newton's cosmic billiards

NEWTON’S COSMIC BILLIARDS THE CONFIDENCE TRICK INFLICTED ON WESTERN CIVILIZATION BY A FEW MATHEMATICIANS

© H. J. Spencer (December, 2017) ABSTRACT The thesis here is that Newton invented a simplistic analogy of the recently introduced game of billiards, popular with the aristocracy since 1470, when it was invented by the French kings. This model of collisions between pairs of billiard balls, once set in motion, was also supplemented by several new concepts, unstated assumptions and wrapped up in a new form of his mathematics (now known as the calculus) that limited widespread understanding and possible critiques to a new priesthood of self-selected mathematicians. Since this analogy was far too simple to reflect the complexity of reality, this model of the Universe must be viewed as an unconscious deception played both on the public and on Newton himself. Everyone has suffered ever since.

HISTORY Physics as a modern science was not launched in Europe until the Seventeenth Century, when Isaac Newton (1642- 1727) merged several ideas that had surfaced in the previous 200 years to formulate the new sciences of kinetics and dynamics. These were published in his masterpiece “The Mathematical Principles of Natural Philosophy” (usually referred to as Principia, one the Latin words in its original title). In terms of its impact on Western Civilization, it must be regarded as one of the most important books written in the last two thousand years. The book was successful in predicting observed planetary motions and concluding that matter in what had been seen as the other-worldly ‘Heavens’ was similar to that found on the Earth itself: all behaving in a similar way and subject to the same timeless ‘Laws’ of ‘dumb’ universal matter. This introduced the image of a mindless recent machinery (a ‘clockwork’) ticking away forever, without any ongoing Godlike intervention and reducing humans to just irrelevant observers. This deadly imagery dramatically reduced the self-confidence of western civilization to one where material selfishness was raised to the highest levels, hidden behind the ego-driven ideology of liberty and individualism. The following sections will try to demonstrate that this innovation was only a Confidence Trick (‘Con Game’) that was played on these intellectual giants themselves, as much as most of the population who came to believe in this new form of public magic. This modern ‘religion’ was obviously ‘true’ because of its exaggerated claims for directly fathering the technologies associated with the industrial revolution, when in fact it was the anonymous efforts of generations of engineers (many of them military) who built on the proven, but independent insights gained from trial and error and following intuitions devoid of mathematical inspiration. Science only started having a broad impact after about 1850, when the steam-engine had been running for 100 years.

BILLIARDS Newton built his edifice on two major contributions from his predecessor and rival, René Descartes (1596-1626); these were his ideas of a Reference Frame and composite algebraic variables. The idea of ‘Reference Frame’ is seen by mathematicians as three invisible lines, mutually set at right-angles to one another, marked with implicit units of distance and ‘defining’ absolute space itself. We can visualize our billiard table being set in the plane of the planets and the sun. We can visualize this by drawing two sets of parallel lines on the table (like a chess board) with the longer side of the table (called the Y-

2 lines or axis) and the shorter side marked with ‘X-lines’. To ease visualization, we can draw these lines about one inch apart with them being numbered from the left-corner. We now place one white billiard ball along the center Y-line, say at a distance 50 inches from the shorter side of the table. The striker then places his ‘red’ (cue-ball) down on the same Y-line but only about 30 inches from the shorter side. These balls must be made of the same material, perhaps ivory, and are of the same size and weight. A second white ball may be placed also on this same line but at a further distance say of 20 inches beyond the first one. Now, we imagine a ‘perfect’ striker who can hit the red ball always with the same force every single time and exactly along the center line. An observer stands near the table with a very accurate stop-watch and signals the striker to begin. He starts his watch as he sees the cue-ball start to move and stops it when it hits the first white ball; for simplicity (but not in reality) each ball is imagined to stop dead immediately when the next ball starts. Let’s imagine that the stop watch reads exactly one second between the first two collisions. Now speed is defined as distance covered per unit time, so we can calculate that the first ball moved off at 20 inches per second. If we were to measure the speed of the second ball after it had been hit, we would observe that it too moves after one and a half seconds, so we conclude it picks up all the motion from the first ball. If we repeat this experiment, we will always achieve identical results, when we can place the balls exactly in the same starting spots. In fact, if we were to substitute a heavier ball (say twice as heavy) for the third ball, we would see that its post-collision speed has been halved. This led experimenters to conclude that the critical ‘quantity of motion’ is the product both of weight (technically called ‘mass’ or “quantity of matter”) multiplied by the speed (actually velocity when directions are included). Newton called this new quantity the momentum of the moving object and built his whole science of motion (“kinetics”) on this idea. This provided a numerical value for Galileo’s original suggestion of inertia, leading to Newton’s First Law of Motion: a moving body maintains its exact momentum unless influenced by another interaction. In fact, when two ‘perfectly elastic’ objects collide they conserve the total momentum before and after the collision. In this billiard example, the striker provides the source of the overall activity. Perfection was also assumed in space since on Earth we always encounter friction that eventually slows down any motion; our billiard table would have to covered by magical cloth to eliminate all friction. So even our science of motion (‘kinetics’) assumes perfect conditions, which are never encountered on Earth.

