Einstein's famous 1905 paper on Relativity applied this principle to Translational Frames, showing it requires the Universal constant c (speed of light) to be the same in all such frames. Were it not, the frame in which c was highest would be the only frame at rest.
But the same principle must require there to be no Preferred Orientation. This leads to the requirement that Planck's constant h be the same in all frames. If the Stern-Gerlach experiment could give results between +h and -h, then the orientation producing the maximum value would be a preferred frame.
And because of that, when Alice and Bob measure entangled quantum particles, their combined results must violate Bell's inequality.
But to my mind, the biggest take-away is that Einstein's Principle of Relativity absolutely requires that conservation can only be on average.
All right, that's a ridiculously condensed summary. Enough to make your head spin :-)
The title paper is for general audiences, and references the original paper at https://www.nature.com/articles/s41598-020-72817-7.pdf
OK, I think I understand that.
> And because of that, when Alice and Bob measure entangled quantum particles, their combined results must violate Bell's inequality.
Could you be slightly less ridiculously condensed here? Give a one-or-two-paragraph, accessible-to-the-semi-layman explanation of why this means the result must violate Bell's Inequality?
> But to my mind, the biggest take-away is that Einstein's Principle of Relativity absolutely requires that conservation can only be on average.
And the same request here. Why does the principle of relativity require that?
> > But to my mind, the biggest take-away is that Einstein's Principle of Relativity absolutely requires that conservation can only be on average. > > And the same request here. Why does the principle of relativity require that?
The way I read this comment was that "the principle of relativity cannot conserve angular momentum on a per-trial basis".
In a Mermin Device a pair of entangled spin particles is set to two Stern-Gerlach experiments. The two particles has net (spin) angular momentum of 0 because that's was the net angular momentum of starting material. But if you measure the angular momentum of the two particles in two non-parallel directions, and if we also require that the only answers you are allowed to get are +hbar/2 or -hbar/2, then the sum of the angular momentum you get by adding +/-hbar/2 times one direction plus +/-hbar/2 times a different direction can never be 0.
If angular momentum cannot be preserved on a per-trial basis, then I suppose it must be preserved on average, because, I suppose if it isn't preserved on average, then I don't think you can say that angular momentum is preserved at all.
> And because of that, when Alice and Bob measure entangled quantum particles, their combined results must violate Bell's inequality.
> > And because of that, when Alice and Bob measure entangled quantum particles, their combined results must violate Bell's inequality. > > Could you be slightly less ridiculously condensed here? Give a one-or-two-paragraph, accessible-to-the-semi-layman explanation of why this means the result must violate Bell's Inequality?
The really short answer is that if we preserve the angular momentum on average then it entails that the correlations we observe from Mermin Device must match the correlations predicted by quantum mechanics, and therefore violate Bell's inequality for the same reason that predictions of quantum mechanics do.
In more detail, if we take the results of a measurement where Alice measures angular momentum in the vertical direction and Bob measures the angular momentum off vertical by theta degrees where Alice gets a result of +hbar/2, then in order for angular momentum to be preserved, Bob's measurement would have to be -cos(theta)hbar/2.
Of course Bob is only allowed to get hbar/2 or -hbar/2, so if we want angular momentum to be preserved on average then when we take an ensemble of trials, and filter out only those trials were Alice measures hbar/2, then the average of all of Bob's measurements for those trials should be -cos(theta)hbar/2. That requires that the probability Bob geting hbar/2 when Alice does is (1-cos(theta))/2 (= sin^2(theta/2)), which I believe is the value predicted by quantum mechanics. Once you have the predictions made by quantum mechanics, a violation of Bell's inequality follows by the usual arguments.
But I have absolutely no idea how to visualise entanglement. Any tips? Or do we just have to shut up and calculate?
Edwin James had some interesting commentary on things like this:
"From his reply to EPR, we find that Bohr's position was like this: 'You may decide of you own free will, which experiment to do. If you do experiment E1 you will get Result R1. If you do E2 you will get R2. Since it is fundamentally impossible to do both on the same system, and the present theory correctly predicts the results of either, how can you say that the theory is incomplete? What more can one ask of a theory?'
While it is easy to understand and agree with this on the epistemological level, the answer that I and many others would give is that we expect a physical theory to do more than merely predict experimental results in the manner of an empirical equation; we want to come down to Einstein's ontological level and understand what is happening when an atom emits light, when a spin enters a Stern-Gerlach magnet, etc. The Copenhagen theory, having no answer to any question of the form: 'What is really happening when - - -?', forbids us to ask such questions and tries to persuade us that it is philosophically naive to want to know what is happening. But I do want to know, and I do not think this is naive; and so for me QM is not a physical theory at all, only and empty mathematical shell in which a future theory may, perhaps, be built."
https://bayes.wustl.edu/etj/articles/cmystery.pdf
...and which he goes on to makes some interesting observations about the Bell Inequalities.
"Just as Bell revealed hidden assumptions in vonNeumann's argument,so we need to reveal the hidden assumptions in Bell's argument. There are at least two of them, both of which require the Jeffreys view point about probability to recognize..."
