Bell's theorem.
It somehow proves that quantum physics is incompatible with local hidden variables, but I could never see an understandable explanation (for me at least) of just how it works.
Yudkowsky's explanation[1] is the first one that worked for me. I later found Quantum mysteries for anyone[2] helpful. The latter has less soap-boxing.
I trust Yudkowsky on many things, but not on that explanation. It's still quite complicated, and a couple of times I miserably failed to reconstruct it over a beer or two. A red flag.
Plus, I'd rather expect at least one professional (QED) physicist exists able to explain it and he isn't one. Mermin is, but the explanation is decidedly less clear.
BTW I came here to say Bell's inequality as well. For me it's as baffling as science could ever be.
I started to read the first one but his insistence that Many Worlds is true was too frustrating. Many Worlds Theorem seems specifically useful at saying "the variables aren't hidden because everything before wavefunction collapses actually plays out in different worlds.
But, we specifically have no way of proving that theory. So now we're back to the essence of the original question - if these things seem random why do we know that they're in fact deterministic without any hidden variables?
Well, I'd recommend to read the whole series. It's not so bad as it sounds. There are so many steps from where you are to appreciating the utter weirdness of Bell's experimental result. Not the weirdness of any theory (or an interpretation, which Many Worlds actually is) but of the basic experimental result.
If you are properly amazed by it, rejecting MWI or any crazy-ish borderline-conspiracy theory seems suddenly a lot harder.
I feel the whole Yudkowsky's QM series in fact served to deliver that one post.
Why isn't the MWI another form of hidden variables (a supremely non-parsimonious one at that), where the hidden variable is which of the many worlds you happen to inhabit?
I think you can make an argument for viewing it that way, depending on exactly what you mean by "you".
But IIUC, one of the remarkable things about MWI is that it would be a local hidden variable theory!
This is a very important property to have because the principle of locality is deeply ingrained in the way the Universe behaves. Note that (almost?) no other quantum interpretation is both realist and local at the same time.
Maybe you wonder, how is it possible that MWI can be considered a local hidden variable theory if Bell's theorem precisely shows that local hidden variable theories are not possible?
I think that it was Bell himself who said that the theorem is only valid if you assume that there is only one outcome every time you run the experiment, which is not the case in MWI.
This means that MWI is one of the few (the only?) interpretation we have that can explain how we observe Bell's theorem while still being a local, deterministic, realist, hidden variable theory.
For it to be local (causality does not propagate faster than light), it must be superdeterministic (all the many worlds that ever will be, already are). For it not to be superdeterministic (many worlds decohere at the moment of experimentation), it is also not local (the decoherence happens faster than the speed of light, across the universe).
If you take the Bell test experiment where Alice and Bob perform their measurements at approximately the same time but very far apart, I think you and I both agree that when Alice does a measurement and observes an outcome, she will have locally decohered from the world where she observes the other outcome.
But I don't see why the decoherence necessarily has to happen faster than the speed of the light.
It makes sense that even if Alice decoheres from the world where she observes the other outcome, the outcomes of Bob's measurement are still in a superposition with respect to each Alice (and vice-versa).
And that only when Alices' and Bobs' light cones intersect each other will the Alices decohere from the Bobs in such a way that the resulting worlds will observe the expected correlations (due to how they were entangled or maybe even due to the worlds interfering with each other when their light cones intersect, like what happens in general with the wave function).
I admit I'm not an expert in this area, but is this not possible?
An awesome question. That is exactly what I have been wondering without being able to put it into words, and this is core of why the MW seems completely uselsess to me as a scientific theory. (As a philosophical one-maybe? But science?)
To be clear, I don't reject Many Worlds at all and in fact consider it a promising candidate due to it sort of "falling out" of the Schrodinger's equations taken literally unless you add complexity.
But the fact remains that it is impossible to prove and it is conveniently well equipped to handle this situation. I'd prefer an argument that presupposes the Copenhagen interpretation as that is when my intuition fails.
>But the fact remains that it is impossible to prove and it is conveniently well equipped to handle this situation. I'd prefer an argument that presupposes the Copenhagen interpretation as that is when my intuition fails.
Is that not like trying to get a better intuition for planetary movement by using an epicycle-based model? The fact that the interpretation is conveniently shaped in a way that a paradox isn't an issue is not a coincidental thing that should be overlooked in the spirit of fairness to alternative interpretations. Regardless, I think my post below is useful for answering your want.
>So now we're back to the essence of the original question - if these things seem random why do we know that they're in fact deterministic without any hidden variables?
The world is only deterministic under Many-Worlds, and it's deterministic in the sense of "each outcome happens (mostly) separately". It doesn't make any sense to try to make sense of the "deterministic" part separately from MWI. MWI is the only deterministic QM theory (unless you're going to consider "superdeterminism", but there's nothing concrete to that interpretation besides "what if there existed a way that we had QM+determinism but not MWI". There's no basis to it, besides a yearning from people that like the abstract idea of determinism and don't like the abstract idea of MWI).
EPR doesn't tell us that the world is deterministic. It tells us that local hidden variable interpretations (where experiments have a single outcome) of QM can't work, because it shows that a measurement on a particle can appear to you to affect the measurement made by someone else on a distant particle. The Copenhagen interpretation response to this is that the wave function collapse must be faster than light. Therefore, the Copenhagen interpretation is not a "local" theory. (The Copenhagen interpretation doesn't give us any answer for who we should expect to trigger this wave function collapse first when two measurements are taken simultaneously at a distance though.)
