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The Trouble with Quantum Mechanics (nybooks.com)
125 points by themgt on Jan 14, 2017 | hide | past | web | favorite | 119 comments

This article presents a very inaccurate view of the realist approach. The universe does not "split" when you make a measurement.

The measurement problem is a solved problem. The solution is that measurement and entanglement are the same physical phenomenon. Measurement is just entanglement extended to a macroscopic system through a process called "decoherence". The net result is that, when you do the math, you recover classical behavior by taking "slices" of the wave function (the mathematical operation is called a "trace"). This has been known for decades now, and provides a coherent and easy-to-understand picture of what is "really" going on. It is astonishing to me that the physics community still bifurcates into two camps: those who think this is common knowledge, and those who are completely unaware of it (or think it's a crazy idea).



https://www.youtube.com/watch?v=dEaecUuEqfc (The same content in a video)



Decoherence is an extremely useful and elegant mechanism for understanding quantum systems, but unfortunately it doesn't solve the measurement problem. At least not to the satisfaction of most practising physicists. The entanglement and trace operation does produce classical probabilities in the observed sub-system. However, it requires you to make a pretty arbitrary division between the observed system and the wider environment. Why is everything not just entangled with everything else up and up the chain until the entire universe is in superposition? The problem of where the quantum world ends and the classical world begins is still unanswered. This is one of the greatest open questions in physics, likely requiring a unification of general relativity and quantum mechanics before it's resolved.

> Why is everything not just entangled with everything else up and up the chain until the entire universe is in superposition?

It is.

I'm going hazard a guess that your next question is going to be: why do I not perceive myself to be in a superposition of states? And the answer is that you are not what you think you are. You think you are a human being, a classical physical object made of atoms, but you aren't. This is a very good approximation to the truth, but it is not the truth. The truth is that you (the thing engaged in this conversation) are a software process running on a human brain. You are a classical computing process, i.e. a process that can be emulated by a classical computing model like a Turing machine. The reason for this is that the kinds of things you do necessarily involves copying information (e.g. the process of reading this comment involves copying information from your computer into your brain) and quantum information cannot be copied. Only classical information can be copied. Your conscious awareness of the existence of physical processes is an emergent phenomenon of accumulating memories, i.e. copying information. Because of this you cannot become consciously aware of your quantum nature, and because of that you cannot demonstrate the quantum nature of any system (to yourself) unless it is isolated from you. You could in principle demonstrate the quantum nature of the rest of the universe if you could somehow isolate yourself from it, but that presents insurmountable practical difficulties.

> The problem of where the quantum world ends and the classical world begins is still unanswered.

Because the question tacitly makes the false assumption that there is a hard boundary between the two. There isn't.

Clearly you have your own unorthodox interpretation of quantum mechanics and you are quite emotionally attached to it. The argument that the universe is really X, but your brain just perceives it as Y because of Z can be made for any X,Y & Z. I don't find it compelling whatever the alleged reason for the disparity (in this case the no cloning theorem). There's also whole host of other issues, if everything is QM why has the brain evolved as a classical information processor, QM is unitary so you need to explain time/thermodynamics ...

Anyway, if you truly believe you have nailed both the measurement problem and consciousness in one fell swoop. Then I suggest you seek some like minded collaborators and a peer reviewed outlet for your ideas.

Returning to your original comment.

> It is astonishing to me that the physics community still bifurcates into two camps: those who think this is common knowledge, and those who are completely unaware of it (or think it's a crazy idea).

As a former member of the physics community I can tell you this is completely false. Everyone is aware of decoherence, it's covered toward the end most of undergrad courses in QM where the density matrix is introduced. I've never met anyone who thinks it solves the measurement problem.

> Clearly you have your own unorthodox interpretation of quantum mechanics

None of these ideas are original with me. All of them can be found in the literature. My only contribution (if I've made a contribution at all) is pedagogical.

> and you are quite emotionally attached to it.

Yes, I am quite emotionally attached to the truth. And yes, it does annoy when people promulgate the myth that QM is hard to understand or contains intractable mysteries when I know it isn't true. It particularly annoys me when people say this and simultaneously ignore the incontestable fact that entanglement and measurement are the same thing, in the same sense that space and time are the same and matter and energy are the same. Yes, all of these things are weird, and yet all of these things are true, and none of them are intractable mysteries or even hard to understand.

> I suggest you seek some like minded collaborators and a peer reviewed outlet for your ideas.

Like I said, these aren't my ideas. But I did submit my paper to Physics Today back when I first wrote it in 2001. It was rejected on the grounds that everything in it was already common knowledge.

> As a former member of the physics community I can tell you this is completely false. Everyone is aware of decoherence

But obviously not everyone is aware of its implications. Your challenging me on this is manifest evidence of that. And for 25 years I have been stumping card-carrying physicists with the EPRG thought experiment. Heck, it took me ten years to find anyone in the physics community who knew the answer! (I even had a chance to pose the question to Freeman Dyson, and he didn't know the answer!)

This is correct. As it is usually applied in practice in the literature, the measurement device decoheres the quantum system and becomes entangled with it --- and at the end of the calculation, Copenhagen interpretation is applied on the measurement device. It works fine in practice, but in the end it is philosophically just the Copenhagen interpretation.

If something is not accepted by the wider physics community, it's very likely the correctness of the thing in question is not that clear.

> in the end it is philosophically just the Copenhagen interpretation

No, it isn't. The wave function never collapses. This is easily demonstrated with a simple thought experiment which is described in the first two references that I link to.

I wrote about the interpretation usually used in published papers, and obviously decoherence alone does not solve the measurement problem as it only shuffles it to the bigger system, you need many worlds / Copenhagen / etc.

I don't bother watching youtube videos of what someone thinks quantum mechanics is about.

You don't have to watch a video. My first reference is to a paper.

Many worlds is just a way of describing the results of entanglement. It doesn't add any structure or dynamics to the wave function. Those worlds are precisely those slices the parent is talking about.

> At least not to the satisfaction of most practising physicists.

This is true, as the parent said - it's not accepted by many physicists.

> However, it requires you to make a pretty arbitrary division between the observed system and the wider environment.

This isn't true. The whole universe is in a superposition and you can reason with decoherence at any level. Literally everything in one "world" including the vacuum of space is entangled with everything else, though to a very small degree.

> The measurement problem is a solved problem.

