How do things move? At first glance this may not seem to be a problem. We tend to take motion for granted. But a long-standing mystery lies behind it. Now new answers are becoming clear, with cutting-edge insights into the nature of space and time and matter.

Philosophy and physics have long studied motion (aka mechanics). Isaac Newton gave us classical mechanics and Max Planck gave us

quantum mechanics. At different scales each tells us how things move. But both assume continuity, the infinite divisibility of space and time at all scales. It is slowly becoming evident to physicists that, at the Planck scale, space must be made of quantized manifolds that are not divisible. So it would seem that when matter moves it must proceed in tiny jumps. This concept plays right into ancient claims that motion is not possible. In his famous arrow paradox, Zeno of Elea sets it up like this: If everything is motionless at every instant, and time is composed of instants, then motion is impossible.

Aristotle answers Zeno. He says space and time are continuous, so subdividing them ad infinitum will resolve the paradox. Two thousand years later, Isaac Newton’s infinitesimal calculus provides the math. With it, one can slice the time step down as near to zero as one likes. Yet this answer leaves a feeling that it buries the problem in math fiction. And if it does resolve the paradox, why do modern mathematicians, philosophers and physicists like Bertrand Russell, Alfred North Whitehead, Hans Reichenbach and Hermann Weyl still need to wrestle with it? Whitehead and Russell are the learned authors of Principia Mathematica. They call it ‘immeasurably subtle and profound.’

The realization that space is quantized and time comes in jumps consigns Aristotle’s answer to oblivion. How then can we answer Zeno? To find out, let’s take a closer look at motion. What exactly happens when something—let’s say an electron—moves? We want to grasp its motion at the Planck scale, which is vastly smaller than the scale of atoms or even of electrons where quantum mechanics rules. This is the scale where things really happen, the scale that takes us beyond Plato’s Cave.

Physics usually treats electrons as indivisible point particles. But the works of theoretical physicist Sundance Bilson-Thompson explains an electron (and each sub-atomic particle of the Standard Model) as composite. It is six twists in what he calls ribbons, paired and braided. In Time One I call them 2-D links between next-neighbor space quanta or flecks. I show how, each Planck time, the universe updates the space quanta and the twists between them. Each twist can move by at most a single space quantum. (One fleck-step per Planck time is the speed of light.) How do we know it’s so? It explains most everything!

The technical term for this kind of universe is foliation. At each foliation, each twist can be in a slightly different position. That is not to suggest we can measure position at Planck scale. At this scale the six twists keep distant company like an erratic bunch of bees with a vague destination. Yet this scale is so small that their electron looks point-like to us. With the universe providing nearly 10⁴⁴ foliations per second, the electron makes its way. Even in a picosecond it can move some 10³² steps (each being 1.6 × 10^-35m). So its progress is now macroscopic and quantum mechanics gives us the odds on the odd properties we see emerging.

But it’s at the Planck scale that we find the false assumption that sets up Zeno’s proposition. His paradox reduces to the question: How do the twists move in between two foliations? The answer’s simple: There is no in-between the foliations. The current foliation is all there is. This is the nature of the universe.

Source: Sundance Bilson-Thompson, “A topological model of composite preons”, http://arxiv.org/pdf/hep-ph/0503213v2.pdf

Image credit: Lunch, http://www.cs.indiana.edu/~hanson/

Caption: 2-D section of a 6-D Calabi-Yau manifold or fleck