B How fast do space-time changes propagate?

[log0]

TL;DR Summary

warp drive space expansion/contraction speed limit

The context is the so called warp drive.

In pop-sci articles I've seen the claim that the speed of light limit only applies to objects in space but not the space-time itself, thus claiming that the expansion and contraction of space by a warp drive has no speed limit.

On the other side, I've seen comments (by a physicist working at CERN I believe) stating that disturbances in space time are limited to c and so is the warping of space-time.

Is there a limit, and what does it mean for the warp drives?

If there is no limit, why are gravitational waves propagating at c?

Btw has anyone ever described the formation of a warp bubble, the process of it taking shape and start moving at FTL?

 

[Ibix]

"Changes in spacetime" doesn't really make sense, because time is a concept provided by spacetime. It's actually quite difficult to come up with a well-defined way of saying what you are trying to say without either resorting to postgrad maths or saying something not really accurate and crossing your fingers behind your back and hoping nobody asks awkward questions. So you are correct to doubt the popsci sources which have chosen the latter option - but it's difficult to do better.

The trick with the warp drive is the negative energy density. It lets you build a spacetime that has a kind of shortcut in it that allows a ship inside that shortcut to get from A to B in less time than anything that goes via any other route. But, despite appearances, nothing is travelling faster than light. It's just a really weirdly "shaped" spacetime.

Gravitational waves don't have negative energy density, so their spacetimes are nowhere near so strange. There aren't any tricky shortcuts to exploit, so they are limited to light speed.

Fundamentally, the issue is that it's very difficult to define "speed" in a general way in curved spacetimes. The only hard and fast rule is that nothing ever overtakes a light pulse. However, it's sometimes possible (if negative energy density is possible, which is doubtful) to arrange things so that it's difficult to tell that I'm taking a shortcut so it looks like I'm travelling faster than light.

Sorry if that comes across as a bit evasive. It's not a topic that we really have language to discuss without grounding it in heavy duty maths. Let's see if anyone else does better.

 

[PeterDonis]

In pop-sci articles

Which are not good sources.

I've seen comments (by a physicist working at CERN I believe)

Where?

has anyone ever described the formation of a warp bubble, the process of it taking shape and start moving at FTL?

No. The known "warp drive" solutions all describe a warp bubble that has always existed, will always exist, and always moves in the same direction at the same speed. In other words, an unphysical thing.

 

[FactChecker]

Although there are many problems with the question, it might be relevant to the OP that the LIGO project results support the theory that gravity waves travel at the speed of light.

 

[pervect]

TL;DR Summary: warp drive space expansion/contraction speed limit

The context is the so called warp drive.

In pop-sci articles I've seen the claim that the speed of light limit only applies to objects in space but not the space-time itself, thus claiming that the expansion and contraction of space by a warp drive has no speed limit.

On the other side, I've seen comments (by a physicist working at CERN I believe) stating that disturbances in space time are limited to c and so is the warping of space-time.

Is there a limit, and what does it mean for the warp drives?

If there is no limit, why are gravitational waves propagating at c?

Btw has anyone ever described the formation of a warp bubble, the process of it taking shape and start moving at FTL?

I don't fully understand the technical details, but General Relativity admits a well-posed initial value formulation, which rules out the propagation of arbitrarily fast influences via gravitation, otherwise there wouldn't be the unique and continuous solution of the field equations that is required for a well-posed initial value formulation to exist.

Some useful wiki references for the technical jargon:

https://en.wikipedia.org/wiki/Well-posed_problem
https://en.wikipedia.org/wiki/Globally_hyperbolic_manifold
https://en.wikipedia.org/wiki/Cauchy_problem

Note that the Cauchy problem is a superset of the initial value problem which includes boundary value problems.

Why does a well-posed formulation of a theory rule out arbitrary instantaneous action at a distance?

Refer to the wiki on the nature of a solution to a well-posed problem.

In mathematics, a well-posed problem is one for which the following properties hold:

The problem has a solution
The solution is unique
The solution's behavior changes continuously with the initial conditions.

Suppose we have spatially separated regions A and B of a space-time, the existence of a unique continuous solution to a set of field equations , such as Einstein's field equations, in the neighborhood of A rules out any influence of region B on the solution near A. If region B could influence the solution near A, there would be multiple solutions near A, not a unique solution.

The very technical details that I am attempting to summarize come from Wald, "General Relativity", chapter 10.

That said, I believe there are some loopholes, such as an assumption that the space-time in question is "globally hyperbolic", an assumption about the causal structure of the space-time.

There are some weird space-times such as that described in what I call "The billiard ball paper", where this assumption fails.

Specifically, see https://journals.aps.org/prd/abstract/10.1103/PhysRevD.44.1077 , "Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory"

Note that according to the abstract, the Cauchy problem of the billiard ball (a generalization of the initial value problem) is ill posed in this spacetime.

This setup is inspired by the grandfather paradox, but with billiard balls. Rather than going back in time and killing one's grandfather, the billiard ball goes back in time (through the wormhole time machine) on a trajectory that one would expect would knock the billiard ball off course so that it couldn't pass through the wormhole. It turns out, however, that solutions do exist for all initital conditions. Some of these solutions, though, the ones the paper calls "dangerous" aren't well posed because the solution is supposed to be unique, and there turns out to be an infinite number of solutions.