Special Relativity: Physics at the Speed of Light

You awaken, and your mind clears. Yes, you are traveling on the inter-stellar freighter Hyperion, outbound to mine anti-matter from a galactic vortex. The automated systems have just revived you from suspended animation. Your assignment – perform periodic ship maintenance.

Climbing out of your hibernation chamber, you punch up system status. All systems read nominal, no issues. That is good. Your ship extends 30 kilometers. Just performing routine maintenance exhausts the mind and body; you don’t need any extra work.

You contemplate the task of the freighter. The Hyperion, and its three sister ships, fly in staggered missions to harvest energy, in the form of anti-matter. Each trip collects a million terawatt-hours, enough to support the 35 billion human and sentient robots in the solar system for a full year.

Looking up at the scanner screen, you see the mid-flight space buoy station about a light-hour ahead. The station contains four buoys, configured in a square, 30 kilometers on a side. A series of eleven stations keeps your ship on course during its two year travel out from Earth.

You check the freighter’s speed relative to the buoys – about 50 percent of the speed of light, but constant, i. e. no acceleration or deceleration. That makes sense – at mid-flight, the freighter has entered a transition phase between acceleration and deceleration.

The Theory of Relativity

Either through deliberate study, or general media coverage, you likely have heard of the Theory of Relativity, the master piece of Albert Einstein. Einstein built his theory in two phases. The first, Special Relativity, covered non-accelerating frames of reference, and the second, General Relativity, dealt with accelerating and gravity-bound frames of reference.

Special Relativity gave us the famous E=MC squared equation, and covers the physics of objects approaching the speed of light. General Relativity helped uncover the possibility of black holes, and provides the physics of objects in gravity fields or undergoing acceleration.

Here we will explore Special Relativity, using our hypothetical ship Hyperion. The freighter’s speed, a significant fraction of that of light, dictates we employ Special Relativity. Calculations based on the laws of motion at everyday speeds, for example those of planes and cars, would produce incorrect results.

Importantly, though, our freighter is neither accelerating nor slowing and further has traveled sufficiently into deep space that gravity has dwindled to insignificant. The considerations of General Relativity thus do not enter here.

Waves, and Light in a Vacuum

Special Relativity starts with the fundamental, foundational statement that all observers, regardless of their motion, will measure the speed of light as the same. Whether moving at a hundred kilometers an hour, or a million kilometers an hour, or a billion kilometers an hour, all observers will measure the speed of light as 1. 08 billion kilometers an hour.

A caveat is that the observer not be accelerating, and not be under a strong gravitational field.

Even with that caveat, why is this case? Why doesn’t the speed of the observer impact the measured speed of light? If two people throw a baseball, one in a moving bullet train, while the other stands on the ground, the motion of the bullet train adds to the speed of the throw ball.

So shouldn’t the speed of the space ship add to the speed of light? You would think so. But unlike baseballs, light speed remains constant regardless of the speed of the observer.

Why?

Let’s think about waves. Most waves, be they sound waves, water waves, the waves in the plucked string of a violin, or shock waves travelling through solid earth, consist of motion through a medium.

Sound waves consist of moving air molecules, water waves consist of moving packets of water, waves in a string consist of motion of the string, and shock waves consist of vibrations in rocks and soil.

In contrast, stark contrast, light waves do not consist of the motion of any underlying substrate. Light travel does not need any supporting medium for transmission.

In that lies the key difference.

Let’s work thought that in the context of the inter-stellar freighter. You rise from suspended animation. Acceleration has stopped. In this case, no buoys exist near-by.

How do you know you are moving? How do you even define moving? Since you reside in deep space, and you are away from the buoys, no objects exist near-by against which to measure your speed. And the vacuum provides no reference point.

Einstein, and others, thought about this. They possessed Maxwell’s laws of electromagnetism, laws which gave, from first principle, the speed of light in a vacuum.

Now if no reference point exists in a vacuum against which to measure the speed of a physical object, could any (non-accelerated) motion be a privileged motion? Would there be a special motion (aka speed) at which the observer gets the “true” speed of light, while other observer’s moving at a different speed would get a speed of light impacted by that observer’s motion.

Physicists, Einstein especially, concluded no. If a privileged reference frame exists, then observers at the non-privileged speed would find light violates Maxwell’s laws. And Maxwell’s laws stood as so sound that rather than amend those laws, physicists set a new assumption – relative speed can’t change the speed of light.

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