Aristotle, always top of the class, wants to be precise: he does not say that the glass is empty; he says that it is full of air. And he remarks that, in our experience, there is never a place where “there is nothing, not even air.” Newton, looking not so much for accuracy as for efficiency of the conceptual paradigm that needs to be constructed in order to describe the movement of things, thinks not about air but about objects. Air, after all, seems to have little effect on a falling stone. We can imagine that it is not even there.
As in the case of time, Newton’s “container space” may seem natural to us, but it is a recent idea that has spread due to the enormous influence of his thought. That which seems intuitive to us now is the result of scientific and philosophical elaborations in the past.
The Newtonian idea of “empty space” seems to be confirmed when Torricelli demonstrates that it is possible to remove the air from a bottle. It soon becomes clear, however, that inside the bottle many physical entities remain: electric and magnetic fields, and a constant swarming of quantum particles. The existence of a complete void, without any physical entity except amorphous space, “absolute, true, and mathematical,” remains a brilliant theoretical idea introduced by Newton to found his physics on, for there is no scientific, experimental evidence to support its existence. An ingenious hypothesis, perhaps the most profound insight achieved by one of the greatest scientists—but is it one that actually corresponds to the reality of things? Does Newton’s space really exist? If it exists, is it really amorphous? Can a place exist where nothing exists?
The question is identical to the analogous one regarding time: does Newton’s “absolute, true, and mathematical” time exist, flowing when nothing happens? If it exists, is it something altogether different from the things of this world? Is it so very independent from them?
The answer to all these questions lies in an unexpected synthesis of the apparently contradictory ideas held by these two giants. And to accomplish this, it was necessary for a third giant to enter the dance.*
THE DANCE OF THE THREE GIANTS
The synthesis between Aristotle’s time and Newton’s is the most valuable achievement made by Einstein. It is the crowning jewel of his thought.
The answer is that the time and space Newton had intuited the existence of, beyond tangible matter, do effectively exist. They are real. Time and space are real phenomena. But they are in no way absolute; they are not at all independent from what happens; they are not as different from the other substances of the world, as Newton had imagined them to be. We can think of a great Newtonian canvas on which the story of the world is drawn. But this canvas is made of the same stuff that everything else in the world is made of, the same substance that constitutes stone, light, and air: it is made of fields.
Physicists call “fields” the substances that, to the best of our knowledge, constitute the weave of the physical reality of the world. Sometimes they may be given exotic names: the fields “of Dirac” are the fabric of which tables and stars are made. The “electromagnetic” field is the weave of which light is made, as well as the origin of the forces that make electric motors turn and the needle of a compass point north. But—here is the key point—there is also a “gravitational” field: it is the origin of the force of gravity, but it is also the texture that forms Newton’s space and time, the fabric on which the rest of the world is drawn. Clocks are mechanisms that measure its extension. The meters used for measuring length are portions of matter that measure another aspect of its extension.
Spacetime is the gravitational field—and vice versa. It is something that exists by itself, as Newton intuited, even without matter. But it is not an entity that is different from the other things in the world—as Newton believed—it is a field like the others. More than a drawing on a canvas, the world is like a superimposition of canvases, of strata, where the gravitational field is only one among others. Just like the others, it is neither absolute nor uniform, nor is it fixed: it flexes, stretches, and jostles with the others, pushing and pulling against them. Equations describe the reciprocal influences that all the fields have on each other, and spacetime is one of these fields.*
The gravitational field can also be smooth and flat, like a straight surface, and this is the version that Newton described. If we measure it in meters, we discover that the Euclidian geometry that we learned at school applies. But the field can also undulate, in what we call “gravitational waves.” It can contract and expand.
Remember the clocks in chapter 1 that slow down in the vicinity of a mass? They slow down because there is, in a precise sense, “less” gravitational field there. There is less time there.
The canvas formed by the gravitational field is like a vast elastic sheet that can be pulled and stretched. Its stretching and bending is the origin of the force of gravity, of things falling, and provides a better explanation of this than the old Newtonian theory of gravity.
Look again at the figure here which illustrates how more time passes above than below, but imagine now that the piece of paper on which the diagram is drawn is elastic; imagine stretching it so that the time in the mountains actually becomes elongated. You will obtain something like the image below, which represents space (the height, on the vertical axis) and time (on the horizontal)—but, now, the “longer” time in the mountains effectively corresponds to a greater length of time.
The image above illustrates what physicists call “curved” spacetime. “Curved” because it is distorted: distances are stretched and contracted, just like the elastic sheet when it is pulled. This is why the light cones were inclined in the diagrams in chapter 3.
Time thus becomes part of a complicated geometry woven together with the geometry of space. This is the synthesis that Einstein found between Aristotle’s conception of time and Newton’s. With a tremendous beat of his wings, Einstein understands that Aristotle and Newton are both right. Newton is right in intuiting that something else exists in addition to the simple things that we see moving and changing. True and mathematical Newtonian time exists; it is a real entity; it is the gravitational field, the elastic sheet, the curved spacetime in the diagram. But Newton is wrong in assuming that this time is independent from things—and that it passes regularly, imperturbably, separately, from everything else.
For his part, Aristotle is right to say that “when” and “where” are always located in relation to something. But this something can also be just the field, the spatiotemporal entity of Einstein. Because this is a dynamic and concrete entity, like all those in reference to which, as Aristotle rightly observed, we are capable of locating ourselves.
All this is perfectly coherent, and Einstein’s equations describing the distortions of the gravitational field and its effects on clocks and meters have been repeatedly verified for more than a century. But our idea of time has lost another of its constituent parts: its supposed independence from the rest of the world.
The three-handed dance of these intellectual giants—Aristotle, Newton, and Einstein—has guided us to a deeper understanding of time and of space. There is a structure of reality that is the gravitational field; it is not separate from the rest of physics, nor is it the stage across which the world passes. It is a dynamic component of the great dance of the world, similar to all the others, interacting with the others, determining the rhythm of those things that we call meters and clocks and the rhythm of all physical phenomena.