Travel 10x the Speed of Light: Warp Drive Explained

[cuberoot]

No true paradoxes, but there might be some interesting things that seem like paradoxes. Though, pole-barn paradox is in the same category, so that's probably what you are thinking of.

The biggest conceptual "problem" with FTL travel is that it violates causality. Causality is a local concept in GR, which is why Warp Drive can exist, but it's a bit hard for people to wrap their mind around global causality violations.

Look at the same pole-barn paradox. It seems like a paradox because order of events appears to switch. But in order for this to happen, the two events must be space-like separated. In other words, closing of the first barn door cannot be the cause of second door opening. If you rig the second door to open only after the first one closed, the pole will ram into the second door in every frame, because the signal required to open the door has not had time to propagate. This is effectively how pole-barn paradox is resolved. Yes, order of events is frame-dependent, but effect always follows cause in every frame.

But if instead of the light beam signal from first door to second I send information with a tiny warp drive ship, the information can actually arrive in time. I can have the second bar door open as response to first door closing, and do so in time for the pole to go through. Now the situation becomes truly bizarre from pole-bearer's perspective. He knows that the second door will only open after the first one closes, but he observes the second door opening before the first door closed. The effect precedes the cause.

That's the sort of "paradoxes" that we can expect with a warp drive.

Notice that these still don't cause any real contradictions. Yes, causality is a frame-dependent concept now. But even though there is a frame of reference in which you can have results of the lottery drawing before the drawing took place, there is no way to make use of that information.

Of course, GR also allows time travel, so apparently, knowing results in advance and being able to act on it would not be a problem either. But that's a separate discussion all together.

So, let's say I am on Earth and I have a ship going away from Earth at a significant fraction of c. What happens if I try to send the lottery numbers to it using the miniature warp drive and have it send them back to me as soon as it receives them, again using a miniature warp drive? Is it not possible to receive the numbers before the lottery draw this way? If not, what exactly would prevent this scenario?

 

[1977ub]

Of course, GR also allows time travel

Hi can you direct me to a reference for this? wiki page mentions "certain unusual scenarios" under which it might be allowed.

 

[cuberoot]

I think I found the answer to my question in the paper "Warp drive and causality" by "Allen E. Everett": http://adsabs.harvard.edu/abs/1996PhRvD..53.7365E (http://exvacuo.free.fr/div/Sciences...tt - Warp drive and causality - prd950914.pdf)

In the space described by Eq.10 there is a region within
one of the bubbles, both in the primed and unprimed coordi-
nates, in which the ‘‘forward’’ light cone runs backward in
time, and CTC’s occur. Suppose a passenger leaves S1 on a
spaceship traveling in the unprimed bubble, starting at
t=t'=0, moving along the line y=y0, and arriving at S2 at
t~=0, t'=T'~=-yBD, at which point the spaceship has
come to rest and the bubble has disappeared. He now travels
the short distance to y=-y0 at subluminal speed through
flat space, and accelerates to sublight velocity B, so as to be
at rest in the primed coordinates. [We assume that this pro-
cess requires negligible time since y<<D and, from Eq. ͑7͒,
B may be small when A is large.] The passenger can then
board a second spaceship bubble and travels back to S1 in the
primed bubble, arriving at t=T1=-BD, thus arriving home
before starting by a macroscopic time interval and carrying a
newspaper reporting on events which have not yet occurred.
This, of course, raises the problems with paradoxes always
associated with closed causal loops. It would appear pos-
sible, e.g., to arrange a mechanism which ensures that a
spaceship will depart from S1 at t=0 if and only if no news
of such an event has arrived from S2 at t<0. This does not
mean that a model of the type introduced in MA is ruled out
as being logically inconsistent, but it does mean that in such
a model there are restrictions placed on the initial conditions.
That is, apparently if superluminal travel through some
mechanism similar to that discussed in MA could actually be
realized, it would imply that the laws of physics include a
principle of consistency, as discussed by Friedman et al. ͓7͔,
which constrains the initial conditions on spacelike surfaces
at times subsequent to the creation of closed timelike curves,
so as to ensure in some way that no contradiction arises; for
example, the initial conditions might guarantee the failure of
the mechanism by which the previous arrival of news of the
spaceship’s departure prevents its later departure from occur-
ring. While not logically inconsistent, such theories appear to
enforce correlations which are certainly counterintuitive.

