[Quantum Mechanics] Explain this theorem, please?

Factual Questions
1

I’m trying to understand how quantum entanglement works, and why it doesn’t require information to travel faster than the speed of light. I’m told that I should look into the No-communication theorem, but Google won’t provide anything not ridden with incomprehensible (to me) equations.

I know it explains why quantum entanglement doesn’t require the transfer of information, and that’s about it.

So, is there anyone here who could explain it to me in more-or-less layman’s terms? Ideally, it wouldn’t have to be dumbed-down to the point where I could’ve just not bothered looking it up in the first place…

Please and thank you, mathematicians, physicists, and idiot savants of the SDMB…

2

Here’s the key sentence of that page:

You have two particles a and b that have entangled. All that means is that the two particles have a pair of traits in common such that one is the opposite of the other. There are presumably an infinite number of possible traits, but let’s be as simple as possible and call one “up” and one “down.” In fact, when it comes to the quantum property called spin, this is exactly one possible measurement.

There’s no way of telling whether a particle is an up or a down until you measure it. When you do, one of the set will be an up and the other will be a down. This is always true. And it’s as random as flipping a true coin. If you measure 1,000,000 particles, on average you’ll get 500,000 ups and 500,000 downs.

So what happens if you entangle a particle and send one zooming off into space. To a measuring station around the star Alpha Centauri, four light years away. Well, let’s say that the particles are photons, which travel at the speed of light. You wait four years and measure particle a. You see that it is an up. So you know that particle b is a down.

So you have information that you didn’t have before. But what can you do with it? If you send a signal to the station at Alpha Centauri, it won’t arrive for four more years. You can’t add to their current information. You can only bring them information as fast as light will carry it.

But what if you think you’re clever and make previous arrangements with the station. Say, as soon as you get the particle measure it. If it’s an up, buy Cosmos stock; if it’s a b, sell Cosmos stock. But the state of any particle is completely random. You might as well have said, in four years flip a coin. If it’s heads, buy Cosmos stock; if it’s tails sell Cosmos stock. You haven’t gained any information at all by the measurement. You’ve just flipped a very expensive coin.

Sending more particles doesn’t help. On average, it’s still flipping a coin. There is nothing you can do with entangled particles that gets information anywhere faster than sending a regular message at light speed.

It’s frustrating. You know that if you measure an up on earth, then the entangled particle, no matter where it is in the universe, even if it is ten billion light years away, will be a down. But you can’t do anything at all with that information. You can’t figure out how the entangled particle “knows” what it should be. You can’t make an entangled particle do anything faster that you couldn’t do by sending an ordinary message. It seems like there should be a way around this, somehow, if you’re just clever enough to think of it, but there isn’t.

No information can be sent faster than the speed of light, and entanglement doesn’t give you a way around that.

That’s all there is to it, but it’s enough to give physicists and philosophers Excedrin headaches.

3

It does however provide a way to generate a cryptographic one-time pad that is identical on both sides and unknown to anybody else. So that if you wanted your data travel to alpha centauri to be very very secure you can just go ahead and send an encrypted message and it’ll take four years to get there. Without entanglement you would have to do public-key negotiation or something like that and the key exchange would take at a minimum 4 years :slight_smile:

4

Good luck :slight_smile:

I have read half a dozen accounts of the EPR paradox/Bell’s inequality* and it sort of fits in my head for five minutes and then falls out. The problem I have is not imagining that a couple of photons a light year apart are connected in some way but Bell’s maths prove that they don’t carry the up/down spin information with them, that would mean hidden variables which are a no-no.

I’m not in any position to answer the OP but I’d like to give it a bump to see if anyone (else thanks E. Mapcase) who can will show up.

5

The standard analogy that’s used to show how this avoids a causality violation is this:

Say you and I have a magic pair of decks of cards. If we both turn over a card, no matter who does it first, no matter where we are, we will always turn up the same card. However, the magic only works when the decks are both perfectly shuffled.

So, how could I send a signal to you through the deck? I’d have to encode the signal into the pattern of cards turning up somehow, and then stack my deck to have that pattern. But as soon as I do that, the magic link is broken and the signal can’t be sent until we both perfectly shuffle our decks, at which point the signal is lost.