-The first postulate of Einstein in his Special Theory of Relativity (STR) states:

“There is no experiment that can be performed in an enclosed laboratory that can detect absolute motion.”

-Certainly the idea of absolute motion is out of reach for modern scientists. There is no way to observe an Aristotle’s grid, or Newton’s fixed stars, or the Michelson-Morley Aether; which are at rest in the Universe, and against which all Celestial motions can be defined.

-This leaves us only able to work with relative motions; that is, we can only define one object’s spatial motion in terms of another object’s spatial position.

-There are a few methods by which relative motion can be ascertained. An observer in a car traveling down the interstate can use a stopwatch to find the time it takes to travel between two consecutive mile posts, then solve for the cars velocity relative to the road by: t = D / v.

-Or, a car traveling down the highway, whose owner is sweating the transmission fluid leak she had found that morning. She noticed that every ten seconds a drop fell into the puddle forming beneath her stationary car. So after traveling a while, she pulls into a rest stop to check the leak; has it increased or decreased, she asks herself. Then she notices it is now not in a puddle, but there is some distance between the drops. She does not think the leak has stopped, but that because of her motion at a certain velocity, this has cased the puddle not to form. She imagines she can determine her car’s velocity relative to the road by measuring the distance between the drops: v = D / t

-As part of his daily commute, a driver on a city expressway determines that at a constant velocity relative to the road, within a preset amount of time, he can travel a certain number of miles: D = vt.

-Each of these scenarios obeys invariance, such that the motion will follow the rule that they take on the most simple form of the equations of motion in that reference frame. However, by using sound waves, which violate Galilean invariance, a new method emerges that also determines relative motion. This method comes from the Michelson-Morley experiment to detect the Aether. I have used sound waves in my previous thought experiment.

-This new method does not take on the simplest form of the equations of motion (velocity, time, or position) in each reference frame. It is identical in both relative reference frames, the one regarded at rest and the other regarded in motion. This method can also be used to address the issues of simultaneity and clock synchronization from Einstein’s STR.

-In other words, one reference frame takes the simple form of the law, while the other reference frame has a more complicated form; and vice versa, depending on whose reference frame the event is being viewed from. Now in my statement, the formulae are identical in both reference frames: whether both are moving; one is moving and one is at rest; or both are at rest. The following considerations give rise to the transformation equations:

♦ Not t = L / c; but t₁ = [(L + vt₁) / c] = [L / (c - v)] identical from within each reference frame. Neither formula makes any statement about the car's motion relative to the moon. (t₁ = t₁ key point for later)