# Minimum travel time

1. Jul 13, 2009

### Tac-Tics

I was considering this the other day, and I'm pretty sure I know the answer, but I want verification that I am not missing anything.

Suppose you are in a rocket ship and you want to travel, say, to a star the nearest galaxy. Is there a minimum amount of time that would require?

Since the speed of light is the ultimate barrier, a naively person familiar with the cosmic speed limit would say, yes. You have a set distance to travel and you have a maximum speed, so there is a minimum time required.

But when you take spacial contraction into account, things change. As you accelerate, the space begins to contract. Even after the star's relative velocity begins to cap out near c, the contraction continues, down to an arbitrarily small length. And so, it should be possible to reach the star in an arbitrarily short span of your ship's proper time.

Am I correct in this reasoning?

2. Jul 13, 2009

### George Jones

Staff Emeritus
Yes.

3. Jul 13, 2009

### Tac-Tics

Sweet 8-D

Just out of curiosity, say this journey started on Earth. As the rocket traveled away from Earth at near c, from the Earth's frame, wouldn't the space ship be contracted back to Earth as its velocity away from Earth increased? The velocity, of course, is always measured as c by the Earth's unchanging frame, so the ship's velocity will always dominate the spacial contraction. But doesn't this contraction need to be taken into account when calculating the ship's flight plan from Earth?