I think this is overselling it slightly. Yes, Everettian style interpretations have helped to shed insight into the reality of the quantum state. Yes, decoherence has helped us to understand physical systems and their interactions with the environment. But if the measurement problem was solved there wouldn't continue to be a swathe of literature on the measurement problem by respected quantum theorists. There are some very good reasons for doubting the validity of many world interpretations. We don't have much of a consensus on what's "really" going on, and I don't believe we will for quite some time.

Indeed it's not that solved. A big problem is as Weinberg puts it

>Several attempts following the realist approach have come close to deducing rules like the Born rule that we know work well experimentally, but I think without final success.

which is kind of the heart of things.

I know of 3 modern ways to derive the Born rule for WMI and all have various reasonable (yet not airtight) assumptions.

In physics you can never really prove anything, but there is no serious technical issues here. Actually probability (the Born rule) is much better defined in WMI then in any other interpretation or even classically.

A related beautiful thing about WMI is that is creates genuine subjective probability inside a deterministic system (the wave function). One thing QM shows us is that we experience real random events, which cannot just come from lack of knowledge. Yet, if you are a computer expert you should know that it's impossible to create real randomness without an outside source. And the universe has no outside sources at all, by definition.

Also, it's clear that the basis of Weinberg's objection to WMI is philosophical if you don't selectively quote him so much. If he was concerned about deriving the Born rule we would talk about the specific assumptions he disagrees with.

Have you aware of Adrian Kent's critiques of (many of) these attempts?


I have read lots of critiques about the Born rule derivations but I've missed this one. Thanks for the pointer. He is only attacking one attempt, the decision-theoretic one.

I have trouble finding his point in this paper because it's so rambling but he seems to be saying:

> It seems prima facie surprising to claim that mathematical analysis could show that Born-weight mean utilitarianism, or any other strategy, is the unique rational way of optimizing the welfare of one’s own, and other people’s, many future selves in a multiverse.

Okay, sure - but it's also just as ridiculous to say that you can prove with no assumptions how a rational agent should act in a classical world.

Actually there is no explanation of probability in the classical world that's as clear as that in a multiverse, where you have actual proportions of outcomes.

All you really need is to assume that branches of equal magnitude have an equal chance of occurring and the Born rule becomes obvious. That seems like a safe assumption to me but you can't prove it beyond all doubt without some axioms of probability.

EDIT: I found a critique of his paper you might also want to read: https://arxiv.org/pdf/1111.2563.pdf

I'm not sure what you mean by "safe". My understanding of Kent's objection is that there's no explanation for why the norm-squared magnitude is related to probability in the first place.

The simplest way to derive the Born rule is to assume "branches" of equal magnitude have equal chances of happening. This isn't controversial because it's a very basic part of QM that is demonstrated by experiments and it seems quite natural too.

Yet even that assumption above can be weakened - that's what the derivations are trying to show to the critics because they find WMI so hard to accept for unrelated reasons.

This is in contrast to the situation in collapse interpretations where the Born rule itself is simply postulated. And in classical mechanics, we need to resort to frequentist explanations which are pretty weak.

So we have already gone quite far beyond the best explanations of probability in any other system.

It is kinda controversial. At least in relation to MWI; the validity and meaning of that assumption forms the basis of much of the criticism of MWI. If there were a rigorous derivation of the Born rule as a logical consequence of a global state undergoing unitary evolution, then I and many others would be much more convinced.

The other part of the problem is how/why observational outcomes occur in a probabilistic fashion in the first place. You keep saying that one or other branch "occurs" or "happens", but in MWI they're all happening. For some reason the observer only experiences one particular strand of their own superposition, and with a somewhat arbitrary probability to boot. It's not like that's the strand they're "actually in" but ignorant of. This is very different from subjective knowledge of a deterministic universe.

What's not controversial is that empirically the equal branches are equally likely. If that can be mathematically derived it probably requires some axioms of probability. But still, it's not a valid objection because the situation is much better than any other theory of probability, like frequentism!

The second problem is easy to see with the classical cloning analogy. Say, someone creates two clones of you and kills the original. Your experience will split, one version for each clone. I think it's clear how that would work classically and how it's analogous to the WMI with equal branch weights.

> If that can be mathematically derived it probably requires some axioms of probability.

I have no problem with axioms of probability being used. I just think you need to be explicit about what the fundamental postulates of the theory are and what is being derived. Clearly, in order to make predictions in line with experiment, a physical meaning must be assigned to the norm-squared of the wave-function. Most modern accounts don't make this a fundamental postulate, so it needs to be derived in a coherent manner.

> it's not a valid objection because the situation is much better than any other theory of probability

Beside the point. If our best theory of nature is flawed then we need to be honest about it.

> like frequentism!

OK- what about Quantum Bayesianism? That's a coherent and consistent account of quantum probabilities. It just lacks in what one can really say about the underlying reality.

> it's clear how that would work classically and how it's analogous to the WMI with equal branch weights.

I think its a false analogy. There aren't actually two copies of you in MWI, just a superposition of two different states. I need an explicit process by which classical probabilities emerge, not an intuitive allusion to how it's kind of like some classical process. A superposition is not classical; that's the whole issue!

We are not being dishonest here. Even if Born's rule was postulated, WMI would still have the most technical merit. Physics can never have a proof anyway.

And the Born rule is just assigning probability to the norm-squared of the wave function, so I'm not sure why you think it's assumed in a derivation of the Born rule itself. That would make the proof a tautology. The assumptions are laid out explicitly for the various proofs throughout the series of papers and critiques.

QBism is all about belief of agents and if you think that's a valid approach than the decision theoretic proof from Deutsch and Wallace shouldn't be hard to accept. Actually a derivation of the Born rule in QBism must take the same form.

A superposition of two different states is two copies after decoherence. They occupy different parts of the wave function and they share nothing, so can't interact. In configuration space (not classical space) they are separated "wave packets".

Just because Steven Weinberg is unaware of or does not accept the solution does not mean that the problem is not in fact solved.

If you are religiously convinced that the QIT interpretation is the only true one that doesn't make it true. For me it is just one of the many interpretations and I think that it is wrong on par with all the others that I'm aware of. If this wasn't the case then the measurement problem and the unification with the relativity theory (or with a theory that supersedes the relativity) would be already solved today. I'm really not in the field, but I don't think that anyone that actively works on QM is debating on solved problems.