PLANETS

Newton’s next step was a gigantic leap of the imagination right off into deep space, where he invented a new science of interactions or “dynamics”. His first step was to expand his dumb billiard ball to the size of a planet (or moon, as needed). Since he did not want to offend his Christian sensibilities he replaced his ‘striker’ with a mysterious force, called gravity that pulled all matter towards one another. He simply assumed that matter possessed this ‘intrinsic’ property (it was called ‘universal) and acted both continuously (as seen on Earth, with the infamous ‘falling apple’) and at a distance – without any touching. This latter he called ‘Far-Action’ and it was the most contentious invention of his solution and even today is usually rejected by most physicists with its substitution of the exchange of invisible intermediaries; “gravitons” in this case and ‘photons’ in the case of light (actually electrical and/or magnetic interactions). Most humans are so in love with their sense of touch that only direct contact (called ‘Near-Action’) is considered possible. My own unorthodox theory, forced me to return to Newton’s original Far-Action for all interactions but now not acting continuously but in a cyclic impulsive manner (like our striker hitting the cue-ball every minute). In the case of electrons, I have calculated this natural interaction rate to occur about a billion * billion times (1024) per second; much too fast for it yet to be seen or measured. Surprisingly, for most folks, assuming that interactions occur continuously (a concept called Force) makes for easier mathematics, so Newton could then prove that

3 smaller astronomical objects move around an ancient geometric curve called an ellipse; a result desired as the German Astronomer Johannes Kepler (1571-1630) has demonstrated about one hundred years earlier that the planets followed such trajectories around the sun. Actually, so does the moon around the earth but its deviation from a perfect circle is only detectable with sophisticated instruments. The ancient Greek mathematicians should have been flattered to see one of their inventions resurface 2000 years later but would have been disappointed that the paths through space were not following the easy and perfect shape: circles. Readers who seek a more detailed historical retelling of this era can check another of my essays, entitled “Good Heavens”.

CONCEPTS

We can see from this story that Newton had to invent several new abstractions that we call concepts. In addition to ‘mathematizing’ the humanly accessible intuitions such as space, time, matter and force. He also had to assume that the same ‘motivations’ operate “above, as below” (such as causality, continuity) at all scales (sizes) of reality. Worse, our billiard experiment assumed we could observe to perfect precision, identical balls are available and confirm that situations persist across time. Well, if humans did not yet have perfect clocks then we could always assume that God was watching at all times and He knew everything perfectly, just like the theologians assumed. I guess the real secret of the success of this method was that it appealed to human vanity that some humans could abstract out of the complexity of nature a simplistic scheme that could be represented symbolically (algebra) from one human imagination to another through a teachable technique known as mathematics that has bedazzled a few intellectuals for thousands of years.

PROBLEMS

Obviously, explaining gravity was a real challenge – in fact, Newton despaired of ever providing a suitable explanation for the rest of his life. Even, today physics has only a mathematical theory from Einstein that involves massive objects ‘bending’ space (how?) to make other large objects to follow these invisible ‘bent’ paths through space (how? – don’t ask embarrassing questions). It was not long before other mathematicians, such as the French mathematicians, LaGrange and LaPlace, had once again abolished time from astronomy by inventing mathematical variations across space that could ‘generate’ equivalent forces – a technique called potential energy. Now the physicists could return to their ancient hoax of pretending that all motion, both past and future, was ‘determined’ leaving the general population with the impression that everything was simply ‘predetermined’. In fact, as Newton knew, this method could NOT be extended to situations involving more than two interacting objects, except in a very few, very special situations; this is called the Three-Body Problem that still defeats scientists today at all levels of nature from astronomical (forcing us to use computer approximations) to the atomic level. The easiest assumption is just to assume that size does NOT matter. If a theory works for planets and seems to work at our human level then it surely works at all scales of the universe? The truth is that physics students learn perfect unreal examples to master the mathematical techniques, where the objects under study are totally isolated from all other sources of interaction; a method called ‘model building’. Even our astronomical observations from Earth can only check directions and have to assume that we are seeing remote objects with exactly straight light lines and our clocks are ‘good enough’. So this clockwork viewpoint (now called ‘Classical Mechanics’) was considered truthful and overwhelmed western educated thought until advanced technology was developed around 1900 that exposed its limitations because our view of atoms was too crude; electrons are vastly smaller than we could ever have imagined, forcing all of us to admit that the real, micro-world is hugely more complicated than we could ever have imagined. This new frontier, called ‘Quantum Mechanics’, has forced physicists to rethink all their mechanical ideas but most still cling to the ‘classical’ assumptions and especially the continuum mathematics invented 300 years ago. The ‘heart of the con’ is to convince

4 people that a method centered on numbers is the secret of the universe. If we can invent theories that calculate numbers and then get experimental scientists to examine these phenomena and develop techniques to generate comparable numbers (“measurements”), so when these two sets of numbers are “close enough” then we have “proved our theories”. We need some more skeptics to rise up and deny that reducing the complexity of the world to a simple abstraction, such as the concept of Number, has no great significance. Really, reducing even a two hour sporting event to a final score is a massive rejection of the vast, uniqueness of life and human interactions. My skepticism is expanded in another essay called “Illogicality”.