lee_smolin's picture
Physicist, Perimeter Institute; Author, Einstein's Unfinished Revolution

The Principle of Inertia

My favorite explanation in science is the principle of inertia. It explains why the earth moves in spite of the fact that we don't feel any motion, which was perhaps the most counterintuitive revolutionary step taken in all of science. It was first proposed by Galileo and Descartes and has been the core of all the successful explanations in physics in the centuries since.

The principle of inertia is the answer to a very simple question: how would an object that is free, in the sense that no eternal influences or forces affect its motion, move?

This is a seemingly simple question, but notice that to answer it we have to have in mind a definition of motion. What does it mean for something to move?

The modern conception is that motion has to be described relative to an observer.

Consider an object that is sitting at rest relative to you, say a cat sleeping on your lap, and imagine how it appears to move as seen by other observers. Depending on how the observer is moving the cat can appear to have any motion at all. If the observer spins relative to you, the cat will appear to them to spin.

So to make sense of the question of how free objects move we have to refer to a special class of observers. The answer to the question is the following:

There is a special class of observers, relative to whom all free objects appear to either be at rest or to move in straight lines with constant speeds.

I have just stated the principle of inertia.

The power of this principle is that it is completely general. Once a special observer sees one free object move in a straight line with constant speed, she will observe all other free objects to so move.

Furthermore suppose you are a special observer. Any observer who moves in a straight line at a constant speed with respect to you will also see the free objects move at a constant speed in a straight line, with respect to them.

So these special observers form a big class, all of which are moving with respect to each other. These special observers are called inertial observers.

An immediate and momentous consequence is that there is no absolute meaning in not moving. An object may be at rest with respect to one inertial observer, but other inertial observers will see it moving-always in a straight line at constant speed. This can be formulated as a principle:

There is no way, by observing objects in motion, to distinguish observers at rest from other inertial observers.

Thus, any inertial observer has equal rights to say they are at rest and it is the others that are moving.

This is called Galileo's principle of relativity. It explains why the Earth may be moving without us observing gross effects.

To appreciate how revolutionary this was notice that physicists of the 16th Century could disprove Copernicus's claim that the Earth moves by a simple observation. Just drop a ball from the top of a tower. Were the Earth rotating around its axis and revolving around the Sun at the speeds Copernicus required, the ball would land far from the base of the tower. QED. The Earth is at rest.

But this proof assumes that motion is absolute, defined with respect to a special observer at rest, with respect to whom objects with no forces on them come to rest. By altering the definition of motion, Galileo could argue that the very same experiment that previously proved that the Earth is at rest now demonstrates that the Earth could be moving.

The principle of inertia was not just the core of the scientific revolutions of the 17th Century. It contained the seeds of revolutions to come. To see why, notice the qualifier in the statement of the principle of relativity: "by observing objects in motion." For many years it was thought that there would be other kinds of observations that could be used to tell which inertial observers are really moving and which are really at rest. Einstein constructed his theory of special relativity simply by removing this qualifier. Einstein's principle of relativity states:

There is no way to distinguish observers at rest from other inertial observers.

And there was more. A decade after special relativity, the principle of inertia was the seed also for the next revolution—the discovery of general relativity. The principle was generalized by replacing "moving in a straight line with constant speed" to "moving along a geodesic in spacetime." A geodesic is the generalization of a straight line in a curved geometry—it is the shortest distance between two points. So now the principle of inertia reads:

There is a special class of observers, relative to whom all free objects appear to either be at rest or to move along geodesics in spacetime. These are observers who are in free fall in a gravitational field.

And there is consequent generalization of the principle of relativity.

There is no way to distinguish observers in free fall from each other.

This becomes Einstein's equivalence principle that is the core of his general theory of relativity.

But is the principle of inertia really true? So far it has been tested in circumstances where the energy of motion of a particle is as much as eleven orders of magnitude greater than its mass. This is pretty impressive, but there is still a lot of room for the principle of inertia and its twin, the principle of relativity, to fail. Only experiment can tell us if these principles or their failures will be the core of revolutions in science to come.

But whatever happens, no other explanation in science besides the principle of inertia has survived unscathed for so long, nor proved valid over such a range of scales, nor has any other been the seed of several scientific revolutions separated by centuries.