15.9. What to Remember from Lesson 15#
15.9.1. The Ether#
That light needed a medium “to wave” in was the undisputed confirmed belief of all scientists for nearly 80 years since Faraday first began his systematic study of electromagnetism. The idea had problems, notably that light has such a high velocity that the stiffness of the ether material had to be millions of times more than that of steel…and yet, it had to be everywhere in the universe–in outer space and in the room you’re in now–without impeding the motions of material bodies going through it.
15.9.2. Detection of the Ether#
Either the ether was dragged along with the Earth as it moves, or is completely stationary were two logical possibilities. Stellar aberration observations suggested that the Earth moved through the ether and it was satisfying to imagine that Newton’s Absolute Space notion had a realization in the ether itself.
So it might be possible to detect the Earth’s motion through that stationary ether by interfering two beams of light in perpendicular directions in the Michelson Interferometer, while, of course, riding on the Earth as it orbits the Sun.
Michelson’s original and then his more precise iteration with Morley at Case detected zero relative speed for the Earth and the ether.
15.9.3. How to Explain the Null Result?#
There was no satisfactory explanation for the null result of the Michelson-Morley experiment. The least unsatisfactory way out was the idea of Lorentz that made use of his notion that atoms exist and that they consist of electrically charged particles who’s electric field would contract due to its motion with the Earth in the direction of its motion. (This particle became became the electron, after its discovery in 1897. Stay tuned.) So, it was concluded by him and by Fitzgerald (who had no model, just the idea) that the physical dimensions of the Michelson Interferometer would shrink due to its motion and the electric fields of its atoms’ interaction with the ether. While not the actual situation, some of the mathematical descriptions that Lorentz worked out have their role in Relativity which is why they are called the Lorentz Transformations, even though they more naturally “fell out” of Einstein’s model.
15.9.4. Galilean Relativity#
This is a simple idea: there is no mechanical experiment that you can perform in an inertial rest frame that would detect whether you are moving or stationary. Working out the mechanics of such an experiment would naturally follow Newton’s laws of motion and any observer who is moving at a constant speed relative to you should be able to use the same Newton’s laws of motion to describe the motion in your rest frame as well. This suggests that Newton’s laws are “invariant” with respect to a Galilean Transformation, which is:
where the \(x_H\) represents an \(x\) coordinate as determined in that “stationary,” Home frame of reference; \(u\) represents the speed of that frame of reference relative to some other frame, called “Away;” and so \(x_A\) represents an \(x\) coordinate of the same event in that moving frame of reference.
15.9.5. Maxwell’s Equations#
While Newton’s laws of motion are invariant with respect to a Galilean Transformation for relatively moving frames of reference, Maxwell’s Equations are not! This manifests itself in many paradoxes which Einstein focused on as troubling.
15.9.6. An Untenable Situation!#
By the turn of the 20th century, there were two great systems in physics, both with highly confirmed mathematical structures: Mechanics was well described by Newton’s laws of motion and Electromagnetism was well described by Maxwell’s Equations, supplemented by Lorentz’s force law.
As firmly established as they were, they had completely different behaviors when they were applied to relatively moving inertial frames of reference.
How can that be?