Why traveling at the speed of light leads to paradoxes

One of the more puzzling aspects of the theory of relativity is that the speed of light is actually NOT relative. No matter what your point of reference is, you always see a ray of light traveling at exactly the same speed, approximately 186 thousand miles per seconds.

To illustrate this concept (and why it's so weird) let's consider two cars traveling down the highway, a hybrid and a new top of the line sports car. The hybrid is traveling down the highway at a fairly sedate sixty miles per hour while the new turbo charged sports car zooms down the highway at a scorching one hundred miles per hour.

When the sports car overtakes the hybrid, and leaves it far behind, the driver of the hybrid perceives the sports car as traveling at forty miles per hour, relative to him. He perceives the sport's car velocity as the difference in the two cars' speed. If the two cars were traveling at constant speed along a sufficiently dark highway with no reference points around them, a passenger in the hybrid could believe that their car was at rest and that the sports car had simply driven past their parked car at forty miles an hour.

This concept is called Gaillean relativity, named after the famous astronomer Galileo Galilei. Galileo postulated that since humans without access to external reference points are only able to detect changes in acceleration (as opposed to speed) a human is unable to tell whether a vehicle traveling with constant velocity is in motion or at rest.

This allows the passenger of the hybrid to be uncertain if his car is parked or in motion. He is aware that the sports car went past him at a speed of forty mph more than him, however without access to external reference points he does not know what the speed of the other car actually was. If the hybrid was parked the sports car was traveling at forty miles per hour. If the hybrid is going one hundred miles an hour, then the sports car must have been traveling at one hundred forty miles per hour.

Conversely, without reference points, a passenger in the sports car can't tell if his car is moving either. He saw the hybrid move behind him at about forty miles per hour but from his point of view, the sports car may be parked and the hybrid was backing up at forty miles per hour.

Without reference points, neither passenger has anyway to tell how fast either car is going. For all the passenger in the hybrid knows, his car is traveling backwards at a constant speed of four hundred miles per hour and the sports car was also traveling in reverse at three hundred sixty miles per hour. He has no way to tell.

In physics we refer to the different perspectives of the passengers in the two different cars as frames of reference.

Normally of course we do have external reference points to rely on. If a man is standing in place on the side of the road he will observe one car traveling at sixty miles per hour and one traveling at one hundred miles per hour. Any school child will immediately conclude that this is the right answer because on planet Earth, we casually consider the point of view of a person who is not moving to be accurate in regard to measuring speed. The "correct" answer is that one car is traveling at sixty miles per hour and the other car is traveling at one hundred miles per hour. This is because on planet Earth we instinctively consider the frame of reference of a person or object who isn't moving to be preferential. Preferential basically means that the perspective of this person is judged to be the accurate default or universal perspective while those that deviate from it are points of view, or simply lacking important context.

Because of this, anyone hoping to pass his elementary school math test realizes that the cars are actually moving at sixty miles per hour and one hundred miles per hour, and the fact that their passengers might not know that is just a piece of useless trivia.

However Einstein's special relativity makes this much more complex. Einstein's theory claims that there is no preferential frame of reference and they are all equally valid.

Imagine a sky diver whose parachute doesn't open. He falls faster and faster toward the Earth far below and will most likely die on impact. However from the sky diver's point of view, it is equally valid to claim that the Earth is rising up to meet him at a faster and faster speed and will slam into him while he is floating motionless in the sky. In relativity, neither perspective is preferential.

To explain why this is so important we need to briefly discuss the speed of light. We've already established that the velocity of objects (such as cars) is relative. If I am traveling at forty miles per hour and see you move pass me at sixty miles per hour, from my frame of reference, you are traveling at twenty miles per hour; this is the difference in our respective speeds. However any experiment that involves light makes this much more complicated.

Let's imagine that we have three cars traveling down a three lane highway. One is traveling at twenty miles per hour, behind it in an adjacent lane, is a car moving at sixty miles per hour, and far behind them both traveling in the fast lane is a car moving at ninety miles per hour.

