Newton – The Urge For Understanding The System Of The World
Posted on April 2, 2008 - Filed Under Arts and Entertainment
What distinguishes Newton among all the natural philosophers is that he understood better than anyone the fact that, if there is an explanation of the harmony of the World at all, it has to be offered in terms of our experience. Otherwise the Man will not understand it. Not understanding it means not learning from it, therefore no possibility of using it!
Like every natural philosopher of his time, Newton saw the explanation of the natural order in understanding the concept of force. What distinguishes him among philosophers is the way of approach towards understanding the force: the analogy. While the force holding the World in harmony was always associated with God’s power, the concept of force itself was formulated in terms of our experience, being entirely derived from this experience. And Newton sought in this experience a fact that might have analogous in the way World was seen as a system. At that time the World was seen as a Copernican System with Sun in center around which the planets are revolving in circular orbits.
Realizing that the Copernican System of the World can be mechanically understood if one accepts a force between Sun and planets, Newton set out to elucidate this force to the point where it can be explained through our experience. It was not an easy task, because this force must transcend the experience to date, in the sense that there was not a material agent that can help accomplishing its effect. But Newton undertook it and finished it with a consistency that cannot be found before him or ever since.
What is the fact of experience chosen by Newton? The human knowledge was familiar with the behavior of a stone tied up to a rope since times immemorial. Perhaps the most notorious recorded event related to such facts is that when David killed Goliath with a sling shot (1Samuel 17:48-51). This incident shows that the Man was able to skillfully use the sling even from old times. As a matter of fact it is known that ancient armies had specialized units of sling shooters.
In swirling a sling the hand feels a force: therefore a force exists pulling the stone away from the hand; this is the centrifugal force. This fact can be tested by anybody on a daily basis. Now, as the common experience shows, we can feel the centrifugal force of the stone only because the hand has to oppose a force in order to keep the stone rotating. In general, our experience shows that whenever a force acts along a direction, there is counterforce acting along the same direction but oppositely. Thus one can infer that there is a force acting centripetally on the stone and opposing to the one we feel at the hand when the stone rotates.
One of the main strokes of Newton’s genius was in using this common fact in an outstanding analogy: the planets of the Copernican System of the World travel around the Sun in closed circular orbits, exactly like our stone around the hand. Therefore they should have more in common with that stone!
The two situations are analogous, but only from a geometrical point of view. The main difference is a physical one: the rope is missing in the case of planets. However, in the case of a sling the existence of rope guaranties the existence of the centripetal force holding the stone in rotation. This turns out to be a real deficiency, because we can think of a centrifugal force acting upon planets and, by analogy, we would be induced to think of a centripetal opposed force. But can we? Can we think of a force acting through space in the opposite sense along the direction Sun-Planet, without any material agent to connect them?
This is, again, one of the crucial moments of our knowledge when the genius of Newton stepped in and delivered an answer that radically changed our thinking. Still appealing to experience, Newton reshaped it by transforming a common fact, which apparently had nothing to do with the force, into the effect of a force.
First, we should say that it was long realized that there are indeed apparent forces that don’t act through the intervention of a material agent, and these are even noticeable on a daily basis: the action of magnets, electricity and, finally, the daily weight of earthly bodies. The moment of analogy between magnetism for instance and the fall of bodies is usually associated with the known anecdote of the falling apple, whereby Newton realized that an essential determination of a force is not the material agent that might happen to be necessary in order to accomplish its effect, but that it is actually a cause of motion. The fall of an apple is completely equivalent with the motion of a magnet in the magnetic field of another magnet. In short, the fall of apple is a motion and should be caused by a force acting on the apple.
Then the next step in analogy is to see that the same cause that makes an apple fall is undoubtedly the cause that keeps the Moon around the Earth and the planets around the Sun. This fact can be seen by first noticing that we can throw the apple, and it describes a trajectory resembling to that of a cannon ball. Then push the imagination a little further, as Newton did, and think of a projectile shot horizontally from places at different altitudes, or at the same altitude with different speeds. If such a missile has enough initial speed, it can engage along a closed circumterrestrial trajectory. This, we may imagine, is the situation of the Moon, minus the initial shooting moment. And if this is the case, then we can push the imagination a little further to think of the Sun and planets in just about the same terms. And so it was!
Because in a round trajectory a body must, according to our experience, undergo centrifugal forces, the planets as well as the Moon must experience a centrifugal force. However, because the planets and the Moon are there forever, completing periodically their cycles, there should be a force upon them, which acts oppositely to the centrifugal force of the planets, otherwise they would be free to wander in space. This is the force of gravitation, the very same acting on apple to make it fall. Now, if the origin of this force is in the Sun, or Earth, as the case occurs, it is obvious that it does not require a material agent in order to help accomplishing its effect. No such agent can indeed be noticed between Sun and Earth or between Earth and Moon. The force, as well as its cause, can only be inferred as existing from the geometrical aspect of the motion of the planets and of the Moon in the way just shown.
