While the vast majority of the equations used on a daily basis by physicists are so difficult to most people who lack PhD's in the subject that it seems as if nothing more than a particularly nonsensical foreign language, there are a few bright spots in the subject - equations which can be utilized even for entertainment value, and by those who know just the most basic concepts of high school algebra.
Einstein's Time Dilation
In Einstein's special theory of relativity, one of his momentous conclusions is the idea of dilation of both space and time. He said that as an object moves faster and faster (i.e. closer and closer to the speed of light), any perception of time within this object slows down accordingly, relative to an object at rest.
Similarly, the same equation can be used to show that from the perspective of an object at rest, a moving object appears to "contract" in the direction of motion as it comes closer to the speed of light.
In other words, if one was able to watch a particularly fast spaceship fly overhead at a speed of 3/4 the speed of light (about 300,000 kilometers per second), to this observer, the spaceship would be measured to be slightly smaller than its actual length, and to any person on board this ship, time would be moving slightly slower.
What manner of complex equation is used to determine the degree to which both of these phenomenon take place?
The Shrinking Factor
It's very simple, actually:
D = √(1-(v²/c²)
Where D is the "shrinking factor," or the percentage of the original size to which time and space shrink. v is the object's velocity, and c is the constant speed of light (300,000 km/s).
Now, even a non-mathematician can perform some fun experiments with this equation. Simply plug in some potential velocities for v and solve for D.
What will be revealed after a few attempts, hopefully, is that this equation really carries with it very little meaning until the speed becomes very close to the speed of light. In other words, at speeds even which seem relatively quick to the human mind, time and space dilation still remain practically zero.
Even at the incredibly quick pace of 100,000 kilometers per second (far faster than anything larger than an atom has ever been propelled by humans), the value of D is .9428. This means that time will have slowed down by about 5% and the length will have contracted by the same amount.
As the velocity approaches very close to the speed of light, however, one may notice a dramatic drop in the shrinking factor. Finally, at monumental speeds (200,000 km/s = 0.75; 250,000 km/s = 0.55; 290,000 km/s = 0.256; 299,999 km/s = 0.0025).
Traveling the Speed of Light?
A student of calculus might notice that this equation seems to imply that at a value equal to the speed of light, there is what is called a limit.
This means that while approaching the speed of light, the values ebb closer and closer to zero at an exponential rate, actually plugging in the values for an object traveling the speed of light reveals an error in the equation. Because it is mathematically pointless to find the squre root of zero, the expression √(1-(v²/c²)) returns a value of just that - zero.
According to Einstein's equation, in other words, an object traveling at the speed of light would have its perception of time drop to zero (suddenly time would become infinite), and its percieved length would drop to zero (it would disappear).
These are two of the important reasons that Einstein declared it a fundamental impossibility to ever travel at or beyond the speed of light (the reader is encouraged to experiment with the equation and see what happens if an object does excede this "magical" limit.)
This equation is a good one for those who are interested in science, but who do not possess the mathematical skills (nor the time to learn them) that would be required for more advance studies. The "shrinking" equation can be pulled out at a moment's notice to have fun by calculating one's own "shrinking" factor in a car or airplane (though don't be surprised when the answer turns out to be 0.99999999996).
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