Let's imagine that at some point these cars will all line up across the highway as the faster cars move past the slowest car. We'll say that at the instant when each car is an equal distance from the end of the road, they each take out a flashlight and shine a beam of light down the road. What speed do you think that ray of light is traveling at?

Well after our prior discussion, it seems logical to assume that a passenger in the car traveling at a constant twenty miles per hour (at rest relative to his passenger) would see his own ray of light dart down the highway at about 186 thousand miles per second. In fact this is exactly what the passenger sees.

You would be well within your rights to assume that the passenger in the car traveling at twenty miles per hour would look at the ray of light fired by the nearby car traveling at sixty miles per and see that ray moving at 186 thousand miles per second plus sixty miles per hour.

However this is completely wrong. The passengers in EACH car all see the ray of light traveling at exactly the same speed. Their own velocity plays no part in it. The speed of light is a constant.

After explaining all that you're probably wondering why I wasted your time with this entire discussion, however, the immutability of the speed of light leads to some really perplexing problems.

Let's imagine three people: Albert, Bert, and Calvin.

Albert is sitting on a desert asteroid perfectly still. Unfortunately for Albert, Calvin has decided to murder Albert. He jumps in his star ship and zooms away from Albert at the speed of light (~186 thousand miles per second) to begin his escape and as he does so, he fires a deadly laser beam at Albert which is also traveling at light speed.

Fortunately the heroic Bert is determined to foil Calvin's evil plan and he jumps in his star ship and rockets off at light speed toward Albert, carrying a laser proof shield to save kind Albert's life.

In this very simple example, we have Calvin who is firing a laser beam at Albert which travels at the speed of light while he is traveling in the opposite direction from Albert, also at the speed of light.

Bert is traveling toward Albert at the speed of light and he has a shield which can deflect the laser. So essentially, Bert is racing the laser beam to reach Albert.

Let's assume that both Bert and Calvin start at the same place and that the laser beam and Bert both have an equal distance to travel.

What will happen? If Bert gets to Albert first, then he can deflect the laser beam with his special shield and Calvin's dastardly scheme will be thwarted. If the laser beam gets to Albert first, poor Albert will be killed instantly.

What will happen? It's important to remember that no matter how fast you are moving (or in what direction) you must always see a ray of light traveling at 186 thousand miles per second relative to you.

Some time later the space police manage to track down both Bert and Calvin and question them. They start with Bert.

Bert tells them a very sad story. He tried to save his friend Albert but even though his ship was traveling at lightspeed, (186 thousand miles a second), when he looked out of his window he saw the laser beam traveling at 186 thousand miles per second faster than him. Remember, no matter how fast Bert is traveling he must see that laser moving at light speed relative to him. This means that the laser struck Albert before Bert got anywhere close to him. Bert has failed in his mission and poor Albert is dead. The space police conclude this will be an open and shut case with this type of damning testimony and proceed to question the wicked Calvin. Calvin is at first unresponsive but then admits he did fire a laser beam at Albert. He saw the laser beam streak toward its target but as fast as the laser beam went, Bert's ship was far faster. He saw Bert's vessel fly toward Albert twice as fast as his laser (because Calvin's ship was moving in the opposite direction as Bert, from Calvin's point of view Bert's ship was moving with a velocity of Bert's speed plus Calvin's speed or ~372 thousand miles per second. Calvin must also see his laser beam moving at 186 thousand miles per second from his reference point) and thus he saw Bert reach Albert long before Calvin's laser beam. Bert has heroically saved Albert's life and Calvin's plan was thwarted.

Now the police are really confused (and I imagine so are you). Is Albert alive or dead? Bert swears that the laser struck Albert before he got anywhere near him but Calvin claims that Bert got there in time to save Albert. Who is correct?

In relativity remember there is no preferential frame of reference so who is correct in their recollections and is Albert alive or dead?