Exploring the Relationship between Lorentz Transformations and Rocket Frames

[accidentprone]

Homework Statement

Consider the Lorentz transformations:

ct' = gct - Bgx
x' = gx - Bgct
y'=y
z'=z

Show that the primed frame corresponds to a "rocket" frame moving at speed v in the x direction relative to the unprimed frame.

(Sorry about my notation: g = gamma)

Homework Equations

The above Lorentz transformations.

The Attempt at a Solution

I understand the Lorentz transformations and the basics of special relativity, but I'm stuck on this question from a past exam. I'm simply not sure how to set about showing this? A few hints in the right direction would be most appreciated!

 

[tiny-tim]

hi accidentprone!

(have a gamma: γ )

hint: in the "rocket" frame, anything in the rocket at a particular value of x' will be at the same x' for all t'

 

[accidentprone]

Hey! Thanks for replying :)

I understand your hint, but I'm still unable to get going on the answer. Could you tell me how I should start answering the problem?
Many thanks again for your time!

 

[tiny-tim]

show us what you've tried, and where you're stuck, and then we'll know how to help

 

[accidentprone]

Ok so I've drawn two graphs - one of x' against y' and one of x against y for the frames and tried fiddling around with them. I think I might be going down the wrong track though! I'm confused as to how I will show what's being asked... Where will v come from?

 

[tiny-tim]

hi accidentprone!

since you're asked to prove something from the equations, i don't see a graph helping, just stick to using the equations …

v should come out as a ratio of x to t ​

 

[accidentprone]

Hey sorry to be posting in an old thread, but I wanted to say that I've solved the problem. I hadn't seen the Lorentz transformations in that form before. My book makes no mention of beta being v/c. Once I knew that it all came together! Thanks for your help.