How Do Lorentz Transformations Confirm a Rocket's Motion in Special Relativity?

[Onias]

Homework Statement

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

Variables: x, x', t, t', y, y', z, z'

Homework Equations

ct' = γct - βγx
x' = γx - βγct
y' = y
z' = z

The Attempt at a Solution

None, I'm not sure what the question is asking of me!

 

[tiny-tim]

Welcome to PF!

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

Variables: x, x', t, t', y, y', z, z'
…
ct' = γct - βγx
x' = γx - βγct
y' = y
z' = z
…
I'm not sure what the question is asking of me!

Hi Onias ! Welcome to PF!

(are those equations part of the question?)

I'm not sure what the question is asking of you, either …

I'd have thought that those equations are the definition of the new frame …

unless they're asking you to say what v is, in terms of γ and β

 

[nlightner]

I understand that frames in special relativity refer to different coordinate systems used to describe the same physical event. The unprimed frame, also known as the "rest frame," is the frame in which an observer is at rest and measures the position and time of an event. The primed frame, on the other hand, is a moving frame that is moving at a constant velocity v in the x direction relative to the unprimed frame.

To show that the primed frame corresponds to a 'rocket' frame, we can use the Lorentz transformation equations:
ct' = γct - βγx
x' = γx - βγct
y' = y
z' = z

where γ = 1/√(1-(v/c)^2) and β = v/c.

We can see that the only difference between the primed and unprimed frames is in the x and t coordinates. This means that the primed frame is moving at a constant velocity v in the x direction relative to the unprimed frame, as expected for a 'rocket' frame.

Furthermore, we can see that the time coordinate in the primed frame, t', is a combination of the time coordinate in the unprimed frame, t, and the position coordinate in the unprimed frame, x. This is a result of time dilation in special relativity, where the time in a moving frame appears to pass slower than in a stationary frame.

In conclusion, the primed frame corresponds to a 'rocket' frame moving at speed v in the x direction relative to the unprimed frame, as shown by the Lorentz transformation equations. This is a fundamental concept in special relativity and helps us understand the effects of relative motion and the nature of spacetime.