Causality, Quantum entanglement, FTL communication etc.

[adam_grif]

It's question time again.

I was under the impression that superluminal communications in QM were disallowed by the No-communication theorem, but recently I've been having people (nobody particularly reputable, of course) claim that the NCT has been disproven, and that as a result, QM permits this kind of FTL communication.

Additionally, I've had the same sorts of people claiming that the double-slit experiment means that information was traveling back in time? Or some crap? I'm thinking they're just talking shit on this one, but I don't have the expertise in physics to refute them decisively.

[Lord of the Abyss]

Additionally, I've had the same sorts of people claiming that the double-slit experiment means that information was traveling back in time? Or some crap? I'm thinking they're just talking shit on this one, but I don't have the expertise in physics to refute them decisively.

I'm not a physicist, but I have read of variations of the double slit experiments called quantum erasure experiments that are sometimes described in pop-sci articles as "erasing information backwards in time". That description might be what these people are talking about.

[Covenant]

They're talking shit. It's immensely confusing, but it's not magic and it's not time-travel. There are currently experiments in place to see what's going on, but in the specific instances you're talking about it's very unlikely retro-causality is being called into play regarding the two-slit experiment.

The problem is that while people can kinda understand atomic physics in a reasonable capacity, trying to comprehend the behavior of odd things like light beams and quantum state and entanglement just go way over people's heads. It's counter-intuitive until you've built a library of concepts in your head to understand quantum behavior with, and as the saying goes, nobody understands it.

You can fire all kinds of shit through a double filter and it acts all goofy, even molecules.

[Kuroneko]

I was under the impression that superluminal communications in QM were disallowed by the No-communication theorem, ...

Well, that's not quite true. That theorem deals specifically with with EPR-type entanglement, and concludes that no superluminal communication can occur in that case, as whatever is done to one does not affect the probabilities of measurment outcomes on the other. So one could reasonably say that the NCT forbids superluminal communication by these means, which covers only a subclass of the possible experiments that could be run.

... but recently I've been having people (nobody particularly reputable, of course) claim that the NCT has been disproven, and that as a result, QM permits this kind of FTL communication.

No. Since NCT is a mathematical theorem following from the formalism of QM, there is no sense in which QM can permit 'this kind' of FTL communication.

In a relativistic context, both FTL and causality is only possible if there is a preferred frame of reference. For quantum field theory, the corresponding statement is that spacelike-separated operators commute, but the essential point remains: when someone wants you to accept claims FTL, that means comes with either time travel or a preferred reference frame. And either of those is a claim large enough to require something more than some mumbling about the NCT not covering all the bases, because they actually do falsify a large chunk of physics: not necessarily NCT, but quantum field theory.

One thing to watch out for in QFT is that just because there some reference to superluminal or tachyonic this or that, does not automatically mean there is actual FTL communication going on. A kind of prototypical example is a line of pendula in a gravitational field, with neighboring pendula coupled together by springs. In a stable rest position (all down), the system acts like an ordinary massive, spinless field. A perturbation spreads outward, but stays localized. But in the unstable rest position (all up), it acts like a field with an imaginary mass, and it is quite correct to say that it has superluminal wave modes. But a perturbation causes the entire configuration to erupt into chaos, but does not actually spread superluminally. A field like that would have the entire future light cone fill up with particles. Spoiler

The Lagrangian of a continuous limit of the pendula can be written as
[1] L = (1/2)(dθ/dt)² - (1/2)(dθ/dx)² - (1-cos θ),
where pendula masses, spring constants, and gravity are chosen to make the extra coefficients unity. The middle term is the elastic potential of the springs, dependent on the difference in the angular positions of adjacent pendula, and the last term is the gravitational potential (as the vertical height of the pendula is proportional to 1-cosθ). Anyway, plugging this into the Euler-Lagrange equation gives
[2] θtt - θxx + sin θ = 0,
so for small perturbations from θ=0, sin θ is approximately θ, this is the canonical Klein-Gordon form with mass-squared = 1. On the other hand, for perturbation from θ=π, the sine term switches sign (sin θ = - sin(π-θ)), and this has the same form except for a mass-squared = -1, i.e., is tachyonic.