Most scientists accept Newton's laws as they describe with an acceptable accuracy most motions. They are replaced by the laws of relativity at speed close to the velocity of light.
Aristotle believed that:
- A heavy body should fall faster that a lighter one because the earth's pull
would be greater on the heavy body.
- Rest was the natural state of any body, and it moved only if a force was
applied to it. From this he deduced that the earth was at rest.
- One can find all the physical laws by pure thought; experiments are not
necessary.
Galileo Galilei had already shown:
- That all bodies -light and heavy- fall at the same speed. Every body in
free fall increase its speed exactly at the same rate.
- The effect of a force on a body is to accelerate it movement, not only makes
it moves.
On the base of Galileo Galilei's experiments, Newton showed that a body in
free fall is subject to a constant force that makes it speed up. In consequence
the effect of a force is to increase the speed of the body, and not only to
put it in motion.
Newton's first law: If a body is not subjected to any force, it will keep
moving in a straight line and at the same speed, or remains at rest.
Newton's second law: when a force acts on a body, the body will accelerate (change its speed) at a rate directly proportional to the force (the higher the force, the greater the acceleration). Moreover, at equal force, the greater the mass of the body, the slower it accelerates.
Newton's law of gravity: two bodies attract each other with a force that is
proportional to the mass of each body but the force decreases in proportion
to the square of the distance between them. This law allows us to calculate
the orbits of the earth, moon, sun, and planets.
To understand the first Newton law correctly we must take into consideration the coordinates of reference. For instance, Newton's law of inertia certainly applies with a good accuracy to the visible fixed stars. But if we use coordinates fixed rigidly to the earth then, by reference to these coordinates that move with the earth, each star describes a circular orbit each day, and this is in apparent contradiction with the law of inertia. If we want the stars to adhere to Newton's first law we must choose the right system of coordinates in which fixed stars do not move in a circle. A Galilean system of coordinates will do it.
Let us assume that a traveller is immobile in a train moving at constant speed and in straight line and an observer is also immobile on the ground. Let us now assume that a bird is flying in such a way that the observer on the ground notices that it is flying at a constant speed (uniform motion) and on a straight line. The traveller in the train would notice that the bird is flying in another direction and at a different speed, but its motion would still be uniform and on a straight line. To generalise the concept we may say: if an object is moving on a straight line and at uniform velocity by reference to a system of coordinates K, it will also be moving on a straight line and at constant speed on another system of coordinates K', provided that K' is on an uniform translation by reference to K.
To generalise even one step further we can say: If K is a Galilean system of co-ordinates, then every other system of co-ordinates K' is also Galilean if its motion of translation is uniform. The mechanical Galileo-Newton's laws hold good for both K and K'. We can even go another step further and enounces what is known as the principle of relativity in the restricted sense: if, relative to K and K' we have a non-rotating uniformly moving co-ordinate system, then the same general laws apply to both K and K' in exactly the same way.
As long as scientists thought that classical mechanics could represents all natural phenomena, the above principle of relativity was considered as fully valid. With the recent advances in sciences, this is not so certain. However the principle represents natural phenomena with a good accuracy in the field of mechanics.
If the principle of relativity (in the restricted sense) is not valid, the description of natural phenomena in the Galilean coordinate systems K,K',K''etc. moving uniformly relative to each other, will not be the same.
From Newton's laws, one derives that rest is relative. For instance, if two bodies A and B are moving away from each other one could say that A was at rest and that B was moving away from A with a speed V. But we could as well say that B is at rest and A is moving with the same speed. Or even that both A and B are moving away from each other with a speed V/2. In other words there is no absolute standard of rest. Newton refused to accept this concept of lack of absolute rest or, better, space, because it did not fit with his conviction that God was absolute.
Newton, as Aristotle, believed that time was absolute. This means that the
measurement of the length of time between two events is the same for all observers.
Einstein's theories changed all this. However, the notion that time is absolute
is accurate enough for everyday life; it is only not true anymore when bodies
are moving close to the speed of light.