Looking at a single object with a fixed angle camera produces similar observations to an entagled pair when the pair is in a similar configuration and where each object in the pair is observed by their own camera except one of the cameras sees a negated result.
In the entanglement experiment described the particles have angular momentum every which way until the angular momentum of one is pinned down by measurement whereupon the other one is also pinned down to the opposite by conservation of momentum. There is still a sort of spooky action at a distance when that happens or perhaps a splitting of the multiverse 'at a distance' into many worlds where the spins point different ways.
Rotational invariance would rotate both the source and the detector, and there would be no surprise that the possible results and statistics over them are unchanged.
The quantum surprise is that rotating the source relative to the detector leaves the possible results unchanged (though the statistics do change).
What's the difference between this and quantum entanglement?
There is a famous test, Bell's inequality [2], that specifically rules out local hidden variable interpretations of QM.
Nonlocal hidden variable interpretations, such as De Broglie - Bohm theory [3], are potentially still on the table, however.
It is somewhat ironic that Bell's theorem is sometimes presented in popular media as a general disproof of all hidden variable theories, in a context where locality is taken for granted -- because Bell himself seems to have been partial to nonlocal hidden variable theories. An article by the same Mermin mentioned in the OP is worth a read, on this subject [4].
[1] https://en.wikipedia.org/wiki/Hidden_variable_theory
[2] https://en.wikipedia.org/wiki/Bell%27s_theorem
[3] https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory
"The Chaotic Ball: An Intuitive Analogy for EPR Experiments"
Say SOMEONE ELSE puts the marbles in two envelopes and sends them to you and your friend in Australia. (it's someone else because we don't actually create the entangled particles, we just "get" them)
The marbles being red and blue (or both red or both blue, depending on what you're measuring) from the beginning would be a LOCAL hidden variable. It's local because it's been predetermined at the moment of creation and the marbles carry the property on themselves and it's hidden because you don't know how/why the person putting the marbles in those envelopes decided those colors and you can't see them until you open the envelope (measure the particle).
This way if you don't open your envelope, your friend's envelope contains a marble that's 50/50 red or blue and the color will be the predetermined one no matter what you do with your marble at home. So whatever decides the marble's color has nothing to do with your marble, it's local to the friend's one.
The actual measurements work differently. It's been experimentally proven many times that at the moment you look at your marble, the other marble's 50/50 probability of being red and blue shifts substantially to, for example 75/25. And that's without it having any way of knowing that you've seen your marble. So there are hidden variables that we don't understand, but they're not local. They somehow affect both marbles.
In real life there aren't only two colors and the probabilities aren't those nice numbers, but you get the principle.
This is completely incorrect, to the point where what you were trying to correct was actually more accurate, though incomplete.
The usual setup is that for any given axis, each person always measures 50:50. Measuring your own doesn't change the odds of the other.
Knowing the _results_ of your own does. For the same axis, the correlation is exact. For axes with an angle theta between them, we get a correlation of R ~ cos(theta/2).
The upshot is that there is no underlying (classical) probability distribution that can give rise to this that can explain things for all measurement axes. This is sometimes glossed as "correlation without correlata".
The rest of your explanation was super easy to grok (thank you!) but this part I can't wrap my head around. If the balls can be red or blue, and it's 50/50 before, how would the probability go to 75/25? I would expect it to either stay at 50/50 (no change) or to 100% (because the other ball is known).
Can you elaborate on this part? This is really fascinating.
I always imagined the two "marbles" as possibly being two similar but differing clocks instead. The clocks will align more or less often depending on how similarly they're set and how fast each run. With this analogy you can come up with any distribution that fits your fancy.
Its probably a silly analogy but it lets me cling my notions of no spooky action.
Same if my friend is opening the envelops.
Now for all the opened envelops if I have got 10 red balls. Now if my friend open the paired envelops, he will probably get 7 blue and 3 red.
My observation of the balls had an effect on his side and shifted probabilities on his side.
If that's what you mean, what does observation or measuring even mean? How do the balls know the envelop has been opened.
In quantum entanglement they are both truly and really random until you measure one. And it's not random in a sense that you closed your eyes when putting them into envelope. They actually both don't have a "selected" color. They "snap into one of two colors" when you measure (look at) one. And the "unbelievable" thing is that when you measure one, the other one immediately snaps into opposite color, no matter how far it is.
If you look at the marble you got and it's red (or blue) the size becomes indeterminate. Focusing now on the size you will find it's large or small, but the color becomes indeterminate. It could be red the next time you look at it.
When you take your entangled marble, look at the color and see it's red you know the other marble is in the "blue" state (and the entanglement is broken). If someone looks at the color of that marble you know they will find it's blue. But if they look at the size before looking at the color it could be large or small (and looking now at the size of your marble will tell you nothing about it) and if they look at the color later it could be red or blue.
In the classical case, if there is a large red marble in one envelope and a small blue marble in the other it doesn't matter in what order you look at the color and the size. You will always know what the other person found.
