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)
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.
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.
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!)
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.
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 don't bother watching youtube videos of what someone thinks quantum mechanics is about.
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.
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.
>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.
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.
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
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.
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.
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.
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!
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".
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 don't have to. But they do have to accept that entanglement and measurement are the same physical phenomenon.
But I am not saying they "have to" - I'm saying that is their reason for not accepting the bare formalism.
> 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.
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.
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 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.
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:
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.
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.
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.
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:
- 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)
"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.
 - https://arxiv.org/abs/1405.1548
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.
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 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
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.
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
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.
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:
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)
- 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 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.
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 (firstname.lastname@example.org). 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.
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.
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.
Observer breaks interference pattern.
for a discussion where people of both sides answered. For an answer that is rather critical towards the Pilot Wave interpretation see
Another skepticall answer is
(The main thing that pilot wave theory clarifies for me is wave function collapse.)
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
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 , 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.  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.
 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.
 This is possible only because there is no limit to how fast Carol's Spaceship can travel.
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.
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.
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.
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.
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.
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".
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?
From our point of view it can very well be sucked in.
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.
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!
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.
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.
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...