I am still not so sure that Bell's theorem and subsequent experiments really do rule out hidden variables.
After all, if I split a coin down the middle and took the two halves to different sides of a continent, it wouldn't be surprising if one was found to be heads and one found to be tails.
It would also not be surprising that if I then repainted one of the halves, the other half would be independent of the repainting and the "entanglement" would be broken.
The difference could be simply in that quantum particles behave differently than having only TWO sides to them, like a coin. But the principle is the same ... that the FTL "spooky" communication never happens even between two particles -- rather, they are correlated because were taken from the SAME PLACE at the same time. We just don't understand how their states work, because they're not just one dimensional states.
I have seen it explained that Bell's theorem does not, strictly speaking, forbid hidden variables. What is says is that if such hidden variables exist, they are irreducibly quantum, at which point the hidden variables become uninteresting. Recall the historical point of "hidden variables" was to recover classicalness out of the quantum. If the hidden variables are also quantum, they're just pointless elaborations that explain nothing and enable nothing, so why bother with them?
(I've also been quibbled with in replies but I'm not sure if those quibbles are correct.)
Put in more interesting terms, a 2-norm probability system can contain states that are fundamentally inexpressible in a 1-norm probability system. See http://www.scottaaronson.com/democritus/lec9.html for a good discussion on what that means. Viewed from that perspective, Bell's Inequality is all but a trivial result; yes, there really is a way in which "quantum" fundamentally differs from "classical" in a mathematically rigorous manner, despite our culture's casual use of the word "quantum".
Bell tests give more correlation than what you're describing could. That's what makes it "spooky".
For example, there are coordination games which can be won with certainty only by using entanglement (or full communication); where just having pre-shared random variables would not be enough (you'd expect to lose now and then). [1]
It's very hard to give analogies for what entanglement is, because of the tendency for any intuitive mechanism to allow either no coordination or too much coordination.
You are confusing two different concepts. Splitting the coin into two faces amounts to collapse of the wave function into physical observables. The two halves have been determined.
The idea with Bell Inequalities is that if Alice and Bob are given entangled particles and some predetermined information (local hidden variables) then when Alice and Bob make specific measurements:
1. For local hidden variables, Alice should see results predicted by the whatever she already knows and won't see Bob's actions having any effect on her results.
2. Without local hidden variables, Alice will find (after the fact) that her results are skewed by (correlated to) the measurements Bob made.
Exhaustive experimentation has been consistent with #2.
Interesting idea and not one I'd ever really considered. Then again, I'm barely even a layman regarding this stuff so there are probably a lot of things I haven't considered yet.
It is important to note here that Einstein was not being translated from German properly into English. 'Spuk' has a meaning akin to spook in the sense of a remote observer; Rather than 'spooky', which is an adjective relating to ghosts.
There are also a lot of assumptions in the no-cloning theorem regarding the nature of quantum operators: that they absolutely must be linear and unitary. This is certainly not the case for research into invisibility or stealth technology, where non-linear optics are standard.
Lastly, the epistemological nature of hidden variables is the property which rules them out. They are referred to as extraneous variables in every other field of science. This has caused problems of overfitting; Biologists can hold excessive faith in Hidden Markov Models. When you dissect Bell's theorem in terms of raw mathematics, it is technically a restatement of the triangle inequality within probability spaces; So it just ensures that the transitive property holds for the variables of a functional system.
> It is important to note here that Einstein was not being translated from German properly into English. 'Spuk' has a meaning akin to spook in the sense of a remote observer; Rather than 'spooky', which is an adjective relating to ghosts.
Einstein's "spukhaft" is very much an adjective relating to the activity of ghosts. If you translate it as "magical", you're not losing much of its meaning.
> It is important to note here that Einstein was not being translated from German properly into English. 'Spuk' has a meaning akin to spook in the sense of a remote observer; Rather than 'spooky', which is an adjective relating to ghosts.
I've never heard this theory before and I don't think it's true. The phrase that Einstein used was "spukhafte Fernwirkung".
