The Zen Anti-Interpretation of Quantum Mechanics
scottaaronson.com
scottaaronson.com
Namely, a hermitian operator is some view of the world, its eigenbasis tells you what you can see from that viewpoint. Two hermitian operators can be incompatible in that they can't be simultaneously diagnolized.
Entanglement is another weirdness that makes perfect sense internally. The tensor product of projective hilbert spaces is not the same as the cartesian product. The segre embedding captures this. Theres more to the geometry of quantum phenomena than naively expected.
The outcome of measurements collapsing to the eigenbasis of a hermitian operator has a beautiful an elegant geometric interpretation. It makes perfect sense really, just not classical sense. Decoherence explains why we see collapse to this set very well.
What is utterly baffling and puzzling is that we only ever see one particular outcome. Decoherence cannot explain that and nothing in quantum mechanics explains that.
IMHO this is the fundamental mistake people make: conflating "I measured spin up" with "spin is actually up". Think about it: what is the evidence that there is actually a correspondence between a measurement and some external reality? There is only one possible answer to that: you can correlate this measurement with the outcomes of other measurements. For example, if you measure the same particle in the same basis twice in a row you will get the same result.
But there is a problem with that: if you actually look at the details you will find that it is actually not possible to measure the same particle in the same basis twice in a row because actually making a measurement requires entangling the particle with a macroscopic system, and you can only do that once. The best you can do is run a particle through a series of filters and look at where it ended up. You can then retrodict that the particle went one way or went another way, but you cannot actually measure its trajectory. In fact, you cannot even know that there even is a particle in your apparatus until the end when you actually measure it.
So the only thing you are left with at the end is a single actual measurement, and a macroscopic arrangement of some experimental setup about which you can tell a consistent story retroactively, but where you do not and cannot possibly have any direct evidence that your story is actually true, i.e. that the particle "actually" was spin up. And this is exactly what QM predicts: the consistent outcomes of measurements is not the result of the particle "actually" being spin up or spin down, but because the macroscopic systems (like humans) which compare the outcomes of their measurements are mutually entangled with each other and so decohere into classically consistent states. So if I ask you what you see as the outcome of the experiment, QM predicts that my perception of your answer will match my perception of the outcome. But it emphatically does NOT say that this outcome is actually real.
If the robot's protocol is to measure the particle twice, it will measure the same outcome twice.
> that the particle "actually" was spin up
I didn't say that it was up, I said that it is up. Very important distinction.
> But it emphatically does NOT say that this outcome is actually real.
Seems like a distinction without a difference to me.
> but you cannot actually measure its trajectory
Bubble chambers do measure particle trajectories. https://cds.cern.ch/record/39474
But you cannot measure the same particle twice. If you think you can, describe the experimental setup for me.
> I didn't say that it was up, I said that it is up. Very important distinction.
Indeed. But by the time you see the outcome of the experiment, the particle you measured doesn't exist any more. So what does "is up" actually mean at that point?
> Seems like a distinction without a difference to me.
It's a crucial difference. Our mental models of our classical universe depend heavily on the continuity of identity, i.e. that there are things in the world with properties that persist across time. This what allows us to say things like, "The vase on the table is green." This presumes that the phrase "the vase" has an actual referent, that referent is a vase, and it is on the table, and it is green. We think this makes sense because we can see the vase on the table, and we can see that it is green.
But in order to see the vase, your eyes have to accumulate a lot of photons, and that takes time. So the vase on the table has to persist at least long enough for your eyes to accumulate enough reflected photons to see it. If you stop looking at the vase, the vase is still there. If you look at it again, the vase will still be on the table and it will still be green.
Particle measurements are fundamentally different. It really doesn't make sense to say "the photon in the left arm of the interferometer" or "the electron in the upper branch of the Stern-Garlach apparatus. If you doubt this, read the following:
http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl... http://blog.rongarret.info/2018/05/a-quantum-mechanics-puzzl... https://blog.rongarret.info/2018/05/a-quantum-mechanics-puzz...
> Bubble chambers do measure particle trajectories
No, they create those trajectories. A particle that is not in a bubble chamber doesn't have a trajectory.
> If you think you can, describe the experimental setup for me.
