From Dance for Two. Alan Lightman. Pantheon Books. NYC NY. 1996.
3-5
Pas de Deux
In soft blue light, the ballerina glides across the stage and takes to the air, her toes touching Earth imperceptibly. Sauté, batterie, sauté. Legs cross and flutter, arms unfold into an open arch. The ballerina knows that the easiest way to ruin a good performance is to think too much about what her body is doing. Better to trust in the years of daily exercises, the muscles' own understanding of force and balance.
While she dances, Nature is playing its own part, flawlessly and with absolute reliability. On pointe, the ballerina's weight is precisely balanced by the push of floor against shoe, the molecules in contact squeezed just the right amount to counter force with equal force. Gravity balanced with electricity.
An invisible line runs from the center of the Earth through the ballerina's point of contact and upward. If her own center should drift a centimeter from this line, gravitational torques will topple her. She know nothing of mechanics, but she can hover on her toes for minutes at a time, and her body is continuously making the tiny corrections that reveal an intimacy with torque and inertia.
Gravity has the elegant property of accelerating everything equally. As a result, astronauts become weightless, orbiting Earth on exactly the same trajectories as their spaceships and thus seeming to float within. Einstein understood this better than anyone and described gravity with a theory more geometry than physics, more curves than forces. The ballerina, leaping upward lightly, hangs weightless for a moment amid flowers she has dropped midair, all falling on the same trajectory.
Now she prepares for a pirouette, right leg moving back to fourth position, pushing off one foot, arms coming in to speed the turn. Before losing balance she gets four rotations. Male dancers, on demi-pointe and with greater contact area, can sometimes go six or eight. The ballerina recovers well, giving her spin smoothly back to Earth and remembering to land in fifth position smiling. Briefly her feet come to rest, caught between the passage of spin and the friction of the floor. Friction is important. Every body persists in its state of rest or of uniform motion unless acted upon by outside forces. Every action requires a reaction.
The ballerina depends on the constancy of the laws of physics, even though she herself is slightly unpredictable. In this same performance last night she went only three and a half turns through her first pirouette, and then took the arabesque several feet from where she takes it now. Regardless of these discrepancies, the atoms in the floor, wherever she happens to touch and at one millisecond's notice, must be prepared to respond with faithful accuracy. Newton's laws, Coulomb's force, and the charge of electrons must be identical night after night – otherwise, the ballerina will misjudge the resiliency of the floor or the needed moment of inertia. Her art is more beautiful in its uncertainty. Nature's art comes in its certainty.
The ballerina assumes one pose after another, each fragile and symmetrical. In the physics of solids, crystal structures can be found that appear identical after rotations by one-half, one-third, one-quarter, and one-sixth of a circle. Crystals with one-fifth and one-seventh symmetries do not exist because space cannot be filled with touching pentagons or septagons. The ballerina reflects a series of natural forms. She is first ethereal, then lyrical. She has struggled for years to develop a personal style, embellished with fragments from the great dancers. As she dances, Nature, in the mirror, pursues its own style effortlessly. It is the ultimate in classic technique, unaltered since the universe began.
For an ending, the ballerina does a demi-plié and jumps two feet into the air. The Earth, balancing her momentum, responds with its own sauté and changes orbit by one ten-trillionth of an atom's width. No one notices, but it is exactly right.
39-44
Time Travel and Papa Joe's Pipe
When astronomers point their telescopes to the nearest large galaxy, Andromeda, they see it as it was two million years ago. That's about the time Australopithecus was basking in the African sun. This little bit of time travel is possible because light takes two million years to make the trip from there to here. Too bad we couldn't turn things around and observe Earth from some cozy planet in Andromeda.
But looking at light from distant objects isn't real time travel, the in-the-flesh participation in past and future of Mark Twain's Connecticut Yankee or H. G. Wells's Time Traveler. Ever since I've been old enough to read science fiction. I've dreamed of time traveling. The possibilities are staggering. You could take medicine back to fourteenth-century Europe and stop the spread of plague, or you could travel to the twenty-third century, where people take their annual holidays in space stations.
Being a scientist myself, I know that time travel is quite unlikely according to the laws of physics. For one thing, there would be causality violation. If you could travel backward in time, you could alter a chain of events with the knowledge of how they would have turned out. Cause would no longer always precede effect. For example, you could prevent your parents from ever meeting. Contemplating the consequences of that will give you a headache, and science-fiction writers for decades have delighted in the paradoxes that can arise from traveling through time.