So, it seems that if these "warp drives" are at all possible and if you can freely use them to travel between arbitrary points then you *can* use them to create real paradoxes just like any other FTL method and so this relies on contrived "consistency maintaining" methods existing in the universe, just like any other FTL method. Am I missing something?

 

[sophiecentaur]

I think I found the answer to my question in the paper "Warp drive and causality" by "Allen E. Everett": http://adsabs.harvard.edu/abs/1996PhRvD..53.7365E (http://exvacuo.free.fr/div/Sciences...tt - Warp drive and causality - prd950914.pdf)



So, it seems that if these "warp drives" are at all possible and if you can freely use them to travel between arbitrary points then you *can* use them to create real paradoxes just like any other FTL method and so this relies on contrived "consistency maintaining" methods existing in the universe, just like any other FTL method. Am I missing something?

Somebody out there must be 'checking' every potential FTL machine as it operates. The logic behind this sort of thing is very difficult to get to grips with. Perhaps future, real warp experiments will resolve it.

 

[DrStupid]

Am I missing something?

No, you are right. As any other FTL travel warp drives would violate causality. But I never understood how they should exceed the speed of light. A warp bubble is a special kind of gravitational wave and therefore should propagate with c at the most. Exceeding the speed of light might be possible by forcing the formation of the warp bubble from outside but not from the ship inside.

 

[AetherCoreGamer]

waitwaitwait... wouldn't there be all sorts of spacedust, stars, planets, and even galixies to account when using this thing? I mean, seriously, even if we were able to get this thing to work, how do we know that we won't run into half the milky way on the way out? *idea slot* if the bubble were to protect us somehow, wouldn't it be like the bug-on-the-windshield effect with all the bugs going 1+ times the speed of light when we got out of the bubble? *end idea slot*
-αether "Science fiction is there to become science fact"
-my dad

 

[PeterDonis]

the principle of what we call a Warp Drive is absolutely solid.

In terms of theory, yes; it's a perfectly valid solution to the Einstein Field Equation.

In practical terms, not so much, since it requires exotic matter (and large quantities of it) to work. Nobody has ever observed exotic matter, and there are good reasons to think that it's impossible to make it.

 

[PeterDonis]

I never understood how they should exceed the speed of light.

They don't, in the only sense that matters in relativity: nothing actually moves outside the local light cones. For example, if a warp drive ship emitted a beam of light that traveled through the warp bubble, the beam of light would reach the ship's destination before the ship itself did.

The warp drive changes the geometry of spacetime so that a timelike path exists joining events that you would ordinarily think could only be joined by spacelike paths. So, for example, it could change the geometry of spacetime between Earth and Alpha Centauri so that a timelike path existed between them that was only a few months long (in terms of proper time), instead of more than 4.3 years long. But there would still be other spacelike paths, not passing through the warp bubble, that would join the same two events that were joined by a timelike path that did pass through the warp bubble.

 

[DrStupid]

For example, if a warp drive ship emitted a beam of light that traveled through the warp bubble, the beam of light would reach the ship's destination before the ship itself did.

I'm not talking about something traveling within or outside the warp bubble but about the bubble itself. How can it propagate faster than light?

So, for example, it could change the geometry of spacetime between Earth and Alpha Centauri so that a timelike path existed between them that was only a few months long (in terms of proper time), instead of more than 4.3 years long.

I have no problem with such a timelike path if the geometry of spacetime between Earth and Alpha Centauri has already been changed. But I do not see how traveling from Earth to Alpha Centauri within a few months should be possible if we start with an unchanged spacetime. We would need to tell the spacetime that it has to change its geometry. Within the still unchanged spacetime this information travels with the speed of light only. That means changing the spacetime would take at least 4.3 years. With this principle it would be possible to build something like stargates or a hyperspace bypass but no superluminal space ships like Enterprise. Star Trek comes up with tachyons to solve that problem but how should it be possible in real world?

 

[PeterDonis]

I'm not talking about something traveling within or outside the warp bubble but about the bubble itself. How can it propagate faster than light?

The bubble doesn't propagate; it's part of the geometry of spacetime, and the geometry of spacetime doesn't propagate, it just is.

I do not see how traveling from Earth to Alpha Centauri within a few months should be possible if we start with an unchanged spacetime.