It's called the Stern-Gerlach experiment. See the section "Sequential experiments" on wikipedia:
https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experime...
> But in order to see the vase, your eyes have to accumulate a lot of photons, and that takes time. So the vase on the table has to persist at least long enough for your eyes to accumulate enough reflected photons to see it. If you stop looking at the vase, the vase is still there. If you look at it again, the vase will still be on the table and it will still be green.
I could similarly say that you cannot look at the same vase twice. By the time you measured the vase, the vase doesn't exist any more. Each photon in fact comes from a different vase. So what does "green" actually mean at that point?
This is an irrefutable philosophical position. It all depends on what you define as the same vase, and what measurement means. There are accepted meanings of these words in QM and those meanings coincide with the conventional meanings in the appropriate limit. I'm happy to use different words though, since you're right that those meanings are not exactly the same as the everyday meanings of those words.
> If you doubt this, read the following:
Have you considered the double slit experiment, where the whole point is the difference in length of trajectory?
Note the following facts, consequence of QM:
(1) the fact that if you bloop spin twice that you get the same result twice
(2) the fact that if you bloop a particle with a more or less spherically symmetric wave function (such as arising from a collision) in a bubble chamber, that you get linear tracks
(3) the fact that a single photon can interfere along paths of different lengths
You've painted yourself into a linguistic corner that makes all these phenomena incredibly difficult to understand, and causes you to make statements that contradict experimental evidence under a non-word-play interpretation of the words.
As for point (3), consider that Maxwell's equations are the quantum theory of a single photon. The reason they also work for macroscopic amounts of light, is that the equations are linear and photons only weakly interact with each other. One shouldn't think of a photon as a particle moving in straight lines at the speed of light. A photon is a wave distributed in both space and time. The wavefront tends to move at the speed of light, but you can't think about it as a point particle moving along trajectories. In some cases you can: there are solutions of Maxwells equations in which a wave packet more or less moves in a straight line at the speed of light, and the probability amplitude is more or less zero everywhere else. But the situation being set up in your experiment, or indeed in the double slit experiment, is not of that form.
Therefore, the outcome of your proposed experiment depends on the shape of the wave packet of the photon and the distance difference. If the wave packet is sufficiently localised in space and time, and the distance difference is sufficiently large, then there will be no interference. The wave packet will travel to the half-mirror and split into two, then those two packets will continue traveling such that they never meet again at the same point in space-time (you can see this by visualising the movie of what happens), and there will be no interference. There will be some probability distribution of observing the photon at a given point on the detector at a given point in time, with two peaks in space-time corresponding to the two wave packets.
If however, you decrease the distance difference so that the two wave packets will overlap in space-time again after the bounce, there will be interference.
No, it isn't. There's a reason that Schroedinger's cat and Wigner's friend and "the measurement problem" are a thing. (And see my last comment below.)
> Stern-Gerlach experiment.
The basic SG experiment setup has two components: the magnets, and a pair of detectors. When you compose multiple SG experiments you compose only one of these, the magnets. The detectors are all moved to the END, AFTER the electrons have transitioned all the magnetic fields. So you are not actually measuring the positions of the electrons at the intermediate stages, only at the end, and only once.
So no, the SG experiment is NOT an example of making two successive measurements on the same particle. Go back a re-read what I originally wrote:
> The best you can do is run a particle through a series of filters and look at where it ended up. You can then retrodict that the particle went one way or went another way, but you cannot actually measure its trajectory. In fact, you cannot even know that there even is a particle in your apparatus until the end when you actually measure it.
In the SG experiment, the magnets are the filters. You will find that ALL quantum experiments have the same constraint.
(BTW, the actual term used by physicist is "preparation". You can use multiple SG magnets in series to PREPARE your quantum system, but you can only actually MEASURE it once. Once you measure it, the wave function collapses, and you no longer have the same system.)
> Have you considered the double slit experiment, where the whole point is the difference in length of trajectory?
Yes, of course. You appear to have completely missed the point. The path-length difference in the experiment I pointed you to is orders of magnitude larger than the standard two-slit experiment. That matters.
> if you bloop spin twice
What does it mean to bloop something? You will find that you will have no more success in defining "bloop" than physicists have had in defining "measurement". Here's a hint: are bloops/measurements reversible?