In the quantum case, if both look at color first they will find complementary colors. If they both look at size first they will find complementary sizes. But the second measurement will be uncorrelated. And if they make the measurements in a different order, everything will be uncorrelated.
Most advocates of the hidden-variables idea believe that experiments have ruled out local hidden variables
Source: https://en.wikipedia.org/wiki/Bell%27s_theorem#Bell_inequali...
A shared RNG seed is essentially entanglement.
This delves more into complex hidden variables, that normal analyses ignore: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC137470/
In order to help you out, after you two have made your guess we are going to give you two a chance to back out and lose nothing. After your prediction we are going to reveal one coin to you and another coin to your partner. Together you and your partner will have an opportunity to back out, but the catch is that you two are not allowed to communicate!
Instead of communicating, you can raise either a red flag or a green flag after seeing your coin. Similarly, your partner can raise either their red flag or their green flag after seeing their coin. If you both raise the same colour flag, the game keeps going and we see if you win or lose. If you both raise different colour flags, the game stops and you lose nothing.
To ensure you don't cheat, we've separated you and your partner by 200 million kilometers and you have one minute to raise one of your flags after seeing your coin, otherwise you lose the game. (Alternatively you are your partner are separated by 400 meters and you have 100 nanoseconds to raise one of your flags.)
Good luck.
---
The above casino game cannot be beaten using envelopes of marbles, but it can be beaten (i.e. positive expected value) using envelopes of entangled particles. See quantum pseudo-telepathy.
https://en.wikipedia.org/wiki/Reinhold_Bertlmann#Bertlmann%E...
The other replies explain why it's wrong, but here's a link to Bell's refutation for good measure
Why is the difference in orientation of the detector necessarily linear? What is the control aspect of this experiment where classical-system shows this linear pattern? Or can the argument be made more fundamentally?
What separates a coherent "quantum" superposition, say, |0> + |1>, from a probabilistic "non-quantum" 50:50 mixture is that I can choose a measurement basis in which the coherent state always yields a definite result, say "1", whereas measuring the mixed state always yields a 50:50 mixture of "0"s and "1"s.
A continuous sweep of the angle of the measurement basis generally results in an interference pattern, the amplitude of which can be used to assess the fidelity of the quantum state.
(I get paid to work on quantum communication and related experiments.)
https://www.youtube.com/watch?v=j6Mw3_tOcNI&ab_channel=Sabin...
What makes people say information travels faster than light with quantum entanglement?
Maybe this will help https://html.duckduckgo.com/html?q=bell%27s%20inequality%20s... I imagine the youtube links might be more comprehensible.
Personally, I'd prefer third party summaries of the thesis when it has been established as an interesting contribution, and the original article to stick to what is actually accepted by the mainstream; or at the very least to be more up-front that this is actually based on a new paper by the author.
That's not to say this paper is wrong - I'm not remotely qualified to judge (and it happens regularly in articles plugged on HN); I just find the way these things are presented as a bit iffy.
If me observing the particle in Australia alters the probability distribution of your particle in USA, can't I only observe the particle when I want to communicate 1 and never observe it when I want to communicate 0?
Edit: thanks a lot for the answers! I guess it boils down to the fact that the Australian guy cannot condition his decision on the (unknown) spin of his particle -- if he could (eg: had access to the local hidden information) then he would be able to update the USA's probability distribution instantaneously and use it to communicate
The crux with quantum mechanics is that you can show (very easily, understandable by the layman, look up the Bell inequality) that in the quantum case the ball only takes on a color the moment you look at it, and so instantaneously is setting the color in the USA as well.
However, the basic setup still applies. You cannot send information by merely observing something.
We don't actually know that this is an accurate description of what is happening, although it is consistent with what is happening.
Very likely, the underlying physical process still operates below the speed of light. "Instantaneous" isn't something that makes physical sense in this context.
https://www.youtube.com/watch?v=dEaecUuEqfc
It is based on this (unpublished) paper:
http://www.flownet.com/ron/QM.pdf
The key insight is that measurement and entanglement are actually the same physical phenomenon. A measurement is nothing more than a very large network of mutual entanglements.
Because physicists can not tell the difference between a particle whose "wave function collapsed" and one that didn't.
The faster than light communication would be equivalent to modulating the collapsedness of a stream of particles by measuring-or-not their entangled counterparts. Since the is no discernable difference between particles pre and post collapse, no information can be transmitted.
The simplest one is that you need to be able to tell the partner when you've made your changes and that you're ready for them to measure
For both theories the physics surrounding them just happens to make their presence undetectable. In the case of the ether, the ether wind just happens to shrink the arms of the Michelson-Morley interferometer by exactly the amount needed to prevent the interference pattern from detecting the ether wind. In the case of hidden variable theories, the predicted joint probability distributions just happen to make the hidden variable values themselves uninferable.
First, if confused more than clarified things. And second, I suspect the principle does apply to all forms of entanglement.
Now if I could only prove that, I'd be on my way to Stockholm. :-)
There are enormous engineering challenges with quantum computing, but no fundamental challenges.
https://spectrum.ieee.org/computing/hardware/the-case-agains...
(I've also just submitted that link to HN separately fwiw)