Appearance of Warp Bubble Internal Volume to Distant Observer

[Onyx]

TL;DR Summary

Questions about how a warp bubble's internal volume would appear to a distant observer at a single moment of their time.

At a single moment of coordinate time $t$, would a distant observer perceive a warp bubble's interior volume as blown up, or would it seem compressed? Looking in the catalogue of spacetimes at the static local tetrad of the Alcubierre metric, the $e^x_{(x)}$ leads me to think that a static observer would see the flat interior differently from the exterior.

 

[phinds]

Doesn't this belong in the science fiction and fantasy section?

 

[PeterDonis]

Doesn't this belong in the science fiction and fantasy section?

The Alcubierre metric is a valid solution of the Einstein Field Equation, so questions about it are on topic in this forum.

 

[Ibix]

Isn't the interior causally disconnected from the exterior? In which case it doesn't look like anything to an observer outside the bubble because they can't see it.

 

[PeroK]

How does one "see" spacetime?

 

[Onyx]

How does one "see" spacetime?

For starters, if they can see the spaceship or other objects in the interior, how would they appear?

 

[Onyx]

Isn't the interior causally disconnected from the exterior? In which case it doesn't look like anything to an observer outside the bubble because they can't see it.

I thought it was only causally disconnected if the bubble moved at apparently superluminal speed. I'm thinking more of a subliminal case.

 

[PeroK]

For starters, if they can see the spaceship or other objects in the interior, how would they appear?

Appearances can be deceptive!

 

[PeroK]

For starters, if they can see the spaceship or other objects in the interior, how would they appear?

For example, try calculating whether you "see" length contraction?

 

[PeterDonis]

Isn't the interior causally disconnected from the exterior?

I don't think this is correct; AFAIK there are no causal horizons in Alcubierre spacetime.

The paths of causal curves that go through the interior won't be what you might expect based on intuitions about ordinary flat spacetime.

 

[Onyx]

For example, try calculating whether you "see" length contraction?

For example, try calculating whether you "see" length contraction?

For example, try calculating whether you "see" length contraction?

By this, do you mean calculate null geodesics starting from the interior and headed toward the observer?

 

[PeroK]

By this, do you mean calculate null geodesics starting from the interior and headed toward the observer?

Possibly. Although I wouldn't have phrased it like that.

 

[Onyx]

Possibly. Although I wouldn't have phrased it like that.

I guess what I'm really thinking about, more than how the observer would see it, is whether the volume elements in the center are contracted compared to the area completely outside the warp bubble. The image here represents the rate of "expansion" that is happening for different spatial points in a constant time hypersurface. Looking at the front, the rate of shrinking gets bigger then gets smaller and then disappears, which suggests to me that the volume remains contracted until it passes through the rear expanding zone. Sorry if anything seems vague, I'm just trying to keep the post short.

 

[PeroK]

How do you compare spatially separated volumes? Isn't volume a summation of local measurements? According to the integral calculus it is!

 

[Onyx]

How do you compare spatially separated volumes? Isn't volume a summation of local measurements? According to the integral calculus it is!

I'm not sure I understand what you are saying here. Is this an answer to my question about the volume inside?

 

[PeroK]

I'm not sure I understand what you are saying here. Is this an answer to my question about the volume inside?

I suggesting you think about what "the volume a distant observer sees" could possibly mean. If you look at a distant house it may look tiny, but that doesn't mean anything. What process are you proposing for a distant observer to measure the volume?

 

[Nugatory]

I'm not sure I understand what you are saying here. Is this an answer to my question about the volume inside?

We are asking you to stop tossing the word “volume” around until you have paused to consider what a slippery concept it is in a curved spacetime. We calculate the volume of a region by integrating infinitesimal volume elements across the entire region…. But this integration requires that we evaluate all the volume elements at the same time, and there is no unique and non-arbitrary definition of “at the same time” in a curved spacetime.

 

[Vanadium 50]

We're swirling down the same trajectory as your past thread. If you don't define how a distant observer measures volume, how can your question possibly be answered?

 

[Onyx]

I suggesting you think about what "the volume a distant observer sees" could possibly mean. If you look at a distant house it may look tiny, but that doesn't mean anything. What process are you proposing for a distant observer to measure the volume?

Well, I maybe the redshifting of light from a stationary source inside the bubble by a stationary observer far away?

 

[PeterDonis]

maybe the redshifting of light from a stationary source inside the bubble by a stationary observer far away?

This tells you nothing about comparing volumes.

 

[Onyx]

This tells you nothing about comparing volumes.

Well, for the process I guess there could be a measurement done by someone inside the bubble and a similar one done by the distant observer, and they could compare them.

 

[Onyx]

We are asking you to stop tossing the word “volume” around until you have paused to consider what a slippery concept it is in a curved spacetime. We calculate the volume of a region by integrating infinitesimal volume elements across the entire region…. But this integration requires that we evaluate all the volume elements at the same time, and there is no unique and non-arbitrary definition of “at the same time” in a curved spacetime.

