Relativity Equations Flashcards
(15 cards)
Lorentz transform for time
t’ = γ(t - βx/c^2)
Lorentz transform for space
x’ = γ(x - βt)
Relativistic Doppler effect towards us
Blue is to
f/f0 = sqrt((c-β)/(c+β))
λ/λ0 same applies
Relativistic Doppler effect going away
Red is away
f/f0 = sqrt((c+β)/(c-β))
λ/λ0 same applies
Galilean transforms
x’ = x - βt
t’ = t - βx
y’ = y
z’ = z
Lorentz transform for velocity
v’ = (v - β)/(1 - vβ/c^2)
v = (v’ - β)/(1 - v’β/c^2)
β = (v - v’)/(1 - vv’/c^2)
Most important is probably the v’ formula
Galilean velocity transform
v’ = v - β
Causality
Δs^2 > 0, time like (inside cone)
Δs^2 = 0, light like
Δs^2 < 0, space like (outside cone)
Energy equation
Ε = γm
Kinetic energy equation
K = E - m
Velocity formula
|P|/E = |V|
Momentum formula (magnitude)
|P| = mv/sqrt(1-v^2)
Mass formula
m^2 = E^2 - |P|^2
4 momentum of a photon, only moving in x-axis
(E, E, 0, 0)
4 momentum of a particle
(E, px, py, pz)
