A Briefer History of Time Read Online Free PDF Page B

the Michelson-Morley experiment showed, cannot be detected. Instead, the theory of relativity forces us to change fundamentally our ideas of space and time. We must accept that time is not completely separate from and independent of space but is combined with it to form an object called space-time. These are not easy ideas to grasp. Relativity took years to become universally accepted even within the physics community. It is a testament to Einstein’s imagination that he was able to conceive it, and to his confidence in his own logic that he worked out its consequences despite the odd conclusions toward which it seemed to be leading.
    It is a matter of common experience that we can describe the position of a point in space by three numbers, or coordinates. For instance, we can say that a point in a room is seven meters from one wall, three meters from another, and five meters above the floor. Or we could specify that a point is at a certain latitude and longitude and a certain height above sea level. We are free to use any three suitable coordinates, although they have only a limited range of validity. It would not be practical to specify the position of the moon in terms of miles north and miles west of Piccadilly Circus and feet above sea level. Instead, we might describe it in terms of distance from the sun, distance from the plane of the orbits of the planets, and the angle between the line joining the moon to the sun and the line joining the sun to a nearby star such as Proxima Centauri. Even these coordinates would not be of much use in describing the position of the sun in our galaxy or the position of our galaxy in the local group of galaxies. In fact, we may describe the whole universe in terms of a collection of overlapping patches. In each patch, we can use a different set of three coordinates to specify the position of a point.

    Coordinates in Space
    When we say that space has three dimensions, we mean that it takes three numbers, or
coordinates,
to specify a point. If we add time to our description, then space becomes space-time, with four dimensions.
    In the space-time of relativity, any event—that is, anything that happens at a particular point in space and at a particular time—can be specified by
four
numbers or coordinates. Again, the choice of coordinates is arbitrary: we can use any three well-defined spatial coordinates and any measure of time. But in relativity, there is no real distinction between the space and time coordinates, just as there is no real difference between any two space coordinates. We could choose a new set of coordinates in which, say, the first space coordinate was a combination of the old first and second space coordinates. So instead of measuring the position of a point on the earth in miles north of Piccadilly and miles west of Piccadilly, we could use miles northeast of Piccadilly and miles northwest of Piccadilly. Similarly, we could use a new time coordinate that was the old time (in seconds) plus the distance (in light-seconds) north of Piccadilly
    Another well-known consequence of relativity is the equivalence of mass and energy, summed up in Einstein’s famous equation E=mc 2 (where E is energy, m is mass, and c is the speed of light). People often employ this equation to calculate how much energy would be produced if, say, a bit of matter was converted into pure electromagnetic radiation. (Because the speed of light is a large number, the answer is a lot—the weight of matter converted to energy in the bomb that destroyed the city of Hiroshima was less than one ounce.) But the equation also tells us that if the energy of an object increases, so does its mass, that is, its resistance to acceleration, or change in speed.
    One form of energy is energy of motion, called kinetic energy. Just as it takes energy to get your car moving, it takes energy to increase the speed of any object. The kinetic energy of a moving object is identical to the energy you must expend in