Spacetime doesn't "change"; it just is.

We would need to tell the spacetime that it has to change its geometry. Within the still unchanged spacetime this information travels with the speed of light only.

There is no such thing as "the still unchanged spacetime". The spacetime geometry just is; it's a 4-dimensional geometry. In the case of the Alcubierre solution, this 4-dimensional geometry happens to have a region in it where the light cones and timelike curves are very different from what we're used to, because of the presence of exotic matter. (Or multiple such regions, if there are multiple warp drives in the universe.)

Given this 4-dimensional geometry, the rule you are alluding to, that the geometry at any particular event is completely determined by the geometry and stress-energy in the past light cone of that event, is still valid. But the configuration of the past light cones of events becomes highly unusual when those past light cones include any portion of the warp bubble. Unfortunately I'm not aware of any good visualization that gets across how this works; but mathematically, it's clear: the Alcubierre solution is a valid solution of the Einstein Field Equation (with exotic matter), and any valid solution of the EFE has the property I just described (this is a mathematical theorem).

 

[DrStupid]

The bubble doesn't propagate; it's part of the geometry of spacetime, and the geometry of spacetime doesn't propagate, it just is.

Let's start with a ship in an almost flat space time. What happens, when the ship starts its warp engine?

 

[PeterDonis]

Let's start with a ship in an almost flat space time. What happens, when the ship starts its warp engine?

The fact that the ship has a warp engine and starts it is inconsistent with the premise that spacetime is almost flat. Spacetime doesn't "change" when the warp engine starts; the 4-d spacetime that describes this scenario already contains all the information about the warp drive, when it starts and stops, and what the light cones and timelike paths look like given the presence of the warp drive (which requires that spacetime is not flat--there must be a high concentration of exotic matter in portions of it, which make it highly non-flat).

This is one of those scenarios that you simply can't think about as "space" changing with "time"; you have to think about it as a 4-d solution right from the start. At least, that's the only way I know of to make sense of it without leading to questions like the ones you're asking, which seem like they ought to be meaningful but actually aren't, because of the highly counterintuitive nature of this spacetime. It's a more intense version of the confusion people get into when they ask how the universe can be "expanding faster than light".

 

[DrStupid]

Spacetime doesn't "change" when the warp engine starts;

Than let's take another step back. Does the spacetime change when the ship is build?

the 4-d spacetime that describes this scenario already contains all the information about the warp drive, when it starts and stops, and what the light cones and timelike paths look like given the presence of the warp drive

That would mean it can't be controlled. I am talking about the usual scenario in science fiction. Captain Kirk choose a destination, Scotty presses some buttons and the ship starts traveling faster than light. I still do not see how this is possible and if I understand you correctly it actually is impossible.

 

[PeterDonis]

Does the spacetime change when the ship is build?

No. Again, spacetime just is--it's a 4-dimensional geometry that already includes all the things that have happened and will happen in a given scenario.

That would mean it can't be controlled.

No, it wouldn't. If the warp drive is controlled, then the 4-dimensional spacetime geometry already includes all the information about how it is controlled--which amounts to information about which regions of spacetime are affected by the presence of the warp drive. If the operator turns the drive on, then the event at which the drive turns on will be part of the boundary of a region of spacetime which is affected. If the operator turns the drive off, then the event at which the drive turns off will also be part of the boundary of a region of spacetime which is affected.

Captain Kirk choose a destination, Scotty presses some buttons and the ship starts traveling faster than light. I still do not see how this is possible and if I understand you correctly it actually is impossible.

I'm not sure you understand correctly. Suppose the Enterprise is on Earth, and Kirk tells Scotty to get the ship to Alpha Centauri in warp drive. Scotty presses the button, and the ship takes off.

Suppose clocks on Earth and Alpha Centauri were synchronized at some time in the past (we assume they are at rest relative to each other), while the Enterprise was far away. Assume also (which I'm not sure is actually a completely valid assumption, but I think it's a good enough approximation) that when the Enterprise's warp drive is turned off, it doesn't affect how clocks and rulers behave in its vicinity. And suppose that the gravity of Earth and Alpha Centauri (and all other objects) is negligible for purposes of this problem (so the only possible source of spacetime curvature is the warp drive).

