Indifference to Motion or Rest

Galileo's Ship§

From Galileo's Ship, we already have our first clue that absolute space may not be physically meaningful. Galileo's thought experiment shows that it is impossible to distinguish between uniformly moving reference frames through any mechanical experiment performed within the ship. A person aboard the ship is therefore logically justified in claiming that they are at rest, since there is no experiment that can determine whether the ship is moving relative to the ocean, which we conventionally choose as our reference frame for "rest."

This does not prove that absolute space does not exist. Rather, it suggests that if absolute space exists, it has no observable physical consequences. Such observations naturally motivate a relational view of space, where only motion relative to other objects has physical meaning.

Indifference to Motion or Rest§

Therefore, the first birth of the concept of inertia begins to take place here.

Prior to Galileo, natural philosophers generally treated rest as a privileged state: if there is no force maintaining an object's motion, the object should eventually come to rest. Galileo's work begins to break this assumption. We can now see that, mechanically, an object does not need to be "at rest" in order to remain in its natural state. In the absence of a net force, an object can continue its motion uniformly.

This gives us a very different way of thinking about motion. Rest is no longer a privileged state of motion. An object moving uniformly and an object at rest are, mechanically, equally natural states.

And this leads to an important consequence: there is no mechanically privileged state of rest. If we are moving uniformly relative to another inertial reference frame, there is no mechanical experiment performed entirely within our own frame that can tell us that we are the ones "really moving."

Newton's First Law§

Do not be afraid to see Newton's name here, because Newton's First Law is, in an important sense, a formalization and generalization of the idea developed through Galileo's work.

Which states:

If no net force acts on an object, then the object remains at rest or continues in uniform linear motion.

Notice what happened here.

Galileo did not simply write down the modern statement of Newton's First Law and call it a law of nature. The idea developed gradually: first, the distinction between rest and uniform motion began to lose its privileged status; then the idea of inertia was developed further; and finally Newton formulated it as a general law of mechanics.

And for readers who have been wondering why this book teaches such a long history rather than going straight to the point, now I can answer the question:

It is to

1. desacralize any false belief about the contribution of individual physicists to physics;
2. really see how to think about physics rather than only what to think;
3. understand that history is actually necessary basic knowledge for learning physics, contrary to the common belief that it is merely a side track. If one learns a theory without understanding the problems and assumptions that gave rise to it, one may know how to apply the theory without understanding when its assumptions are appropriate, why the theory was needed in the first place, or when it is necessary to move beyond it.

Newton's Second Law§

We have now reached the question that Galileo's mechanics left open.

If an object can remain at rest or move uniformly without requiring a force, a force then must changes it motion.

Displacement alone cannot tell us that a force is acting. An object can change its position without being acted upon by any net force.

Velocity alone cannot tell us either. An object can have a non-zero velocity and continue moving uniformly without any net force.

What matters is the change in velocity and Newton turned this idea into a quantitative law later. Force is therefore no longer simply another kind of motion, nor is it something required to maintain motion. It is what produces a change in motion.

This gives us a remarkable conceptual reversal from the physics before Galileo.

Motion does not need a cause. Change in motion does.

Galileo had already begun to separate motion from its supposed cause. Newton completed this separation by giving us a quantitative relationship between the cause and the change:

$$\text{force} \longrightarrow \text{acceleration}$$

Galileo's Direction-Dependent Laws§

There is, however, still a problem with Galileo's picture.

Although Galileo has begun to remove the distinction between rest and uniform motion, he still treats motion differently depending on its direction.

Consider a falling object.

For Galileo, falling is not the result of a force acting upon the object. It is simply a natural motion governed by its own law: the object accelerates downward uniformly.

Why does Galileo refuse to call this acceleration a force?

Because force, in his physical philosophy, must have some observable mechanical effect. A force is something that can be experienced through an interaction: we can push, pull, resist, or otherwise observe its mechanical consequence. But when an object is simply falling, there is no corresponding mechanical interaction that Galileo can identify as a force acting upon it. The falling is therefore treated as a law of nature rather than as the effect of a force.

This leaves Galileo with laws of motion that are still direction-dependent. Horizontally, an object can maintain uniform motion; vertically, an object naturally accelerates as it falls.

This is particularly clear in projectile motion: the horizontal component follows uniform motion, while the vertical component follows the law of falling.

Coincidence? ( Optional Read Up )§

For those who have heard about General Relativity, you may notice something fascinating here: Einstein also treats free fall as motion that does not require a gravitational force. A freely falling object is, locally, in an inertial frame.

So, historically, we have something rather interesting:

Galileo → Newton → Einstein

Galileo and Einstein arrive at surprisingly similar ways of thinking about free fall, while Newton's mechanics sits between them and interprets falling through the concept of gravitational force.

And the similarity goes even deeper than this.

The same pattern will appear when we talk about space and time. Newton believed in an absolute space and an absolute time: there exists a privileged background against which true motion can be defined. Galileo's developing mechanics, on the other hand, already points us toward the idea that there is no mechanically privileged state of rest. Einstein will later take this much further: there is no absolute frame of reference from which the universe's motion can be judged.

Galileo → Newton → Einstein.

In both cases, Galileo and Einstein end up surprisingly close to each other, while Newton sits historically between them.

Coincidence?

We will come back to this.