The Structure of Space and Time, and the Indeterminacy of Classical Physics

TL;DR

This paper explores the vagueness in the structure of space and time, deriving principles of inaccuracy and randomness in classical physics, and relating these to quantum mechanics and entropy.

Contribution

It introduces the concept of vague intervals for space and time, and derives a principle of complementary inaccuracy, connecting classical physics with quantum indeterminacy.

Findings

Vague intervals represent location in space and time.

A principle of complementary inaccuracy between position and velocity.

Classical systems exhibit inherent randomness despite deterministic laws.

Abstract

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and other considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning.