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The determinism of Laplace

When we look at the determinism of Laplace, we are immersed in his biography and, inevitably, we find the figures of the French Revolution. For the mathematician Pierre-Simon Laplace was associated with the greatest, Mirabeau (MP Third State author of the famous « We are here by the will of the people and we will leave only by the force of bayonets), of Alembert (one of the founders Encyclopedia), Condorcet (mathematician member of the national Assembly), Bailly (astronomer, the first to take the oath of palms game), Lavoisier (the father of modern chemistry), Monge, Legendre and Lagrange (the great mathematicians of the time) and then Bonaparte (to whom he passed the competition gunner) …. Laplace merges with the history of France.

All his life, he sought a place in the sun, a pension of a particular academy, abusing his relationships (d’Alembert who found him his first paid teacher post), jealous of his great competitor (Legendre) he sometimes plagiarized, and highlighting (too probably) his extraordinary aptitude for mathematics.

Newton as a starting point

Newton was for him a starting point. The English scientist had put into equations of planetary motion (but also the apples that fall on the heads of scholars), discovering, by the way, the properties of a particular and universal force: the gravity . Newton also noted irregularities in the motion of planets. This irregularity could, in Newton, make the whole system unstable and even lead eventually to the collision of planets or fall into the sun. 

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solar system

Newton had described gravity as a force that each body exerts on another, proportional to the product of the mass of the bodies, and inversely proportional to the square of their distance:

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gravity

But Newton was careful to explain the origin of this force. Divine intervention was still necessary for him, in particular to adjust gravity at a fair value to prevent the solar system from collapsing or to periodically correct the irregularities in the running of the planets.

The determinism of Laplace

Newtonian mechanics remained simple when one considered that two bodies interact (the earth and the sun) and the easy equation to solve. When a third body (eg the moon) was introduced, it was complicated. If we added all solar system bodies, complexity was such that mathematics reach their limit. Laplace attacked this problem and found the first solutions : the solar system was put into equations. Laplace showed that the orbits of Jupiter and Saturn, for example, increased and then reduced by a period of 929 years. The solar system therefore remained stable long-term. The corollary of the work of Laplace was that the universe was written in advance : it was fully determined. Knowing the initial conditions, we could well determine the location of all objects at any time in the future as in the past. Everything was determined ! It was the birth of the Laplacian determinism. Incidentally, Napoleon ordered the absence of God in his works:

The celestial mechanics Treaty

  • How expensive Laplace, you give the laws of all creation and, throughout your book, you do not speak once the existence of God! Napoleon pointed out to him
  • Sire, said Laplace, I had no need of that hypothesis.

Everything was said. First, God was only a hypothesis. On the other hand, we could do without describing the Universe ! This is a deep determinism widespread.

We must consider the present state of the universe as the effect of its previous state and as the cause of the one that follows. An intellect which at a given instant knew all the forces with which nature is animated, the respective positions of the beings that compose it, if indeed it were vast enough to submit these data to analysis, embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom. Nothing would be uncertain for it, and the future as the past would be present to its eyes. Pierre-Simon Laplace.

To say that God does not exist, there is not a … He is the worthy heir of materialists, such as:

  • Epicurus and Democritus who were not atheists, but thought that the gods did not intervene in the functioning of the Universe;
  • Descartes (the principle of inertia: every effect has a cause and vice versa)
  • Leibniz (God created a perfect world he no longer has to intervene)
  • and the king of materialists, Baron d’Holbach . How not to be deterministic after reading his system of nature ?

In a dust swirl pupil a strong wind; some confused it seems to us, in the most awful storm excited by opposing winds that raise the waves, there is not a single molecule of dust or water that is placed randomly, which has its sufficient cause to occupy the place where it is located, and which strictly act the way it should be. A surveyor who would know exactly the different forces at work in both cases, and properties of the molecules that are driven, shows that, according to the data causes, each molecule is exactly as it should be, and can not act otherwise than she does. Baron d’Holbach

Determinism today

To say that everything is determined does not invalidate the hypothesis of God. For sure, one can predict the future, but it does not answer a fundamental question: where does the gravity comme from and why it takes this particular value? It is the same for the speed of light or the mass of the electron (and others). It is shown in quantum mechanics that a small variation of the values ​​of these constants leads to a sterile universe. Everything behaves as if the values ​​had been « settled » so that the universe is stable and it allows the emergence of life. So determinism can lead to a certain intuition of God that would have set the constants ….

Heisenberg and the end of determinism?

One of the major assumptions of Laplace is to perfectly know the initial conditions including the speed and position of all objects. But Heisenberg, with his uncertainty principle (or rather indeterminate), showed that a quantum level, that are not possible: the more we know the speed, the less we know the position and vice versa. Knowledge of the initial conditions is not possible and determinism a chimera at the microscopic level.

The formation of the solar system

Laplace was first postulated that the solar system is formed from a huge gas nebula turning on itself. In the center, a denser area is formed, driving under the influence of gravity to the constitution of the sun. Gas continued to turn around, is organizing filament, like the rings of Saturn. E These filaments are cooled and condensed into balls that formed the planets in passing, Laplace solved one of the puzzles of astronomy: it explained why the planets move all in the same direction and in coplanar orbits (located in the same plan).

Black holes

He was also the first to postulate:

  • objects outside our Galaxy (Milky Way), as other galaxies (as Andromeda);
  • but also of massive celestial bodies exercising an attractive force such that even light could not escape: and he described the first black holes, two hundred years before Hawking .
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