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By Root 2124 0

dimensions in which we find ourselves immersed. Although it sounds abstract, the notion of time as a dimension is actually concrete. When we want to meet someone, we tell them where "in space" we will expect to see them—for instance, the 9th floor of the building on the corner of 53rd Street and 7th Avenue. There are three pieces of information here (9th floor, 53rd Street, 7th Avenue) reflecting a particular location in the three spatial dimensions of the universe. Equally important, however, is our specification of when we expect to meet them—for instance, at 3 P.M. This piece of information tells us where "in time" our meeting will take place. Events are therefore specified by four pieces of information: three in space and one in time. Such data, it is said, specifies the location of the event in space and in time, or in spacetime, for short. In this sense, time is another dimension.

Since this view proclaims that space and time are simply different examples of dimensions, can we speak of an object's speed through time in a manner resembling the concept of its speed through space? We can.

A big clue for how to do this comes from a central piece of information we have already encountered. When an object moves through space relative to us, its clock runs slow compared to ours. That is, the speed of its motion through time slows down. Here's the leap: Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed—that of light. This is a strange idea; we are used to the notion that objects travel at speeds considerably less than that of light. We have repeatedly emphasized this as the reason relativistic effects are so unfamiliar in the everyday world. All of this is true. We are presently talking about an object's combined speed through all four dimensions—three space and one time—and it is the object's speed in this generalized sense that is equal to that of light. To understand this more fully and to reveal its importance, we note that like the impractical single-speed car discussed above, this one fixed speed can be shared between the different dimensions—different space and time dimensions, that is. If an object is sitting still (relative to us) and consequently does not move through space at all, then in analogy to the first runs of the car, all of the object's motion is used to travel through one dimension—in this case, the time dimension. Moreover, all objects that are at rest relative to us and to each other move through time—they age—at exactly the same rate or speed. If an object does move through space, however, this means that some of the previous motion through time must be diverted. Like the car traveling at an angle, this sharing of motion implies that the object will travel more slowly through time than its stationary counterparts, since some of its motion is now being used to move through space. That is, its clock will tick more slowly if it moves through space. This is exactly what we found earlier. We now see that time slows down when an object moves relative to us because this diverts some of its motion through time into motion through space. The speed of an object through space is thus merely a reflection of how much of its motion through time is diverted.6

We also see that this framework immediately incorporates the fact that there is a limit to an object's spatial velocity: the maximum speed through space occurs if all of an object's motion through time is diverted to motion through space. This occurs when all of its previous light-speed motion through time is diverted to light-speed motion through space. But having used up all of its motion through time, this is the fastest speed through space that the object—any object—can possibly achieve. This is analogous to our car being test-driven directly in the north-south direction. Just as the car will have no speed left for motion in the east-west dimension, something traveling at light speed through space will have no speed left for motion through time. Thus light does not get old; a photon that emerged