Preserving causality in the most general way.

[MTd2]

I was trying to think in general means to localy preserve causality. By "means", it means to include (or not) varying speed of light and faster than light sign propagation. By varying speed of light, it means that light speed can localy depend on the most generical parameters you can get.

Don't think in terms of special relativity and space time, just any general cases 3 and 4 manifolds.

Go as crazy as you can get, as long as you are mathematicly consistent. Don't worry about trying to get realistic physics right now.

 

[Haelfix]

Thats a question with a large literature attached to it and depends who you ask.

Typically you want to ensure that microcausality is ensured (a statement about commutators of operators vanishing outside of the light cone), but you can make it more specific in some contexts.

Usually if the classical theory has a nice causal structure, it implies the quantum picture ensures microcausality, but that can be a little controversial as well.

 

[Fra]

I admit I didn't quite understand the objective of the post. Are you inviting to brainstorming??

Here's a quick&dirty one! focused on the conceptual part.

My take on this, is via what's measurable from an inside observer. And if one starts to define the notion of locality, as referring not to spacetime, but to the information space, then a measure of locality can be thought of as a measure of distance between two observers information. As a kind of information divergence.

Then it follows from the choice of abstraction, the any non-local observations simply aren't likely. Because the observation itself, implies projection onto a local observer. (Where local refers to observerID, not to spacetime "points").

Then the remaining problem is that different observer while maintain a sort of local causality, may totally disagree with other observers. And IMO, this disagreement or "inconsistency" manifests itself as physical interactions and "forces" between observers. (And ultimately between subsystems of the universe, since any subsystem can be abstracted to an observer, that observes "the rest of the universe")

The environment (defined as the closest neighbourhood or interacting observers) puts a selective pressure on every observer, to either by internal re-equilibrations come into agreement, or to disintegrate. A kind of self-preservation.

In this way, to have confidence observations of non-local phenonomena, is to estalibsh with high confidence, that an unlikely event has occured. It somehow contains an internal tension, which I choose to interpret as physical interactions/forces. However inertia probably prevents instant changes. Of course, if an unlikely event is repeatadly observerd! then anyone who is updating his priors will see that the result of this is deformation of the priors. I think it's the same with non-locality and locality.

Edit: Maybe analogous to the idea with gauge invariance that interactions are sort of identified with differences in gauge choices. So from a third observer observing the interactions between many observers, he sees gauge invariance, but still notes that the relative gauges inside the system are related to interactions.

It seems to suggest that there is no gague invariance in the "inside view" (from withing the interaction), but only from an outside view (a weakly coupled observer)??

/Fredrik

 

[MTd2]

Hmm,

Let's then say that I am considering a non-quantum theory, to make matters simpler. I am also not concerned with the nature of information, interactions, or anything that is realistic, except for the fact that it preserves microlocality.

So, I will say something that I have in mind. Galilean space and time and mikowski space-time are both microcausaly causal. Yet, on galilean space, the speed of light is infinte, that is, it is as if the light-cone has an angle /theta of 180º of aperture.

So, how, or what is the most general transformation can one make, by preserving microcauality?

Besides, by preserving microcausality, that, can I simultaneously, in the same space time point, use 2 light-cones? 3-light cones? a finite number of light cones? A continuous of number of them?

And yes, I want to brainstorm :).