I am absolutely not religiously convinced that QIT is the only true explanation. In fact, I explicitly say at the end of my talk that it is not, that multiple-worlds is equally valid, and which you choose is a matter of personal preference. But if want to argue that no solution exists (and this is Weinberg's claim) then you have to consider all of the solutions on the table, and Weinberg does not. He deliberately ignores the fundamental (and IMHO ultimately clarifying) fact that entanglement and measurement are intimately related (and are in fact the same physical phenomenon). It is entirely unsurprising that anyone who ignores this fact ends up believing that there is a big mystery. But in fact there is no big mystery. There are only people who are mystified because they are ignoring (or ignorant of) this crucial fact.

> There are only people who are mystified because they are ignoring (or ignorant of) this crucial fact.

I don't think that's the only reason people are mystified. From what Weinberg says, and I've heard from other physicists, when you get to the root of the issue they just won't accept a multiverse theory.

It has profound philosophical consequences, so I guess they go looking for ways to make their understanding of QM fit their strongly held preconceptions. Some avoid this fact you just mentioned, but others fight the Born rule derivations or wrongly apply Occam's Razor or have more original objections.

> they just won't accept a multiverse theory

They don't have to. But they do have to accept that entanglement and measurement are the same physical phenomenon.

These things are not unrelated :) If you accept that there is only the wave function as in the bare formalism, either an infinity of worlds or zero worlds, like in QIT, are the logical outcomes.

But I am not saying they "have to" - I'm saying that is their reason for not accepting the bare formalism.

> These things are not unrelated :) If you accept that there is only the wave function as in the bare formalism, either an infinity of worlds or zero worlds, like in QIT, are the logical outcomes.


> But I am not saying they "have to" - I'm saying that is their reason for not accepting the bare formalism.

Well, OK, but then the burden is on them to come up with something better. QM is one of the most thoroughly tested scientific theories of all time. If you want to call yourself a scientist you can't legitimately reject it just because it doesn't make you feel warm and fuzzy inside.

Maybe I agree with you, but science is built on philosophy, which is not rigorous - but based on fuzzy feelings of what is right.

The fact that we accept QM because it predicts the outcome of experiments is philosophy. So I could theoretically imagine someone holding the belief in our universe being what it seems higher than mathematical sense.

Yet my primary point is physicists are just human and have all the same irrational tendencies as the rest of us. You can't ignore their feelings if you hope to convince them of something.

In your everyday experience, you are constantly bombarded with overwhelming evidence that space and time are two completely different things, that matter and energy are two completely different things, that life is much too complex and well adapted to its environment to have arisen without an intelligent designer, and that the sun revolves around the earth. And yet, none of these things are true.

Likewise, you are constantly bombarded with overwhelming evidence that you are a classical physical entity living in a classical universe. But that is not true either. It's a very good approximation to the truth, good enough for most day-to-day purposes, but it is not the truth.

You can choose to accept these facts, or you can choose to bury your head in the sand. But you cannot legitimately say that there is a "problem with quantum mechanics" when in fact what is going on is that you have chosen to bury your head in the sand. There is no more a "problem" with quantum mechanics than there is a "problem" with relativity, evolution, or the Copernican theory. There is no intractable mystery here, only people who choose not to accept what the math is telling them.

I don't think that's been solved either or most physicists for that matter. I've read some of the attempts and they are not terrible good.

I don't think Ron Garret even touched on the Born rule, Everett of many worlds just hand waves and assumes it. The attempts I've seen are basically of the form that if the rule was different from the probability equaling the absolute amplitude squared then reality wouldn't come out as we find, so it must be so, which is not much of an explanation in my book.

FYI, I am Ron Garret.

It's true that I don't talk about the Born rule or multiple worlds in the paper, but I do talk about multiple worlds in the video (at the end, during the Q&A) and in the blog posts I linked to above.

As for the Born rule, what kind of an explanation are you hoping for? Some things can't be explained beyond, "That's just how it is." For example, why do the fundamental physical constants have the values that they have?

Maybe this will help:



Two of the appealing arguments for many worlds type interpretations are that the number of required assumptions is small, and that it gives a reasonable physical intuition for why measurement outcomes occur as they do. Having to bolt on the Born rule weakens both of these.

In fact, I would even go so far as to say that if you are going to merely "enforce" the Born rule without justification, then you are no longer proposing an Everettian interpretation. The whole point of these interpretations is that simply "unitary quantum mechanics" describes the whole universe.

I agree that bolting on the Born rule seems a weakness of the many world view. It would be nice if you could say everything follows the Schrodinger equation and hence the probabilities naturally come out the way they do but it doesn't seem to work that way very easily.

Everett himself however seems to basically "enforce" the Born rule without justification so I guess that would be Everettian.

See https://www-tc.pbs.org/wgbh/nova/manyworlds/pdf/dissertation... page 34

>we define a square-amplitude distribution, Pi...

Probability is a funny thing to deal with. Say you have an experiment where you push a button and a red light or green comes on based on some quantum effect but the green light is 1000x more likely. In many worlds you'd end up with different worlds with an observer seeing one or another but it's tricky to see how the 1000x thing comes in.

Well the Copenhagen interpretation traditionally requires the act of an 'observer'. I.e., you are not allowed to perform that act of summation on the set of orthonormal vectors in N dimensional Hilbert spaces until an "observer" observes. (That's where that stupid cat came into play and the 'uncertainty' of it being both dead and alive simultaneously until it's 'observed'.) Until this discrete event occurs, the wave function doesn't "collapse" and we're just living in statistical la-la land.

The disagreement lies in "I can mathematically apply the trace function, I'm just not quite sure when".

Alternatively, according to the Everett interpretation (to which I subscribe, and to which you seem to as well) quite a few reputed physicists do believe that the universe "splits" (though not in an actual literal sense, there's nothing ripping the universe physically in two) every time an "observation" occurs and there are lots and lots of occurring simultaneously taken from various frames of reference. This actually makes a lot of sense. Let Sean Carroll https://youtu.be/ZacggH9wB7Y convince (the plural) you.

The wave function never collapses. This is easily demonstrated with a simple thought experiment that is described in the first two references that I link to.

This is going in circles. You still need to put in Born's rule by hand somewhere. If you can explain the origin of Born's rule we'll have gotten somewhere. I also don't understand why you call a trace a slice. It's an ensemble average. Try deriving the density matrix formalism by coupling a small system to some collection of ancillae and you'll see that it doesn't really add anything. The trace is just convenient notation for the operator sandwich of closed quantum systems... it's just that your closed system is now an open system tensored with a bath.

