Special Relativity

Question 1

What is a frame of reference?

Answer 1

A coordinate system where the observer is at rest with respect to the coordinate origin.

Question 2

What is an inertial frame?

Answer 2

When an object has no acceleration when no forces are acting on it, so it moves at a constant velocity or is at rest to other inertial frames.

Question 3

What is a non-inertial reference frame?

Answer 3

Can have fictitious forces, so the object can accelerate without known forces acting on it.

Question 4

What assumption is made in Galilean relativity?

Answer 4

That time follows a universal clock for all inertial frames.

Question 5

In frame S’ an object is moving with velocity u’, what is u in frame S?

Answer 5

u = u’ + v
a = a’

Question 6

What are the Newtonian axioms on absolute time and space?

Answer 6

1. All inertial frames have a universal time
2. Absolute space remains fixed to the universe

Question 7

(ε0μ0)^–1/2 = ?

Answer 7

c

Question 8

How can the speed of light be estimated using astronomical observations?

Answer 8

Observing the eclipses of Io by Jupiter:
An eclipse creates a pulse of duration T from start and stop in measured light intensity.
T was longer when the Earth was travelling away from Jupiter.
Using the distances involved, c = ∆D/T

Question 9

How did Fizeau measure the speed of light?

Answer 9

Using a spinning toothed wheel and a mirror.
The ω of the wheel was set so light passing through the gap would be blocked by the next tooth.
Using the size of the gap, t = ∆θ/ω and c = 2d/t

Question 10

What is the aether?

Answer 10

A medium fixed to absolute space and time where light travels at speed c.

Question 11

What is the Michelson-Morley experiment?

Answer 11

An interferometer was built to measure a difference in the speed of light depending on which direction light was travelling through the aether.
The interferometer split the light to travel along 2 perpendicular arms of equal length, each with mirrors reflecting light back to a detector which measured interference patterns between the two beams caused by difference in their speeds.

Question 12

What should be observed in the Michelson-Morley experiment on Earth?

Answer 12

Since it is the speed of Earth through the aether affecting light’s speed, the difference in time should be the same as observed in Earth’s frame or the aether’s frame.

Question 13

What was the result of the Michelson-Morley experiment?

Answer 13

There was no shift detected, despite the resolution precise enough, providing strong evidence against the existence of the aether, and that the speed of light does not change due to motion.

Question 14

What was a limitation of Lorentz’s work?

Answer 14

The local time in the moving frame was not considered real, as only the aether time was considered as the true time.

Question 15

What were Einstein’s two postulates towards relativity?

Answer 15

1. The laws of physics must be the same in all inertial frames
2. The speed of light in a vacuum is the same in all inertial reference frames

Question 16

What frame is the proper time interval measured?

Answer 16

The inertial frame in which two events occur at the same location.

Question 17

What does a Lorentz factor significantly higher than 1 mean?

Answer 17

That the velocity is very fast.

Question 18

What is the proper length?

Answer 18

The length measured by an observer at rest relative to the object.

Question 19

What direction does length contraction happen?

Answer 19

In the direction of motion, observations of other spatial dimensions are unaffected.

Question 20

How does the decay of muons provide evidence for time dilation and length contraction?

Answer 20

Muons are created by collisions of atmospheric atoms with cosmic rays, which are very high speed. Saying that v ≈ c, the proper length can be estimated that a Muon travels on Earth before it decays as we know the mean lifetime.
While the length in Earth’s rest frame is the proper length, the proper time interval must be found using the time dilation relation.
The measured lifetime at rest is too small for the muons to reach the ground, but muons are measured in the ground, showing that in Earth’s rest frame the time interval is larger than the proper time interval.

Question 21

What is the difference between a Galilean transformation and a Lorentz transformation?

Answer 21

The Lorentz transformation accounts for time dilation and length contraction, and is always valid.

Question 22

When is the Galilean transformation valid?

Answer 22

When v &laquo_space;c, βc = v, and γ → 1, as then ∆t′ → ∆t and time dilation is negligible.

when v &laquo_space;c, u reduces to u = u’ + v.

Question 23

What is a worldline?

Answer 23

An objects path through spacetime.

Question 24

What does a straight worldline show?

Answer 24

A constant velocity in an int

Question 25

What is boosting a reference frame?

Answer 25

Comparing motion in two inertial frames and showing the proper time interval by transforming a frame so both events are at the same x value.

Question 26

What is a spacetime interval ∆s^2?

Answer 26

The length of a line between two events in space and time.

Question 27

When is the spacetime interval invariant?

Answer 27

When it is the same in all inertial frames, when the proper time interval is invariant.

Question 28

What is the zeroth component of a 4-vector?

Answer 28

Time

Question 29

What is the minkowksi inner product?

Answer 29

A·B = A0B0 – A1B1 – A2B2 – A3B3

Question 30

What does the Minkowksi inner product do?

Answer 30

Outputs the same scalar value in any inertial frame. So the inner product of a 4-position vector with itself is the invariant spacetime interval.

Question 31

What is the Lorentz transformation of a 4-vector?

Answer 31

Transforming a 4-vector from one inertial frame to another by multiplying it by the Lorentz transformation matrix.

γ –γβ 0 0
–γβ γ 0 0|
|0 0 1 0|
0 0 0 1

Question 32

What is an objects proper velocity?

Answer 32

Using the proper time interval, it is w = dx/dτ.

Question 33

What is 4-momentum?

Answer 33

P = ( γmc, γmux, γmuy, γmuz)

Question 34

When is the binomial expansion of the Lorentz factor valid?

Answer 34

When β &laquo_space;1