The Errors of the Past

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An error in science would be anything that leads to or might lead to an incorrect conclusion. Such errors can take many forms — the failure to consider all the relevant data, relying an unproven scientific principle, using an improper assumption, employing un-calibrated or poor equipment, and so on.  And since no one is immune from making mistakes now and again, part of the Scientific Method must carry with it the requirement that verification be done by several others.  It is not enough for a single scientist to do only one experiment to confirm a hypothesis and have that be the final word.


The Five Historical Errors, given in no particular order.  

Error #1

No one verified Du Châtelet’s results experimentally.  When she released her findings, they were ignored. This was partly due to her gender and because no one at the time had much interest in Vis Viva.  Naturally a error of this type is meaningless if she got it right.

Error #2

When Descartes developed momentum, he did not have the ability to measure velocity exactly; precision in the 17th century was science fiction, not fact.   He merely supposed that motion was a conserved quantity but, it is not.    The Welcome Page for this website demonstrates the fact that Descartes' supposition was wrong.

Error #3

The third error occurred years later after Vis Viva became more than a minor curiosity. At some point, scientists finally realized that momentum, the sole objection to mv2, had no merit when it came to Vis Viva. With no respect for Du Châtelet or even much knowledge of her, scientists simply elevated Leibniz’s Hypothesis to an accepted physics principle by default.

This is still done today; a great many experts use the fact that mv is incapable of representing mechanical energy as actual proof for the Work Energy Theorem. This would be laughable if it were not so sad and a gross violation of the Scientific Method.  Additionally because the Work Energy Theorem can be derived mathematically, some see this as further evidence or, sadly, actual proof.  One such derivation can be found on this website, "Deriving the Work Energy Theorem" and is a simplfied version of the one Maxwell published in 1877.

Error #4

Compounding the third error was the failure to examine all possible mathematical options for Vis Viva. This third error traces its origins back to Leibniz’s who focused all his attention on mv2 never once considering an equally viable candidate for Vis Viva — the product of mass (m) and speed (s). With no directional notation, ms (a non-directional version of momentum if you wish) passes the "Explosion Scenario".  If two halves of a metal sphere accelerate away from one another as in an explosion, the mathematical sum of ms is always positive just as it is for mv2 or ½ mv2. In short, the product of mass and speed cannot be as easily dismissed as momentum; it can only be rejected by some other means, specifically testing if its prediction is true or not.

Objections to the use of ms, regardless of what they may be, can only be described as both historically and scientifically naïve. Historically, such objections date back to Descartes who was the first to reject the product of mass and speed. Ironically, he dismissed ms for the very reason Leibniz embraced mv2. Since then, physicists generally do not use the word “speed” but, they always use it in one particular situation — the speed of light. This means no one should automatically reject the concept and word “speed”.  And finally there is the fact that mechanical energy is itself non-directional so, there is no reason not to use non-directional variables in its mathematical form.

Error #5    Du Châtelet’s Monumental Blunder

Du Châtelet and her work on Leibniz's proposal is the perfect case study why experimental verification is vital and that it should be done by others plural. In short, she failed to consider time for the variable it is. Evidently, Du Châtelet did not have as firm a grasp on Newton’s Laws of Motion as she believed. One has to factor in time to produce the impulse / momentum equation from Newton’s 2nd Law. Almost as importantly, she did not have access to the technology necessary to perform the experiment in the manner it was conducted. Imagine, or do the experiment Du Châtelet performed — dropping small metal spheres from a few meters high into a soft uniform clay bed that was probably at best a meter deep. See if it is possible to measure the differences in time the spheres take to stop moving once they contact the clay with any degree of precision. Try with a stop watch or any modern means; then try using the state of the art timing technology of her era — pendulum based clocks.

When a metal sphere first contacts the clay and is traveling at velocity v, it immediately begins to slow down and continues to do so until it comes to rest. A sphere traveling at 2v also begins to slow down and must perforce slow down to v before coming to a stop. Time passes for the sphere that begins at v and even more time for the one that begins at 2v. This means that for every change at the beginning of the experiment — initial velocity of the sphere — there are two corresponding changes once the sphere reaches the clay — depth of penetration and time to stop moving (distance and time). The only variable Du Châtelet measured and considered was how far the spheres sank (distance) and that means her conclusion has no scientific value whatsoever. The failure to take into account half the experimental data — time — is the worst blunder a physicist could make. Granted, not all data may have the same value in all experiments; often, some facts are far more important than others. However, there can be no greater error than failing to measure both time and distance in any experiment involving motion.

Interestingly, a modern version of the s’Gravesande Experiment is well known, not so much in physics but elsewhere. It is called the “Stopping Distances of Automobiles” and is often mentioned in Drivers Education Classes.  In any discussion relating to stopping distances, time is rarely if ever mentioned.  Anyone with access to an automobile, a stopwatch, and a tape measure can perform this version of the s’Gravesande Experiment. Simply get an automobile up to various velocities on a road with no traffic and then slam on the brakes. While doing this, measure how long the vehicle takes to stop in terms of time and how far it moves during the deceleration process. Even a poorly conducted series of experiments will conclusively demonstrate that time, just like distance, is a variable.

What Can We Conclude?

Given these five historical errors of varying importance, the only proper conclusion is that the validity of the Work Energy Theorem should be re-visited by today's physics community.   Additionally and along with these five specific errors, others have crept in and may be added to this website sometime in the future.  However before exploring more about the errors of the past, it might be a good idea to take a good look at an "Ironic Experiment".   The word, "ironic" is used because the experiment examined is of the kind Du Châtelet performed and when done properly, it produces an entirely different conclusion to the one she made. 

Please note that whenever someone makes a bold claim, as this website does, physicists demand verifiable and concrete evidence.   This site complys.  That proof exists using the "Ironic Experiment".  It represents far more evidence that was ever provided historically for the Work Energy Theorem or Vis Viva. 

For Comments, Questions, or to report any errors I may have made please email me at



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