Some might consider the chief elements of Einstein’s Special Theory of Relativity – the dilation of both space and time – to be a sort of “Cosmic Speed Limit,” and indeed, this does seem to be the case. For it is partly because of these two principles, which have become two very well-tested facets of science in the past century, that we have come to realize that, barring unforeseen breakthroughs, nothing will ever travel at or faster than the speed of light. In this sense, I suppose these principles are somewhat depressing, in that they seem to limit human potential, as far as the exploration of our universe is concerned.

On the other hand, time and space dilation are extremely interesting and can be very fun to study, so perhaps it all cancels out in the end.

## Adding Velocities

What exactly are these principles, and how do they relate to the principle of relativity? You see, as Einstein was exploring the idea of the speed of light as a perpetual constant (to denote this he used the term “C” in his equations, which became shorthand for the speed of light, roughly 300,000 km/s), he realized that he had to find a way to reconcile the fact that different observers, even traveling at very different speeds, both measured the speed of a single source of light to be the same. In the minds of most logical thinkers, the speed of anything should be measured in relation to our speed relative to that thing. In other words, if one car is moving down the road at 50 per hour and another car, traveling 55 miles per hour passes it, their speed *relative to each other* is only 5 miles per hour. If the second car was replaced by a ray of light, however, that light would pass by the car at exactly the speed of light, no matter what the car’s speed.

This surely seems bizarre to most people today, just as it did in the early twentieth century. Einstein, though, using techniques developed by Maxwell and Lorentz in decades prior to his 1905 breakthrough, began to come to terms with this fact, and even figured out how to explain it.

Einstein’s conclusion was this: Time and space are not absolutes. They are not invariable, nor do they always retain the same values. The only way the speed of light can possibly remain constant is if, as an observer travels at different speeds, that observer’s own perception of time and distance must change as well. Skipping past some of the complex mathematics (actually, it’s not *too* complex when compared to other fields of physics), Einstein concluded that as a person moves faster, their own perception of time slows down accordingly (though normally to such a small degree that it is hardly even measurable, unless one is moving very quickly). Furthermore, the faster one travels, the smaller they would appear to an outside observer – contracted in the direction of motion. If this was the case, then according to Special Relativity, as one’s perception of time and distance changed according to their speed, light could always be measured at the same speed.

## Finding the Shrinking Factor

How, exactly, does this prevent us from ever traveling the speed of light? Simple. The dilation equations that Einstein published look like this:

S = √(1 - v²/c²)

It is fairly simple to use – just enter in your speed (v) and solve for “S”, which gives you your “shrinking factor” (remember that “c” stands for the speed of light – 300,000 km/s). If your shrinking factor ends up as .75, then you will have shrunk down to three quarters of your original size and time will have slowed down accordingly. So far, so clear.

Generally, with any speed human beings have been able to attain, the shrinking factor is very small, somewhere on the order of 0.99999. We hardly shrink at all, and time keeps moving. This number continues to stay very small until one begins to approach the speed of light. Then things start to get very peculiar.

Now, let’s say that you want to find out what would happen if you traveled the speed of light. Plug in the numbers and you end up with a problem: S = 0. You’ve just shrunk down to absolute nothing and time has stopped. You don’t exist, and it seems that you will be forced to stay that way for eternity. Not exactly a pretty picture – but fortunately, it doesn’t appear possible, either, so we don’t really have to worry. If we *could* get over that little speed hump, however, the numbers start becoming even stranger, and, some have conjectured, time begins to move backward and whatnot… but it doesn’t appear that anyone will experience that anytime soon, either.

For now, it is important to appreciate the fact that Einstein was finally able to solve the problems with light, and he was able to show the world that time and space were more flexible than they appeared.

Not bad for a mere patent clerk in Switzerland.

For more on the mathematics of time and space dilation, visit the Suite101 article, Solving Time and Space Dilation.

References:

Einstein, A. (1905). On the Electrodynamics of Moving Bodies. *Annalen der Physik* .

Einstein, A. (1961). *Relativity: The Special and the General Theory - A clear Explanation that Anyone can Understand.* New York, NY: Random House.

Gardner, M. (1962). *Relativity Simply Explained.* Mineola, NY: Dover Publications, Inc.

Davies, P. (1995). *About Time - Einstein's Unfinished Revolution.* New York: Simon & Schuster.

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