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When you bring up the history of anything, you are talking about its origins and its evolution.  Dates and locations, naturally, play a role but, history is about the individuals and the actions they took.  This page recounts the actual history of momentum and the Work Energy Theorem without any editorial comments.  Once that is done, we can use the gift of hindsight to see if there were any mistakes, significant or otherwise, were made.      


We start with French scientist, mathematician, and philosopher Rene Descartes (1596 - 1650).  He developed momentum while living inIce skating Holland. Descartes located there after hearing of Galileo Galilee’s (1564 - 1642) difficulties with the Church.  Galileo's problems began after writing a book that supported a sun-centered universe.  It happened to conflict with Catholic Doctrine and so, he was subsequently charged with heresy.   And to avoid any chance of a similar fate, Descartes thought it best to move in Holland.  Although it was primarily a Catholic nation, it also had a large Protestant population and thus was a relatively safe haven for anyone whose views might conflict with Catholic Doctrine.

One of Descartes’ interests involved motion. He was hoping to describe in mathematical terms how objects moved.  His benchmark for success was simple and it began with the supposition that motion was a conserved aspect of the universe. He reasoned that if two objects were to collide, the amount of motion before they met would be the same as the amount after the event.

Unfortunately, precise measurements were more of a dream than a reality some four hundred years ago.  Descartes could judge speed but not very accurately.  He could however measure weight reasonably well and thus was able to know how much mass an object had.  Descartes’ first attempt to describe motion began with the product of weight (mass) and speed. It is not very difficult to get the idea that motion might very well be represented by how much stuff there was in an object and how fast it is moving.   But as so often occurs in life, his initial results were rather disappointing.  The product of mass and speed failed horribly for inelastic collisions. The values he calculated before such collisions bore no resemblance to the values he calculated after the event. Elastic collisions were an entirely different situation; Descartes’ observations and calculations seemed to indicate there might be some hope if he could only make the right adjustments.

Around the time Descartes was pondering how to proceed further, he was tutoring the son of an acquaintance.  The young man’s name was Christian Huygens (1629 - 1695) and it was he who offered an interesting observation into Descartes’ motion problem. Descartes listened to and embraced the young student’s thoughts —  the addition of direction.  Descartes went on to modify his initial mathematical model ever so slightly from the product of mass and speed to the product of mass (m) and velocity (v).  The addition of a directional component which amounts to changing speed to velocity, worked perfectly for both elastic and inelastic collisions. He went on to name his creation “momentum” from a Latin word of identical spelling, a word that had the meaning of “moving power”.

The Original Hypothesis

In 1687, English mathematician and scientist Isaac Newton (1642 - 1727) published the first edition of his seminal work, “The Principia”. In England, the Catholic Church’s influence over scientific matters was virtually nonexistent. This was due in large part to the rifts created with the Church by Henry VIII (1491- 1547) to circumvent Catholic rules regarding divorce. Also by this time and extending throughout the rest of Europe, the Catholic Church had eased their scientific restrictions. However, despite this increased scientific freedom, a religious influence still existed within the European scientific community if only based on a fear of the afterlife. Newton, for one, referred to the “Almighty” in his book, not once but several times.

NewtonNewton’s book begins with a section entitled “Definitions”. The first one refers to mass stating that it is proportional to weight. He essentially states that weight and mass are closely related but not the same thing. This is immediately followed by a definition for “quantity of motion” — momentum (mv). A few pages later, Newton pens a section entitled, “Axioms, or Laws of Motion”. When Newton’s now famous Three Laws of Motion are combined, they describe the Law of Conservation of Momentum. This was the basis upon which Descartes had developed momentum — his original supposition.

Newton, as the most prominent scientist of his era, had his share of detractors. One of the less vocal of these was Huygens, the same individual Descartes had once tutored and who had assisted in the development of momentum. By this time, Huygens had become a scientist in his own right achieving a measure of fame throughout Europe and particularly in France. While living in Paris, Huygens befriended and tutored someone who became Newton’s archrival — German born scientist, mathematician, and philosopher Gottfried Von Leibniz (1646 - 1716). One of the best-known disputes between Leibniz and Newton revolved around calculus. Another and the one of particular interest in the development of the Work Energy Theorem involved momentum.

