# Exploring Relativistic Compression: What Happens to the Space Between Ships?

• intervoxel
In summary, when a convoy of spatial ships leaves the Earth at a speed v, each ship is relativistically compressed in the direction of movement. This results in shorter gaps between the ships in the frame of the Earth. However, whether these gaps are shorter than before the acceleration depends on how the ships synchronized their acceleration. In cases where the convoy just passes by the Earth, an observer on Earth will find both the distance between ships and the total length of the convoy to be length-contracted. But if the convoy actually leaves the Earth, each individual ship must start at rest and accelerate, making the relationship between the distances between ships more complex. This is known as the "Bell's spaceship paradox" and more information can be found by searching for

#### intervoxel

A convoy of spatial ships leaves the Earth at a speed v. Each ship is relativistically compressed in the direction of movement. What happens to the space between the ships? Is it compressed too?

intervoxel said:
A convoy of spatial ships leaves the Earth at a speed v. Each ship is relativistically compressed in the direction of movement. What happens to the space between the ships? Is it compressed too?
In the frame of the Earth the gaps are shorter than in the convoy frame. Whether they are shorter than before the acceleration depends entirely on how the ships synchronized their acceleration.

intervoxel
You can start with an easier case: A convoy of ##n## spaceships flies past the Earth at constant speed. An observer in one of the spaceships finds that the length of each ship is ##L##, the distance between the nose of one and the tail of next is ##D##, and the total nose-to-tail length of the convoy is ##n(L+D)-D##.

An observer on Earth finds both ##N## and ##D## to be length-contracted.

It gets more complicated if the convoy "leaves the earth" instead of just passing by. In this case, each individual ship must starts out at rest on Earth and must accelerate to start moving away. In this case, the relationship between the distances between the ships will, as A.T. says, depend on how thevships synchronize their acceleration.

Google for "Bell's spaceship paradox" and check the FAQ here for more about the second, kore complex, case.

intervoxel