Equations

Question 1

In a collision with a stationary particle and a moving particle, what are their momentums?

Answer 1

Stationary has 0 momentum, moving has a momentum of p

Question 2

In a collision with a stationary particle and a moving particle, what are their energies?

Answer 2

Stationary has an energy of E=mc^2, moving has an energy of E^2=p^2c^2+m^2c^4

Question 3

In a collision where both particles are moving in opposite directions, what is the initial momentum?

Answer 3

0

Question 4

When finding things like minimum energy or mass required, what is the condition we use for products of reaction?

Answer 4

Products are stationary unless told otherwise

Question 5

How to deal with E^2 and p^2 in natural units?

Answer 5

E^2-p^2=m^2 (when using natural units)

Question 6

Another use of E^2 and p^2?

Answer 6

S=(sum of E)^2-(sum of p)^2

Question 7

How to prove velocity lorenz transformation?

Answer 7

u=dx/dt which is rewritten as dx/dt’ x dt’/dt which is written as (dx/dt’)/(dt/dt’) and sub in values

Question 8

Proof of space time invariant?

Answer 8

Define S’ and sub in respective lorenz transformations until we find S

Question 9

Time like intervals?

Answer 9

S^2>0 and |r|<c|t| and events may be connected

Question 10

Light like intervals?

Answer 10

S^2=0 and |r|=c|t| and events may be connected

Question 11

Space like intervals?

Answer 11

S^2<0 and |r|>c|t| and events are not connected

Question 12

How to prove relativistic energy?

Answer 12

dE=dp/dt x dx/dt x dt then apply the product rule

Question 13

Easiest way to find velocity as a fraction of c?

Answer 13

Find p/E

Question 14

Which rest frame does time dilation/length contraction occur in?

Answer 14

Moving objects rest frame, not the Earth rest frame

Question 15

How does the invariant work across Lab and CMS frames?

Answer 15

(E^2-p^2)_LAB = (E^2-p^2)_CMS