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.
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.
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.
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.
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".
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/
Classical entanglement, which is not good enough to explain quantum entanglement.
In QM, experiments show us that entangled particle spin probabilities vary non-linearly with the angle between detectors (even if those detectors are far apart).
This means that either: 1) locality is broken.. state is somehow transmitted faster than the speed of light between particles. 2) realism is broken.. god plays dice with the universe
But there's also a 3rd, which is: the choice of detector angle is not an independent variable (a necessary assumption for Bell's inequalities to hold).. instead the state of the universe is pre-determined and the experimenter's choice of detector angle is known beforehand so there is no need for spooky action at a distance. This isn't a very popular explanation since it provides no reason as to why we don't see this weird lack of independence elsewhere.
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.
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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?
If you told me causally this detector which measures electrons/photons/whatever and varies by the cosine of the orientation, I don't think any (non-physics person) would bat an eye; it seems like a pretty normal thing a sensor might do.
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?
> Knowing the color of one marble is enough to know the color of the other marble
I guess so.
> without information travelling between the marbles?
The marble colours are in sync on measurement. Somehow that info has travelled instantaneously. You just can't use it to send information, at all..
above is just my understanding. I have no background in this. Just a programmer.
Maybe this will help https://html.duckduckgo.com/html?q=bell%27s%20inequality%20s... I imagine the youtube links might be more comprehensible.
The problem comes in when the angle between your two measurements is anything else. The chance that the measurements match is based on the cosine of that angle. There's no way for this to happen if the measurements are independent.
If you try to write two equations, where the first equation takes the secret particle state and first angle and gives you 1 or 0, and the second equation takes the secret particle state and second angle and gives you 1 or 0, you won't be able to reproduce the odds you get in the real world. Only equations that know both angles will work.
The thing about the change of "colour" in this analogy is you don't know in which direction it changes. So let's say you observe you "marble" through a "purple filter", which gives has:
- a 50% chance of being transparent to your marble (corresponding to a red-blue superposition marble collapsing to a purple marble)
- a 50% chance of being opaque to your marble (corresponding to red-blue superposition marble collapsing to a green marble).
The issue is that when you learn your marble is purple, while you know with 100% certainty the marble in australia is green, there is no way you can send information to Australia using that. This is because the other 50% of the time, your marble will be green, and the marble in Australia is purple.
So if I'm sitting in Australia, when I measure the marbles in my envelopes with purple filters, all I see is purple marbles 50% of the time and green marbles 50% of the time no matter what measurements you are performing at your end. So you can't send me messages by performing measurements at your end because you can't change the statistics of those measurements.
But you'll know the answer to every measurement I performed, if you've measured the other marble with a purple filter too.