W’-s^^’Qn18/CHROIVICLESnTIME by Jocelyn Tomkinn”I wanna go back and do it all overnBut I can’t go back I knownI wanna go back ’cause I’m feeling so muchnoldernBut I can’t go back I know”n— Popular song by Eddie Moneyn(1986, CBS Inc.)nMostly we take space for granted so long as we havenenough of it. But what about time? The Romans saidn”tempus fugit” and said it all, or at least most of it. It isndifEcult to say more without getting tautological; but we cannsay that time has only duration so it must be one-dimensional.nThe natural division of time into past, present, andnfuture, which we often picture as a straight line with a pointnmarking the present, the past stretching back along the line,nand the future stretching ahead, expresses time’s one-n]ocelyn Tomkin is on the staff of the astronomyndepartment at the University of Texas.nyy^’flJii^^^^^.^^-w 5n^ ‘U’l, i^z.nnndimensional nature.nWhat about space and time? How are they related? Antough question; it’s fair to ask if it is meaningful. Is there anynreason to expect them to be related? Common sensensuggests that, indeed, they must be linked together somehow.nFor instance, when we make an appointment to meetnsomeone we state not only a place, but also a time.nBut as to what the relationship might be, this is much lessnclear. The fact that Isaac Newton did not get it right suggestsnthat the situation is far from straightforward. Only at thenbeginning of this century, stimulated by the discoveries ofn19th-century physics, did physicists realize exactly how timenfits into the scheme of things. The world doesn’t consist of anthree-dimensional space with time as a separate unrelatednentity, but is a fusion of space and time in which time is thenfourth dimension. Hermann Minkowski, who first discussednthe properties of unified space-time, opened his address tonthe 1908 Assembly of German Natural Scientists andnPhysicians with a clear statement: “The views of space andntime which I wish to lay before you have sprung from thensoil of experimental physics, and therein lies their strength.nThey are radical. Henceforth space by itself, and time bynitself, are doomed to fade away into mere shadows, and onlyna kind of union of the two will preserve an independentnreality.”nMinkowski did much more than merely state that time isnthe fourth dimension. He tamed time by showing how tonconvert an interval of time into an equivalent of space and sonput things on a quantitative footing, like a good scientistnshould. He demonstrated that the conversion factor is thenspeed of light. Thus an interval of time is equivalent to thendistance that light travels during that time. Because of light’snenormous speed (186,000 miles per second), a little time isn”worth” an immense distance — one second corresponds ton186,000 miles, for example. We all know that “time isnmoney,” but nobody says that “distance is money,” sonperhaps, in a way, folk wisdom anticipated Minkowski.nThe establishment of the relationship between time andnspace does not imply that time is a type of space. It isn’t.nTime and space by themselves “are doomed to fade awayninto mere shadows” in Minkowski’s eloquent phrasing, butnnonetheless they are separate shadows; time is time, andnspace is space.nDevelopments since Minkowski’s time have confirmednhis space-time description of the world. Einstein’s theory ofngeneral relativity, which is a theory of gravity, adoptsnMinkowski space-time as an essential preliminary ingredient.nEinstein did not “explain” gravity any more thannNewton “explained” gravity, but he did provide a betterndescription of gravity. Einstein’s theory does everything thatnNewton’s does, and then some.nEinstein did not modify or extend Newtonian theory butntook an entirely new approach in which Newton’s gravitationalnforce is superseded by curvature of space-time. FromnEinstein’s viewpoint the apple didn’t fall on Newton’s headnbecause of a gravitational force between the apple and thenEarth, but because the mass of the Earth curves space-timenin the Earth’s vicinity, and the apple’s falling was anmanifestation of this curvature. The space-time that is beingncurved by the Earth’s presence is Minkowski space-time. Innouter space, far away from massive bodies like the Earth,n