Comes down to definitions of words: same "system" (by which you mean wave function) vs same particle. See bubble chamber: particle interacts with several atoms along a trajectory. Sure, you can claim "the wave function has collapsed after the first interaction", so it's "not the same system"...but then you're just saying that measurement affects the wave function...well, yeah, it does. Or you can say that the bubble chamber "is just a series of filters"...ok sure, everything that happens is just a series of filters, with sufficiently broad interpretation of that phrase.
> You appear to have completely missed the point. The path-length difference in the experiment I pointed you to is orders of magnitude larger than the standard two-slit experiment. That matters.
Seriously? I explained in detail what will happen in your proposed experiment as a function of path length and why the explanation comes down to the same thing as with the double slit. You completely ignored this, and then say that I completely missed the point...I honestly find your behaviour quite rude.
Perhaps at the scale we're considering, the observer is coupled to the outcome.
Maybe I've misunderstood something, but isn't that the explanation of an Everettian many worlds interpretation?
That the observed "collapse" is really just the entangling of the observer with the system?
The blog post has a link to a transcript of Sidney Coleman's lecture "Quantum Mechanics in Your Face". https://arxiv.org/abs/2011.12671
The section on the cloud chamber through to the end does assert a reasonable answer this. (pp 9-12).
Actually, there is an answer to this. See e.g. https://arxiv.org/abs/quant-ph/0503009
tldr: if information is transferred from a microscopic quantum state to a macroscopic one, one always gets a collapse of the wave function.
Your observations, thoughts, etc, exist in the domain of eigenvalues of measurement operators applied to a quantum state and the universe itself is a massively entangled state vector in hilbert space. There is no decoherence at all. Instead, anything you can conceive of doing or measuring is actually a linear quantum operation taking a well described state in hilbert space from one state to another. What we actually see, and observe, and perceive is all just computation in the domain of the eigenvalues rather than the underlying true state of the universe as a vector in hilbert space.
The fact that you remember a consistent history is because your 'remembering' is itself one such eigenvalue of a measurement operator applied to a massively entangled set of histories and you only think you get one result because that thinking itself occurs in the domain of the eigenvalues rather than the true state.
The maths is what it is and does what it does, and if you play with things at that scale you can build a new intuition, but it just isn’t like the macroscopic world.
Just as scaling up from bits and NAND gates can become like virtual reality.
> The sun and stars trace arcs in the sky. One interpretation is the earth is the center of the universe, and the sun and stars move around it. Another is the sun is at the enter, and the earth and stars move around it. I can predict where the sun will be at any time of day, and day of the year based on these observational charts. The motion of celestial bodies is what it is, and doesn't need an interpretation
The flaw here is that by understanding more deeply what's going on with this analogy, we can learn so much more about the cosmos, like explaining the motion of planets etc etc. By not seeking an interpretation of quantum mechanics' observations, we limit ourselves.
Furthermore I don't agree that people are limiting themselves because of a lack of an interpretation, on the contrary my personal observation is that people are limited precisely because they either seek an interpretation or are clinging to one.
Historically, this line of thinking is common in science. You might be right here; science has advanced far in the last century, but I urge you to exercise skepticism that we've really hit the bottom. Nearly all claims of this type historically have been wrong!
> the endpoint where you intuitively understand exactly what a Many-Worlder, Copenhagenist, or Bohmian would say about any given issue, and also how they’d respond to each other, and how they’d respond to the responses, etc. but after years of study and effort you’ve returned to the situation of the baby, who just sees the thing for what it is.
But the sun being the center of the universe is a physical theory. It makes testable predictions. We can learn something about the universe from such a theory. On the other hand, most of the interpretations of quantum mechanics are metaphysical theories closer to religion than science. They do not make testable predictions or allow us to learn about the cosmos. They may be interesting thought experiments but they teach us as much about quantum mechanics as debating heaven and hell teach us about death.
[IANAP]
a) are almost universally honest about the empirical difficulties in their field,
b) are reasonably exploring the possible theoretical options to hopefully create testable predictions for a future experiment/telescope (science is hard)
c) have made major advances in mathematics, with important (and testable) applications outside of string theory
I feel like you’re projecting the attitude of one sometimes unscrupulous scientist (Brian Greene) onto the entire field. Although laypeople’s fascination with string theory has died down it is still a vital and vibrant field.