If human experience was, at the time of Newton, enough in order to accommodate new facts like the action of a force without any material means between the bodies, it was however not sufficient to accommodate the consequences of these new facts. Those consequences are far beyond any experience, and even by today’s standards for that matter. First and foremost it had to be proved in a logical manner that, under the assumption of an existing centripetal force opposite to the centrifugal one, the motion of planets has indeed the geometric form of the Keplerian motion. This is nowadays a simple algebraic exercise, but in his time Newton had many challenges to overcome, as one can see just by simply browsing the “Principia Mathematica”. In the hands of Newton this problem led to the known system of Classical Dynamics, as usually taught in schools today. It is based on three fundamental axioms, whose role may be easier to understand if we offer their story.
The rigor of knowledge in the times of Newton was that of the Euclidean geometry: construct everything by a logical pursuit starting from a minimal set of axioms. These axioms have to be truths detached from experience, unprovable by that logic, but organically necessary for the pursuit itself. Their coming into existence can be seen as follows.
First of all, Newton needed a quantitative expression of the force of gravity. He inferred it from Huygens’ expression of the centrifugal force by noticing that the experience shows that an action upon matter in a point is always resisted by a reaction in the same point. Based on this he deduced that the force of gravity goes inversely with the square of the distance between two bodies, but he also realized that there is here a logically unprovable assumption: the principle of action and reaction. This became the Law III, known also as the Third Principle of Dynamics: “To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”
Secondly, Newton needed to prove that under the action of a force permanently directed toward a center, a point body follows a circular trajectory. Now, in a circular trajectory it is the velocity of the body that changes its direction in every moment of the trajectory, and this change is always directed along the radius, toward the center of trajectory. It is then only natural to assume that the force acting toward the center is in relationship (more exactly it is proportional) with this change in the velocity.
This is not a logically easy task mainly because one might rightfully ask: would the motion of a planet be different without the assumed force of gravitation? In other words, what is the trajectory of motion under no force? Thus Newton had to assume the form of motion under no force, and this became the Law I, known also as the First Principle of Dynamics: “Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.” It was inferred from the observations on the same old stone tied on a rope and rotated horizontally over our head. If we cut the rope during rotation the stone will continue to move in a straight line along the tangent to the circle of motion imposed by the rope. David must have known and mastered perfectly this fact! So Newton resolved that he had to accept the logically unproven fact that, when no forces act upon it, a body moves in a straight line with constant speed if it is not resting, in which case the speed is zero.
This will put the variation of speed in any point of the trajectory among the cases of the existence of forces acting upon our body, but that’s all; it will not say anything about the relationship between the variation of the velocity and the acting force. Here Newton introduced the Law II, which is a purely mathematical fact, known also as the Second Principle of Dynamics: “The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.” This is actually the exclusive mark of the Classical Mechanics as we know it today: the acting force induces a proportional variation of velocity along the line of action.
The Classical Dynamics is always taught and learned by starting from the three axioms that were called, even by Newton, Laws of Motion. While this is the order of things established by Newton himself, and is indeed logically the most economical in acquiring the necessary working knowledge and skills, it has however the shortcoming of hiding the true source of inspiration of those Laws of Motion. So much is lost from the initial warmth of Newtonian creation, that nowadays not many scientists even think that there was a superior motivation behind the construction of this system. As a matter of fact, the Science doesn’t even seem to consider taking note of this aspect of the problem otherwise than as a historical curiosity. However, behind the pure Science there is a message of Classical Mechanics. It can be learned by analyzing the reason of being of Mechanics. And that reason is gravity.
The three axioms above took care of the facts which have to be supplied in order to start the Science, so to speak. However, they couldn’t take care of the consequences of this Science, once started. When one talks about consequences, one usually understands the marvelous explanations provided by the Classical Mechanics that emerged from the three axioms. This was, indeed, quite a message! There is however a hidden message too.
In the analogy with the cannon ball, which indicated that the planets are acted upon by the same force of gravitation that acts upon apple, we don’t know anything about the initial moment of the motion of a planet, the way we know about the cannon ball. There is no axiom of Classical Mechanics to supply the initial conditions of the motion of planets. Why? Simply because the initial conditions are collaterals: we can solve the problem of motion, find the orbit in general terms, and then particularize it by initial conditions. The Classical Mechanics concentrated upon the form of the orbit, but the problem is that one cannot see how a planet was shot like a cannon ball! This fact created the modern Cosmogony, which is far from perfect in explaining the facts. But analyzing the cosmogonic theories, it occurred to us that perhaps the message is different: look for the initial conditions of a planet motion in the Sun!
Another “left over” of the Classical Mechanics is the problem of action of gravitational force itself. We maintain that the action is directed toward the center of the orbit, according to our experience. However, when we calculate the orbit based on this assumption, it turns out that its center and the point toward which the force acts are quite different. Historically this fact led to the critique of the concept of force, and later on to the General Relativity. Nevertheless the question remained: is the force of gravitation acting “laterally” too? Perhaps the message here is that the planets’ motion is done under the “lateral” action of gravitation!
Nicolae Mazilu, PhD Physics and Engineering, occasionally (very often lately!) writer regarding unsettled problems. Usually perceiving these in places where everything seems to be settled: Classical Mechanics, Cosmology, Thermodynamics, Heat Transfer, Continuum Mechanics, Astrology, Relativity.
Related Posts
Comments
Leave a Reply
