Relativity 2

Question 1

Are energy and momentum conserved in relativity?

Answer 1

NO

Only the 4-vector relativistic momentum is conserved (within a single inertial frame).

Question 2

What is a key property of four vectors?

Answer 2

The dot product of a four vector with itself is equal to the first component squared - the second component squared (dot product with itself if second component is a vector).
The dot product of a four vector with itself is invariant in all inertial frames.

Question 3

What is the momentum four vector in relativity?

Answer 3

mgamma(c,v) = (energy/c , relativistic momentum 3-vector)

Question 4

What is the relativistic expression for energy?

Answer 4

mgammac^2

Question 5

What is a relativistic expression for kinetic energy?

Answer 5

(gamma - 1)*mc^2

Question 6

What is the relativistic expression of momentum?

Answer 6

gammamv

Question 7

What is the dot product of the relativistic momentum four vector with itself, expressed in terms of the invariant mass?

Answer 7

M^2 * c^2

Question 8

What is a relativistic expression for energy in terms of the invariant mass?

Answer 8

E^2 = (c^2 * p^2) + (m^2 * c^4)

Question 9

How is the invariant mass defined?

Answer 9

sqrt((the dot product of the momentum 4-vector with itself)/c^2)
The invariant mass is constant throughout all frames.

Question 10

What is the energy of a photon?

Answer 10

cp

Question 11

What is the momentum of a photon?

Answer 11

E/c

Question 12

How can the energies (e.g: mass energy, kinetic energy…) be extracted from the relativistic energy (gammamc^2)?

Answer 12

Binomially expand gamma