2.1 Relativistic Eqns of Motion

Question 1

What must the relativistic equations obey for low speeds?

Answer 1

Newtonian mechanics when v

Question 2

What do we mean by proper time?

Answer 2

τ - Time in the comoving frame

- All observers agree on it

Question 3

What is the invariant scalar for the proper time?

Answer 3

dτ = dS / c = dt/γ

Question 4

What is the four force equal to?

Answer 4

F = γ(v . f / c , f) = γ(1/c dE/dt , f)

Question 5

What is f equal to in the four force tensor

Answer 5

f = γ dp/dt

Question 6

Why does the time component of the four force have two forms

Answer 6

f(0) = γ dp(0)/dt and p(0) = E/c
= γ(1/c dE/dt )
= γ(v . f / c)

Question 7

What is the 0 component of the 4 momentum equal to? p(0)

Answer 7

p(0) = E/c

Question 8

What is the Faraday tensor equal to? F^(alpha beta)

Answer 8

0 -Ex/c -Ey/c -Ez/c
Ex/c 0 -Bz By
Ey/c Bz 0 -Bx
Ez/c -By Bx 0

Question 9

How is the contravariant Faraday tensor different to the covariant?

Answer 9

Covariant has - EX/c on the column

Contravariant has -EX/c on the row

Question 10

How can the Faraday tensor be split up into two blocks?/

Answer 10

The first row and column is the time like block of the electric field
The 3x3 in the bottom right is the space like block of the magnetic field