How Do Lorentz Transformations Relate to Rocket Frames in Special Relativity?

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Homework Help Overview

The discussion revolves around the application of Lorentz transformations in the context of special relativity, specifically relating to a "rocket" frame moving at a constant speed relative to another frame. The original poster expresses uncertainty about how to demonstrate the relationship between the transformations and the rocket frame.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how to apply the Lorentz transformations to show the relationship to the rocket frame but is unsure of how to start. Some participants suggest focusing on the equations rather than graphical representations and question how velocity is derived from the transformations.

Discussion Status

Participants are actively engaging with the original poster's questions, providing hints and suggestions for approaching the problem. There is a mix of attempts to clarify concepts and explore different methods of reasoning. One participant has reported successfully solving the problem, indicating some productive direction in the discussion.

Contextual Notes

There is mention of confusion regarding notation and the relationship between beta and velocity, which may affect the understanding of the transformations. The original poster also notes that their textbook does not cover certain aspects of the transformations, which could contribute to their difficulties.

accidentprone
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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!
 
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hi accidentprone! :smile:

(have a gamma: γ :wink:)

hint: in the "rocket" frame, anything in the rocket at a particular value of x' will be at the same x' for all t' :wink:
 
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!
 
show us what you've tried, and where you're stuck, and then we'll know how to help :smile:
 
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?
 
hi accidentprone! :smile:

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 :wink:
 
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.
 

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