Relativity 1

Question 1

What is an inertial frame of reference?

Answer 1

Inertial frames of reference are not accelerating relative to one another, so all laws of physics are invariant between frames.

Question 2

What are Einstein’s 2 postulates?

Answer 2

1: The “laws of physics” are invariant between all inertial frames of reference. (-> equivalent experiments give the same results)
2: The speed of light (in a vacuum) is the same in all inertial frames of reference.

Question 3

What are the lorentz transformation equations?

Answer 3

x = gamma(x' + vt')
t = gamma(t' + {v/c^2}x')
x' = gamma(x - vt)
t' = gamma(t - {v/c^2}x)

Question 4

What is gamma equal to in relativity?

Answer 4

gamma = 1/(sqrt{1-[v^2/c^2]})

Question 5

Derive the equation for time dilation.

Answer 5

delta t = gamma * delta t’

Question 6

Derive the equation for length contraction.

Answer 6

delta x = delta x’ / gamma

Question 7

Derive the equation for velocity transformations in the x and y directions.

Answer 7

Check notes

Question 8

Derive the doppler relativistic doppler effect equation.

Answer 8

Delta t = gamma * delta t’ * (1 + v/c)

Question 9

How is the spacetime interval between two events (delta s) defined?

Answer 9

(delta s)^2
= (c * delta t)^2 - (delta x)^2
= (c * delta t’)^2 - (delta x’)^2

Question 10

Why is the spacetime interval useful?

Answer 10

The spacetime interval between two events is invariant of inertial frame.

Question 11

What is the “proper time” interval?

Answer 11

The spacetime interval divided by c.

Equal to the time on a clock constantly at rest in the frame (delta x = 0).

Question 12

How can the total spacetime interval of a path be calculated?

Answer 12

Integrate
->
Total spacetime interval = the integral of (c/gamma) with respect to time