That definitely makes sense because even with the two stationary observers their clocks will still run differently. But I've also seen it described very objectively, like in this article:

https://en.wikipedia.org/wiki/Interior_Schwarzschild_metric?wprov=sfla1

Is it just more straightforward when dealing with a diagonal metric?

 

[PeterDonis]

I guess there could be a measurement done by someone inside the bubble and a similar one done by the distant observer, and they could compare them.

What kind of measurement?

 

[PeterDonis]

I've also seen it described very objectively, like in this article

That article talks about the Schwarzschild metric, which is static, so there is a sensible notion of "stationary observers". The Alcubierre metric is not, and there is no sensible notion of "stationary observers".

 

[Onyx]

What kind of measurement?

Measure with clocks how long it takes to get from one point to another.

 

[Onyx]

That article talks about the Schwarzschild metric, which is static, so there is a sensible notion of "stationary observers". The Alcubierre metric is not, and there is no sensible notion of "stationary observers".

Because even a person far away at rest with respect to their frame is not at rest with respect to the bubble person's frame?

 

[Vanadium 50]

We are two dozen messages into this thread, and we still don't have a definition for what you are asking.

 

[Ibix]

Measure with clocks how long it takes to get from one point to another.

How will you measure the speed of whatever is crossing the bubble in order to convert time taken into distance travelled? Will you have to correct different amounts depending on where the bubble is? And will distant observers in different states of motion and/or position agree on any of it?

Because even a person far away at rest with respect to their frame is not at rest with respect to the bubble person's frame?

No, because the spacetime isn't stationary so there isn't an invariant notion of what you mean by "space". All of the questions in this thread stem from this fact. You need to define "space" before you can start to answer the question, and you have considerable latitude over how to do that - probably enough that the answer to your question is either yes or no depending on how you choose your definition.

 

[PeterDonis]

Measure with clocks how long it takes to get from one point to another.

What point to what other point? What will this measurement tell you?

 

[berkeman]

(Thread prefix level changed A-->I for now)...

 

[Nugatory]

Measure with clocks how long it takes to get from one point to another.

That requires some additional assumptions that you may not be aware of. We need some rule for relating times on the two clocks (“when the in-bubble clock reads X the distant clock reads Y”) before they can be compared - otherwise we just have two unrelated intervals from two unrelated clocks. This rule is called a “simultaneity convention” and it is pretty much an arbitrary assumption; depending on what we assume we can get pretty much any answer to your question we please.

There are similar difficulties with defining distance: the distance between two points in space (remember, a point in space is a line in spacetime) depends on where they are at the same time.

Because even a person far away at rest with respect to their frame is not at rest with respect to the bubble person's frame?

There is no meaningful way of comparing the velocities of two objects far enough apart that curvature effects matter. I can be at rest in some local frame, and you can be at rest in some other local frame, but unless the two overlap (in which case they’re really just one frame) our relative velocity is undefined so we cannot be said to be or not be at rest relative to one another.

I have already suggested that you stop tossing the word “volume” around until you can precisely define it in the context of this problem. You may want to be similarly careful with “velocity” and “distance” - the ordinary meaning of these words depends on hidden assumptions about flat spacetime.

 

[Onyx]

How will you measure the speed of whatever is crossing the bubble in order to convert time taken into distance travelled? Will you have to correct different amounts depending on where the bubble is? And will distant observers in different states of motion and/or position agree on any of it?

No, because the spacetime isn't stationary so there isn't an invariant notion of what you mean by "space". All of the questions in this thread stem from this fact. You need to define "space" before you can start to answer the question, and you have considerable latitude over how to do that - probably enough that the answer to your question is either yes or no depending on how you choose your definition.

Specifically, would this involve redefining the spatial coordinates to something else?

 

[Onyx]

We are two dozen messages into this thread, and we still don't have a definition for what you are asking.

It's clear that I don't understand what I've been asking as well as I thought.

 

[George Jones]

Summary: Questions about how a warp bubble's internal volume would appear to a distant observer at a single moment of their time.

At a single moment of coordinate time $t$, would a distant observer perceive a warp bubble's interior volume as blown up, or would it seem compressed? Looking in the catalogue of spacetimes at the static local tetrad of the Alcubierre metric, the $e^x_{(x)}$ leads me to think that a static observer would see the flat interior differently from the exterior.

It's clear that I don't understand what I've been asking as well as I thought.

Answers to your questions might be given in (the figures of) "Detailed study of null and time-like geodesics in the Alcubierre Warp spacetime" by Thomas Muller and Daniel Weiskopf,

https://arxiv.org/abs/1107.5650

 

[PeterDonis]

Specifically, would this involve redefining the spatial coordinates to something else?

I would suggest that you stop thinking in terms of coordinates and start thinking in terms of actual physical measurements. Which means actual physical measurements that you can describe in detail.