# What is the proof of the law of inertia?

An object in motion will stay in motion unless acted on by an outside force; ditto for an object at rest. Perhaps poorly stated, that is the law of inertia. As I understand it, it is pretty fundamental–atleast for macro type objects.

Question: What is the proof of this law? Is it taken as given because it stands to reason? What’s the straight dope?

At one time it was thought that all objects would eventually come to rest regardless, until Galileo noticed a ball that rolled down an incline rolled up the opposite incline at nearly the same height; the smoother the incline, the closer the height. Galileo reasoned that the difference between the heights was caused by friction acting on the ball. If there was no friction, the ball would attain the same height over and over again, virtually forever. If there’s no incline on the other side, the ball will roll off and travel virtually forever.

Newton expanded on this in his first law of motion by saying that a force is not needed to keep an object in motion. The ball does not come to rest beacuse of the absence of force, but the presence of it: friction. In the absence of force, the body remains in motion.

[QOUTE]An object in motion will stay in motion unless acted on by an outside force; ditto for an object at rest. Perhaps poorly stated, that is the law of inertia. As I understand it, it is pretty fundamental–atleast for macro type objects.
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…in an inertial(not accelerating, that is) frame of reference.

I don’t think there’s an experimental proof of this fact.
Our observations of the planets, though, provide good evidence of Newton’s second law, namely,
F=ma
Setting F=0, you get a=0, which is the result we want.

There are tons of experiments that bear out the law of inertia. Any time a physicist uses F=ma they are testing it, essentially. As mic84 points out, the law of inertia is just a special case where F=0 and therefore a=0. (If you can show me a planet that’s not accelerating, though, I’ll give ya a million bucks.)

In an interial frame! I mean, a planet that’s not accelerating in an inertial frame!

(I sure as hell hope I can post this before someone comes after the prize!!!)

Taking F=ma and setting F=0 yields a=0. That makes sense, I never thought if it that way. But that also sounds sort of definitional to me. Define Force to be anything that causes acceleration, then by definition no Force=>no acceleration. Instead of a proof we have an identity.

Did that make sense? I’m assuming I’m mistaken; where’s my error?

Thanks for the replies. I’ve been wondering about that.

If it can’t be proven axiomatically, but only demonstrated experimentally, why isn’t it known as the theory of inertia?

Force isn’t only something that causes acceleration, it’s also anything that changes velocity, i.e., pushes or pulls. Without the pull of friction, the object travels indefinitely. Without the push of additional force, the object won’t accelerate. Inertia just says that velocity won’t change spontaneously, both slowing down and speeding up are due to a force changing the velocity.

You’re right, if you define force this way, the law of inertia just follows. OTOH, you could see force as something fundamental(since there are only three of them, it’s reasonalbe). Then F=ma is meaningful, but there’s no “proof” of it, just experimental evidence.

You cannot “prove” physical laws nor theories. To do so would require observation and/or experimental verification over all time and space.

A physical “law” is simply a summary of observations.

A theory is an explanation of one or more observation(s).

To use a chemistry example, it has been observed that a given chemical compound always contains the same proportion by mass of each of its constituent elements. After this was observed to be true for every chemical compound so analyzed, the observation was deemed important enough to be summarized as the “Law of Definite Proportions.”

Soon thereafter, Dalton proposed an explanation for why the aforementioned law was always observed to hold true. His theory is called “Dalton’s Atomic Theory.” The theory hypothesizes that all elements are made up of atoms that combine to form elements.

While the language of physics is often stated to be that of mathematics, physics itself is not mathematics. So far as I am aware, there are no axioms in physics. Everything is based on experimental observation.

Thanks for the explanation.

To address the OP directly, as I stated in my last post, you cannot prove physical laws. You can only gather more observations that support a law and do not disprove it.

While laws cannot be proved, they can be disproved. One example is the “Law of Conservation of Mass.” This law was experimentally invalidated with the advent of nuclear physics.

The fact that we can send satellites into high orbit, and they stay there for a very long time, is a pretty convincing demonstration of inertia.

Pravnik

The definition of acceleration is the rate of change of velocity. So if something is accelerating, it’s velocity is changing.

GTPhD1996

An alternative viewpoint:

The “law of inertia” (which can be stated alternately as the ‘conservation of momentum’) can actually be immediately inferred from the hypothesis that space is homogeneous.

In other words, the “law of inertia” is a direct consequence of the fact that space itself ‘looks’ the same at every place in the space-continuum. Thus, in the absence of other objects, a given object has no way to tell where it is in space, because everything looks the same–furthermore, it doesn’t have any way to tell if it is moving (if you were floating by a perfectly clear, flat piece of glass, but couldn’t touch it, could you tell how fast you were going? or if you are even moving at all?). If the object has no way of knowing how it is travelling through ‘space’, how could it alter its path.

This, of course, isn’t a “proof”, but it’s one way that theorists might think about it. Well, at least theorists who ignore relativity and quantum physics.

Yes, that’s true. But how is that different from what I said?

Don Roberto has it correct. Conservation of momentum/energy/mass is comes from the translation symmetry of space-time. A good general relativity textbook will cover this in more detail than you want. This pushes back the question to “why space-time is homogenous?”. I don’t know the answer to that one.

This principle is also useful in regions of space that are not homogenous. The best example is within the lattice of a crystalline solid (e.g. metals). The atoms with the solid are positioned in a three-dimensional pattern. This means that space looks the “same” only if you move in certain directions for certain distances. These restrictions mean that the momenta of particles (e.g. electrons) are conserved only for certain types of motion. This is the basis for all microscopic descriptions of solids.

GTPhD1996, the definition of acceleration is the rate of change of momentum, ie. F = d/dt (mv). If the object’s mass is constant, the definition reduces to yours. Rockets (mass decreasing) and rolling snowballs (mass increasing) are conspicuous counter-examples.

F stands for force, not acceleration.

Per Karl Popper, the hallmark of a scientific theory is falsifiability. What this means is that scientists don’t spend their time trying to “prove” something to be true, but rather think of ways to falsify or disprove a certain theory. A theory is falsifiable if it can make a testable prediction. For the case of inertia, we can have a simple test: go to space and release a ball with initial linear velocity v. The Law of Inertia predicts that the ball will travel in a straight line. We make this prediction on paper here on earth.

Now you carry the actual experiment by going aboard the space shuttle. Then record the results. Compare your experimental results with your theoretical prediction.

Do we know for sure that the law of inertia is true? What we do know is that nobody has shown it to be false yet (as far as I know). It’s the best model we’ve got so far. That’s what scientists do: try to find better and better models of nature.