Every marksman knows that if a bullet misses its target, the gun was not aimed correctly. The statement seems trite, yet it conceals a deep truth. The fact that a bullet will follow a definite path in space from gun to target, and that this path is completely determined by the magnitude and direction of the muzzle velocity, is a clear example of what we might call the dependability of nature. The marksman, confident in the unfailing relationship between cause and effect, can estimate in advance the trajectory of the bullet. He will know that if the gun is accurately aligned the bullet will hit the target.
The marksman's confidence rests on that huge body of knowledge known as classical mechanics. Its origins stretch back into antiquity; every primitive hunter must have recognized that the flight of a stone from a sling or an arrow from a bow was not a haphazard affair, the main uncertainty being the act of projection itself. However, it was not until the seventeenth century, with the work of Galileo Galilei and Isaac Newton, that the laws of motion were properly formulated. In his monumental work Principia, published in 1687, Newton expounded his three famous laws that govern the motion of material bodies.
Cast in the form of mathematical equations, Newton's three laws imply that the motion of a body through space is determined entirely by the forces that act on the body, once its initial position and velocity are fixed. In the case of the bullet, the only significant force is the pull of gravity, which causes the path of the bullet to arch slightly into a parabolic curve.
Newton recognized that gravity also curves the paths of the planets around the Sun, in this case into ellipses. It was a great triumph that his laws of motion correctly described not only the shapes but also the periods of the planetary orbits. Thus was it demonstrated that even the heavenly bodies comply with universal laws of motion. Newton and his contemporaries were able to give an ever more accurate and detailed account of the workings of the solar system. The astronomer Halley, for example, computed the orbit of his famous comet, and was thereby able to give the date of its reappearance.
As the calculations became progressively more refined (and complicated) so the positions of planets, comets and asteroids could be predicted with growing precision. If a discrepancy appeared, then it could be traced to the effect of some contributing force that had been overlooked. The planets Uranus, Neptune and Pluto were discovered because their gravitational fields produced otherwise unaccountable perturbations in the orbits of the planets.
In spite of the fact that any given calculation could obviously be carried out to a finite accuracy only, there was a general assumption that the motion of every fragment of matter in the universe could in principle be computed to arbitrary precision if all the contributory forces were known. This assumption seemed to be spectacularly validated in astronomy, where gravity is the dominant force. It was much harder, however, to test in the case of smaller bodies subject to a wide range of poorly understood forces. Nevertheless Newton's laws were supposed to apply to all particles of matter, including individual atoms.
It came to be realized that a startling conclusion must follow. If every particle of matter is subject to Newton's laws, so that its motion is entirely determined by the initial conditions and the pattern of forces arising from all the other particles, then everything that happens in the universe, right down to the smallest movement of an atom, must be fixed in complete detail.
This arresting inference was made explicit in a famous statement by the French physicist Pierre Laplace:1
Consider an intelligence which, at any instant, could have a knowledge of all forces controlling nature together with the momentary conditions of all the entities of which nature consists. If this intelligence were powerful enough to submit all this data to analysis it would be able to embrace in a single formula the movements of the largest bodies in the universe and those of the lightest atoms; for it nothing would be uncertain; the future and the past would be equally present to its eyes.
Laplace's claim implies that everything that has ever happened in the universe, everything that is happening now, and everything that ever will happen, has been unalterably determined from the first instant of time.
The future may be uncertain to our eyes, but it is already fixed in every minute detail. No human decisions or actions can change the fate of a single atom, for we too are part of the physical universe. However much we may feel free, everything that we do is, according to Laplace, completely determined. Indeed the entire cosmos is reduced to a gigantic clockwork mechanism, with each component slavishly and unfailingly executing its preprogrammed instructions to mathematical precision. Such is the sweeping implication of Newtonian mechanics.
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