Why can't we Travel Faster than Light?
By Clint W.


In Calculus, there is something called the intermediate value theorem, which basically states that for any continuos function, between any two points, every real intermediate value is attained by the function. So, if a function contains the point (5,3) and the point (9,12), y has every real number value between 3 and 12 on the interval between x=5 and x=9, assuming this function is continuous.

In motion, we do not expect this at all. Velocity is described by something called "meters per second" (or, more prevalently, miles per hour) which, once you break it down to the smallest possible unit of time, indicates a body moving some distance in the transition between one real value of t (we will call it a moment) and the next. This would all be good and well if every object moved with the same velocity, because we would simply have to regard the distance traversed between one moment and the next as the smallest possible distance in our universe (we'll call it a quantumeter), but of course everything does not travel with the same velocity. Therefore, it appears that some objects literally jump from one point in space to the next in a single moment. This peculiar concept led me to considerable thought.

In 1865, James Clark Maxwell set forward the idea that light was an electromagnetic disturbance that moved away from an observer at a constant rate regardless of the motion of the observer (a strange concept indeed!). Later, Einstein used this truth to go about dismantling everything we knew about the universe with the theory of relativity which proposed that light traveled at the fastest velocity possible in the universe. This brings us to our question: why is the velocity of light the fastest possible velocity in the universe?

This is not to be confused with the question "Why does light travel at the fastest possible velocity in the universe?". This question can be answered relatively easily, even using Newtonian physics. Newton states that the kinetic energy of a particle is equal to its velocity squared times its mass. Since a photon (the particle that composes light) is massless, it is free to attain any velocity at all as this would seem to require no additional energy. 0 g times any real velocity squared is still zero joules.

Let us recap. We know that light travels at a constant velocity, and we are quite certain that this velocity is the fastest possible velocity in the universe. We also know that displacement as we know it seems to defy the rules of continuity since an object being displaced more than one quantumeter in one moment would necessarily mean that object never occured in the intermediate positions. but now it might occur to you there is a very simple way to reconcile physics and Calculus...

What if velocity was merely a probability function, expressing the likelihood that an object will move at all in a moment (which, remember, we are defining as the very smallest possible unit of time)? This would mean that when you are traveling very close to the velocity of light, you are not actually moving any further in one moment than if you were traveling much more "slowly", but rather, you have a greater probability of moving at all in any given moment. Seeing as how there are likely to be an overwhelming number of moments in even one second, it would make sense why this effect were all but unnoticeable... if you flip a fair coin a billion times, the percentage variation from the coin landing on each side 50% of the time would be negligbly small.

This would also explain why a speed limit would occur in the universe: light, with a velocity of c, would have a 100% probability of moving a quantumeter in any given moment, meaning that in every moment it moves one quantumeter, and, further, meaning the intermediate value theorem would hold. There could be no velocity greater than c because a probability greater than 100% simply has no meaning.

Therefore, we have reached the conclusion of my thought. It very well could contain some blaring oversight which will lead to me being ridiculed the rest of my days. However, allow me to share the bit of inspiration which began this train of thought.

Let us look at one of Einstein's equations for kinetic energy of a particle undergoing translational (rather than rotational) motion. As such, E is the kinetic energy of the particle, m is the mass of the particle, c is the constant for light and v is the velocity of the object. Notice the section at the bottom where we have velocity squared over the speed of light squared. We have a fraction in which the bottom number will always be larger (and sometimes much larger) than the number on top, leading to a number between 0 and 1. Sounds a lot like a probability to me.

From there my crazy brain took over until I finally came to my conclusion. Could it be that velocity squared divided by the speed of light squared represents the probability that an object will move during a given moment?

Of course, the hard part would be proving this crazy idea. I think I have a basic notion of how you would go about creating evidence for the concept, but it would take some very accurate instruments: You would need to set up an apparatus, apply very specific forces to a particle (just enough to set it along at a specific velocity and then to keep it there). Plus, you would need a way to measure, with great precision, how long it takes to travel between two points. Then you would need to repeat this many many times and compare your results with those you would expect to get if velocity were actually a probability function. Creating these "expected results" would be fairly easy using computer simulations. If the standard deviation of the "expected results" matched well with that of the experimental results, that would be one step toward proving this crazy idea.