> You still need to put in Born's rule by hand somewhere

I'm not sure what you mean by "putting Born's rule in by hand". We're talking about interpretations here. Born's rule is just an empirical fact. Do you mean that I need to explain why the probabilities are the square of the amplitude? That's kind of like asking me to explain why the speed of light has the value that it has. It doesn't have an explanation. It's just part of the Way Things Are.

But I can make the following heuristic arguments:

1. Outcomes are probabilistic because this is the only way that classical behavior can emerge from the wave function, and without classical behavior you can't copy information, and without copying information you can't have discussions like the one we're having. It's an anthropomorphic argument (actually it's a info-pomomorphic argument :-)

2. The probabilities are the square of the amplitude because that is how you get a useful mathematical model of reality. It is simply an empirical fact that destructive interference happens, so if you want to build a mathematical model of that you need something that can take on negative values. You can't have negative probabilities in classical reality, so the underlying reality must be something other than classical probabilities. The square root of the probability is just the simplest mathematical model that explains the observations.

Maybe this will help: the technical paper that my position is based on is here:


There are a few ways to derive the Born rule within WMI. None are perfect but their assumptions are fairly reasonable and most importantly the handling of probability is better defined than in classical mechanics or Copenhagen, so it's not a reason to discount the theory.


Relevant for those who are interested in the topic: Two rather unusual interpretations if quantum mechanics:

- De Brogle-Bohm theory: https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory

- Gerard 't Hooft - The Cellular Automaton Interpretation of Quantum Mechanics: https://arxiv.org/abs/1405.1548 (see also https://en.wikipedia.org/wiki/Superdeterminism)

the Automaton interpretation sounds like something I would enjoy reading. But considering that I do not have the time this week nor enough knowledge in the subject, could you perhaps provide me with a quick summary as to what it is about?

My understanding is this: Hooft is an "instrumentalist" as described in this article. He does not believe that quantum mechanics describes "what's really going on" and is interested in classical models that explain why QM makes such good predictions.

"Superdeterminism" is a very interesting perspective that Hooft feels could resolve this dilemma. Others feel that superdeterminism is not falsifiable, so there's no point in discussing it.

I came across this interesting article on stackexchange from a few years ago: http://physics.stackexchange.com/questions/34217/why-do-peop...

The first response is from Peter Shor, presumably the discoverer of Shor's algoithm. Kinda cool that such intelligent people with the highest academic credentials use a public forum.

Actually the kind of superdeterministic theories proposed by t'Hooft are falsifiable. From [0] "If engineers ever succeed in making such quantum computers, it seems to me that the CAT is falsified; no classical theory can explain quantum mechanics." By "such quantum computers" he means computers that can run Shor's algorithm. "...but factoring a number with millions of digits into its prime factors will not be possible – unless fundamentally improved classical algorithms turn out to exist."

[0] - https://arxiv.org/abs/1405.1548

't Hooft's approach is the only superdeterministic theory I've heard of, so it's worthwhile for the novelty alone.

I've never been pursuaded by arguments that science is impossible in a superdeterministic world though. The fact that all current observations are consistent with a superdeterministic world and yet we still came up with a viable theory already proves that science is possible in such a world.

The physics stack exchange has basically two populations: people learning physics and asking introductory questions, and experts gathering to discuss detailed questions. It's really an example of a great egalitarian online community.

I think most people are "realists" as Weinberg mentions in his article. A lot of people (including myself) have bashed on so-called "instrumentalists" like Hooft, but after reading this Weinberg article, I am grateful for people like Hooft who are not here to "give up" and accept that there are necessary unknowns, and that there might be something going on underneath it all -- the Einstein way.

As far as I know Loop quantum gravity is an alternative to string theory and says nothing about how to interprete quantum mechanics (though it better should reproduce its predictions). But convince me to be wrong.

Let me give example why physics is hard, using most simple example.

Ever encountered term observer (like observer in inertial frame)?

Well, it turns out, observer in physics means whole laboratory with established procedures of measuring time and length, not observer as you would mean in everyday life. And established procedure, what is that? Say, how do you measure time when certain event happened? It turns out, you can measure time only locally, and for this you need to have synchronized clocks spread out in your lab in points of interest. Some more philosophically inclined physicist would say that time means synchronized clocks. And how do you synchronize clocks? Well, it has to do with speed of light but I will stop here.

And this is for the most simple term. Imagine something more complicated. Now imagine hundreds of people writing papers and books with only partial understanding, and signal to noise ratio :-)

End of rant :-)

I know that Eliezer Yudkowsky is very controversial and some of his statements cannot be taken seriously, but I really liked his sequence of articles on QM. It made it a little bit more accessible to me, who knows very little about it.

I cannot judge how accurate it is; but from googling around, it doesn't seem he does any strong errors. Also he makes some very strong statements in the end which I found preposterous (mainly, that Bayes reasoning is better than scientific reasoning, and that Bayes reasoning must lead to Many Worlds theory).

The sequence is here


One of the issues with engaging with Yudkowsky's posts is how verbose his arguments are. Fortunately, for something as well formalized as quantum mechanics, there's a succinct counter-example: A formalism of quantum mechanics that makes perfect sense with neither the idea of wavefunction collapse nor some abundance of ontologically dubious and extravagant entities (alternate universes you can never observe). That formalism is relational quantum mechanics.

Accessible overview: https://plato.stanford.edu/entries/qm-relational/ In particular, this overview addresses the fundamental difference between Everett's theory and Rovelli's theory.

Original paper: https://arxiv.org/abs/quant-ph/9609002

A fluffy paper by the same author about QFT and its relational nature: https://arxiv.org/abs/hep-th/9910131

In short: The way you can evade the difficulties MWI addresses completely by changing one premise of the problem: that physical systems have states independent of their observers. In relational quantum mechanics, there is no universal wavefunction because there is no external observer of the universe. Call it the zero worlds interpretation. How parsimonious!

There is an element of Yudkowsky's sequence that deals with relative configuration spaces, but this is a subtly different concept and is really just a discussion from a clever guy unequipped with the right concepts about the difference between, say, affine spaces and vector spaces or torsors and groups. The idea that there is a configuration space independent of the observer is the assumption he misses.

In general I find Yudkowsky's extreme certainty in his own arguments to range from amusing to obnoxious. It's not hard to find places where uncertainty creeps in. It doesn't come from mistakes in his reasoning because what he considers he is usually meticulous about considering, but from what he doesn't consider.

This is a really good description of the measurement problem. It takes all the sides of the debate seriously, which is hard for most physicists to do. If you think about quantum mechanics all day every day, you're almost bound to settle on one interpretation as your working model, and it becomes hard to take the others seriously.

