apply. Or money. Conservative thinking often opposes both education and science. (But that’s a whole other conversation.)

I couldn’t keep up with your speculation about spin and electric currents. I get the sense you’re saying spin *isn’t* a physical characteristic of quantum systems, but I’m sure I’m misunderstanding. A lot of my thought is linked to the Stern-Gerlach experiment with silver atoms in a magnetic field. I agree there are multiple ways to formalize that mathematically, but the physical behavior fascinates the ontologist in me.

Therefore, talking about such small size scales struck a chord. I was a fan of string theory when it first took off (I bought into Brian Greene’s hype), but over the years I’ve lost faith in it (and Brian Greene). But I’ve imagined that if something along the lines of string theory was true, that might give “particles” a physical orientation (down at the string theory scale) that shows up as spin.

As I mentioned in the other thread, the thing about spin that impresses me is what happens with multiple measurements, the way each measurement seems to affect — “collapse” — the wave-function. I imagine the magnetic field used in the spin measurement might align that physical orientation. I know Dirac (I think? or was it Pauli?) calculated quantum spin couldn’t be physical because it would require spinning faster than light speed, but was he thinking down at string theory scales?

I do take what I believe to be your point about measurement statistics. The three results we get of each specific particle are assigned probabilities based on myriad similar test results, so there’s an implicit assumption about reality built in. FWIW, I do think we build a reasonable model of reality from repeated tests. (But like I said, maybe I’m not keeping up with your point here.)

I’m perceiving two distinct key ideas here, one about the role of noise, the other unifying CM+QM. A third aspect involves a signal analysis approach. I find the noise ideas attractive, and I’ve mentioned I’m on board with quantum reconstruction. Signal analysis isn’t something I’ve had much exposure to, so that’s the most opaque part for me. After I get a chance to check out the video and paper I might be able to come up with something intelligent to say.

A fellow coder! I went from being a hardware guy to being a software guy. Retired a bit early when The Company stopped taking custom corporate software seriously. I was a tailor and they were increasingly buying off the rack. The “open office” bullshit was the final straw…

]]>”(I am very skeptical the idea of wave-function is meaningful for macro objects.)” The idea of a state for a macro object makes complete sense. What I think is in question is whether we can perform something like a fourier transform measurement in hardware for a person. Section 7.3 of AlgKoopman is kinda whimsical, but it points out that we can perform an “is the cat dead or alive?” measurement, and we can perform a “can the cat be resuscitated/killed?” measurement, but performing both at the same time is tricky. The eigenstates of “is the cat dead or alive?” are clearly dead and alive, but the eigenstates of “can the cat be resuscitated/killed?” are something like half-dead±half-alive, which I think are not nonsense if we think “can the cat be resuscitated/killed?” is not nonsense.

The sequence of slides in the talk at IQOQI is so graphic that I don’t think I can do justice to a conversation about the Bell inequalities until you’ve had a quick look at the first 20 minutes. I found it very helpful to have a close look at what was once the best experiment around and to see how we can talk about it if we focus on signal analysis and events, the selection of subsets of the actually recorded data, and the various algorithms that are applied to compute statistics. Some people have found the slides telling. Also, you can meet *Frank*, who some people have even quite enjoyed. I emphasize, however, that I personally don’t care much whether we thread faster-than-light communication or superdeterminism or whatever else into our models, because I think our models are massively underdetermined by the experimental data. Given that I think a plethora of models is possible, I’ve felt happy enough not obsessing over one in particular.

Philip Ball’s 20 questions example is one of the best, but it’s not statistical. My view is more that when we set up an experiment that is constructed to produce many millions of events per hour, of course there will be statistics. How those statistics are arrived at may not be accessible, but we can think of it as enough that they are arrived at. Perhaps there’ll be an almost perfect frequency, but the timings of events are more likely to be somewhat random: that still means, however, that there will be an average rate, standard deviation, and higher moments, et cetera. When we change *anything* about the experiment, there will be a small change of those statistics. We’ll be able to tell, after a few years of data, that someone substituted a titanium bolt for a brass bolt, say, because of slight resonances in the statistics over time. We can perform an equivalent of an MRI of the whole apparatus, but, like an MRI, it takes time to collect enough data and the environment has to be sufficiently controlled. Obviously this is different from what you’ll find in books about QM, because in those there are particles all the time, even though we know for sure that talking about particle properties often doesn’t work at all well; the events that might be naively supposed to be caused one-for-one by particles are barely mentioned!

If we record the signal levels out of dozens of devices, giving us TeraBytes of data, all that data is jointly collected, effectively as single data points for trillions of measurement operators. We could say that those trillions of operators do not commute and there’s a collapse of the state after every single measurement, but because all those measurements are jointly collected we *could* also say that the state was effectively a classical state and all the measurement operators commute. The first picture, with collapses, is effectively Heisenberg’s version of the Copenhagen Interpretation, whereas the second picture, without collapse, is effectively Bohr’s version of the Copenhagen Interpretation: recorded results are classical. Single data points for each of trillions of measurement operators doesn’t give us very good statistics(!), so we have to apply algorithms that consolidate those data points into subensembles that we think are similar enough that we can model every entry in the subensemble as measurement results for the same measurement operator. We have to keep track of whether the selection of a given subensemble is compatible with the selection of all the others or not.

We can certainly fill in between the single data point data, satisfying our “strong ontological leanings” and our desire for “trying to visualize some skeletal idea of what’s “really” going on” but if we construct incompatible subensembles then we can’t necessarily fill in between the results of those algorithms. We can have models that fill in between the Terabytes of recorded data when we think of them as single data points for an equal number of measurement operators, but after we have applied some complicated set of algorithms that consolidate that data as large numbers of samples associated with relatively few measurement operators that don’t commute, we can’t. [I said that twice, but I can’t decide which to delete.] Of course models that consistently fill in between single data points for trillions of measurements in the presence of significant noise are wildly underdetermined by the recorded data, so we should be careful not to take any particular model too seriously, but if it helps the imagination enough, it seems to me OK.

It’s perhaps worth saying that I think this places all the noncommutativity in the algorithms we use to analyze the actually recorded signal levels, each of which is effectively a transformation of the Terabytes of recorded data. Much of what those algorithms do is effectively nonlocal and they may subtly encode an a priori ontology — which is OK if so, but it’s good to understand what assumptions have been encoded. I should also mention that I’ve recently come to think that the above account can inform Everett’s relative state interpretation, which I never thought I would hear myself say, however I think MWI is just wrong. The idea of worlds splitting, so that measurement results are different in different worlds at later times, is AFAICT contrary to the mathematics of QM when there’s only unitary evolution of the state over time (in which case both worlds would have to give exactly the same result for the same measurement, for *every* measurement).