About Time

Albert Einstein was the hero of my youth, not just for inventing Relativity, but even more for his unorthodox approach to life. He was a one-worlder who saw far beyond the petty concerns people and nations have in their day-to-day affairs. Ultimately, even though his pacifist and socialist views were dismissed by his generation and its descendants, I think he was on the right track. I follow him by having (what I call) a Utopian point of view. So it is very difficult for me to criticize the ideas of one of History's truly great and important people, especially one whose ideas I still do not fully understand.

Nonetheless, there is something wrong with General Relativity: most likely, the assumption of continuity. Prof. Einstein was born and rooted in the Victorian age, even if he lived and grew beyond it. General Relativity uses Riemannian geometry which assumes space is continuous, which makes it incompatible with Quantum theories which assume things occur in lumps. Quantum theories have very little to say about whatever bounds or lies outside things. Yet Quantum Mechanics is by far the more powerful theory in explaining the world of our everyday experience, except for the gravitational properties of things.

The Victorians brought Newtonian science to its peak by developing and applying the Calculus. 19th Century mathematicians invented a theory of Real and Imaginary numbers which underlies the Calculus, hence much physical science. Along with those developments, 19th Century mathematicians, such as Riemann and Lobachevsky, invented new geometries which denied ancient Euclidean axioms, yet shared with the ancient one the notion of the continuity of space. The fullness of space and time is still illustrated in Heraclitus saying, 'one cannot touch same river twice.' On that view, there are no holes in the fabric of space-time; every part of it is in touch with every other part. The idea of continuity implies that one can always get there from here.

Most people are familiar with the Einsteinian notion of space-time warp which explains gravity. Material bodies interact with a webbing ("space-time") which is "bent" by the presence of gravitating bodies. Since electromagnetic phenomena can be interpreted as photons in motion (due to the deBroglie equivalence of particles and waves, which is a further result of Einstein's E=mc²), photons also bend space-time. In 1919, Einstein's famous prediction that the Sun would make starlight travel around it in a seemingly warped path was verified. Since then, gravity is endlessly illustrated by billiard balls sitting on trampoline surfaces.

But careful consideration of those pictures - Einstein's picture - always reveals there are two classes of things: bodies and "space-time." Gravitating bodies are depicted as timeless entities which also have a spatial description; i.e., they fill a space. In the illustrations, "space-time" is somehow separate from material bodies. This must be a hangover from the Newtonian clockwork conception of the Universe, which imagines some sort of absolute space and time in which bodies and immaterial light waves travel. It was that conception which brought about the late Victorian controversy concerning the ether, which was dispelled by the astounding result of the Michelson-Morley experiment: light travels everywhere at a constant speed, c. Consequently, the pictures of warped "space-time" are incorrect because the bodies themselves contain space-time. A better picture would show the bodies as enveloped by the sheet of "space-time," but even that fails to reveal the depth of the problem, that every point in a body is a piece of space-time. So, if space-time is represented by a two dimensional sheet, the body is just a figure inscribed in (not on) the sheet. When the interaction of bodies and space-time is so described, the meaning of Relativity becomes difficult to understand. That is, Einstein's General Relativity is most easily explained by reference to earlier intuitions of Newtonian space and time.

The Quantum Mechanical concept of gravity is entirely different from the classical picture, and avoids the difficulty of being explained by reference to Newtonian objects. In Quantum Mechanics, the interactions of particulate things are explained as the exchange of other particulate things. The notions of "space" and "time" are not explicit or defined, even if they are parameters in equations of state. That is, things are described as a sequence of states, which are a sequence only because (we prefer to) observe them that way. Thus, when a certain electronic transition occurs near an atomic nucleus, photons are emitted which may interact with other physical objects. Similarly, massive bodies interact by an exchange of gravitons.

Here it is important to note the particle-wave duality taken into account in Quantum Mechanics. Photons can be described as lumps or as space-filling waves. In the same vein, gravitons must have an alternate description as gravity waves. When we introduce the parameter time, both entities are seen as traveling in space. But, "internal" to the space filling wave and anything else that travels at the speed of light, there can be no time. The wave "sees" itself as a distribution of its energy, not as an advancing wave front. Interference patterns that imply electromagnetic waves are in more than one place at a time are only puzzling when we introduce the parameters of space and time. When the Universe is considered sub species aeternitas, none of that is a problem.