Then along comes relativity theory and says that both of these are equally right. There is no "center" and therefore when making calculations you should just pick whatever center - frame of reference, that is - makes the calculations simpler. For example, you'll have a much easier time doing the math of planetary motion if you pick the sun as your frame of reference, but you could pick the earth if you wanted to.
However, if you want to calculate the movements of stars in the Milky Way, you should no longer use the sun as your frame of reference - instead, use the center of the galaxy.
However, dropping the idea of a universal center, it's false that the Earth is the center of the solar system, i.e. the other major objects in the solar system don't revolve around the Earth, even though it's possible to produce a consistent Earth-centric model that works like that.
Relativity doesn't say that both an Earth-centric and solar-barycentric models are equally correct, since the Earth-centric model is not an inertial frame, and Earth's contribution to spacetime curvature is one of the smaller ones. Both special and general relativity allow us to draw reliable conclusions about which models better represent reality, as opposed to just making accurate predictions.
As such, this example provides better support for the idea that interpretations matter, than that they don't. It suggests that the situation with quantum interpretations may well be similar. You can make accurate predictions under any sufficiently complete interpretation, but that doesn't mean that there isn't an interpretation that's a better fit to reality than others. We may just lack the ability to determine that yet.
Aaronson's take is similar to the "shut up and calculate" take in the sense that it explicitly ignores or rejects the question here. It's an anti-knowledge position - it's saying we should be happy with what we already know, and simply work within that framework, ignoring deeper questions. It's the position of an engineer rather than a fundamental research scientist.
I'm fairly sure it does. Of course, you'll get the same answer either way - the earth moves in an elliptical orbit around the sun and contributes a tiny amount of the total inertia of the system. But you can use either the sun or the earth as your frame of reference to calculate this.
It's explained quite well on wikipedia so I'll just quote that here:
> Albert Einstein and Leopold Infeld wrote in The Evolution of Physics (1938): "Can we formulate physical laws so that they are valid for all CS (=coordinate systems), not only those moving uniformly, but also those moving quite arbitrarily, relative to each other? If this can be done, our difficulties will be over. We shall then be able to apply the laws of nature to any CS. The struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either CS could be used with equal justification. The two sentences, 'the sun is at rest and the Earth moves', or 'the sun moves and the Earth is at rest', would simply mean two different conventions concerning two different CS. Could we build a real relativistic physics valid in all CS; a physics in which there would be no place for absolute, but only for relative, motion? This is indeed possible!"[47]
> Despite giving more respectability to the geocentric view than Newtonian physics does,[48] relativity is not geocentric. Rather, relativity states that the Sun, the Earth, the Moon, Jupiter, or any other point for that matter could be chosen as a center of the Solar System with equal validity.
> Relativity agrees with Newtonian predictions that regardless of whether the Sun or the Earth are chosen arbitrarily as the center of the coordinate system describing the Solar System, the paths of the planets form (roughly) ellipses with respect to the Sun, not the Earth. With respect to the average reference frame of the fixed stars, the planets do indeed move around the Sun, which due to its much larger mass, moves far less than its own diameter and the gravity of which is dominant in determining the orbits of the planets (in other words, the center of mass of the Solar System is near the center of the Sun). The Earth and Moon are much closer to being a binary planet; the center of mass around which they both rotate is still inside the Earth, but is about 4,624 km (2,873 mi) or 72.6% of the Earth's radius away from the centre of the Earth (thus closer to the surface than the center).[citation needed]
> What the principle of relativity points out is that correct mathematical calculations can be made regardless of the reference frame chosen, and these will all agree with each other as to the predictions of actual motions of bodies with respect to each other. It is not necessary to choose the object in the Solar System with the largest gravitational field as the center of the coordinate system in order to predict the motions of planetary bodies, though doing so may make calculations easier to perform or interpret. A geocentric coordinate system can be more convenient when dealing only with bodies mostly influenced by the gravity of the Earth (such as artificial satellites and the Moon), or when calculating what the sky will look like when viewed from Earth (as opposed to an imaginary observer looking down on the entire Solar System, where a different coordinate system might be more convenient
https://en.m.wikipedia.org/wiki/Geocentric_model#relativity
See in particular this sentence:
> It is not necessary to choose the object in the Solar System with the largest gravitational field as the center of the coordinate system in order to predict the motions of planetary bodies, though doing so may make calculations easier to perform or interpret.
