Time and Motion

Pierre Duhem

Time and motion are intimately related, because there can be no motion without time. In fact, Aristotle understood it the other way around, thinking that if there were no motion, there would be no time. He defined time in terms of motion, as the number of changes in terms of before and after. And the basic motion, upon which all others depend, would be the rotation of the sphere of the fixed stars.

·         Saint Augustine, in his Confessions, dedicated Book XI to the philosophical study of time. He rejects Aristotle's theory, denying that time depends on the existence of motion, and doubts that time exists outside our minds, although his famous quote reveals his uncertainty about time: What is time? If no one asks me, I know; if I want to explain it to a questioner, I don’t know.

·         Averroes considers that the sensation of time is linked to the perception of our existence, which is subject to change: Whenever we perceive any motion, we feel that we exist with an existence subject to change… from which the sensation of time arises for us.". And he adds, to adapt his ideas to those of Aristotle, that this is a consequence of the movement of the heavens.

Guillermo de Occam

·         According to William of Ockham's nominalist conception, motion is simply a name designating a set of concepts... first, the moving object... second, what the moving object acquires or loses... But for local motion to exist, it is not necessary that the place acquired by the moving object be a place that actually exists; it is enough that it be a conceived and merely hypothetical place... time cannot be defined. (Pierre Duhem, Chapter 4 of Volume VII of Le Système du Monde).

·         While Aristotle sees time as a property of the real world (motion) that the human soul measures, Kant defined time as an a priori form of human sensibility, that is, a structural framework that the mind imposes to order our perceptions. The external world exists independently of us, but we see it framed within time. For Kant, time does not originate from experience or the external world, but is a pure intuition, a subjective structure of the subject. Everything that human beings experience must necessarily pass through the filter of time in order to be understood.

·         For Newton, time is absolute, the same for all beings in the universe: Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time. (Philosophiae Naturalis Principia Mathematica).

·         In Einstein's theory of relativity, time is not absolute, but depends on the state of rest or motion of the observer making the measurement. Every moving body will measure a proper time interval, which differs from the interval measured by an external, stationary observer, according to the following expression:

where t is proper time and t₀ is the time measured by an external observer, which will always be greater than t, since v (the speed of the moving object) is always less than c (the speed of light), so the square root is always less than 1. Note that the proper time of a hypothetical object traveling at a speed greater than that of light would not be negative (it is often mistakenly said that time would run backward). It would be imaginary, because t₀ would be multiplied by the square root of a negative number.

·         Finally, with the Big Bang theory, a new definition of absolute time has emerged: cosmic time, the time elapsed since the Big Bang. Although we cannot perceive it directly, except in our immediate surroundings, this time exists and is related to the expansion of the universe, taking the same value at all points in the universe that measure the same temperature of the cosmic microwave background radiation.

In short: time and movement are intimately related, but after so many centuries and so many theories, we still don't understand time. I think the best approximation is still Saint Augustine's famous phrase.

The same post in Spanish

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Manuel Alfonseca