Weinberg mentions the quote by Eugene Wigner regarding the importance of consciousness in the section on instrumentalists. However, I see it is being fundamental to realist's interpretation also. I subscribe the the realist approach, which I view as meaning nothing special happens when a human makes an observation - it is just quantum mechanics as usual. This has interesting implications. The key is that the observer is not outside the system, he is a part of it. His wave function becomes entangled with the system when the measurement is made. But what makes this difficult to analyze is that we don't know what it means for the observer to say "I see the result was *". What physical process allows the observer to be aware of the measurement?

We can make a simplifying and unsatisfying assumption - the observer has a register in his head which records the result of the measurement. Here, it is easy to imagine this register is part of the wave function just like the object being measured. As mentioned above, the wave function for this register is entangled with the object being measured so the measurement and register value are correlated. In our model this corresponds to the person independently thinking each of the possible results, which some people call multiple universes.

But this simple register is not what goes on inside the brain. Not knowing this makes it difficult to accurately model the measurement process.

EDIT: for clarity

In the realist interpretation, even without people, you wind up in entangled states after measurement of a spin (where by "measurement" I mean: allow a giant classical system to interact with a spin and tilt a pointer on some gauge to / wind up with some register holding + or -). It's perfectly possible to formulate the realist ideas without any consciousness or insistence that the measurements register in a brain or observer.

Yes, I agree you can formulate the realist ideas, because the observer is nothing special at all. And I also think this is how the world works. But from an experimental verification point of view I think you really need a model for what the brain does to say you understand how a measurement is made. What is a theory without verification?

Granted his quote used the word formulate, but I interpret the comment as referring to not just writing some rules but also having some justification for them.

What is wrong with the Pilot Wave Theory intepretation? I'm ok with FTL information transfer, and so Bell's inequalities are satisfied.

And anyway the other interpretations DO NOT rule out FTL information transfer. For example if one entangled electron flies into a black hole then we would be able to know its spin by measuring the other one even if light from it won't reach us.

Also there is this:


>I'm ok with FTL information transfer

Which will lead to the conclusion that Special Relativity (which was extensively validated) is either wrong or incomplete.

I have seen a revival of Pilot-wave theory here on HN, but the real conclusion (a real particle pushed around by the enigmatic pilot wave or quantum potential or whatever) is as bizarre or as satisfying as saying particle is in a superposition. Also, I haven't seen anyone satisfyingly explain, in a classical-deterministic sense, the Delayed Choice Quantum Eraser Experiment (also, see the the Wheeler Thought Experiment)

There is the silicone oil droplet phenomena which is a classical version of the pilot wave, and it does reproduce some quantum behavior, including the double slit. That a pilot wave has been discovered (granted at macro scale) does make one reconsider.


It does not, really. The macroscopic realisation is not particularly surprising (although it is quite awesome and original). If you put a ball floating on top of a wave you will observe the predictions from a mathematical model of that system, which is exactly what the pilot wave theory is, and there is nothing surprising here. Moreover, the macroscopic model simulates something which by definition is an unobservable construction in the quantum model. It does not simulate any inherently quantum behavior (classical waves is a thing we already knew exists).

Nobody tells that walkers are simulate all quantum behavior and doing that correctly. However, they helps to understand some of quantum puzzles. For example, droplets have spin. Can you predict behavior of the classical droplet spin in compare to the puzzling quantum spin?

But you can do the same with classical setups that mimic some effects from the typical quantum mechanical formulations. Those classical experiments are indeed amusing and interesting, but they do not illuminate the "quantum puzzles", no matter whether they are modeled after pilot wave theory or after quantum mechanics. And very importantly, those amusing demonstrations do not scale! Sure, you can mimic with classical contraptions the pilot wave (or the wave function) of a single particle, but the nice intuitive demonstrations fail when you try to scale it up to more particles (or anything that would be exhibiting the interesting, nontrivial quantum behavior).

So, your prediction for walker droplet spin is that walkers, in kind of Stern and Gerlach experiment, will behave like classical magnets, not like quantum particles, right?

No, they would behave like a ball floating on top of a wave and given that there are waves involved there will also be interference patterns. There is nothing quantum here. Sure, in one particular way it looks like a quantum particle (to the extent of a cargo cult), but in all the important ways it does not (entanglement, computational power, generalisation to multiple particles).

I asking about outcome of Stern and Gerlach experiment. It's binary thing. Make public prediction, please.

Certainly, but then please first pose/define the question clearly. What do you call a macroscopic Stern-Gerlach experiment with balls floating on top of the waves of a fluid? It would be an amusing toy problem to work out if you define it for me. However, it does not change the main argument: there is nothing quantum in macroscopic experiments with water waves - interference does not imply "quantumness".

Lets define experiment as following (excuse me my bad English, please):

- vibrating bath with non-conductive, non-magnetic, non-paramagnetic, non-diamagnetic fluid;

- vibrating bath is wide enough to avoid excessive interference with reflected waves from bath sides;

- vibrating bath has regular pattern on top of fluid, without any irregularities in space of experiment;

- small charged droplets of fluid on top of bath;

- north and south poles of a magnet are placed horizontally, without touching of bath fluid or droplets, e.g. at sides of bath, OR over fluid, OR under bath;

- an apparatus creates droplets of same size with random spin in all 3 dimensions;

- droplets are forced to walk through the batch, starting at center line between north and south pole and following that line;

- without magnetic field applied, droplets must walk straight;

- an detectors to measure decline of droplet path from center line must be installed at end of magnetic pole.

I expect that, when magnetic field is applied, droplets will slide completely to left or completely to the right, like electrons in Stern-Gerlach experiment.

It's not a quantum experiment, of course, but it can provide insight on nature of quantum spin.


Sorry, droplets must be charged, not magnetic. Updated.

The main point of the Stern-Gerlach experiment was that the electrons hitting the screen were forming two distinct dots instead of a long spread out line, therefore proving that the angular momentum is quantised. In your example you will instead have simply a spread-out distribution because there is no quantisation of the angular momentum of your droplets.

The pilot wave usually refers to the spatial degrees of freedom, especially in these classical mock-ups with balls on top of waves. They do not properly addressed internal degrees of freedom like spin.

Unrelated to those macroscopic mock-ups, pilot wave theory actually has serious problems with the description of anything that is not a spatial degree of freedom.

You can still use pilot wave theory to describe the quantum behavior of the coordinates of a particle. But even then, the classical mock-ups we are discussing will not show anything inherently quantum - it will simply produce some interference patterns, that can be explained classically.

P.S. side note: An important part in the Stern-Gerlach experiment was that the magnetic field was not homogeneous, because it is the gradient of the field, not the field itself that causes the electrons to move.

IMHO, Stern-Gerlach experiment demonstrates interaction of magnet field with guiding wave mediated via particle, so I expect that magnet will steer particle-wave into same spots, thus will demonstrate «quantum» behavior of particle spin at macro level.

Without disrespect I insist that you are wrong about that. The spin degree of freedom is "internal", unrelated to the position of the particle. The pilot wave does not influence that spin, and if you have a big ball on top of a wave, that wave does not care about the angular momentum of the ball. The ball is big and classical, hence its angular momentum is (practically) not quantized.

The thread got a bit long, but if you are really interested in learning about this I would be happy to continue the discussion through email (stefan.krastanov@yale.edu). You probably also need proof of some kind of qualification on my part - my online profile does prove that I work at a respected institute doing research on that topic.

As far as I know there is no analog of entanglement in these experiments. If someone has heard or read something in that regard, I'd be interested in a reference!

Nobody even tried to entangle two walkers. AFAIK, uncharged non-magnetic particle without any inclusions (e.g. bubbles) has spin and phase of vibration only. How to entangle them?

Moreover, spin is 3d, walker is 2d, phase is 1d, while our Universe is 3d. It's like studying of 2d/1d projection of 3d world.

> Which will lead to the conclusion that Special Relativity (which was extensively validated) is either wrong or incomplete.

Not necessarily. The simplest relativistic pilot wave theory requires only a preferred foliation of spacetime.

This is seemingly unappealing to most physicists, but recent work has shown that the wave function itself contains just such a structure, so the needed foliation is present in every interpretation of QM.

Did you saw double slit experiment reproduction in 2D macro?: https://www.youtube.com/watch?v=nsaUX48t0w8

Observer breaks interference pattern.

> What is wrong with the Pilot Wave Theory intepretation?


> https://www.quora.com/Why-dont-more-physicists-subscribe-to-...

for a discussion where people of both sides answered. For an answer that is rather critical towards the Pilot Wave interpretation see

> https://www.quora.com/Why-dont-more-physicists-subscribe-to-...

Another skepticall answer is

> https://www.quora.com/Why-dont-more-physicists-subscribe-to-...

What I personally do not like about pilot wave theory is that in the many body versions of the theory that I've seen, you still need a wave function that depends on the positions of all the particles. That is, the "pilot wave", unlike physical fields like electric or magnetic fields, is not a function of location in spacetime, nor is it attached to a particle, but to all particles. This means in a certain sense the amount of information in a given space grows exponentially with the number of particles. To me this has always been one of the mysteries of QM, and in pilot wave theory it is as much of a mystery.

(The main thing that pilot wave theory clarifies for me is wave function collapse.)

Still better than world-splitting at every instant. Isn't it?

Yes, I would agree with that!

There is no information transfer in your black hole example. Entanglement can not be used for FTL communication no matter the interpretation you choose.

As for why pilot wave theory is not popular: it generalises poorly. Sure, you can build a multi-particle theory or even field theory on top of it, but they are clumsy to work with and after their initial study they did not show any promising way forward that was not available to the typical approach to quantum mechanics.

Edit: Wiki article about why entanglement does not provide FTL communication even if naively it looks like it should be possible https://en.m.wikipedia.org/wiki/No-communication_theorem

Do you understand the arguments that the ability to send a signal faster than light allows you to send that signal backwards in time? I've never met anyone who who understood special relativity but was OK with that.

How so? Why should faster-than-light travel imply a reversal of the arrow of time? Can you explain the reasoning?

This is an intuitive way of thinking about this without diving into the math. Here are the postulates: speed of light (c) is same for everyone. And there is no special reference frame; your physics is as good as the physics of your friend moving away from you in a space-ship in a constant velocity v. Now consider that your friend is actually moving in a spaceship away from you. He has an experimental setup with him using which he measures speed of light. You are sitting at home postulating about his experiment. Consider he is moving at velocity v, so is his experiment equipment. How can he arrive the same result (3*10^8 m/s) for speed of light? You conclude that only way is that whatever clock he is measuring the experiment with is running slower than yours (velocity=distance/time, he is measuring less distance, so time must be less too). Now imagine he is going at the speed of light. (The actual equations breakdown at this point, but you can imagine he is infinitesimally close to speed of light). How is he arriving at c? Only way is time is not passing for him (according to you). Now imagine he is going faster than speed of light. At this point, the equipment he is sending photons with is traveling faster than photons itself! How does he arrive at c? His clock must be running backwards! And keep in mind, your friend in all these cases is happily measuring speed of light as c without any of these conundrums you have. And now you can publish a paper claiming that your friend travelled back in time! Did he really do that in a "Back to the future" kind of way? Perhaps not.

I did used to ponder over this sort of mystery, but I realized the actual answer to this lied at the particle level as explained in QED by Feynman: A positron can be treated as an electron traveling backwards in time. When it collides with an electron, the two create a photon. Should you ever come close to the speed of light, one way to "exceed" it would require a collision with your anti-matter self, resulting in (self-obliteration and...) photons from everyone's else's point of view. Of course, assuming my understanding is correct, it's also possible that you transform into your anti-matter self... bizarre. Going forward again would require some similar interaction, but I seem to recall formulating a thought experiment where this violates causality, making either the whole idea impossible even from a Relativistic standpoint or forcing some denial of causality, which would make other dependencies on causality (such as science itself) unreliable.

This wiki page [1] explains why whether two events happen at the same time depends on your reference frame. If you can send signals faster than light then you can send a signal to an even far away and cancel that event. In another reference frame the sending of the signal would have happened after the far-way event has already happened. Hence, due to the "relativity of simultaneity" FTL communication is equivalent to sending messages to the past.

[1]: https://en.wikipedia.org/wiki/Relativity_of_simultaneity

By sending a message in two opposite directions, we can achieve 2c speed of information transfer. How that is possible?

No, we can not, but the reason might seem subtle. S sends the same information in opposite directions to A and B. So A learns what B learns, but A can not use that to tell something to B, that S did not already know. A can not influence B, rather it is S that influenced both A and B.

No, sorry, I can't explain the theory of relativity in one paragraph. It takes a book. Spacetime Physics, by Taylor and Wheeler, explains it very well with only high school level maths.

Thanks for the reference.

The idea behind relativity is that the speed of light is constant in all reference frames. [0]. In order for this to work, we "warp" spacetime depending on the velocity of the observer.

More concretely, imagine Alice and Bob are moving away from each other at 50% the speed of light. They both observe event some event, X, occur and note the location in space-time. If Alice observes that X occurs in the location (t,x,y,z), then we can compute precisely where and when Bob observed the event occurring (t',x',y',z'). This conversion is known as the Lorentz Transformation [1], and can be derived mathematically from the assumption that the speed of light is constant regardless of reference frame.

Where this gets weird is the case where Alice and Bob observe 2 events: X and Y. In this case, it is possible that they will disagree about which event happened first. Once you accept this, it should become clear why causality requires some speed limit. You can do the math based on the Lorentz Transform and confirm that this limit is the speed of light. Intuitively, this is a direct consequence of the fact that we defined the Lorentz Transform to make the speed of light constant.

In case the need for a speed limit is not obvious, let as pretend that it does not exist. Suppose that, from Alice's perspective, X happened before Y. Further, suppose that Carol happened to be in a spaceship that passed by X at the instant it occurred, moving at a velocity that would take her by Y at the instant it occurred. [2] From the perspective of Bob, Carol would have traveled backwards, going from Y to X.

We can make this situation even worse by considering Carol's perspective. Recall that we defined Carol as starting at X and traveling to Y. In the same way, we can define Dave as starting at Y and traveling to X (recall that, if we were Bob, we would be convinced that Y happened first, so with a fast enough ship, Dave and make it in time). In this situation, both Carol and Dave exist at Y, so Carol can give Dave a copy of her diary of the trip. However, after Dave makes the trip to X, he will meet Carol again, so he can give her a copy of her diary of the trip she is about to take.

[0] This means that if I am on Earth, and you are in a space-ship moving at 99% the speed of light (from my perspective), and we both measure the speed of light, we will arrive at the same answer.

[1] https://en.wikipedia.org/wiki/Lorentz_transformation

[2] This is possible only because there is no limit to how fast Carol's Spaceship can travel.

> From the perspective of Bob, Carol would have traveled backwards, going from Y to X.

So what? It's Bobs problem.

FTL electrons, in medium where speed of light is much less than c, are traveling exactly as you described.

Suppose Carol has a clock. At X it reads 0, and at Y it reads 100 (100 units in the future). From Bob's perspective, Carol's clock would also read 0 at X and 100 at Y despite the fact that she was at Y first.

In other words, as Carol travels 'forward' in Bob's time, her clock runs backwards. Or, from Carol's perspective, Bob's clock would be running backwards.

This isn't actually a problem in relativity, but is the definition of time travel.

No, it's not a time travel. Bob will see that Carol travels backward and Carol will see that Bob travel backward, like we see EM emission from FTL electron in reverse order. FTL electron is not moving back in time, nor Bob or Carol.

The notion of "backwards" in time is a bit fuzzy once you get into relativity, so the three person example I gave may not clearly show it.

However, in the four person example, Dave is able to hand Carol her diary of the trip that she is about to make. If that is not time travel, I do not know what is.

It's very unlikely. If Dave has Carol diary, then Carol made the trip already, so Carol will notice empty fuel tanks and big holes in the shield. She will may have problems with memory, but she is not stupid.

No she didn't. X is the point in spacetime where Carol begins her trip. From her perspective, Dave came from the future.

The only reason that this cannot happen is that X and Y are so far away in space, and close in time, that it is impossible to travel between them.

Sorry, I cannot follow you here. Maybe it's well known thought experiment, but I'm unable to find it.

Because events that have a spacelike separation -- that is, they are close enough together in time and far enough apart in space that even travelling at the speed of light you couldn't be present at both -- have no absolute order. Depending on your frame of reference -- how fast you're travelling and in what direction -- you might see two such events (let's call them A and B) as simultaneous, as A happening before B, or as B happening before A.

This is commonly illustrated with the following scenario. Imagine Alice is sitting by the train tracks. Her friend Bob comes past riding on top of a train, sitting exactly in the middle of the car's roof. As he passes Alice, they high-five (presumably Alice is on a raised platform of some sort). A split second later, Alice sees lightning strike each end of Bob's carriage at exactly the same moment. Thanks to some very precise measuring equipment, Alice is able to determine that the two lightning strikes occurred at the very moment that she high-fived Bob. At that point, Alice was exactly halfway between the two points that were struck, so it makes sense that the light from those strikes reaches her at exactly the same time.

Alice also knows that Bob would have seen lightning strike the front of the car before it struck the back of it: the light from the front strike would have passed Bob on its way to Alice, and the light from the rear strike would have passed Alice on its way to Bob.

Now let's look at it from Bob's view. As Alice concluded, he sees the lightning strike the front of the car first. But (a) he's exactly the same distance between the two strike-points, and (b) the speed of light is always the same for any observer. So if he sees the light from the strike at the front first, that means the front was struck first. Bob has a different order of events from Alice.

Which order is the "right" one? Answer: both. Or, if you prefer, neither. There are no grounds to prefer Alice's view over Bob's, or vice versa. You cannot say that one lightning strike "really" happened first, or that they "really" happened simultaneously.

To complete the picture, let's imagine Charlie riding another train car on the set of tracks the other side of Bob's, travelling in the opposite direction to Bob. At the exact moment Alice is high-fiving Bob, Charlie is also exactly lined up with them and smacks Bob on the back of the head. For reasons similar to but opposite to Bob, Charlie will first see lightning strike the rear of Bob's car and then the front, which means that in his (equally valid) frame of reference, the rear strike happened first.

Now imagine someone or something used FTL travel to go from the front of Bob's car to the rear, leaving at the moment the front was struck by lightning and arriving at the moment the rear was struck. In Bob's frame, this would be unremarkable, except for the exceptional speed (ignoring for the moment any adverse environmental effects -- Google "what-if xkcd relativistic baseball" for a flavour of what those might be). But in Charlie's frame, this would be travel backwards in time, as the arrival at the rear would occur before the departure from the front.

Wouldn't the entanglement just break? The preassure would rip the electron apart to begin with. I'm not sure if that erases entanglement already or if the quarks needed to be annihilated. Either way, are the known laws of physics applicable inside a black hole at all? I don't think so.

The entanglement does not break. The entire black hole becomes entangled with the electron left outside (which is less exciting than it sounds).

