Chapter Two

Galileo’s Relativity

Aristotle

Alfred North Whitehead, the brilliant and somewhat mercurial 20^th century philosopher and mathematician once said, “The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.”

In many ways the same can be said of Aristotle regarding science.  Though he used the philosophical tool of reason rather than the modern approach of experimentation, it can safely be maintained that Aristotle covered every aspect of the physical world in his voluminous and brilliant writings.

The main difference in the stature of the two greatest figures of classical Greek thought is that while philosophy is forever, science or “natural philosophy” as it was called until a century ago is in a constant state of change.  Many modern people proudly call themselves “Platonists” today.  In mathematics, a Platonist is one who believes that math is discovered rather than invented by humans.  By contrast, nobody calls themselves an “Aristotelian” today and for a very good reason.  He was simply wrong about a lot of things.

One of the things he was most wrong about was his notions about space, time and motion.  According to Aristotle:

1. “Being at rest” was the natural state of motion of any object. If an object were in motion, then there must be some agent that is responsible for that motion. And when that agent stops, the motion stops.
2. There is a privileged being: The Prime Mover. He is the first agent, responsible for moving objects, which, in turn, move other objects.
3. The Prime Mover, he argued, must be at Absolute Rest. By “absolute” rest, we mean that all observers will universally agree on that state of rest.

Aristotle didn’t seem to understand that it was the force of friction that caused moving objects to come to a rest.  Instead he thought that everything would always be at rest unless a force was continuously applied to it.  Aristotle was no vagrant.  From simple observation of the way things work around us, his conclusions were both perceptive and correct.  To arrive at a different conclusion required a new form of logic and thinking which took mankind an additional two millennia to develop.

Galileo’s Principle of Relativity

Galileo formulated the principle of relativity in order to show that one cannot determine whether the earth revolves about the sun or the sun revolves about the earth. The principle of relativity states that there is no physical way to differentiate between a body moving at a constant speed and an immobile body.

Galileo’s Principle of Relativity is generally stated somewhat as follows:

“Any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments.”

It is of course possible to determine that one body is moving relative to the other, but it is impossible to determine which of them is moving and which is immobile. The laws of physics are identical in systems moving one at a constant velocity in relation to the other, so that one cannot conduct any physical experiment capable of indicating if the body is immobile or in motion.

A common experience most of us has had is sitting in a train in the train station.  When the train immediately next to you appears to move it is difficult to determine whether it is your train or the other that is actually moving.  If the moving train is travelling at a constant speed, there would be no experiment one could perform from within the train that would answer the question either.  A dropped coin in either train would behave exactly the same.

In fact, there is no meaning to the concept of a moving body, without reference to its movement relative to another body. All velocity is only relative velocity.  Remember the example in the previous chapter about the solitary ball in an otherwise empty universe?  We said that it was incapable of motion because there would be no way to detect its movement.  This is a classic use of Galileo’s theory of relativity.

The Law of Inertia

But Galileo didn’t stop there.  In order to answer his critics to his theory that the Earth moves around the sun he developed the law of Inertia which can be stated as follows:

A body will preserve its velocity and direction so long as no force in its motion’s direction acts on it.

His critics had contended that if Galileo was correct that the earth moved, how could it be that a stone dropped from a tower would fall straight down.  If the Earth was moving, the stone should fall at an angle!

In his response to their contentions, Galileo likened the sailing ship to the moving earth.

If we drop a stone from the mast of a sailing ship, where would the stone fall?

Galileo showed that the stone would fall to the base of the sailing ship’s mast and that on the moving earth too; the stone will fall to the base of the tower, as can be seen from experience.

Galileo understood this phenomenon on the basis of his theory of Inertia which he had developed as a result of his experiments with inclined planes.  He placed two tracks for balls opposite each other and equally inclined them towards each other in a “V” shape.  He observed that when he rolled a ball from any chosen height on one plane that the ball would rise to precisely the same height on the other plane absent a small loss to friction. 

From this he concluded that friction aside, an object in motion would continue at the same speed and direction forever, unless acted on by an external force.

Both these discoveries overturned forever the Aristotelian theory of motion that had held sway from the dawn of scientific thought.

Today Galileo is mostly remembered for being the champion of the Copernican theory of the solar system over the Ptolemaic theory had also stood since the first century AD.  In fact, his greatness as a scientist far exceeded even this historical achievement.

His theories on inertia and relativity would ultimately become` the pillars on which the new physics of the 20^th century would be built.