Does opening and closign a wormhole to send a message within seconds across the galaxy violate causality?
Wouldn't different observers disagree about the order of events and what effected what? Is that observation just an illusion after all?
Update: Note that the Wormhole is stationary in both places and that both places can be considered to be in the same frame of reference. Also I am not sending matter, but information in form of light through the wormhole to simulate FTL-Communication.
Does opening and closign a wormhole to send a message within seconds across the galaxy violate causality?
There is no violation of local causality. For every event there is a neighborhood on which everything looks normal, but the neighborhood might be very small.
Lots of things can be different between local and global. For instance energy can be locally conserved but there might not even be global energy and if there is it might not be conserved. Same with charge, locally it is absolutely conserved, but globally it doesn't have to be.
Wouldn't different observers disagree about the order of events and what effected what?
Now it seems like you are confusing two issues. In special relativity when two events are spacelike separated then two frames will disagree about which happened first (in their frame) but they will say that neither caused the other or even influenced each other.
That said, if you have tachyons in special relativity then the reinterpretation principle applies. In which case the two frames can argue about which caused which. But in special relativity there is a frame where they are simultaneous so there isn't a straightforward answer like you seem to assume.
And as for entanglement if you go with a realist (and nonlocal)/quantum mechanics, it isn't one causing the other it is the spin state continuously changing (in configuration space) based on the Hamiltonian which also changes the spatial wave in configuration space. So you just have a nonlocal thing, the wave (defined on configurations) and it all evolves according to be same Schrödinger equation, it isn't one thing in one place causing another it is a wave that is already everywhere and more than everywhere it is in configuration space. And all parts of it evolve based on just the values assigned to configurations near it. So it is local in the sense that only nearby configurations affect the value or spin at a given configuration. But the object itself isn't a thing with properties in real space and in particular that means there isn't a wave at each point in spacetime so no obvious connection to wormholes.
Those are the kinds of situations where people bring up spacelike separated causality and ordering outside general relativity.
In general relativity you can go local and then it is as simple as Minkowski space for the causality. Or else you can try to orient via curves between events. Which allows you to define different kinds of causality in terms of different kinds of curves. For instance of you use curves who always have a tangent and who's tangents are always future pointing you get one kind of causality but other kinds are possible.
For instance, if you allow yourself to use curves who always have a tangent and who's tangents are always future pointing and timelike (i.e. not lightlike) you get a different kind of causality.
Also I am not sending matter, but information in form of light through the wormhole to simulate FTL-Communication.
If you use the kind of causality that allows lightlike paths they could potentially be causally connected and if you use the kind of causality that only allows timelike paths them they might not be causally connected. But this is just semantics about the kind of ordering you assign to things. And some spacetimes don't have a sense of future (an orientability) to even allow either of those examples to be defined.
But you might have some misconceptions about wormholes. You might want to think of a donut with a fairly small hole. From the top side near the hole there are two routes to a point on the bottom side near the hole. The fast route is through the hole, the long route is to head out across the top of the donut down the side and then head across the bottom. That is what a wormhole is like, it isn't teleportation and locally nothing looks weird. There are just long ways and short ways between places. So in a sense if there is a wormhole between two places they are just closer than the other paths make it look.
So it can be like a sphere. Most people taking random paths wouldn't even hit the sphere. And if there wasn't a wormhole the surface of the sphere would be close to the opposite side of the sphere but if it is a wormhole then one side of the sphere is really close to the other side of the sphere. And if this seems magically go back to the donut. There is a circle on the top enclosing the hole and one on the bottom. If there was no hole the circle edge would be close to the other side of the circle but since there is a hole going in in that direction take you to the circle on the bottom side.
So locally nothing looks weird at all. Well, to be honest, if the wormhole is traversable there might be some weirdness. Normally curves get closer because of gravity and in a traversable wormhole it looks like you need some exotic matter with a negative energy density and things would look a bit weird near them, just like things would look a bit weird near a negative mass star. But not strictly locally. Strictly locally everything is still boring (well except you talk about opening and closing it, that seems really weird like maybe impossible). So it's just the nonlocal effects near the exotic matter that are weird. Very subtle.
But the whole issue is subtle because you are piecing together a local theory into a global whole.
To me, if wormholes can exist without braking causality, so can any FTL communication. No?
In one sense it isn't faster than light since in each local region it is regular lightspeed communication.
But FTL communication is a problem for causality in special relativity only if you can do FTL that is faster than light in different frames. Otherwise it could be a reinterpretation thing.
And the same exact problem occurs with wormholes. Imagine three locations and have two frames at each location (frames a and a' at location A frames b and b' at location B and frames c and c' in location C).
Let the wormhole AB go from near A to near B and be at rest for a' and b.
Let the wormhole BC go from near B to near C and be at rest for b' and c.
Let the wormhole CB go from near C to near A and be at rest for c' and a.
Each of them might seem very benign. But depending on how those frames a,a' and b,b' and c,c' are moving (and thus how the wormholes AB, BC, and CA are moving) then there might be a curve that goes around always lightlike but starts and stops at the same event.
So the seemingly nice wormhole is dangerous if you can have multiple wormhole and they can be at rest to arbitrarily moving observers.
You could probably do it with just two wormholes but now the objection applies to warp drives too and having three allows the paths to be straight and still not cross in case you want to have special tracks laid down. The warp drives have issues about getting on and getting off. But I don't know how big a deal that is compared to other concerns.
Where am I wrong: 1) Different observers can disacree about order of events 2) Only if those events are so far apart that not even light can travel between them 3) That is, they don't have a causal connection as nothing can travel faster than light 4) Disagreeing about their order does not hurt causality because of that. 5) Wormholes mess up with this, as even events far apart can be causally connected by the worm hole. So two observers will disagree about the chain of events.
Why are people ordering events when they aren't in the future of each other (when there isn't a future pointing path between them)? It is meaningless. When there is a wormhole they are not far apart. And no one disagrees about what casually affects what because that depends on paths of curves and everyone agrees on that. a frame is like a basis of a vector space it can help you compute real things but it has no physical meaning because you can pick any one you want to compute physical things. This "order" assigned by frames is not a physically meaningful concept. The idea of whether there Ade curves and paths from on to the other where the curve is lightlike or timelike is relevant. And physically meaningful and two frames agree on that.
And frames are local anyway. And a frame is just a basis for a small region. It doesn't mean anything. They do not disagree about whether a curve goes from one to the other. They do not disagree about whether the curve has a tangent. The do not disagree about whether the tangent is lightlike or timelike. No one disagrees when you stick to the real concepts. The frame dependent concepts are just teachers and experts pandering to people that don't want to learn the real stuff.
The issue for causality is not about how two frames might disagree about stuff that isn't physical (and anything two frames disagree about isn't physical) the problem for causality is whether a point is in its own future. That is a real issue. If there is a curve from itself to itself with a tangent everywhere and the tangent being lightlike or timelike at each event on the curve. And this can happen if you went through multiple wormholes that are all as nice as you one.
