SPECIAL THEORY OF RELATIVITY

In the Special Theory of Relativity, published in his so-called “miraculous year” of 1905, Einstein turned the question around and asked: what must happen to our common notions of space and time so that when the distance light travels in a given time is measured, the answer is always 300,000 km/s? For example, if a spaceship fires a laser beam at a piece of space debris flying towards it at half the speed of light, the laser beam still travels at exactly the speed of light, not at one-and-a-half times the speed of light. He began to realize that either the measurement of the distance must be smaller than expected, or the time taken must be greater than expected, or both.

In fact, the answer is both: space “contracts” and time “dilates”, and both space and time are therefore relative concepts, with only the unvarying speed of light providing the bedrock on which the universe is built. This revolutionary idea flew in the face of the long-held notion of simultaneity (the idea that events that appear to happen at the same time for one person should appear to happen at the same time for everyone in the universe) and suggested that it was impossible to say in an absolute sense whether two events occurred at the same time if those events were separated in space.

In a nutshell, the Special Theory of Relativity tells us that a moving object measures shorter in its direction of motion as its velocity increases until, at the speed of light, it disappears. It tells us that the mass of a moving object measures more as its velocity increases until, at the speed of light, it becomes infinite. It also tells us that moving clocks run more slowly as their velocity increases until, at the speed of light, they stop running altogether.

Thus, one person’s interval of space is not the same as another person’s, and time runs at different rates for different observers travelling at different speeds. To some extent, the faster you go, the slower you age and the slimmer you are! The reason this is not obvious in everyday situations is that the differences at everyday speeds are infinitesimally small, and only really become apparent at speeds approaching that of light itself (“relativistic” speeds). The closer the speed of an objects approaches to the speed of light, the more warped lengths and time intervals become.

(Click for a larger version) At relativistic speeds, space “contracts” and time “dilates” (Source: Time Travel Research Center: http://www.zamandayolculuk.com/cetinbal/ HTMLdosya1/RelativityFile.htm)

A couple of other examples may help to make the effects of relativity fully clear. Experiments have been carried out where two identical super-accurate atomic clocks were synchronized, and then one was flown around the world on an airplane while the other stayed at home. The clock which travelled recorded marginally less passage of time than the other (as predicted by the theory), although the difference was of course minimal due to the relatively slow speeds involved.

If it were possible to travel in a spaceship at 99.5% of the speed of light, however, a hypothetical observer looking in would see the clock moving about 10 times slower than normal and the astronaut inside moving in slow-motion, as though through treacle. An ultra-short-lived muon particle, which habitually travels at 99.92% of the speed of light, actually lives about 25 times longer and travels 25 about times further than it theoretically should for this same reason.

A corollary of all this is that, if it were possible to exceed the speed of light, then it would also be possible to go back in time, which raises the possibility of time-travel paradoxes (where a person goes back in time and interferes in their own past or kills their own grandparents, etc), although some scientists believe that some as yet undiscovered law of physics may intervene to prevent such paradoxes. Actually, special relativity does not forbid the existence of particles that travel faster than light at all times, and there is a hypothetical sub-atomic particle called a tachyon, which does indeed spend its entire life travelling faster than the speed of light, but it is currently still hypothetical.

(Click for a larger version) In the "twins paradox", a space traveller returns to Earth younger than his twin (Source: The Reference Frame: http://motls.blogspot.com/ 2007/02/resolving-einsteins-twin-paradox.html)

Another paradox associated with the dilation of time is the so-called “twins effect” or “twins paradox”, where an astronaut returns from a near-light speed voyage in space to find his stay-at-home twin many years older than him (as travelling at relativistic high speeds has allowed him to experience only one year of time while ten years have elapsed on Earth). This is considered a paradox in that each twin sees the other twin as travelling, so each should see the other aging more slowly, but one twin (the one which experienced acceleration and deceleration) really does age less.

Essentially, then, the Special Theory of Relativity can be boiled down to its two main postulates: that physical laws have the same mathematical form when expressed in any inertial system; and the speed of light is independent of the motion of its source, and will have the same value when measured by observers moving with constant velocity with respect to each other. Not such a scary proposition at first glance, perhaps, but it does lead to some rather interesting implications, which we will begin to consider in subsequent sections.