Physicists are, of course, horrified at the though of causality violation. Differential equations for the way things should behave under a given set of forces and initial conditions would no longer be valid, since what happens in one instant would not necessarily determine what happens in the next. Physicists do rely on a deterministic universe in which to operate, and time travel would almost certainly put them and most other scientists permanently out of work.
But even within the paradigms of physics, there are some technical difficulties for time travel, over and above the annoying fact that its existence would altogether do away with science. The manner in which time flows, as we now understand it, was brilliantly elucidated by Albert Einstein in 1905. First of all, Einstein unceremoniously struck down the Aristotelian and Newtonian ideas of the absoluteness of time, showing that the measured rate at which time flows can vary between observers in relative motion with respect to each other. So far, this looks hopeful for time travel.
Einstein also showed, however, that the measured time order of two events could not be reversed without relative motions exceeding the speed of light. In modern physics the speed of light, 186,000 miles per second, is a rather special speed; it is the propagation speed of all electromagnetic radiation in a vacuum, and appears to nature's fundamental speed limit. From countless experiments, we have failed to find evidence of anything traveling faster than light.
There is another possible way out. In 1915 Einstein enlarged his 1905 theory, the Special Theory of Relativity, to include the effect of gravity; the later theory is imaginatively name the General Theory of Relativity. Both theories have remarkably survived all the experimental tests within our capability According to the General Theory, gravity stretches and twists the geometry of space and time, distorting the temporal and spatial separation of events.
The speed of light still cannot be exceeded locally – that is, for brief trips. But a long trip might sneak through a short cut in space created by gravitational warping, with the net result that a traveler could go between two points by one route in less time that light would require y another route. It's a little like driving from Las Vegas to San Francisco, with the option of a detour around Death Valley. In some cases, these cirsuitous routes might lead to time travel, which would indeed raise the whole question of causality violation.
The catch is that it is impossible to find any concrete solutions of Einstein's equations that permit time travel and are at the same time well behaved in other respects. All proposals either require some unattainable configuration of matter, or else have a least on nasty point in space called a 'naked singularity' that lies out side the domain of validity of the theory. It is almost as if General Relativity, when pushed toward those circumstances in which all of physics is about to be done away with, digs in its heels and cries out for help.
Still, I dream of time travel. There is something very personal about time. When the first mechanical clocks were invented, marking off time in crisp, regular intervals, it must have surprised people to discover that time flowed outside their own mental and physiological processes. Body time flows at its own variable rate, oblivious to the most precise hydrogen master clocks in the laboratory.
In fact; the human body contains its own exquisite timepieces, all with their separate rhythms. There are the alpha waves in the brain; another clock is the heart. And all the while tick the mysterious, ruthless clocks that regulate aging.
Nowhere is the external flow of time more evident that in the space-time diagrams developed my Hermann Minkowski, soon after Einstein's early work. A Minkowski diagram is a graph in which time runs along the vertical axis and space along the horizontal axis. Each point in the graph has a time coordinate and a space coordinate, like longitude and lattitude, except far more intereresting. Instead of depicting only where something is, the diagram tells us when as well.
In a Minkowski diagram, the entire life history, past and future, of a molecule or a man is simply summarized as an unbudging line segment. All this on a single piece of paper. There is something disturbingly similar about a Minkowski diagram and a family tree, in which several generations, from long dead relatives to you and your children, move inevitably downward on the page. I have an urgent desire to tamper with the flow.
Recently, I found my great-grandfather's favorite pipe. Papa Joe, as he was called, died more than seventy years ago, long before I was born. There are few surviving photographs of other memorabilia of Papa Joe. But I do have this pipe. It is a fine old English briar, with a solid bowl and a beautiful straight grain. And it has a silver band at the base of the stem, engraved with three strange symbols. I should add that in well-chosen briar pipes the wood and tobacco form a king of symbiotic relationship, exchanging juices and aromas with each other, and the bowl retains a slight flavor of each different tobacco smoked in the pipe.
Papa Joe's pipe had been tucked away in a drawer somewhere for years, and was in good condition when I fount it. I ran a pipe cleaner through it, filled it with some tobacco I had on hand, and settled down to read and smoke. After a couple of minutes, the most wonderful and foreign blend of smells began wafting from the pipe. All the various tobaccos that Papa Joe had tried at one time or another in his life, all the different occasions when he had lit his pipe, all the different places he had been that I will never know – all had been locked up in that pipe and now poured out into the room. I was vaguely aware that something had got delightfully twisted in time for a moment, skipped upward on the page. There is a kind of time travel to he had, if you don't insist on how it happens.