Calculating Spatial Separation Using Lorentz Transforms: Homework Solution

[Mugen Prospec]

Homework Statement

Two events occur at the same place in a certain inertial frame and are separated by a time interval of 4 seconds. What is the spatial separation between these two events in an inertial frame in which the events are separated by a time interval of 6 seconds?

Homework Equations

Lorentz Transforms

The Attempt at a Solution

I really have no idea where to start. I know its not that hard I am just drawing a blank

 

[gabbagabbahey]

Homework Statement

Two events occur at the same place in a certain inertial frame and are separated by a time interval of 4 seconds. What is the spatial separation between these two events in an inertial frame in which the events are separated by a time interval of 6 seconds?

Homework Equations

Lorentz Transforms

The Attempt at a Solution

I really have no idea where to start. I know its not that hard I am just drawing a blank

Hint: What quantity involving both time and position is invariant under Lorentz transforms?

 

[Mugen Prospec]

I know the speed of light is invariant. The way I worked it was putting it through the Lorentz time transform solving for v. then put that v in the x Lorentz transform

 

[gabbagabbahey]

I know the speed of light is invariant. The way I worked it was putting it through the Lorentz time transform solving for v. then put that v in the x Lorentz transform

Sure, $c$ is Lorentz invariant, but it doesn't invole time or position, so that doesn't help. What about the spacetime interval $\delta s^2$?

 

[Mugen Prospec]

Could you give me maybe a walk through on how to find that or even the problem. I am really at a loss, I missed a week of classes because i was sick.

 

[gabbagabbahey]

Could you give me maybe a walk through on how to find that or even the problem. I am really at a loss, I missed a week of classes because i was sick.

I'm not here to teach a week of coursework. Read the section in your text that talks about spacetime intervals and then try the problem.