Newton's laws of motion can be summarized as:
First law: an object that is at rest will stay at rest unless a force acts upon it. An object that is in motion will not change its speed unless a force acts upon it.
Second law: the rate of change in the motion of an object - denoted by the symbol a - is directly proportional to the applied force F and inversely proportional to its mass m: a = F/m.
Third law: all forces between two objects exist in equal magnitude and opposite direction. If an object A exerts a force FAB on a second object B, then B simultaneously exerts an equal but opposite force FBA on A: FAB = −FBA.
Newton's law of universal gravitation:
Every point mass (m1) attracts every other point mass (m2) in the universe with a force (F) which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. F = G.(m1.m2)/r2
According to Newton, everything in our universe was composed of tiny, hard, indestructible particles, called point masses, which could be assembled in an unlimited number of different ways to shape thus all the material objects we encounter in the world. That idea possibly sheds light on his preference for alchemy experiments. Light also, according to Newton, consisted of tiny hard particles; corpuscles. His particle view of light would be reconfirmed, in a certain way, by quantum physics in de 20th century.
Important assumptions of Newton about space, time and matter are:
The space in which the universe "takes place" is absolute. Everything in the universe moves relative to that fixed absolute "stage".
Time is absolute and objective. Clocks will run at the same speed everywhere in the universe in every situation.
Space and time are both continuous. This means, they cannot be divided into their smallest parts.
Everything exists independent from the observer and is therefore an objective fact.
Everything in the universe - including light - is composed of utterly small particles.
According to current insights Newton has turned out to be wrong in all these assumptions. This does not diminish in the least his undeniably important contributions to science.
With his theory of gravity and his laws of motion, Newton was able to explain why, among other things, the moon did not fall on the earth, how low and high tide came about, and why heavy and light objects fell equally fast in a vacuum. Newton, incidentally, had no real idea what caused gravity and found it extremely unsatisfactory that he had to assume a force that applied at a distance ('Hypotheses non fingo' - I do not make up any hypothesis).
Newton thus created a mathematical model of our environment with immense predictive power. Its enormous success has led us to equate reality with its mathematical model. The accurate predictive power of Newton's theories affected the thinking of all scientists coming after him in a very deep way. It still affects current thinking. Yet, already in the time of the ancient Greeks, there had been scholars pointing to serious problems with this vision of reality.
Zeno of Elea (ca. 490 BC) and his paradoxes
The assumption by Newton that space and time are continuous is in direct contradiction with the insights of Parmenides and Zeno of Elea. They expressed their ideas by formulating paradoxes that are not as easy to disprove as results of incorrect reasoning, as one might think.
Parmenides was Zeno's teacher. To support the message of his teacher about the impossibility of diversity and change, Zeno produced a number of paradoxes that are still known today. With his paradox about the impossibility of movement, Zeno disputed in fact the idea that space is continuous and that each distance can be divided unlimitedly into smaller and smaller pieces. His most cited paradox is the idea of the arrow that will never reach its target because it must therefore travel an infinite number of distances of its trajectory. There exists even an interesting quantum effect that is named after Zeno and his paradox, to be discussed later.
By applying mathematics, we thought we had eliminated Zeno's paradox: after all, in mathematics the sum of an infinite series can be finite: (1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... ad infinitum) = 2. However, is the physical world indeed equally mathematical in character up to infinitely small details? Do physical infinities exist? The mathematical proof of the finiteness of the sum an infinite row of numbers uses limit values at infinity. In the real world we only reluctantly accept infinities. Consider the idea of black holes that imply infinities, singularities, by their existence. Accepting their existence was surely not immediate and their existence is still hypothetical in the sense that we do not find or create any black holes in our laboratories [10]. Or do we? The mathematical "proof" of the logical error in Zeno's paradox is a good example of how we allow our concept of reality to be dictated by mathematical models. Anyhow, Zeno's paradox appears not so easy to be reasoned away and keeps popping up its mocking face.
Zeno did not mean to say that the arrow won't reach its target in our experience. His paradox was meant to support his message that reality must be an illusion. This idea seems perhaps far-fetched, but it will turn out that it offers an excellent road sign of how to understand and solve the difficult interpretation problems that quantum physics presents to us.
In this connection, Democritus, a contemporary of Zeno, should also be mentioned. Democritus was a Greek philosopher who proclaimed the hypothesis that all matter consisted of very small indivisible particles, called atoms. The idea behind that was related to that of Zeno and Parmenides, namely that infinity is not a characteristic of nature. You cannot, therefore, keep splitting a piece of matter endlessly in two. This splitting will always come to an end. Therefore, Democritus is viewed as the father of the idea of the atom. Incidentally, Zeno in his turn did not wholly agree with the ideas of Democritus.
Pierre-Simon Laplace (1749-1827)
The influence of Newton's theory on philosophy and theology was enormous. With the right mathematical instruments everything seemed computable and God could be sidelined in his creation with regard to direct interventions. And, of course, with God everything that had to do with church and religion. Some people who did not like the position and the demands of the church preferred that idea, as did Pierre-Simon Laplace, a French mathematician and astronomer. He is the one who replaced the geometry-based classical mechanics with analytical methods which facilitated mechanics calculations considerably.
Laplace is known for his hypothetical demon [11] who knows exactly the starting positions, masses and speeds of all objects in the entire universe and is able to use this knowledge to calculate the course of all events in the universe. The demon is hypothetical. He does not have to exist for the final conclusion of Laplace: all matter - including past and future - has ultimately fixed knowable properties and will therefore obey Newton mechanics for 100%. The universe becomes a gigantic clockwork from which chance is vanished. According to Laplace, coincidence as we experience it, therefore only exists for humans because they do not have sufficient information and computing power to calculate everything in advance.
This turned coincidence and also man's free will into an illusion. People, animals and plants became nothing more than very complex machines. Which is an idea that is still strongly expressed by many in the current scientific community. Fortunately, our legal system is still based on free will, meaning that we basically assume that the offender did have a choice. The judge will not easily honor your lawyer pleading that weaving errors in your DNA caused you to take a grab out of the supermarket till. It is however striking that when something goes wrong in a company's administration,