Are the Spaceships' Worldlines Straight in Relativity?

[MeJennifer]

Consider a space station A traveling on a straight worldline.
Four smaller spaceships, B, D, E and F, leave this spaceship by igniting their rockets in a north, south, east and west direction at the same time. And by looking out of the observatory deck one can clearly see that all four spaceships increase their distances between the space station in different directions.

The chief scientist on the space station has a discussion with juniors about space-time and claims that it is possible that the spaceships B, D, E and F have a completely straight wordline from the moment they took off.
Is he right?

 

[JesseM]

Consider a space station A traveling on a straight worldline.
Four smaller spaceships, B, D, E and F, leave this spaceship by igniting their rockets in a north, south, east and west direction at the same time. And by looking out of the observatory deck one can clearly see that all four spaceships increase their distances between the space station in different directions.

The chief scientist on the space station has a discussion with juniors about space-time and claims that it is possible that the spaceships B, D, E and F have a completely straight wordline from the moment they took off.
Is he right?

Are you asking about general relativity or special relativity? Like I said on the other thread, my understanding is that diffeomorphism invariance in GR means that any smooth coordinate system is equally good, and for any given worldline you can find a coordinate system where that worldline is "straight" (i.e. its coordinate position doesn't change with coordinate time).

 

[MeJennifer]

Are you asking about general relativity or special relativity? Like I said on the other thread, my understanding is that diffeomorphism invariance in GR means that any smooth coordinate system is equally good, and for any given worldline you can find a coordinate system where that worldline is "straight" (i.e. its coordinate position doesn't change with coordinate time).

I am asking about reality.

 

[JesseM]

I am asking about reality.

No you aren't, because curved vs. noncurved is not a coordinate-independent question, and only coordinate-independent statements are considered to be objective statements about "reality" in physics.

 

[pervect]

I would generally interpret "straight worldline" as "following a geodesic in space-time".

If the space-ships are accelerating because they are thrusting with their rockets, they aren't following a geodesic.

I would interpret / describe the scenario by saying that the spaceships, which are accelerating by firing their rocket engines, are not following a geodesic, while the space-station, which is not firing any rockets, is following a geodesic.

If the spaceships cut their thrust after having acquired some velocity relative to the space-station, they will then be following a geodesic, because they are not being acted on by any external force.

If there is some other intent to the question, please clarify it.

 

[JesseM]

I would generally interpret "straight worldline" as "following a geodesic in space-time".

Ah, I didn't think of that interpretation. OK then, there is a clear-cut answer to whether something is following a geodesic or not, because this depends on the metric rather than the coordinate system. But a coordinate system where a geodesic is a straight line in terms of coordinate position vs. coordinate time is not privileged over one where it is not (and many commonly-used coordinate systems wouldn't have this property, like Schwarzschild coordinates where an orbiting object would not be moving in a straight coordinate line).

 

[MeJennifer]

Ah, I didn't think of that interpretation. OK then, there is a clear-cut answer to whether something is following a geodesic or not, because this depends on the metric rather than the coordinate system. But a coordinate system where a geodesic is a straight line in terms of coordinate position vs. coordinate time is not privileged over one where it is not (and many commonly-used coordinate systems wouldn't have this property, like Schwarzschild coordinates where an orbiting object would not be moving in a straight coordinate line).

Ok then, replace everywere "geodesic" for "straight worldline" if you think it makes a difference.

 

[JesseM]

Ok then, replace everywere "geodesic" for "straight worldline" if you think it makes a difference.

Yes, in that case I was agreeing with pervect's answer.