Then there will be a region of spacetime to the past of the warp drive starting which is flat; this region will be bounded by a surface of simultaneity in the mutual rest frame of Earth and Alpha Centauri, which we will call the surface $t = 0$. An instant after $t = 0$, according to Earth clocks, the warp drive turns on. We assume that the ship's clock also reads $t = 0$ an instant before the drive turns on. At some later time $t = T$ by the ship's clock, the ship is in the vicinity of Alpha Centauri and the drive turns off. We assume that, because of the warp drive, $T$ is much less than 4.3 years.

Now, what will clocks on Alpha Centauri read when the Enterprise arrives? According to the Alcubierre solution, they will read $T$ (at least approximately; IIRC the Alcubierre solution is actually a family of solutions that give somewhat different answers to this question, but all of them are much less than 4.3 years, so we can just use $T$ as a representative value). This is the sense in which the Enterprise has traveled "faster than light". But spacetime in the region between the event of the ship leaving Earth and the event of it arriving on Alpha Centauri is highly curved, in a way that makes the Enterprise's worldline timelike everywhere, so that it never travels "faster than light" in a local sense; it will never outrun a light beam that starts out co-located with it.

 

[DrStupid]

No. Again, spacetime just is--it's a 4-dimensional geometry that already includes all the things that have happened and will happen in a given scenario.

Does that mean you assume future to be predefined?

Then there will be a region of spacetime to the past of the warp drive starting which is flat

OK, it seems I wasn't precise enough. It's not spacetime that changes but the geometry of different regions of spacetime differ from each other.

But spacetime in the region between the event of the ship leaving Earth and the event of it arriving on Alpha Centauri is highly curved

That means we have a region of spacetime between Earth and Alpha Centauri and t<0 with flat spacetime. Another region of spacetime between Earth and Alpha Centauri and 0<t<T is highly curved. That's what I mean with the change of spacetime in my postings above. My problem is: Why does the region of spacetime at Alpha Centauri change (from the view of a local observer) from flat to highly curved within t<=T<4.3 years? In my opinion it can't be caused by Kirks decision to travel to Alpha Centauri because this information would take at least 4.3 years to reach Alpha Centauri.

 

[PeterDonis]

Does that mean you assume future to be predefined?

GR is a deterministic theory, so whenever we are talking about a GR model, the entire spacetime is "predefined".

we have a region of spacetime between Earth and Alpha Centauri and t<0 with flat spacetime. Another region of spacetime between Earth and Alpha Centauri and 0<t<T is highly curved. That's what I mean with the change of spacetime in my postings above.

But this is not a "change of spacetime"; it's just a fact about the spacetime geometry that the curvature is not the same everywhere. And thinking of it as a "change" is leading you to make incorrect inferences; see below.

Why does the region of spacetime at Alpha Centauri change (from the view of a local observer) from flat to highly curved within t<=T<4.3 years?

Spacetime doesn't change. See above.

If what you really mean is "a region of space between Earth and Alpha Centauri changes from being flat to being highly curved", this sort of thinking works OK for nearly flat spacetimes, but it doesn't work for highly curved spacetimes like the warp drive spacetime. See below.

it can't be caused by Kirks decision to travel to Alpha Centauri because this information would take at least 4.3 years to reach Alpha Centauri.

It would if spacetime were flat everywhere, yes. But this spacetime is not flat everywhere. The region of the spacetime that is curved (because of the warp drive being on) is curved in a way that allows the causal consequences of Kirk's decision to reach Alpha Centauri when clocks on Alpha Centauri read much less than 4.3 years. There's no way (that I'm aware of) to correctly model this as "space changing with time"; that type of model is simply an approximation, that works OK in flat or nearly flat spacetimes, but doesn't work in the kind of highly curved spacetime that you get when a warp drive is present.

(The reason the "space changing with time" model is only an approximation is that it leads you to a chicken-and-egg problem. A particular event can only causally influence events in its future light cone; but which events are in its future light cone depends on the geometry of spacetime. So thinking of the geometry of spacetime itself as "propagating" at a speed that's limited by the light cones is a logical circle that can't be closed: the light cones are determined by the very thing whose "propagation" is supposed to be determined by the light cones. The only way to rigorously avoid this problem is to look at the entire 4-d spacetime geometry "all at once" as a self-contained solution to the Einstein Field Equation. But in cases where the spacetime curvature is small enough everywhere, you can think of the light cones as being "fixed" to a good approximation, and then think about how curvature propagates within those approximate light cones, and get answers that are close enough for many purposes. A warp drive spacetime is one of those where the curvature is not small enough everywhere for this to work.)

