Relativistic

Question 1

What is the lorentz transformation for x and x’ ?

Answer 1

x’ = γ (x -ut)
x = γ (x’ -ut’)
Can include Δx and Δx’
A Galilean transformation with γ

Question 2

What is the lorentz transformations for y and z ?

Answer 2

y = y’
z = z’
Can include Δ for both

Question 3

What is the lorentz transformation for t and t’ ?

Answer 3

t’ = γ (t - (ux)/c²)
t = γ (t - (ux’)/c²)
Can include Δt’ an Δt

Question 4

What is the equation for space time intervals?

Answer 4

(Δs)² = (cΔt)² - ((Δx)² + (Δy)² + (Δz)²)
(Δs)² = (cΔt’)² - ((Δx’)² + (Δy’)² + (Δz’)²)

Question 5

What is the equation for length contraction?

Answer 5

L = γL’

Question 6

What is the equation for relativistic energy?

Answer 6

E = mc²γ

Question 7

What is the equation fo relativistc momentum?

Answer 7

p = mvγ

Question 8

What is P.P equal to in the rest frame?

Answer 8

P.P = m²c²
(lowercase p is relativistic momentum)

Question 9

What is P.P in the general frame?

Answer 9

P.P = E²/c² - p.p
(lower case p’s are relativistic momentum)
Thus m²c² = E²/c² - p.p
m²c^4 = E² - p²c²
Thus E² = m²c^4 + p²c²

Question 10

What is the equation for relativistic kinetic energy?

Answer 10

Ke = γmc² - mc²

Question 11

What is the equation for the energy of a particle?

Answer 11

E² = m²c^4 + p²c²

Question 12

What is the energy of a particle equation apply to?

Answer 12

All particles.
eg: a photon has no mass, only the E² = p²c² applies.
A staitionary particle has no momentum thus only rest energy of E² = m²C^4 applies

Question 13

What are the 3 types of relativistic collisions?

Answer 13

Totally elastic
Totally ineleastic
Radioactive decay

Question 14

What is a Totally elastic collision?

Answer 14

A collision where momentum and kinetic energy are conserved.

Question 15

What is a Totally inelastic collision?

Answer 15

A collision where the particles stick together.
Momentum is conserved

Question 16

What is a Radioactive decay?

Answer 16

A particle splits into multiple parts.
(There is no classical counterpart)

Question 17

Why can a geometric point travel or rotate faster than C?

Answer 17

Because it holds no information

Question 18

What is Special relativity based on?

Answer 18

Principle of Relativity:
The laws of nature are identical in all identical frames of reference.

“Special bit”:
The speed of light in empty space always has the same value.

Question 19

What is a Lorentz contraction?

Answer 19

L’ ≤ L
Because 1 ≤ γ

Question 20

What is the “Proper Length”?

Answer 20

The length of an object in its rest frame

Question 21

What is the Lorentz transformation for V and V’ ?

Answer 21

v’ = (v-u) / (1-uv/c²)
v = (v’-u) / (1-uv’/c²)
u is speed of frame of reference