That's exactly the point I made above.
That was my point. Saying "the earth moves in an elliptical orbit around the sun" is not compatible with what you wrote previously, "both of these are equally right," when one of the statements in question is that the Sun and planets move in orbits around the Earth.
This part of the Wikipedia quote underscores this:
> Relativity agrees with Newtonian predictions that regardless of whether the Sun or the Earth are chosen arbitrarily as the center of the coordinate system describing the Solar System, the paths of the planets form (roughly) ellipses with respect to the Sun, not the Earth.
The quote you provided describes the same distinction I was making: there is a predictive equivalence between a geocentric and heliocentric model, i.e. either coordinate system can give the correct results; but, the two models do not provide equivalent explanatory power.
For example, in the geocentric model, you have to explain why planets undergo both prograde and retrograde motion. If you're trying to go beyond simple prediction to understand what's happening, you need an interpretation of the model, beyond just treating it as a black box that spits out predictions.
The only correct interpretation of the model is the one in the two quotes above.
To bring this back to the original discussion, it seems extremely likely that e.g. the Copenhagen interpretation is much like the geocentric one - its notion of "collapse" is almost certainly something due to our perspective as macroscopic quantum objects interacting with microscopic quantum objects, much as prograde and retrograde motion are a result of our geocentric perspective. Even though one can make correct predictions under Copenhagen, it may be a red herring from an explanatory perspective.
This isn't an analogy though, it's a direct consequence of relativity theory. It's the reason the word "relativity" is in the name.
This follows from heisenberg uncertainty. If a world is an assignment of a position to every particle, it cannot also assign them momentum: If you see position as fundamental then momentum is a phenomenon that exists "between-worlds" rather than inside them. And conversely if you see momentum as fundamental than position exists "between-worlds". When such fundemental things cannot exist in a single world, than I doubt that we can either.
I think that qm summarized in one sentence is the no-cloning theorem https://en.wikipedia.org/wiki/No-cloning_theorem
The connections to linear logic are very interesting. One can make the connection form qm to constructive math.
The no-cloning theorem isn't unique to quantum mechanics. As with many quantum paradoxes, you can translate it into an equivalent statistical paradox. The classical version of the no-cloning theorem is the statement that there's no operation that transforms one sample from a Bernoulli distribution with unknown parameter p into two independent samples from that distribution.
Since there's classical no-cloning, it's a very bad idea to define quantum mechanics as that-thing-with-a-no-cloning-theorem. That definition isn't able to distinguish quantum mechanics from statistics.
After that sentence I was really expecting your Wikipedia link to point here: https://en.wikipedia.org/wiki/Koan
Michel Bitbol is quite a thought provoking scholar (at least for me). Unfortunately there aren't many of his books translated in English.
Space is emergent because: spooky action at a distance. Time is emergent because: delayed choice quantum eraser experiments.
I even thought at one point I'd try to write a summary of his argument for Wikipedia but failed. It's not the most simple of things.
The end bit I was thinking was "the fact is that a spin-two field has this geometrical interpretation; this is not something readily explainable--it is just marvelous." In section 8-4. But the math leading up to that is tricky.
A smiliar cool idea that I encountered in a string theory course, is when you have tachyons. They seem pretty bad because you can gain energy by creating more tachyons, and your spacetime would decay. But what it really means is that you have chosen a "wrong" spacetime, and you can transform the tachyons away by choosing a different background. (Handwaving here since I'm just an experimentalist ;-))
There are so many equivalences between quantum theory and probability theory, beyond "QM is an extension of probability to complex numbers" and "square the amplitude to get the probability". For example, look at Feynman's path integral - where you sum up all possible ways to go from A to B, to get the transition amplitude. You can do a wick rotation (t -> it) and get a new expression related to a classical random walk. I hear you can even use a version of it in finance mathematics.