So, let us suppose we can dispense with space-time as in General Relativity and space and time as in Newtonian physics. Let us suppose the Universe is composed of things which are observed to have certain characteristics, such as mutual attraction (gravity). These things are sometimes seen as matter and sometimes as energy, but they are either or both on account of E=mc² (Einstein's enduring contribution). This supposition is to throw away the lingering notions of space and time as somehow independent entities in which the things of this Universe are imbedded or by which they are connected. I stubbornly stick to Ernst Mach's discipline: we rely on what we observe, on experiment. That, after all, is where Einstein started. What we observe are bodies and energies.

Time is an inferred dimension. We have no direct perception or intuition of time. We measure the passage of time as the motions of things we observe; the tick of a clock. Without motion, there can be no time, which implies that the entire empirical content of "time" is motion. If so, then "time" is a euphemism for the observed motions. Of course, human beings ascribe a more imminent presence to time; i.e., we reify it. Reification is an ancient practice, a natural habit, which we do to all sorts of things, such as souls, minds, gods, etc. as well as space and time. It is that habit which engenders the ball and trampoline diagrams supposedly illustrating the operation of Relativistic gravity. But, there is no ball or trampoline any more than there is any space or time, except in our imaginations. To assert the existence of time is to make the same sort of mistake which results in philosophical dualism: it is to claim the existence of an unobserved, possibly unobservable, entity or factor which makes it so. Thus, reification of time is the same sort of practice as supposing there are souls, gods, etc. But such suppositions are not useful in getting things done.

It is legitimate to note the passing of time, for in this case we are marking down our observations. It is legitimate to say 'the time is ...' because this is a shorthand for a certain reading of the clock. But, it is not legitimate to say that there is any time apart from its measurement. Of course, some sort of claim could be made about a separate entity we call "time" if one believes the Universe is continuous. The belief in continuity implies there is a filling between the things we observe; that, in principle, we could at least measure time in as small quantities as we like. The difficulty with such a belief is that our understanding of the micro-Universe, of Quantum Chromodynamics, denies it. The microscopic Universe is made of particles, which also have wave properties, with nothing between them. According to our modern physical understandings, there is no underlying clock.

Gravity is another chimera. The matter and energy of our experience responds to gravitational forces, but only because a certain configuration of this Universe allows it. At an earlier epoch, during the Big Bang when everything was highly compressed, either gravity didn't exist or it did not operate as it does now. This is not as difficult a notion as it seems at first. Consider electromagnetic phenomena: not everything interacts with electrons, light waves or magnetic fields. There lumps of things which are unaffected by the presence of electromagnetic energy. It is as if such things were color blind. Similarly, gravity need not affect anything unless it is somehow endowed with the ability to "see" it. According to my readings in physics, the Higgs particle now being pursued has something to do with things that have mass. Gravity is invisible to things that do not have mass or its equivalent, energy.

Thus, space-time as hypothesized in General Relativity rests on shaky foundations. Einstein's results are valuable - we want to keep them - but they must be set on different moorings. During the last decade, there has been a drift toward multiple Universes (e.g., Lisa Randall's Brane theory) based on an 11-dimensional geometry. Such a theory is said to quantize gravity and reconcile the contradictions between Quantum and Relativistic theories. That sort of theory also gives meaning to Stephen Hawking's admission, that information is not lost in a black hole if one integrates over all histories; i.e., one has to account for each packet in all of its alternative appearances (possibly in Multiverses).

Space, time and gravity are only what seems to us in our Universe. Following Robert Frost, all of us have taken the path "less traveled by," the one which defines our Universe. Still, Frost's poem acknowledges the other paths not in our direct experience. The present problem is not what is space-time, but how do we expand our experience to include the paths not taken?

Posted 03/27/2008 10:25:55 AM                Last update: 03/27/2008

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