This will be a continuation of an exposition of Einstein’s theory of special relativity, by Russell Stannard. A mission controller who observes the astronaut whom he is communicating with, will see time passing slowly for the astronaut. The astronaut himself will experience time as normal. Does this mean that the astronaut sees time speed up for the mission controller? This would allow us to see who is “really” moving and who is “really” stationary. It would mean that the astronaut was really moving and that the controller is stationary.
This would violate the principle that for inertial all motion is relative, however. Instead, the astronaut will conclude that the controller’s clock is moving more slowly than his, just as the controller has concluded that the astronaut’s clock is moving more slowly than his. But how is this possible? Keep in mind that the clock comparison is not a side-by-side comparison. Initially, the astronaut and controller may have synchronized their clocks.
The controller then founds out how the astronaut’s clock is doing by waiting for a signal to be emitted by the astronat’s clock. He then adds the transmission time to the reading of the clock. This allows him to calculate what the time is on the other clock at that time, as opposed to the reading of his own clock. This allows him to conclude that the other individual’s clock is running slowly. Both will conclude that the clock of the other individual is running more slowly. This is known as the twin paradox.
But what if we were able to compare the clocks side by side? Either the clocks, when compared, will be the same time, or one will be found to be slower than the other; but it would be absurd to say that each of the two is slower than the other. The muons described in the initial experiment provide us with our answer. The muons travel in a circular path and play the part of the astronaut. They begin at a specific point in the laboratory, engage in their circuit and then return to the point at which they began. The traveling muons will have been found to age less than the others, and this demonstrates whose clock is moving more slowly.
But does this not entail a violation of the principle of relativity? After all, we seem to have determined whose clock was “really” moving. Since the principle only applies to inertial observers, the principle is not violated. The astronaut occupied an inertial frame of reference during his steady speed as he traveled away from earth, and likewise again on his return. However, when the spacecraft makes its return, the rockets were fired, causing the ship to no longer occupy an inertial reference frame.
Since Newton’s law of inertia no longer applied here, only the observer in the initial frame during the entire trip (the controller) could be justified in applying the time dilation formula. This means that when he concludes that it is the astronaut’s clock who has been running more slowly, that is what one will find when the two are compared. It is because of the period of acceleration undergone by the astronaut that the symmetry between both observers is broken, resolving the paradox.
Indeed, the astronaut knows that he has not stuck to the condition of remaining in a steady or inertial state for the entire duration of the trip. As he travels at a steady rate away from the controller, the latter’s clock appears to be moving more slowly than his own. The astronaut can conclude that the controller will fall even further behind as he begins to travel back to the controller. In light of this, how could the controller’s clock get ahead of the astronaut’s? Is there any way the astronaut could have determined in advance that the controller’s clock would be ahead of the astronaut’s? Yes, there is.
In fact, things become even more complicated when talking about the speed of the craft and its distance from earth when it reaches another planet. True, the mission controller is capable of determining in advance how long the journey will take, thanks to his clock. The astronaut can do something similar. But does not the astronaut have a different time as a result of time dilation? Does this not mean that he will find that he has arrived too soon? After all, he could not possibly have covered the distance at the astronaut’s speed at the latter’s reduced time. This means that he must be the one really moving after all, thus violating the principle of relativity.
How is the dilemma solved? Both observers are agreed with respect to their relative speed. Instead, the problem has to do with their estimates of the distance from the earth to the planet. Consider that both individuals have their own time. He has his own estimate of the distance, meanwhile, while the astronaut has his own estimate of the distance. The two measures of distance differ in the same ratio as the times differed. Therefore, the astronaut is content about his arrival at the planet. The astronaut’s clock is slower than his because the astronaut has not traveled as far as the controller says the astronaut has. The astronaut says that the journey time is 4/5 of what the controller says it is, since the astronaut insists that he has traveled 4/5 of this distance. Therefore, the astronaut’s estimates of both time and distant are internally consistent. Indeed, the same is true of the controller; his own estimate of his time and distance are internally consistent.
Thus, relativity theory affects not only time, but also space. For the astronaut, everything moving relative to him is “contracted” or squished. This is true of both the distance between earth and the planet, as well as to the shape of the earth and of the planet as well. They are no longer spherical. Distances in the direction of the motion are contracted. This means that distances at right angles to this motion are unaffected. This is known as “length contraction.”
It should come as no surprise that what applies to the astronaut also applies to the controller . Distances moving relative to him are contracted. Suppose the craft is traveling at such and such a speed. The length of the craft will be 4/5 of what it initially was prior to its blastoff. This is true, not only of the craft, but its contents. The astronaut will not feel himself flattened, however. This is because space itself has contracted. Indeed, the atoms themselves will be contracted, reducing in size in the direction of the motion, and therefore no longer needing as much space to fit inside his body. But should the astronaut not see that everything in the craft is squashed? No, because the astronaut’s retinas are squished in the same ratio, along with the scene he is observing.