relativity

Question 1

proper time/distance

Answer 1

time/distance in reference frame of moving object

Question 2

time measured by observer with relativity

Answer 2

Δt = Δt_p/ √(1 - v²/c²) = γΔt_p

γ = 1/√(1 - v²/c²)

observer time is always longer than proper time

Question 3

Length measured by observer with relativity

Answer 3

L = vΔt_p = vΔt/γ

L = L_p/γ = L_p√(1-v²/c²)

Length observed is always longer than length at rest

Question 4

relativistic doppler effect

Answer 4

f_obs = f_source√(1+v/c)/√(1-v/c)

frequency increases as object approaches, decrases as it moves away

Question 5

lorentz transormation S -> S’ for time (moving observer)

Answer 5

t’ = γ(t - [v/c²]x)

t’ -> moving frame
t -> rest frame

Question 6

lorentz transformation S -> S’ for distance

Answer 6

x’ = γ(x - vt)

Question 7

lorentz transformation for time S’ -> S

Answer 7

t = γ(t’ + [v/c²]x’)

Question 8

lorentz transformation for distance S’ -> S

Answer 8

x = γ(x’ +vt’)

Question 9

lorentz velocity transformation (S -> S’)

Answer 9

u’_x = ( u_x - v )/( 1 - [u_x* v] / c²)

• u’_x -> observed velocity of moving object from moving frame of reference*
• u_x -> velocity of object from stationary reference frame*
• v -> velocity of moving frame of reference*

Question 10

Lorentz velocity transformation (S’ -> S)

Answer 10

u’_x = ( u_x + v )/( 1 + [u_x* v] / c²)

• u’_x -> observed velocity of moving object from moving frame of reference*
• u_x -> velocity of object from stationary reference frame*
• v -> velocity of moving frame of reference*

Question 11

relativistic linear momentum

Answer 11

P = γmv = mv/[√(1 - u²/c²)]

Question 12

relativistic kinetic energy

Answer 12

K = (γ - 1)mc²

Question 13

relativistic total energy

Answer 13

E = K + mc² = γmc²

Question 14

energy/momentum relationship for relativistic particle

Answer 14

E² = p²c² + (mc²)²