"However, both particles have the property from their inception, and so no faster-than-light or non-local interpretation should be needed."
This is incorrect, both particles have a superposition of k and ~k (to use your terminology). It is not the case that when the wavefunction collapses, we just suddenly find out the "internal state" of the particle. This "internal state" simply does not exist until the wavefunction collapse has occurred.
The "no faster than light" doctrine refers specifically to the transfer of information. And no information, in the strictest sense, has been transferred. Think of it like this: try to imagine how you could communicate with someone using quantum entanglement. If you can communicate something, then information has been transferred. But you can't. All you know is that if your particle is k, then theirs is ~k.
Now, you could make up a rule book that says "if my particle is k, then I'll do x, and you'll do y" but that rule book will have to have been shared between both parties before hand, at less than the speed of light.
Edit: should just mention I'm not an expert here, and articles like this are always interesting. Finding loopholes in our conventional understanding. But it's important to know just /what/ our conventional understanding is first to realise why things like this are important.
Even with such a preshared rule book you wouldn't get any FTL communication. You could crate a pair of random number generators this way which will always give the same result. Certainly useful for cryptographic purposes but sadly not direct communication.
Agreed; that's what I was trying to say. Perhaps it's disingenuous to frame the problem in this way (that is, talking about rule books and the like), but I was just trying to make it more relatable to normal human experience.
> both particles have a superposition of k and ~k (to use your terminology). ... This "internal state" simply does not exist until the wavefunction collapse has occurred.
What would the implications be if particles did have an internal state?
It would be a violation of Bell's theorem as we currently understand it. In other words, it can't happen, unless our understanding is wrong. (For more info, the wiki on Bell's theorem has been linked to elsewhere in this thread.)
But when you "collapse the wavefunction" and "create" the internal state of the particle, do you also create the internal state of the other one that is entangled to it? Do you create it instantaneously?
You see, the problem is not whether you can transfer information in human readable form (though if you could that would certainly be a huge problem with relativity!), but whether any effect that propagates faster than the speed of light exists.
You'll have a hard time explaining that in the frame of wavefunction collapse, I think.
This is incorrect, both particles have a superposition of k and ~k (to use your terminology). It is not the case that when the wavefunction collapses, we just suddenly find out the "internal state" of the particle. This "internal state" simply does not exist until the wavefunction collapse has occurred.
The "no faster than light" doctrine refers specifically to the transfer of information. And no information, in the strictest sense, has been transferred. Think of it like this: try to imagine how you could communicate with someone using quantum entanglement. If you can communicate something, then information has been transferred. But you can't. All you know is that if your particle is k, then theirs is ~k.
Now, you could make up a rule book that says "if my particle is k, then I'll do x, and you'll do y" but that rule book will have to have been shared between both parties before hand, at less than the speed of light.
Edit: should just mention I'm not an expert here, and articles like this are always interesting. Finding loopholes in our conventional understanding. But it's important to know just /what/ our conventional understanding is first to realise why things like this are important.