Thrawn Rickle 79THE COSMIC SPEED LIMIT REVISITED© 2004 Williscroft 
Professor Albert Einstein actually developed two theories of relativity: the Special Theory of Relativity in 1905, and ten years later the General Theory of Relativity in 1915. For you non technical readers, remember that for scientists and engineers, the word “theory” means a “modelderived” solution. When a scientist wants to describe what you call “theoretical,” he uses “hypothetical.” According to the Special theory, matter, the stuff that makes up everything around us — air, furniture, ground, water, cars, etc. — behaves quite differently when it moves at high speed than when it is at rest. When you fire a bullet from a gun, although it is not at all obvious, the speeding bullet gets heavier. The amount is so small that it cannot be measured by any laboratory device we have, but this is only because a speeding bullet really is moving quite slowly, when compared to the speed of light. If you were to accelerate the bullet so that it was moving at some significant fraction of light speed, its increase in mass would be very apparent. Furthermore, if you were to accelerate it to the speed of light, its mass would become infinite, an obvious impossibility, since it would take an infinite amount of energy to get this infinite mass to light speed. This characteristic, strange as it seems, is one of the fundamental facts of the universe — things that move fast increase their mass; they get heavier. This becomes a practical matter in a cyclotron where subatomic particles are accelerated to very high speeds. As their speed becomes a significant fraction of light speed, they become very much heavier so that the accelerating magnets have to be given a great deal more power just to keep things going. A second interesting effect for objects moving at very high speed is that a speeding object gets thinner in the direction it is moving. As before, this effect can only be observed when the object is moving at a significant fraction of light speed. If you were to move an object at the speed of light, it would become infinitely thin, a third impossibility. This effect also has practical implications in highspeed particle research. A very fast moving particle of known size actually appears thinner than when it is at rest. Sensors must be calibrated to take this into account, or they can’t even see the particles. Another strange effect at high speed is that time slows down for a rapidly moving object. Several years ago, the amount of this slowing was physically measured when a satellite was orbited containing a highly accurate atomic clock, while the twin of the clock remained on the earth’s surface. Even though the satellite’s speed still was slow when compared to light speed, it was sufficiently fast for the slowing of the satellite’s time to be measured by the two identical clocks as their initially synchronized times began to move apart. Another way to look at this phenomenon is to view an object moving through spacetime as a simple vector. Imagine a grid with velocity laid off on the vertical axis and flow of time laid off on the horizontal axis. A real object can be represented as an arrow starting at the zero point, and pointing up into the grid. According to Einstein’s Special Theory of Relativity, the length of this arrow or vector is constant, represented by the speed of light. This means that in the spacetime continuum (as opposed to just space) all objects have constant motion; all objects move through spacetime at exactly the same rate. On the vector diagram, this is equivalent to saying that the object is represented by a vector, an arrow with constant length.
RELATIONSHIP OF SPACE AND TIME IN THE UNIVERSE In our diagram, the direction the vector points and its constant length (which is fixed by the speed of light) determines the amount of the vertical component, the “space” velocity, and the amount of the horizontal component, the “time” velocity. From the tip of the arrow, draw a line straight across to the velocity axis to get the space velocity component. Drop a line straight down from the arrow point to the time axis to get the time velocity component. In effect the object’s total constant velocity through spacetime is the “vector sum” of the velocity through space and of the movement through time.
HOW WE NORMALLY EXPERIENCE SPACE AND TIME For objects in our normal existence, the vector or arrow on the grid points nearly horizontally, because the object’s speed — its velocity component on the vertical axis of the diagram — is very small, even for highspeed aircraft and satellites. Because of this, the vector consists mostly of the time component. Any small changes we make to the vertical axis of the diagram have very little effect on the horizontal part of the vector.
SPACE
AND TIME AT VERY HIGH VELOCITY Since the length of the vector does not change, as we add more velocity to the “space” component, to the vertical axis, the vector begins to swing upward, so that we see increasing reduction of the horizontal component, the “time” element. In other words, as the velocity through space increases, in order to maintain the constant length of the vector, the motion through time decreases.