 

[DrStupid]

If what you really mean is "a region of space between Earth and Alpha Centauri changes from being flat to being highly curved", this sort of thinking works OK for nearly flat spacetimes, but it doesn't work for highly curved spacetimes like the warp drive spacetime.

What I mean is this:

Then there will be a region of spacetime to the past of the warp drive starting which is flat; this region will be bounded by a surface of simultaneity in the mutual rest frame of Earth and Alpha Centauri, which we will call the surface t=0.
[...]
But spacetime in the region between the event of the ship leaving Earth and the event of it arriving on Alpha Centauri is highly curved

For t<0 the spacetime between Earth and Alpha Centauri is flat and for 0<t<T it is highly curved. All I currently understand is that you do not like the term "change of spacetime" for this fact about the spacetime geometry but I do not want to discuss semantics. I try to understand why these regions of spacetime are different - especially if (and if yes how) this can be caused by an event at Earth and t=0.

So thinking of the geometry of spacetime itself as "propagating" at a speed that's limited by the light cones is a logical circle that can't be closed: the light cones are determined by the very thing whose "propagation" is supposed to be determined by the light cones. The only way to rigorously avoid this problem is to look at the entire 4-d spacetime geometry "all at once" as a self-contained solution to the Einstein Field Equation.

Yes, this avoids the problem but it doesn't solve it. You still need to explain how the spacetime geometry around the spaceship during the flight results from the decision of the captain. For the case that you deny his freewill just replace him by a mechanism similar to Schrödinger's cat (which is widely agreed to be really randomly).

 

[JesseM]

This is one of those scenarios that you simply can't think about as "space" changing with "time"; you have to think about it as a 4-d solution right from the start.

Are you talking specifically about a spacetime containing closed timelike curves? A spacetime with a single warp bubble doesn't contain any (I think Alcubierre showed this in his original paper, though with multiple bubbles moving in different directions there are CTCs), so in that case can't one foliate the spacetime into a series of 3D hypersurfaces, and use the ADM formalism to describe how spatial curvature of the 3D hypersurfaces changes with time?

 

[PeterDonis]

this avoids the problem but it doesn't solve it. You still need to explain how the spacetime geometry around the spaceship during the flight results from the decision of the captain

And that's what the Alcubierre solution to the Einstein Field Equation does. It shows how the causal structure of the spacetime permits the events that take place in the region of spacetime along the ship's path from Earth to Alpha Centauri to all be causally connected to the event where the captain makes his decision. Unfortunately I don't have a handy quick visualization of how this works, but that doesn't mean it's not a valid solution.

 

[PeterDonis]

Are you talking specifically about a spacetime containing closed timelike curves?

No, just a single Alcubierre drive. (I'd rather not open the additional can of worms that comes into play when you have multiple warp drives in relative motion. )

can't one foliate the spacetime into a series of 3D hypersurfaces, and use the ADM formalism to describe how spatial curvature of the 3D hypersurfaces changes with time?

Sure. But there's no guarantee that the "speed of propagation" of changes in the spatial curvature will not appear to be "faster than light" in this formulation, just as the apparent "speed of recession" of galaxies from one another in the universe can be "faster than light". In both cases, the key physical reason is that the spacetime (or at least the portion of it in question) is highly non-stationary, so there is no way to foliate it with 3D hypersurfaces that all have the same geometry, and the "speed of changes in the geometry" from one hypersurface to another can in principle be arbitrarily fast. (If they are, then the light cones will also appear to "expand" arbitrarily fast; so you can still use the light cones to verify that nothing actually moves faster than light in the sense that matters. But it all will still appear highly counterintuitive.)

 

[DrStupid]

And that's what the Alcubierre solution to the Einstein Field Equation does. It shows how the causal structure of the spacetime permits the events that take place in the region of spacetime along the ship's path from Earth to Alpha Centauri to all be causally connected to the event where the captain makes his decision.

That sounds like I need to take a closer look at the Alcubierre solution. I wasn't aware that it includes the creation of the warp bubble.