Special Relativity

Question 1

Galilean Invariance

Answer 1

Laws of physics are the same for all intertial frames

Question 2

Galilean Transforms for 2 frames, S and S’. S’ is moving at u relative to S. And the inverse

Answer 2

• t =t’
• x = x’ + ut’
• y = y’
• z = z’
• Inverse is t’ = t etc
• Inverse is x’ = x - ut

Question 3

Galilean Addition of Velocities for 2 frames S and S’. S’ is moving at u relative to S

Answer 3

v = v’ + u

Question 4

Lorentz Transformations for 2 frames, S and S’. S’ is moving at u relative to S. And the inverse

Answer 4

• t = γ (t’ +ux’/c^2)
• x = γ (x’ + ut’)
• y = y’
• z = z’
• Inverse, Swap t and t’, x and x’, turn u into -u

Question 5

Length Contraction Equation

Answer 5

• γ Lu = L0
• Lu is length in frame where it is moving at speed u
• L0 is length in rest frame

Question 6

Time Dilation Equation

Answer 6

• ∆tu = γt0
• tu is time in frame where it is moving at speed u
• t0 is time in rest frame

Question 7

Relativistic Addition of Velocities and Inverse

Answer 7

• v = (v’ + u) / (1 + uv’/c^2)
• To inverse, swap v and v’ and u into -u

Question 8

Relativistic Kinetic Energy Equation

Answer 8

• KE = (γ-1)m0 c^2
• m0 is rest mass