Entaglement, locality, and information

[hideelo]

As far as I understand, given that there is such a thing called entanglement, we know that there are non-local interactions. The line that this is usually followed with is "since no information traveled faster than light , locality isn't violated".

I have a few interrelated questions about this. As far as I know in GR, we demand that all real particles travel through spacetime with tangent vectors which are non-positive. No mention of information, it's a constraint on allowed tangent vectors of particles.

We have another assumed condition on "causality" which takes explicitly that two regions in spacetime which can be connected by timeliness or null curves are said to be in causal contact with each other. This also makes no reference to information, but does seem to have a notion that causal interactions do not propagate faster than light. What distinguishes causal interactions from non causal ones?

A final question, what is information, and why would it be the measure of what can and cannot travel faster than light?

 

[atyy]

There are two notions of causality, one not relying on information and the other one relying on information.

For the one that does not rely on information (the sense in which classical relativity is a theory of causality), quantum entanglement breaks it - ie. reality is nonlocal or weirder.

For the one that does rely on information, quantum entanglement does not break it. Here the notion of information is simple. Two observers widely separated make measurements. Can I, making measurements on my side, figure out what he is doing? It turns out that in quantum mechanics, I cannot. Since none of his actions make any difference to the outcomes of my measurements, he is unable to transmit any information to me.

 

[hideelo]

I'm sorry, I really don't see how that clarifies anything

 

[secur]

all real particles travel through spacetime with tangent vectors which are non-positive.

That's using a Lorentz signature like ( -, +, +, +) of course

causal interactions do not propagate faster than light. What distinguishes causal interactions from non causal ones?

Non-causal would be the ones that do propagate faster than light, i.e. non-local. The only one I know of is entanglement. Many physicists would argue it doesn't really qualify, but perhaps we can treat that as a nit for this question.

A final question, what is information, and why would it be the measure of what can and cannot travel faster than light?

That's clarified by atyy's answer

 

[bhobba]

As far as I understand, given that there is such a thing called entanglement, we know that there are non-local interactions.

That's incorrect.

You need to study Bells Theorem:
http://www.drchinese.com/Bells_Theorem.htm

Thanks
Bill

 

[atyy]

I'm sorry, I really don't see how that clarifies anything

As you said in your original post, there are two notions of causality
(1) one notion involves "real" causality and does not involve any notion of information - using this notion, QM is nonlocal
(2) a different notion is usually said to involve information - a better term may be that it is an "operational" notion of causality - using this notion, QM is local

A good paper reviewing the different notions of causality is http://arxiv.org/abs/1503.06413. In section 5.1 they explain Bell's theorem in terms of the realist notion of causality, and in 5.2 they explain it in terms of the operational ("information") notion of causality.

There is some debate over the historical interpretation of Bell's work in that paper, but the physics itself is not controversial.