Another example is superluminal signaling. It would seem like something superluminal is going on with entanglement. But nature conspires just so that we cannot use it for transmitting information. A beginner would try to explain it classically - imagine you have two boxes, and put a marble in one. Now find the marble in one box, and obviously it will not be in the second. But classical analogies cannot give the same statistics as QM. (Sorry, it's been a while, I have difficulties recalling the argument :-).)
Anyway it seems like there must be an underlying reality that is "non-local" (in that it is not concerned with x, p, t, because these are emergent), and of which QM emerges as a statistical limit. There is an interesing idea from Gerard 't Hooft that this is a cellular automaton - the math seems to work out, but personally I feel that it should be a field theory (without any great justification as I'm just an armchair theorist).
I would think being emergent has something to do with a structure being present in a system which is not a fundamental part of the description. Something like thought being emergent from connecting a group of neurons.
Calling x, p, t, emergent, when they are co-ordinates in the conventional formulation of QM, is not this. I wouldn't call time emergent in the description of a simple harmonic oscillator, and I wouldn't call frequency emergent either.
Could you elaborate on what you meant?
So the fundamental description of the world would be some strange configuration space, which is neither classical nor quantum. And the physical world would sit "on top".
If the universe was like this, and you'd try to form a hidden variables QM theory using the wrong, i.e. physical variables x, p, t, you'd automatically get either nonlocality + infinitely many variables, or very convoluted dynamics (like Bohmian mechanics). Which is exactly what you see.
Another reason for me to believe that a description below QM and spacetime is possible, is because QM looks like a statistical limit of something. I find it very odd to identify that QM is the extension of probability theory to imaginary numbers, and then not ask: Probability theory of what?
This nicely sums up every explanation on this topic I've ever encountered.
There's an interpretation of QM called hidden variables theory that essentially states that the probabilistic nature of quantum behaviour is due to QM being emergent behaviour from lower variables that we haven't discerned. It isn't in vogue, but it fits a systems perspective perfectly. Through this lens QM is a dynamical system, though perhaps not chaotic (I'm still not sure as to the boundary between dynamical and chaotic behaviour given both imply complex nonlinear causality).
But then, a big issue with QM is that it's unintuitive, so that's probably confirmation bias on my part.
One of the koans I worked with recently:
""" A monk once went to Högen of Seiryo before the midday meal to ask for instruction. Högen pointed to the bamboo blinds with his hand. At that moment, two monks who were there went over to the blinds and rolled them up in the same manner. Högen said, "One has gained, one has lost." """
A key aspect to the koan is that by "in the same manner" it is meant that there is actually no difference between them in any normal sense; Högen doesn't have access to some inner state of the monks that we don't have. But Högen was a great Zen master and knew what he was doing.
By understanding other people’s interpretations you can translate between the “assembly languages” for their minds.
You know what they will say, you know how they will react, you know what counter-arguments they will produce. You know how to paraphrase your words so they agree or disagree with you. You know how they think.
He has predictive models for other minds.
There is nothing to “understand” about QM at face value. Because “understanding” is always about prediction.
IF I will be able to reproduce these effects in human scale experiments by myself AND derive my own formulas from these experiments, which will closely describe the results of quantum experiments, THEN we both will trust each other that we understand QM. Otherwise, it's a religion with rituals in math, not a science. 40+ years without much progress clearly demonstrates that.
https://www.wolfson.cam.ac.uk/about/news/there-just-one-fund...
(Direct link to journal article can be found within.)
Also, this is just me but how does the speed of light constrain the speed of motion if quantum physics are non-local? There's no such thing as a speed limit if you can teleport information.
What I'm saying is that people (who understand stuff I can't begin to comprehend) seem to dismiss out of hand an interpretation that includes nonlocality, but presumably it doesn't conflict with anything else that we actually observe whether you treat it one way or the other. It doesn't contradict all our physics with light speed limitations because it's defined consistently in the first place.
I'm just taking this on faith, but it appears that there is no issue of reality being this or that, but more of an aesthetic problem where something implying faster than light action is just unpleasant because it seems like a universal principle isn't so universal.
I want to read something popularized about what you get if you decide that an interpretation with nonlocality is just fine.