Length Contraction & Time Dilation: Relative Velocity Impact?

[sqljunkey]

So an object moving close to the speed of light will be length contracted. Does that mean the distance it covers also contracts in length? From the traveling object's point of view it's surrounding's would contract as he sees them moving along.

In these scenarios wouldn't velocity be a relative component too? will the two frames of reference disagree about the velocity? given that time and space has been different.

 

[BvU]

Generally: yes, yes and yes. You want to formulate a bit more precisely (in particular who is the observer drawing such a conclusion), but you will learn that quickly enough when you do exercises.

Check out the MIT game -- it's fun

 

[Ibix]

Apart from the sign, the two frames agree on the velocity of the other. In general, velocities are related by the relativistic velocity addition formula.

 

[sqljunkey]

Okay. To be sure I understand this right, the distance the rocket traveling at near speed doesn't contract for an observer at rest right, only the rocket contracts

 

[Ibix]

Yes. The rocket sees itself as normal and the distance to its destination contracted. Observers on Earth see themselves as normal and the rocket length contracted

 

[sqljunkey]

I doodled a sketch here. Let's say there is a light clock 299792458 meters tall (or one light second) and instead of moving horizontally it moves vertically, with speed .999999c . Along this y-axis that it's moving it contracts to 24,486.42 meters. Wouldn't it be close to 1 second when the light traveled from the bottom of the light clock to the top of the light clock, since now the ceiling of the clock contracted. Instead of taking 570 something seconds if it was traveling horizontally ?

 

[Ibix]

You need to work out the duration of a complete cycle of the clock - from bottom to top and back down. Then you should get the same answer in both cases.

Edit: if you don't, post your maths and we'll see where you went wrong. I recommend working in units of seconds and light seconds. Then the speed of light is 1.