If experimenters disprove Many Worlds, they've also disproved Copenhagen. These are exactly the same equations after all.
Theoreticians choose very different mindsets about the same equations, which (they say) somehow create them grounds to form various new hypotheses. As far as I know neither approach was very fruitful so far in terms of new science, so people try multitude of others.
What I've meant to say above, I have much trouble using Copenhagen to understand Bell's experiment. MWI fits the bill here for me.
AFAICS it was published in the American Journal of Physics in 1981 but it's addressed to the general reader. It requires no knowledge of quantum physics.
I have seen the example with the polarized lenses in a few places, but they dont explain why (imo) the simplest explanation does not apply. Namely that the lens itself might disturb the phase of the light, which would then mean it can pass through the next lens.
Only if you take away the middle lens, not the third.
Here's what I would have thought happens: After the first lens, you get polarized light, 90deg offset from the last lens, so no light passes. Then you introduce a 3rd lens in the middle, 45deg offset. This could alter the polarization (maybe it widens the band, or introduce some greater variance, shifts it who knows), and this is why now some light will pass through number 3.
No need to create any light
The short answer is this. Suppose thread OP gave you and I a box each. Each box has a some knobs to choose some settings, and if one chooses a setting and presses the GO button, a number pops up on the screen. We go far away from each other so that, due to the finite speed of light, it takes quite a while for any information to travel between the boxes. We do this, because we don't want the boxes to communicate live, even though thread OP might have recorded the same data into the memory drive of both boxes.
Then we choose some settings and press GO and record whatever number pops up. We do this many times so we each have a nice frequency chart. Now Bell proved that if you live in a local hidden variable universe, the correlations between these numbers is upper bounded, no matter how you choose settings on the boxes. Then, he also gave a prescription for choosing the settings, such that if you live a in quantum universe, the correlations between these numbers will be higher than the upper bound.
The rest is mathematics, which cannot really be simplified without leaving the reader unsatisfied.
So what I don't understand is, if both of us take an identical Gemalto token / Yuvikey, we can be light years apart and get the same sequences, no? Is the explanation that these will have one type of distribution vs if they had real "spooky movement at a distance" they have a clear different distribution? EDIT: what about this one: https://arxiv.org/abs/quant-ph/0301059
The distance is part of the proof, but not really part of the mystery.
I'm going to throw out an analogy that gets at what's observed and why it's surprising, but doesn't relate to the physics of spin, momentum, position or anything that's actually under observation in these experiments.
It's as if we have a pair of dice, and I throw my die and you throw your die many times. In a classical world, if I throw a three, it has no influence on what you throw; you're equally likely to throw 1-6. But in the quantum world it's as if when I throw a one, your die still has the expected uniform distribution, but when I happen to throw a three, you're a little bit more likely to throw a three. Your die is fair if I happen to roll a one, but it's weighted if I happen to throw a three.
Back in the real world, this is the strange behavior that is observed in experiment. Schroedinger's equation predicts the probabilities perfectly. But Bell shows that it's far from intuitive.
Here's the thought experiment that sold me on how weird this stuff is.
Imagine explorers on Mars find the ruins of an ancient alien civilization. In those ruins they find several small devices that have three buttons. Beside each button are two colored lights. red and blue. Above the buttons is a display. The linguistics team figured out enough alien writing to tell that the buttons are labeled with the alien's equivalent of A, B, and C, and that the display is a numerical display that goes from 0 to 38413 displayed in base 14 (which fits with other evidence found that the aliens have two hands with 7 fingers).
There is also some kind of docking station, which can hold two of the devices, and has a single button.
If two of the devices are placed in the docking station and its button is pressed, all the lights briefly flash on the devices, and the counter resets to 0. The lights stay on until the device is removed from the dock. Nothing happens if only one device is placed in the dock.
To try to figure out what these devices do, pairs are placed in the dock, reset, and then given to a couple people who go off and press the device buttons are record what happens.
Here is what those people observe.
1. If they press one of the buttons (A, B, or C), exactly one of the two lights next to that button comes on. When the button is released, the light goes out, and the counter goes up by 1, until it reaches 38413. After the next press/release, the counter goes blank and the device is unresponsive until reset again in the dock.
2. As far as anyone can tell, there is no pattern to which light lights. It acts as if pressing a button consults a perfect true unbiased uniformly distributed random bit generator to decide between red and blue.
3. When they compare their results with those of the person who had the box that was their box's dock mate for reset, they find that if on each person's n'th press
-- if they both pressed A, or both pressed B, or both pressed C, they got the same color light.
-- if one of them pressed B, and the other pressed either A or C, they got the same color light 85.36% of the time.
-- if one of them pressed A and the other pressed C, they got the same color light 50% of the time.
4. These results do not depend on the timing between the two people's presses. Those correlations are the same if the people happen to make their n'th press at the same time, or at wildly different times. Even if one person goes through all their presses before the other even starts, their n'th presses exhibit the above correlations.
5. These results do not depend on the distance between the boxes. If a box pair is split up, with one person taking theirs back to Earth while the other remains on Mars, and the two then run through all their presses at nearly the same time, completing quickly enough that there can be no communication between the two boxes during the run due to speed of light limits, they still exhibit the correlations.
Challenge: try to figure out how such boxes could be built without using quantum entanglement. Assume the aliens have nearly unlimited storage technology, so you can include ridiculously large tables if you want, so you can even propose solutions that involve the dock
preloading the responses for every possible sequence of presses (all 3^38414 of them). Anything goes as long as it produces the right correlations, and does not involve quantum entanglement.
