Special Relativity

Question 1

Galilean transformation of x to x’?

Answer 1

x = x’ + vt, or x’ = x - vt

Question 2

Equation for Lorentz factor?

Answer 2

γ = 1/√(1-β^2 )

Question 3

Equations for time dilation and length contraction

Answer 3

∆t=γ∆τ and L= L_p/γ

Question 4

Equation for the space-time interval?

Answer 4

∆s^2 = (c∆t)^2 - ∆x^2 - ∆y^2 - ∆z^2

Question 5

Equation for the Lorentz transformations (component form)?

Answer 5

X′0 = γX0 - γβX1 and X′1 = -γβX0 + γX1

Question 6

Equation for the Lorentz transformations (derived form)?

Answer 6

c∆t’ = γc∆t - γβ∆x and ∆x’ = -γβc∆t + γ∆x

Question 7

What are the invariant quantities in special relativity?

Answer 7

X.X = ∆s^2 and P.P = (mc)^2

Question 8

Total energy at relativistic speeds?

Answer 8

γmc^2

Question 9

What is the relativistic energy-momentum relation?

Answer 9

E^2 = (mc^2)^2 + (pc)^2

Question 10

Equation for relativistic velocity addition?

Answer 10

u = (u’ + v)/[1 + u’v/c^2]

Question 11

What important property in Galilean relativity implies relativity of simultaneity?

Answer 11

t = t’