Spooks at government agencies are not the spirits of dead people; they are merely remote observers. The word ghost is translated as geist, like in the word 'poltergeist'.
Really? For me it looks overly complicated and going in circles. After all it boils down to: "You have two boxes that generate exact same sequence of random bits, no mater how far away they are. How can you use it for communication? There is no way."
No the idea is pretty simple. You give entangled particles to Alice and Bob who are a non-trivial distance away from each other.
Alice performs an operation to send a bit of information to Bob via the entangled property. Bob still gets random results from his measurements. If Bob saw a signal instead of randomness this would be FTL communication.
Instead Bob and Alice compare notes after the fact and Bob finds that if he knows what Alice did, now he can find a signal in his data. This after the fact comparison is what scuttles FTL communication. Bob doesn't know anything until after the "sub-light" communication.
Alice could instead transmit her information using "sub-light" communication to Bob at the same time she performs the entangled operation, but Bob still doesn't know anything (measurements look random) until the "sub-light" information reaches him.
I tend to read it as the steps taken in a thought process to try to use quantum entanglement to achieve FTL communication. Personally this is one of my favorite learning methods, since you go through the motions of a discoverer rather than getting the finished thought served.
The book "About Time" (Davies 1995) is written like this, and I love it :)
So wait, if you can refresh the probabilities of a quantum property by making a second type of measurement (as described by the video in the article), why wouldn't this work? Here's how you might send information between two entangled particles via some property:
To send a 0 via property A:
1. Clear your measurement of property in A by measuring property B
2. Measure property A again
3. If A is not in state 0, goto 1
4. The other entangled particle should now read state 0 too
To send a 1 via property A:
1. Clear your measurement of property in A by measuring property B
2. Measure property A again
3. If A is not in state 1, goto 1
4. The other entangled particle should now read state 1 too
Maybe it would take a few more tries than expected occasionally, but if you give enough time to loop say, 10 times between measurements of the second particle, that's only a (1/1024)/2 = 1/2048 chance that the information is wrong! That's probably reliable enough for reasonably good error detection [1]. As long as the amount of time needed to get the first particle into a given state is less than the amount of time needed to send a photon to the second particle, it would seem that you could send information faster than c.
A measurement is any interaction between particles. In the case of entangled photons, a measurement consists of allowing the photon to be absorbed by an atom. You only get one such measurement; any new photon emitted by that atom will have a spin which is no longer entangled with the spin of it's original twin. (Actually, they were more like anti-twins; one was up when the other was down, and visa-versa.)
Even assuming you had two larger particles (let's say atoms) which were entangled, allowing you to make multiple measurements, nothing you change about one of them is communicated back to the other. If you measure a property of your atom you may also be able to determine the value of that property for the other, but in doing so you change the atom. You flip the spins of the electrons, or of the atom as a whole, etc. This is what "clearing your measurement" means; you no longer have any good information about that property. If you then remeasure that property, it's value is no longer correlated with the twin particle.
The author, Chad Orzel, is the author of the book, "How to Teach Physics to Your Dog", which I thoroughly enjoyed. The chapter in which he explains the Bell Theorem I had to read twice, but I eventually got it.
He also wrote a sequel, which I haven't read yet, titled, "How to Teach Relativity to Your Dog". The cover art is hilarious if you know what a light cone is.
Bummer, so much so sub space communication. It does sound like it would be useful for extremely safe encryption where the two parties would have an ever changing shared key.
After all, if I split a coin down the middle and took the two halves to different sides of a continent, it wouldn't be surprising if one was found to be heads and one found to be tails.
It would also not be surprising that if I then repainted one of the halves, the other half would be independent of the repainting and the "entanglement" would be broken.
The difference could be simply in that quantum particles behave differently than having only TWO sides to them, like a coin. But the principle is the same ... that the FTL "spooky" communication never happens even between two particles -- rather, they are correlated because were taken from the SAME PLACE at the same time. We just don't understand how their states work, because they're not just one dimensional states.