Posts Tagged ‘Holonomy’

Constructing TIME

June 3, 2014

How does one usually define time? Well, I will argue, it’s constructed by machines.

This has major consequences in physics, to be evoked some other time: Cosmic Inflation theory uses time, but has forgotten to define it. Thus a philosophical-historical review is in order.

The concept of time was developed experimentally over several millennia.  Time was important in agriculture: it allowed predicting when to do some specific activities essential to agriculture (planting, irrigation works, etc.).

Mayan Calendar: No Time, No Hydraulic Civilizations

Mayan Calendar: No Time, No Hydraulic Civilizations

The Mayas, and the Babylonians discovered that astronomy, observing stars and planets, allowed to predict the seasons. Thus, they defined time. The Mayan civilization depended upon highly technological seasonally constrained hydraulics, so time was of the essence. The Mayans thrived for millennia before an inordinate drought brought ecological catastrophe and the consequential mayhem (7C to 9C).

Shortly after the equal sign was invented (circa 1500 CE), time appeared in the equations of the Seventeenth Century physics. Time was fundamental to the equations of classical mechanics that described both how mechanical forces and gravitation-imparted trajectories: every dynamical phenomenon was a function of time, and its acceleration, the double derivative relative to time, was the force.

This classical time allowed to determine longitude in navigation. The more precise the time, the more precisely navigators knew where they were in the middle of the ocean. This (new) mechanical notion of time had grown from astronomical time, and was found, de facto, to be identical with astronomical time.

Mathematics and physics were deeply entangled. Time is truly an injection of the Real Line into the space(s) the equations are about. The concept of Real Line is implicitly central to calculus. Calculus was developed for physics.

However, in the Nineteenth Century, equations were derived for a force that was not found in Classical Mechanics, Electromagnetism.

(17 C) Gravitation is what one could call (until 1916!), a “point force”: a planet of mass M can be replaced by a point of mass M (that’s Gauss theorem; it caused lots of trouble to Newton).

Electromagnetism was more complex than gravitation.  Faraday drew lines of force lovingly (and was despised for it). Maxwell transformed them into “field” equations.

A “field”, just as a field of wheat. The Electromagnetic field could turn in circles on itself, or make lobes.

Sometimes, electric charges behave like “point forces” too. But magnetic charges could not be found: they were never like point (“monopoles” in modern jargon). However, electricity would turn into magnetism, and varying magnetism into electricity. Electromagnetism was exasperatingly complicated.

A journalist asked Faraday what use the fact that a varying magnetic field created electricity had. Faraday retorted: ”What’s the use of a new born baby?

All our industry now rests on this new born baby. (By the way, Michael Faraday was directly supported personally by the top plutocrat in Britain, the king.)

A field is non local. Whereas it looked as if gravitation did not need to be described by a field (an impression Einstein would change, but that’s besides the points made here), it was certainly not the case for electromagnetism.

Any force generates an acceleration, hence a dynamic, hence a trajectory. So classical mechanics generated a notion of time (it had turned out that time from a mechanical force, a spring, was the same as from gravitation).

Similarly for electromagnetism: it’s a force, so it defines a notion of time. However, even classically, electromagnetism was non-local. So the clocks defined by electromagnetism are non-local. I call them holonomic. (Adjusting classical time to electromagnetic time is called Special Relativity; it turned out that gravity needed to be made into a field, and that time needed to vary with speed so that physics was independent of speed.)

This notion of non-local time, it turned out, was another excellent torpedo against Cosmic Inflation, and the naivety that helped built it. More later…

Patrice Aymé