I Finally Get Relativity — Part II

Welcome back! If you made it through Part I, I will assume that I still got the ball and everything there made sense to you — or you’re just a glutton for punishment! Either way, things are about to get real weird, real fast! Here goes…

Enter Einstein

By the 20th century, Einstein and many other physicists would introduce a slew of concepts that would knock all this “universality” on its ear! First of all, there were many experiments into the behavior of light and electromagnetic phenomena at this time, and the results didn’t fit with Classic Newtonian Mechanics. Second, there were observations of Mercury’s orbit that didn’t conform to Newton’s theory of Universal Gravitation (more on that in the next installment).

Much like the pre-Copernican revolution, an impending scientific breakthrough was previewed by scientific confusion. Whenever observations don’t fit with accepted theories, those theories are about to change!

To summarize it succinctly, by the 19th century, scientists realized that light was an electromagnetic (EM) phenomenon. Today, it is understood that this is due to the nature of light, which consists of photons (positively-charged electrons) that behave as both a particle and a wave. These discoveries were decades away during the 19th century, but scientists nevertheless understood that light and electromagnetism were related.

Thanks to the experiments of people like James Clerk Maxwell and Dutch physicist Hendrik Lorentz, scientists also understood that electric and magnetic forces behaved as fields and exerted forces on point charges. These were summarized in Maxwell’s Equations (1861–62) and the Lorentz Force Law (1895). The experiments conducted by these and other scientists also yielded highly-accurate estimates for the speed of light — which we now know to be 299,792,458 m/s (1.079 billion km/h; 670.6 million mph).

Ah, but there’s was a snag! These many experiments also showed that the speed of light was constant. It didn’t matter if the source was moving relative to the observer or not — the speed always came out the same. This contradicted what Galileo said about reference frames and the relativity of it all. After all, if the observer were moving towards the source, wouldn’t it appear to be moving faster? And if this same observer were moving away from it, wouldn’t there be a measurable decrease in the velocity?

In response, scientists began to postulate that space must be filled with some invisible “aether” that allowed light to propagate, but also slowed it down. This made sense since experiments going back to Classical Antiquity indicated that light behaved as a wave. If that were the case, light would travel through this “aether” in the same way that sound travels through air or ripples across a pond. Alas, this necessitated that scientists measure the effect of this “aether” to determine its properties.

A famous example was the Michelson-Morley Experiment (1887) conducted by American physicists Albert A. Michelson and Edward W. Morley. Using a chamber and a series of mirrors, they attempted to measure the speed of light from different angles — a horizontal one corresponding to Earth’s rotation towards the Sun and a perpendicular one. If such an “aether” existed, then the Earth’s movement through it (and towards the Sun) would result in a noticeable difference with the horizontal beam.

Special Relativity

However, the experiment yielded the same result as the rest: the speed of light was the same in all inertial reference frames. This is where Einstein made his stand in 1905 in a famous paper titled “ On the Electrodynamics of Moving Bodies,” which resolved Maxwell’s Equations on electromagnetism with Newton’s Laws of Motion and introduced Einstein’s Special Theory of Relativity. This theory came down to two postulates:

• The laws of physics are identical in all non-accelerated inertial reference frames
• The speed of light in a vacuum is constant, regardless of the motion of the observer or light source

What did this mean? For starters, into the confusion caused by experiments not aligning with theory, Einstein cut through the crap and told scientists to trust the experimental results! But to get there, Einstein had to overturn a lot of conventional thinking. Lucky for him, he did not need to reinvent the wheel. He merely had to synthesize the experimental data and resolve it with established theory.

A key aspect of Einstein’s breakthrough was something Lorentz had come up with. While examining all the experiments concerning the behavior of light, Lorentz theorized that in an inertial reference frame, things become distorted along the path of travel (aka. Lorentz Transformations). When applied to objects approaching the speed of light, this meant that its measurable speed does not speed up or slow down. The passage of time does!

Like his predecessor, Einstein related how this worked using a clever (and updated) metaphor. Picture this: a person is standing in a train car and holding a mirror. There’s another mirror on the floor directly beneath them, and the two are reflecting a beam of light back and forth. Assuming it was possible to observe the light traveling in real-time, the person in the train cart would see it bounce directly up and down without any delays, always moving at a constant speed of c.

To an external observer viewing from the side of the tracks, the light would appear as a zig-zagging beam, constantly trying to catch up to the mirrors. But they would also record a constant speed of c. Naturally, this situation would make little sense to the observer watching the train. Because the mirrors are moving, the light bouncing back and forth would need to catch up to them, which would impose a delay (even if it was just a few nanoseconds).

However, if both observers were to check the time, the person in the train would notice that their watch was slightly behind that of the other person. The difference would be immeasurable, but if the moving reference frame were going a fraction of the speed of light, the difference would be quite noticeable. In short, the person in the moving frame has experienced time at a slower rate, just slow enough to let the light “catch up” and maintain a constant velocity of c.

This effect is known as “time dilation,” which states that for objects approaching the speed of light, the passage of time slows. Alas, Einstein and his contemporaries still held to the Conservation of Energy Law, which states that energy is never destroyed or created, merely converted. This led him to formulate the famous equation E=mc2, which states that an object’s energy (E) is equal to its mass x its acceleration towards the speed of light.

Time & Space

This equation has a few notable consequences. First, it states that as an object accelerates towards the speed of light, its inertial mass will increase. Ergo, an exponentially greater amount of energy will be required for the object to keep accelerating. This also means that the speed of light is absolute since it would take an infinite amount of energy to reach c since the object’s mass would become infinite in the process!

Another startling consequence was how mass and energy are interchangeable in this equation. If you switch mass and energy around in the equation, the outcome is still the same. This came to be known as the principle of Mass-Energy Equivalence, which states that energy and mass are essentially two sides of the same coin. As if that wasn’t enough, Einstein’s Special Theory of Relativity also revolutionized the way scientists thought of space and time.

Previously, scientists had assumed that a three-dimensional geometry of the Universe was independent of time. In other words, space and time were separate! But by showing how time was relative to the observer in a moving reference frame, Einstein was proposing a four-dimensional geometry of the Universe where three dimensions of space were combined with one dimension of time — aka. Spacetime!

Almost immediately, Einstein’s Special Theory of Relativity caught on like wildfire. Not only did it resolve electromagnetism with Newton’s theories of motion. It also did away with extraneous explanations like the need for an “aether.” In the coming years, Einstein would take this a step further in the hope of resolving Special Relativity with gravity to create a more generalized theory of how the Universe works.

Stay tuned!

Originally published at http://storiesbywilliams.com on January 19, 2022.