Special Relativity

Question 1

What was Descartes theory of light?

Answer 1

Light is a corpuscle/particle with its colour determined by intrinsic rotation of the particle about its axis.

Question 2

What was Hooke’s theory of light?

Answer 2

Light is a vibratory motion transmitted through a medium in a series of wave fronts like ripples in a pond.

Question 3

What did Huygens argue about the particle theory?

Answer 3

The particle theory was inconsistent with what happens when two light beams intersect and proposed a model of light as disturbances in an elastic medium.

Question 4

Why was Newton critical of Hooke’s theory?

Answer 4

Due to its failure to account for refractive phenomena.

Question 5

How did Young’s double slit experiment support the wave theory of light?

Answer 5

The interference fringes on the screen proved light was wavelike in nature.

Question 6

What does Maxwell’s theory of light say?

Answer 6

There are two types of field (magnetic and electromagnetic). The first can be associated with a magnet or charge carrying wire and the second from a stationary wire. In Maxwell’s theory, there is a set of equations that such fields must satisfy and together these equations imply we can think about E and B fields as behaving like waves propagating in a particular manner. Electromagnetism allows us to define light as a propagation of fields which it does without reference to the medium through which it propagates. In Maxwell’s theory light is defined in terms of constants, these being the permittivity and permeability of some medium.

Question 7

What was the medium in Maxwell’s theory thought to be?

Answer 7

What was called the ether. This ether allowed us to define an absolute inertial rest frame called the ether frame and to define the speed of light relative to this frame as c.

Question 8

What does the ether imply in terms of rest frames?

Answer 8

It implies that there is a privileged standard of rest

Question 9

What was the speed of light considered to be in the ether theory?

Answer 9

The speed of light in this medium was like any mediums, light should always propagate at the same speed for ether stationary light. This is the speed of light in free space c

Question 10

Why was the Michelson Morley experiment conducted?

Answer 10

If the effect of the ether being dragged is taken into effect, there should be small but detectible consequences for the isotropy of the two way measured speed of light when measured on Earth. This would therefore be able to prove or disprove the existence of the ether.

Question 11

What was the method used in the Michelson Morley experiment?

Answer 11

Using a 2 arm inferometer, they could conduct a precise experiment that measured the relative time difference in terms of the relative fringe shifts between two beams of light. One split into the perpendicular direction and the other in the parallel direction.

Question 12

What were the results of the Michelson Morley experiment?

Answer 12

No fringe shift was observed (null result) which seemed to contradict Maxwell’s theory of light as the existence of the ether defined a rest frame and relative to which the Earth was moving seemed necessary to make physical sense of the equations.

Question 13

What did some physicists (Fitzgerald, Lorentz and Lamor) propose in response to the results of the Michelson Morley experiment?

Answer 13

They considered issues with the motion of bodies held together by EM forces as an explanation, specifically the hypothesis that we should understand the motion of material bodies relative to the ether as having effects on their length and breadth. The idea then was to obtain the null result in terms of the contraction of the arm of the inferometer parallel to the motion of Earth. If the relevant factor of the contradiction is fixed to be the square root of one minus v squared over c squared, then this precisely cancels the effects of motion relative to the ether on the times for perpendicular vs parallel travel to the mirror and back. This was the contradiction hypothesis.

Question 14

What were Einstein’s thoughts on the results of the Michelson Morley experiment?

Answer 14

He was convinced of Lorentz’s approach to the optics of moving bodies but did not like that he had to introduce the Lorentz contraction to explain the experiment. He thought it felt unconnected to the rest of the theory. He found it preferable that the failure of the experiment and similar experiments for detecting the motion of matter relative to the ether was that the speed of light is the same in all inertial reference frames.

Question 15

What year was Einstein’s Annus Mirabilis and what were some of his discoveries?

Answer 15

1905 and he wrote:
- On the electrodynamics of moving bodies
- The paper that presents E = mc^2
- His proposal of the idea of energy quanta
- A new determination of molecular dimensions giving a relation between the coefficients of fluid viscosity with and without suspended particles
- The paper that developed a stochastic model of Brownian motion
- His work on the foundations of statistical mechanics, filling in the gaps in the mechanical foundations of thermodynamics
- His work on the photoelectric effect

Question 16

What crucial step was needed for Einstein to come up with special relativity?

Answer 16

He needed to drop the assumption that the ordinary Newtonian law of addition of velocities was correct. This law implies that c is constant with respect to any other inertial frame moving with respect to the first.

Question 17

What are Einstein’s two postulates in special relativity?

Answer 17

The principle of relativity and the principle of constancy of the velocity of light.

Question 18

What did the principle of relativity state?

Answer 18

The laws of physics take the same form in all inertial frames.

Question 19

What did the principle of constancy of the velocity of light state?

Answer 19

The velocity of light in a vacuum is the same in all inertial frames regardless of the state of the motion of the source.

Question 20

What was Einstein’s notion of simultaneity?

Answer 20

That it was defined operationally within any given inertial frame by a network of clocks and rods. The rods are assumed to be rigid and give an observer stationed at any point a means to measure the length of other objects by superposition of its length. Clocks are assumed to be definite time at the point in time they are stationed.

Question 21

When are 2 clocks considered asynchronous in special relativity?

Answer 21

In a return trip taken by light between the two clocks A and B, the light ray leaves clock A at time ta and arrives at B at time tb and is instantaneously reflected and arrives back at A at time ta’. The clocks are considered asynchronous only if:

tb - ta = ta’ - tb

Question 22

What does Einstein’s notion of simultaneity mean for coordinate systems?

Answer 22

It means that 2 events are synchronous when viewed from one coordinate system will not be synchronous when viewed from a system moving relatively to this system.

Question 23

If there is an observer on a train and an observer on the ground and the observer on the train shines a light beam that is reflected back, what will the observer on the train see?

Answer 23

The observer sees the two light flashes emitted simultaneously from the ends of the train which are equidistant. The light from both ends arrive at the same time.

Question 24

If there is an observer on a train and an observer on the ground and the observer on the train shines a light beam that is effected back, what will the observer on the ground see?

Answer 24

The observer must see two flashes arrive at the central observer at the same time but for her, the light flashes have travelled different distances. All agree on the speed of light so she concludes hat the flashes were not emitted simultaneously.