Sure, plenty of thing break if we start talking about unknowns, like the black hole evaporation for instance, but today's physics has a pretty good idea what happens if we just drop one of the electrons in the black hole and measure the other one. We just learn the spin of both of them at the same time, but we can not choose the value (it is random) hence there is no communication and no "weird peeking into the black hole".

> if one entangled electron flies into a black hole then we would be able to know its spin by measuring the other one even if light from it won't reach us

All the arguments here mention what happens under SR but wouldn't GR be more appropriate? If an electron flies into a black hole, from the frame of reference of the observer doesn't it appear to get closer and closer to the black hole event horizon over time, but never actually enter? It only enters a black hole from its own frame of reference, doesn't it? So the outside observer would never see it enter the black hole, and light from the electron would always reach us.

Or is my understanding of General Relativity effects near a black hole event horizon wrong?

Thanks, I wanted to add that, too, but wasn't sure about it. I still am not, because this opens another can of worms. Can a black hole then not grow if from our POV nothing ever enters?

I thought that from the POV of the object falling into the black hole, time stretches.

From our point of view it can very well be sucked in.

It is the other way around. From the POV of the object falling they just fall in. Look up Preskill's work for explanation of how it works when entanglement comes into play.

Then how is it different than just splitting a coin, throwing the other half far away and then looking whether you have heads or tails? There is never any spooky action at a distance.

This is a pretty great question with a fairly subtle answer. It is not much more than just flipping a coin, indeed!

See section "4. Relativistic Causality" of http://www.scottaaronson.com/democritus/lec11.html for the best explanation I know of. This entire book "Quantum Computing Since Democritus" is absolutely great if you want to understand these topics.

See also https://en.wikipedia.org/wiki/No-communication_theorem


Think of it this way: We've got two players, Alice and Bob, and they're playing the following game. Alice flips a fair coin; then, based on the result, she can either raise her hand or not. Bob flips another fair coin; then, based on the result, he can either raise his hand or not. What both players want is that exactly one of them should raise their hand, if and only if both coins landed heads. If that condition is satisfied then they win the game; if it isn't then they lose.

They can win 75% of the time if they just never raise their hands. Using a shared entangle state they can "cheat" and win 85.3% of the time by using a specific protocol, because they rely on some new form of correlation. But they still can not use this correlation to send messages (see the no communication theorem). Naively (this naive intuition does break!), you can imagine them having two slightly correlated coins - sure, after Alice flips hers she knows Bob's result, but she did not decide the result of her coin so she can not use it to send information to Bob.

But here you have two independent coins. My question is, how is entanglement fundamentally different than having two sides of the SAME coin but not looking until later?

Let's forget how this looks like two correlated coins and focus on your question.

Yes, if Alice and Bob just measure the spin of their corresponding electron, indeed it just looks like half of a precut coin. But if they want to win the game they will do something more complicated. (side note: To use the typical physicist terminology, this precut coin is a hidden variable - something set inside of the electron even before its measurement.)

But Alice and Bob can do something more interesting, something that permits them to win the game we described more often than 75% of the time. This involves Alice measuring the spin of the electron in a projection different than the one in which Bob is measuring (this is part of the "specific protocol" that I mentioned in the previous post). So while Alice is checking whether the result is h=Heads or t=Tails, Bob is checking whether the result is h+t or h-t. Now the two electrons seize to behave like the two parts of the same coin (and this is what permits them to win the game more often than 75% of the time). Explaining how exactly they use this protocol would take too much space, but you can look it up in the link to the book I provided.

P.S. However, as explained in the previous post, this does not permit them to send messages to each other.

P.P.S. Again, Section 4 of the linked page explains this in details!

An electron is a lepton, it isn't made up of quarks. What does it mean to rip it apart?

That would be an embarrassing blunder of me.

Pilot wave theory only postpones the question of "what is a wave function and how does it collapse?", it doesn't actually say anything new. I think Wigner's Friend is really no fundamentally different than Schrodinger's Cat.

It seems that the scientific method has led us to a theory that is beautiful, accurate, and yet utterly incomprehensible. Until we can explain exactly what happens during a wave function collapse, I think QM will remain that way.

It doesn't seem that way to me. Decoherence is understood pretty well; although not every detail is completely worked out it explains our experience and the subjective appearance of collapse. It's just approximate though and hence we get quantum interference.

The reason you think it's incomprehensible is that a lot of smart people have trouble accepting what we called reality is only one of many classical "worlds". It's a philosophical concern; technically there are no major issues and it's not that hard to understand.

The reality of QM won't be commonly accepted until we find a way for people to accept that the universe isn't what they expected or we change their expectations.

Wave functions do not collapse in the realist view, as explained in the article. The cost, however, is a giant explosion of alternate possibilities all having equal reality, summed in superposition.

But, the point is, there is at least one interpretation of QM where the wavefunction never collapses: it just evolves unitarily according to the Schrodinger equation, forever.

I had three semesters of QM in grad school and I still have trouble with it.

Well, the OP author is arguably the greatest living physicist, so it's not surprising that 3 semesters isn't enough :)

"Anyone who says that they understand Quantum Mechanics does not understand Quantum Mechanics" - Richard feynmann (might be paraphrased)

They overcharge you if your license is from two simultaneous states.

> In this musical analogy, the act of measuring the spin somehow shifts all the intensity of the chord to one of the notes, which we then hear on its own.

People can accept that measurements and observables are operators which act on the wave function (which can be expressed as a linear combination of eigenstates of the operator in question). People can even accept that some observables cannot be measured simultaneously, because they do not commute, and cannot share eigenstates.

People cannot accept that particles can only be found in eigenstates of the observable in question, without some mechanism to explain why this happens. If a particle's measured value can only be one of the eigenvalues of the operator, it begs the question "which eigenvalue is it going to show us?". Alternatively, if nature let us measure the expectation value instead of "one of the eigenvalues", then quantum mechanics would not be "weird" at all. Too bad, nature isn't like that, or maybe, be thankful that it is.

> But if the corrections to quantum mechanics represented by the new terms in the Lindblad equations (expressed as energies) were as large as one part in a hundred million billion of the energy difference of the atomic states used in the clock, this precision would have been quite lost. The new terms must therefore be even smaller than this.

I always see people (physicists) complaining about String Theory, etc. because they play around in regimes which are too small for us to actually work with. We have observed macroscopic effects which are due to a build-up of quantum mechanical effects (superconductivity, solid state, etc.). It would be expected that a correction to quantum mechanics would also make macroscopic predictions...

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