Extraterrestrial Civilizations - Isaac Asimov [113]
The “common sense” that makes it so difficult to accept the limitation is based on our experience with everyday phenomena. We notice that if we keep pushing an object, it goes faster and faster and faster. In fact, Newton’s second law of motion specifically states that this is so and that an equal push will always result in an equal speedup regardless of how fast the object is already moving. It would therefore seem that no matter how fast we make an object move, we can always make it go still faster by giving it an additional push. Indeed, careful observation and measurement bear this out under ordinary circumstances.
But that is because we deal with objects that go only a tiny fraction of the speed of light, and under such circumstances Newton’s second law does indeed hold as far as we are able to measure and “common sense” reigns supreme.
The truth is, though, that if we give an object a push and make it speed up, and then give it a second push of just the same size, the amount by which the object speeds up the second time is not quite as high as the first time. Some of the force of the push goes into increasing the speed, yes; but some goes into increasing the mass as well.
At ordinary speeds, so little of the force goes into increasing the mass that that portion is undetectable. As the speed goes higher and higher, however, a larger and larger fraction of the force goes into increasing the mass and a smaller and smaller fraction into increasing the speed, according to a formula worked out by Einstein. When the speeds are high enough, so much of the force goes into mass and so little into additional speed that we begin to notice that Newton’s second law and “common sense” aren’t working anymore.
It wasn’t until the opening of the twentieth century that scientists knew of any objects that moved fast enough to begin to show the imperfection of the second law. The fast-moving objects then discovered were subatomic particles, and careful studies of these tiny objects showed that Einstein’s equation relating force and speed was exactly right.
By the time the speed of any object gets close to the speed of light, hardly any of the force applied to it goes into additional speed. Almost all of it goes into additional mass. The speeding object becomes much more massive, but hardly any more speedy. In the end, even if you put an infinite amount of force into the speeding object, you can only serve to give it an infinite mass and raise the speed only to the speed of light.
That means that even if you accelerate to maximum speed in an instant by some magic device, it would still take you 4.40 years to reach Alpha Centauri. If you could then decelerate to zero in an instant, turn around, accelerate to maximum speed in an instant, it would still take you 8.80 years to make a round trip.
In actual fact, you would have to accelerate to a very high speed, and that would take a long time if you confine yourself to an acceleration low enough for the human body to endure. It would then take an equally long time to decelerate so that it would be possible to land on a planet in the Alpha Centauri system.
The need to accelerate and decelerate would add about a year to the time it would take to reach a star if we were to travel at the speed of light all the way. Another year would have to be added on the return, and a third year, perhaps, for the time taken in exploration.
Thus, if we count in acceleration, deceleration, and exploration, the time taken to go to any star and return is the speed-of-light round trip plus three years.