Leibniz proposed a bold new concept he called “Vis Viva” meaning living force and he believed it to be a far more important scientific concept than momentum. He gave Vis Viva the mathematical form mv2, an expression that his mentor — Huygens — had been among the first to investigate. And like mv, the product of mass and the square of the velocity is conserved for elastic collisions. Leibniz would say that mv2 was more than an inferior cousin to momentum which is the only one of the two expressions conserved in all collisions. He realized mv2 failure as a conserved expression for inelastic collisions meant something far more profound.

To understand Leibniz’s reasoning one need only consider what occurs in an explosion (the Explosion Scenario). Interestingly, an explosion can be thought of as being an inelastic collision in reverse. Instead of objects colliding and uniting in some way as occurs during an inelastic collision, an explosion begins as a single object that breaks into pieces which then fly apart. Consider a hollow metal sphere containing a quantity of gunpowder. Leibniz would state that the explosive mixture contains a particular value of Vis Viva that can be determined by igniting the gunpowder and observing the results. In the simplest possible scenario, half of the metal sphere accelerates to the left and the other half to the right. The amount of Vis Viva would then be calculable by knowing the mass of the two halves and their velocity.

Leibniz seemed to understand, as every physicist quite properly does today, that momentum was an impossible option for Vis Viva, absurd actually. In the Explosion Scenario where the half-spheres fly apart, the momentum of the half-sphere moving to the left added to the momentum of the other half-sphere produces a null result (no net momentum). Moreover, no matter how much gunpowder is used, the net momentum after the explosion is always the same — zero. With mv2 representing Vis Viva, a positive value always manifests. With more gunpowder, the amount of Vis Viva increases; with less, Vis Viva diminishes.

At the time, Leibniz did not have a complete grasp of what his hypothesis meant or would mean in the future. He did not realize that Vis Viva would extend well beyond motion and its immediate causes — the concept of energy as it is widely understood today. He believed Vis Viva represented a previously unknown type of conservation — the forerunner of today’s Law of Conservation of Energy.

Newton did not subscribe to Leibniz’s radical new idea and as the leading scientist of the day, a great many others followed his lead. Newton took Leibniz’s proposal as an insult meant to devaluate his Laws of Motion and suggested that regardless of anything, mv would be a far better mathematical choice for Vis Viva. Leibniz did not take kindly to this and ridiculed Newton by stating if Vis Viva had the form mv, God would have to intervene in the universe from time to time. A scientific controversy ensued and one intense enough to spread throughout Europe. Two factions formed; on one hand, English and French scientists backed Newton, and thus Descartes as well. On the other hand, the Germans stood by their countryman — Leibniz — while scholars from other nations were split between the two views.

Leibniz’s reference to God further illustrates the religious influence that still remained a part of Natural Philosophy, the term used before the word “physics” became commonplace. Leibniz believed in a God that created a universe that was self-perpetuating. Newton found comfort in having the Almighty play a role in keeping the universe moving. Today, physicists are supposed to avoid such religious arguments; they are certainly not part of the modern Scientific Method.

At the time, Leibniz’s proposal was so radical that many scholars had great difficulty grasping it. Thinking in terms of energy is commonplace today; before acceptance of Leibniz’s hypothesis, scientists thought only in terms of individual phenomenon with no known means of unifying them. The arguments back then were centered on religious and philosophic notions; there was no known or widely accepted experimental evidence to suggest mv2 was a better expression for Vis Viva than mv, or vice versa.

A number of years later, after Newton and Leibniz had gone on to meet their maker, the controversy had faded from broad scientific discourse.  And this is when a most unlikely individual took it upon herself to resolve the one time heated dispute — Emilie Du Châtelet (1706 - 1749), a Frenchwoman and Aristocrat. She had interests far beyond those usual for a woman of her station and time. Du Châtelet understood mathematics and was up on all the latest advances in science. She understood Newton’s book, “The Principia”, certainly well enough to be the one who translated it from Latin into French. She also had a firm grasp on Leibniz and his philosophic views. Du Châtelet had every appearance of an informed unbiased scientist, an almost ideal judge to decide the matter. Unfortunately, her gender was a liability given the era in which she lived. Today, the fact of being a woman is meaningless. Yesterday, it was an entirely different matter; she generally had to hide her skills and ambitions from all but a precious few confidants and allies.

