# Is the distance relative also?

1. May 3, 2010

### xponential

From the special theory of relativity, I understand that time is not absolute but relative according to the speed of observer. For instance, suppose there are two watches, one put inside a spaceship which rotates the earth and the other is just stationed on earth and both of them are synchronized firstly to have the same time reading. Let's consider now that the spaceship rotated the earth 100 times at half the speed of light and then stopped. Then, if we looked at the current time readings on both watches, they will be significantly different.

Is that also applied to distance? If there is a device in the spaceship which tells to those inside it how much distance (in km) the ship has been moving so far (like the one in the car), and after the ship was stopped, will the reading of the device be different (i.e. much less) than if we got the length of the spaceship's path around the earth and multiplied it by 100 (since there were 100 rotations)?

Last edited: May 3, 2010
2. May 3, 2010

### Ich

Welcome to PF!
Of course. It will show ship time * 0.5*c, that's the definition of velocity. This is less than 100 orbits as seen from earth.

3. May 4, 2010

### JDługosz

How does such a device work?

You can't watch the space go by.

Scenario 1: if you have a relativistic train and you count the number of rail ties that you pass, you will get the same number as the observer at the station. However, if you examine them through a trapdoor in the bottom of the train, you will measure them to be closer together. If you use the shorter span as your basis, then sure you saw a shorter distance in your voyage.

Scenario 2: at speed, you use RADAR to find the range to your destination. You find a much shorter distance than you did when you measured it before starting out. At the end of the journey, which value to you report in your log book?

4. May 7, 2010

### xponential

I think it should be, then, the shorter value.

JDługosz & Ich, thank you very much for the clarification.

Last edited: May 7, 2010