Time Travel, Part One

This essay was substantially too long for a single post, so I divided it into two sections. Today's section deals with the problems special relativity poses to time travel. Tomorrow's will deal with the possiblities general relativity and alternative geometries open up for time travel.

The question of whether time travel is possible can be divided into three parts: first, whether travel into the future is possible; second, whether travel into the past is possible; and third, whether some sort of curvature of time would make travel into the past possible, since it is also our future. The first, travel into the future, is possible, since special relativity allows for the twins paradox, in which time passes much more slowly for a person who travels close to the speed of light relative to a given inertial frame. The second, travel into the past, appears to be impossible, since it would require that a body be accelerated past the speed of light. The third would be the only way to travel into the past, but it would require alternative geometries of spacetime that may or not exist, and would imply paradoxes that perhaps cannot be overcome. I will deal with each of these in turn, referring primarily to special relativity, and what it teaches us about the equivalence of inertial frames.

Time travel into the future is in some sense possible. By accelerating to high speeds and then returning to Earth, it would make our time slow down significantly. This is not "true" time travel, as envisioned by Wells, in which the traveller simply disappears at one point in time and reappears at another point in time. In some sense, we are travelling to the future all the time - travelling to high speeds would simply enable us to survive the trip past our natural life spans. An immortal being with infinite patience would not have any interest in this process. It would, however, enable a traveler to travel, say, one thousand years in only a one-year "trip". As a traveller approaches the speed of light, he or she sees the original frame of time slow down according to a Lorentz transformation, t=1/(1-v²/c²)^½. As one can see, as v approaches c, the denominator approaches zero, and the time elapsed approaches infinity. If one then returned to one's original inertial frame, much more time will have passed in the original frame than in one's own. The traveller could then travel back to Earth, again slowing time relative to the traveller's frame, and would return with only a small amount of time elapsed relative to the time passed on Earth. This is known as the "twins paradox", as two twins, one of whom boards such a time-travelling space ship, and another who waits at home, would be very different ages by the time the travelling twin returned. As such, time travel to the future of a sort is possible, in the sense that a person can hasten the Earth's time relative to himself or herself, and take a shorter trip through spacetime.

Time travel to the past is more complicated and most likely impossible. Though one may be able to "slow time down" relative to oneself (or speed it up, if one somehow managed to put Earth on a spaceship and send it away very, very fast), this is far from causing time to go backwards. No matter how much one slows down time, it is just slowed down. However, looking at the original transformation, t=1/(1-v²/c²)^½, one can see that if v were higher than c, the denominator would become imaginary. This would enable the traveller to travel back through time. It seems that if one had an even faster spaceship, one could leave earth and then return at an even earlier time. Unfortunately, acceleration past the speed of light is not possible, as the Lorentz transformation applies to mass as well as space and time. Let m be the mass of an object relative to a measuring frame, and let m₀ be its mass relative to its own frame. In this case, m= m₀/(1-v²/c²)^½. Just as with time, relative mass would increase toward infinity as the object approaches the speed of light, as the denominator would approach zero. It would take an infinite amount of force, then, to accelerate an object to or past the speed of light relative to a given frame, and it is impossible to generate an infinite amount of force. Therefore, no object can travel faster than the speed of light, and travel backwards in time would be impossible through the "acceleration method" we used to travel forward in time. While an object may take an infinite amount of force to accelerate to the speed of light, analogously, an object that was already travelling faster than the speed of light would take an infinite amount of force to decelerate to c. Hence, one would need to take into account one's "starting speed". These theoretical "faster than light" particles have been called "tachyons" (from the Greek word tachys, meaning "fast"). However, no one has ever seen evidence of these tachyons, though whether this is because they do not exist or because their backwards travel makes them impossible to interact with is uncertain. Were they even to exist, it would not solve the problem that we are not ourselves travelling faster than the speed of light, and could never accelerate to such a point.

To be concluded tomorrow...