Du Châtelet contemplated for a time how to resolve the controversy and had little success. Then, as she was looking at what others were doing that might help, a solution turned up in the form of an experiment Dutch scientist Willem s’Gravesande (1688 -1742) had devised. He had many years earlier been on a junket to England on behalf of his country. While there, he had occasion to meet Newton and became enamored by the world’s greatest scientist. So great was his fascination for Newton that s’Gravesande abandoned his legalDuchatelet career for a scientific one.

By modern standards, the s’Gravesande Experiment is extremely simple, even childish when comparing it to experiments done at today's high schools.  His experiment consisted of nothing more than dropping small metal spheres from various heights into a soft clay bed and measuring how deeply they sank. When Du Châtelet performed this experiment for herself, she discovered the depths to which the spheres sank into the clay always followed a predictable pattern. In short, if a sphere was moving twice as fast as another identical sphere, the faster sphere would penetrate the clay four times as far. If the faster sphere travelled three times as fast, it would sink nine times deeper. It was a very dramatic result that Du Châtelet took as nothing less than absolute proof that Leibniz’s hypothesis was valid and that Vis Viva had the mathematical form he proposed.

Du Châtelet exploited one of the two key differences between mv and mv2. The first is that momentum is a directional expression; mv2 is not. The second difference, the one she focused on, was that an object’s momentum directly relates to velocity. Double an object’s velocity and its momentum doubles; treble its velocity and its momentum increases by a factor of three — an obvious linear relationship. With mv2, it is an entirely different situation; the value this expression produces is always related to the square of the object’s velocity. In simple terms, mv2 produces non-linear values, values easily distinguishable from those momentum gives.

Du Châtelet had what Leibniz did not — experimental evidence. She had changed a single factor — the velocity of a sphere as it reached the clay — and it produced a result that bore no resemblance to momentum’s linear relationship with velocity. She went on to publish her findings to a scientific community that at the time had little to no interest in Vis Viva.

Years later, scientists began to re-consider the value of Vis Viva. The transient nature of Leibniz’s hypothesis started to make sense and they began using mv2 to represent Vis Viva. By this time, scientists were universally able to grasp that mv, as a directional expression, was utterly incapable of representing Vis Viva. Du Châtelet’s contribution was cast aside and her name all but erased from the history of physics. Her gender had always been an issue in a science thoroughly dominated by men, men with egos and wives that knew nothing of such elite matters.

Today's Work Energy Theorem

As the nineteenth century began, English scientist, Thomas Young (1773 - 1829) renamed Vis Viva with his introduction of a new term – energy. In his famous series of lectures, circa 1805, Young explained energy’s relationship to height. He pointed out that an object that falls from a height twice as great as another identical object has a value of energy twice as great. This relationship between height and energy had the effect of aligning mv2 with the modern understanding of force acting through a distance (displacement). In these lectures, Young did not modify Vis Viva’s original mathematical form but the stage was set. In 1829, French scientist and engineer Gaspard Gustave De Coriolis (1792-1843) publishes a Paper, "On the Calculation of Mechanical Action", in which he changes mv2 to ½mv2 and coins the word “work” to describe the idea of force acting through a distance.

After De Coriolis, others added to the understanding of energy. One of the most notable was James Prescott Joule (1818-1889) who wrote a Paper in 1844 entitled, "On the Mechanical Equivalent of Heat". In it, Joule equated thermal energy with mechanical work and for his efforts, scientists named the basic unit of mechanical energy in his honor, the "joule".

The Obvious Conclusion

By taking the history on face value, the validity of the Work Energy Theorem looks pretty good.  And so, it is easy to get the idea that the scientists of the past got it right.  However, when we use the gift of hindsight a number of errors spring into view.  If you did not see them, know that you are in pretty good company; no one has spotted them in centuries.

Click on the "The Errors of the Past" to continue.



For Comments, Questions, or to report any errors I may have made please email me at SurprisedOwl@gmail.com.


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