# Simple relativity

During the summer break, I got involved in the issue of whether time was relative, but before I can discuss that, I need to be sure readers understand what relativity is. Most would consider relativity to be essentially mathematical. Not really. The principle of relativity is quite simple, and goes back a long way. In Il Dialogo, Galileo pointed out that if you were below decks in a boat, you have no idea how fast it was going, nor for that matter, in what direction. You could get up on deck and work out how fast you were going relative to the water, but there is no absolute velocity, for if you can see land, you may have a different velocity if there is a tidal flow or current. Then, of course, the earth is rotating, orbiting the sun, the sun is orbiting the galactic centre, and the galaxy is also moving relative to other galaxies. The point is, unless there is a fundamental reference there is no absolute velocity, but only a velocity relative to something else, and that depends on your perspective. As Einstein once remarked when on a train, “The Zurich Railway Station is approaching, and will shortly stop outside the train.” Bizarre though that may sound, that encompasses relativity.

The simplest way to look at this is to answer the question, “Where are you?” There are two probable answers. One is “Here!” Not very helpful when half the population answer the same way, in which case “here” is a different place for different people. The second answer is to give an address, or coordinates. The means you are defining your position as being at some distance from something else. Velocities represent the rate of change of position, and are vectors, which means they have magnitude and direction. Coming and going have quite different effects. Think of standing in the middle of a road and there is a car on it. However, when direction is properly taken into account, velocities are additive, at least in Galilean relativity. Suppose we have two fleets of ships heading to each other. Each is entitled to consider itself as motionless in its own frame of reference, with the other fleet approaching at a velocity that is the sum of the vectors in a third frame of reference.

James Clerk Maxwell gave physics a huge problem by writing his equations of electromagnetism in the form of a wave equation, when he found the velocity of his wave was more or less equal to the known speed of light. Accordingly, he stated that light was an electromagnetic wave that travelled at velocity c. The problem was, relative to what? His equation equated the velocity to constants that were properties of space itself. Still, if the waves moved through something, namely aether, they would have a velocity relative to the aether. When Michelson and Morley carried out an experiment to measure this, they found nothing. (Actually, they found a very small velocity, but that was put down to experimental error because it did not reflect the earth’s movement properly.) For Einstein, the velocity of light was constant to any observer, and there was no aether, nor any absolute motion. Making sense of this involves mathematics that are a little more complicated than those of Newtonian physics, and now we have a problem as to what it means. The interpretation most people accept was proposed by George Fitzgerald and Hendrik Lorentz, and involved space contraction in the direction of motion. The basis of this can be imagined by considering two space ships flying parallel to each other, and going in a fixed direction. Suppose one sends a signal to the other that is reflected. The principle of relativity is from the space-ships’ point of view, the other ship is stationary, but from an external observer, the signal does not go directly to the other ship, but rather travels along the hypotenuse of a right-angles triangle, which now requires Pythagoras’ theorem to untangle the maths. Complicated?

There are some seemingly absurd results obtained from relativity, but it should be noted that these arise from what different observers, each travelling at near light speed, interpret an event they see. The complication is each sees the light coming to them at the same velocity, and this leads to some more complicated maths. Strange though it may seem, the equations always give correct agreement with observation, and there is little doubt the equations are correct. The question then is, are the observations and equations being properly interpreted? Generally speaking, the maths have taken relativity quite some distance, using a concept called space-time, and in that, time is always relative as well. It would generally be thought to be near impossible to solve anything of significance in General Relativity without the use of space-time, so it must be right, surely? In my Gaius Claudius Scaevola trilogy I make use of the time dilation effect. To fix a problem in the 23rd century, a small party of Romans have to be abducted by aliens in the first century. They travel extremely close to the speed of light, and when they return, they arrive at the right time, having burned through 2,200 years, and have aged a few years. Obviously, I believe time is relative too, don’t I? More next week.