SPACE
AND TIME AT LIGHT SPEED If we rotate the vector all the way to the vertical, all of its velocity through spacetime consists of the vertical component — velocity through space, and the object would be moving at the speed of light; none of the vector velocity would consist of the horizontal component — movement through time. In other words, if an object were to move at the speed of light, time would cease to exist for it, another obvious impossibility. We see this effect clearly in subatomic particle research, where once again these effects have practical significance. If you fire a radioactive particle with a halflife of a microsecond at a target, you can move the target far enough away from the source that the particle will decay before it hits the target. But if you fire the particle with a speed that is a significant fraction of light speed, because time slows down for the fast moving particle, it arrives at the target before it decays, whereas calculations that ignore this effect indicate that it should have decayed before arriving at the target. In other words, the “timedilation” effect must be considered when running experiments using radioactive highspeed particles. Here is another, more practical example of how timedilation can affect real people in the real daytoday world. Imagine that we live sufficiently far into the future so that travel between stars is routinely possible. People can purchase tickets for transport from Earth to the Sirius doublestar system, for example, about nine lightyears distant. Let us imagine that you are onehalf of a twin set—say two brothers. You are both the same age, of course. One of you decides to take the grand tour out to Sirius, stay there for a year, and then come back. The other prudently decides to remain safely on Earth. In any real example like this, we would have to discuss how we intend to accelerate the starship to near light speed, from where we might obtain fuel, etc. For our thought experiment, however, we’ll just assume that somehow humans have developed the necessary technology to accomplish this. We will assume some time accelerating to speed, and finally some time decelerating back to normal speed, during which the traveling twin ages at approximately the same rate as his brother. Of course, during his time in the Sirius system he will also age at the same rate. But for the time spent near light speed both on the outbound and the return trips, the traveling twin’s time line will nearly stop. If we generously allow six months to accelerate and six months to decelerate on both the outbound and return legs, plus the year in the system, for three years the traveling twin will age at about the same rate as his brother back on Earth. If they really get close to light speed, the “subjective” time experienced by the traveling twin will be several weeks at most on each leg, say a month and a half out and the same back, for a total of three months, during which time the brother on Earth will age eight years for the outbound leg and another eight years for the return leg. Thus, upon the traveling twin’s arrival back on Earth, he will have aged three years and three months, while his twin brother will have aged nineteen years and three months. The implications of this very real phenomenon are astounding. Once you have accelerated to near light speed, the difference between “rest” time and “subjective” time reaches astonishing heights, so that—at least hypothetically—a traveler could cross a significant part of the known universe and return, having aged only several years, while millions or even billions of years would have passed back on Earth. To people on Earth or on any other planet for that matter, it would seem a form of time travel, but only moving forward. The traveler, on the other hand, would experience a normal “subjective” lifetime, but with each trip out and back, would leap into the future by an amount dependent upon how far and how fast the traveler went. This ultimately would develop into two entirely different societies. The one would consist of people living at “rest,” with respect to their universe, like we do today. The other would consist of people who continuously leaped forward in time. By properly calculating the jumps and intervals, they would be able to synchronize aging or catch up with another person, or fall behind, but all the while living a normal span of “subjective” life. Yet these people would appear as immortals to people trapped in the “resttime” universe, since they would appear from time to time during a regular lifetime, without any apparent aging or other signs of time passing. Each of these effects becomes more pronounced as the object’s speed approaches light speed. In fact, at light speed, an object’s mass becomes infinite, time stops, and it becomes infinitely thin — things which obviously cannot happen in any real universe. Hence, in the world in which we really live, nothing can exceed the speed of light — the cosmic speed limit. It may turn out that there is no way to bring about an acceleration to near light speed. If this turns out to be true, then our discussion becomes nothing more than a pleasant distraction. If, on the other hand, we eventually discover how to accelerate to near light speed and maintain ship’s integrity, and the million and one other things that will become necessary to accomplish this task, then we humans will be able to spread throughout the known universe. Who knows what we may discover; what we may become?
