Einstein's Universe Homework #4

In what frame of reference are the laws of electromagnetism valid, according to Einstein?

According to Einstein, the laws of electromagnetism are valid in any frame moving at a constant velocity or in all frames that are in uniform motion.

What are Einstein's two postulates of special relativity?

Einstein's first postulate of special relativity states that the laws of physics are the same in all inertial frames of reference in uniform motion (constant speed). Einstein's second postulate states that the speed of light is independent of the motion of the source or observer.

Describe the analogy between the two light beams in a Michelson interferometer and the two people swimming up and downstream and across and back in a river.

It was believed that the beams of light created by Michelson's interferometer would take different amounts of time to travel the same distance because of the ether wind. The ether wind (the ether is the medium of the wave) would treat each wave differently because of the different directions they were traveling in. This can be compared to two people swimming up and downstream and across and back in a river. It would take the swimmers different amounts of time to swim the same distance because the water (the medium in this case) would treat each swimmer differently depending on which direction they were swimming in. The current in the river is like the ether wind.

What is the Michelson-Morley experiment? What was it designed to measure? Did it succeed in measuring what it was designed to measure? Include a description of a Michelson Interferometer.

The Michelson-Morley experiment was designed to measure the motion of the Earth through the ether. A single beam of light was split into two beams that ran perpendicular to each other. The Michelson Interferometer was the instrument that split the beam in two. The purpose of the tool was the produce interference between two light beams. The Interferometer works by splitting a beam of light into two equal amplitude beams. One beam hits a fixed mirror and the other hits a movable mirror. This gives different beam lengths which then converge creating an interference pattern. The two beams traveled the same distance and were then reflected against mirrors so that they could return into one singular beam. When the two waves combine once again, there is inference. Michelson wanted to use this interference to measure differences in the time it took to travel due to ether wind. The experiment was repeated many times and failed every time.

List the properties that the ether must have and why it must have them. Identify any apparent contradiction between these properties.

The ether was considered the medium in which all waves are relative to. Maxwell's equations raised the question, if light is moving at speed c, what is it moving relative to? The ether answered this question but because it must accommodate multiple types of waves, it has odd and contradictory properties. It must be tenuous, frictionless, transparent, and flexible so that it minimizes resistance, but it also must be stiff and strong to maximize wave speed. How can the ether both is tenuous and strong? This is a big contradiction.

According to Einstein, with respect to what does the speed of light move at speed c?

The question, "with respect to what does the speed of light move at speed c?", baffled physicists for a long time before Einstein came up with answer. Before Einstein, it was believed that the ether was light's medium. Einstein claimed that the ether was unnecessary and dangerously misleading. He stated that light propagates through not through a material medium (like the ether) and instead it moves through empty space. Light waves are different from all other waves physicists had encountered because they all require a physical medium.