The Lorentz transformations

Question 1

What are the Lorentz transformations from S to S’?

Answer 1

x’=γ(x-ut)
y’=y
z’=z
t’=γ(t-ux/c^2)

Question 2

What are the Lorentz transformations from S’ to S?

Answer 2

x=γ(x’+ut’)
y=y’
z=z’
t=γ(t’+ux’/c^2)

Question 3

What is the equation for γ, the Lorentz factor?

Answer 3

γ=1/√(1-u^2/c^2 )

Question 4

What is the length contraction equation?

Answer 4

Lu=L0/γ
Where Lu is the length in the moving frame and L0 is the length in the rest frame

Question 5

What is the time dilation equation?

Answer 5

Δt_u=γΔt0
Where Δt_u is the time interval in the moving frame and Δt0 is the time interval in the rest frame

Question 6

What is the relativistic doppler effect?

Answer 6

f_A/f_0=1/(γ(1+u/c)) with L moving away from A
f_A/f_0=1/(γ(1-u/c)) with L moving towards A
With f_A the frequency in the rest frame of an observer and f_0 the frequency in the rest frame of the source
λ_A/λ_0=γ(1±u/c)

Question 7

For the twin paradox what is the result?

Answer 7

Alice, who goes into space ages less than Bob by a factor of 1/γ

Question 8

What is the equation for relativistic velocity addition for S’ to S?

Answer 8

v=(v’+u)/(1+uv’/c^2 )

Question 9

What is the equation for relativistic velocity addition for S to S’?

Answer 9

v’=(v-u)/(1-uv/c^2 )