Pedestrian Physics 13

Space

“Void” is a subject for metaphysics, philosophy and theology. It has no place in physics except as a foil for “reality”

“Space” and “Void” are not synonyms. Space has structure. It is a concept that has been with us since heathen-old. Even Aristotle, although he rejected the concept of “Void”, believed in the reality of space. “A body occupies place,” he said, “but place is not a part of the body, Remove the body, and place is left behind.”

All through antiquity and the middle ages there was only one Space. Euclid’s space was timeless and endless.

The idea of multiple spaces, and spaces in motion, is fairly modern. It was born with Descartes’ Analytic Geometry. He defined space, not by the body occupying it, but by the matter surrounding it. This space was not left behind when the co-ordinate system moved; it moved along with it.

The idea culminated with Newton. His laws of dynamic were applicable to “Inertial Space”, only. In all other cases, one has to make allowance for local conditions before applying his laws. So, what is an inertial space? It is a space where Newton’s laws are valid!

Newton stated that if there were one inertial space, there would be a multitude, at rest with, or moving relative to it. He wondered if there might be one space at absolute rest, spawning all the others. He firmly believed this to be the case and that this system might be anchored beyond the distant stars, He supported his claim with the famous “bucket experiment”. It is an argument that is hard to follow but we have another experiment that is neither hard to follow, nor difficult to replicate. It is there for anyone to see; the most awe-inspiring experiment in all of Mechanics:

Foucault’s pendulum.

A swinging pendulum has to obey the law of conservation of angular momentum. His pendulum did, but it did not take its bearings from the ceiling where it was suspended, nor from the floor where it made its mark; nor from the closed walls surrounding it. It took its bearings from the distant, invisible stars!

For this reason, if for no other, I believe in an “absolute” space. I believe our Universe is finite, with a finite amount of mass. As such, it qualifies for Newton’s definition of an isolated mechanical system writ large: The sum of momenta must be constant, and since there is no reference point outside the universe, it must be zero, there must be a center of gravity, of motion, that anchors all resting systems. This belief is not shaken by the fact that, as practical matter, we cannot identify absolute rest. We are restricted to compare relative motions, even when we confine our research to inertial systems.

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The idea of multiple spaces raises conceptual problems if we, like Einstein, jump nilly-willy from one reference frame to another.

While velocity and momentum and static force are vectors with values that change in magnitude and direction with change of reference frames, static mass is a scalar and invariant. Kinetic energy, and with it dynamic mass, depends on velocity and is not invariant under change of reference system.

Energy cannot be created, nor destroyed, with an arbitrary selection of reference frame. There must be a price.

The price is irrelevance. As long as you do not interact with the object and as long as you are consistent, the absolute numbers you assign are of no consequence.

A car crash is a car crash, whether observed by a passenger on a moving train, or an orator on a soap box.