Einstein's missed opportunity to rid us of 'spooky actions at a distance' (opens in new tab)

> 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.

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?

I think I have a reasonable mental model of how certain QM processes work by visualising waves in transit coalescing as particles when measured.

But I have absolutely no idea how to visualise entanglement. Any tips? Or do we just have to shut up and calculate?

Invariance under velocity changes boosts the whole apparatus. And speeds less than C are observable, and do change w.r.t. an unboosted observer.

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).

This is fairly far from my field, but as I understand it, that would be a hidden variable interpretation of QM [1], and specifically in that analogy a local hidden variable theory. That's what Einstein himself wanted.

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

[4] https://cqi.inf.usi.ch/qic/Mermin1993.pdf

The way I understand it, this is exactly the simplified (and incorrect) explanation.

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.

It's not my field, but I remember reading that your example doesn't represent entanglement because when put into envelopes, one marble is already red and another blue.

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.

You could have something similar to quantum entanglement if these were some strange kind of marbles which cannot have a well defined color and size at the same time and are magically linked.

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.

This would be a 'local hidden variable' theory. According to wikipedia these have largely been ruled out:

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...

Welcome to Bell's Casino. You and your partner will be playing our famous two-coin game today. We have hidden two coins under these two opaque cups. You and your partner are to guess the orientation, heads or tails, of both of the coins. Guess correctly and win $1. Guess incorrectly and lose your $1 bet.

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.

This argument is called "Bertlmann's Socks"

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

http://cds.cern.ch/record/142461/files/198009299.pdf

Wikipedia's Simple English page on Bell's inequality actually has a nice overview of a simplified way of thinking about quantum entanglement: https://simple.wikipedia.org/wiki/Bell%27s_theorem

If you do the experient with an entangled source and two Stern Gerlach detectors oriented the same way it's not so interesting a bit like the marbles in envelopes - either they both red of green. The interesting bit is if you rotate them a bit the correlation varies like cos(the angle) between them. So correlation 1 at 0 degrees, 0 at 90 degrees, -1 at 180 degrees and about 0.98 at 10 degrees. But how does nature or whatever know the angle between them when they are far apart? In most 'hidden variables' scenarios the correlation at 10 degrees is more like 0.89 or a linear change and that is basically the essence of Bell's theorem and experiments - you can't get the correlations without the particle at one end kind of knowing the set up at the other, or 'non locality' as Bell called it.

What seems to be missing from the replies posted so far is the notion of coherence, and the choice of measurement basis.

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.)

Sabine Hossenfelder gives the best explanation to address this that I've found

https://www.youtube.com/watch?v=j6Mw3_tOcNI&ab_channel=Sabin...

The phenomenon is statistical. In your example (which is a bit too simple but still), the analogous surprise would be something like each party guesses what's in the envelope before they open it, and the accuracy of their guess is too high to explain by chance.

actually the marbles change colour every 1 second and you can take them really far apart, meaning one can go at a really high speed and distance trough universe, so the time would have dilated for it. when you open them both have same color

Roughly speaking: if you can see your marble through a purple filter, the one in Australia will turn out to be perfectly green.

Apparently this common explanation is wrong. If you actually measure one, the other actually changes. Although you can't use that to send information, so einstein's faster-than-c restriction isn't violated.

Maybe this will help https://html.duckduckgo.com/html?q=bell%27s%20inequality%20s... I imagine the youtube links might be more comprehensible.

I agree, motivation is important (because it reflects on the quality of the content).

I have a bag with two balls, one red, one blue. I randomly send one of the balls to Australia, one of the balls to the USA. The moment you look at your ball in Australia, you also know the color of the ball in the USA. How would you use that fact to send information?

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.

This is a Google Tech Talk I gave about this about 8 years ago:

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.

When the person at the other end looks at their particle, and sees it either 1 or 0 and has no other information, how do they know if you've looked at your particle or not?

This is my favourite explaination. I have had this bookmarked for over 10 years and keep coming back to it:

http://www.felderbooks.com/papers/bell.html

>> Does someone have a good explanation/intuition for why you cannot exploit quantum entanglement to send information faster than light?

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.

Initially, your particle in Australia and its entangled twin in the USA exist in a superposition of 0 and 1. When you "measure" the state of your particle, you force it to assume a definite state, and entanglement forces the other particle to assume e.g. the opposite definite state ("spooky action at a distance"). This allows you to synchronize information across large distances, but you cannot send anything, because you cannot chose the outcome of the quantum measurement.

Entanglement works like synchronized clocks. You can't send information, but you can coordinate actions to a similar effect. Much like you can coordinate actions of separate groups using synchronized clocks with no communication except for passing time.

you have to send classical information to get useful stuff out of the entanglement like quantum teleportation.

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

When I wrote my original post I seriously considered adding the restriction to 'entangled spin states', but then decided not to.

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. :-)

For quantum computing to be impossible, basically all of quantum mechanics would have to be wrong.

There are enormous engineering challenges with quantum computing, but no fundamental challenges.