WHAT’S MASS? It is not an easy question. An answer for inertial mass was given seven centuries ago. Astoundingly, it’s still the foundation of our most modern physics. Let me explain.
Momentum, force, and inertial mass were defined from trajectory deviation, first. This, I will show below, is incredibly modern (the idea is found in Riemann ~ 1860 CE next). This was all in Buridan’s work, in the Fourteenth Century (14C). Jean Buridan postulated the notion of motive force, which he named impetus. Consider this, from Buridan’s Quaestiones super libros De generatione et corruptione Aristotelis:
“When a mover sets a body in motion he implants into it a certain impetus, that is, a certain force enabling a body to move in the direction in which the mover starts it, be it upwards, downwards, sidewards, or in a circle. The implanted impetus increases in the same ratio as the velocity. It is because of this impetus that a stone moves on after the thrower has ceased moving it. But because of the resistance of the air (and also because of the gravity of the stone) which strives to move it in the opposite direction to the motion caused by the impetus, the latter will weaken all the time. Therefore the motion of the stone will be gradually slower, and finally the impetus is so diminished or destroyed that the gravity of the stone prevails and moves the stone towards its natural place. In my opinion one can accept this explanation because the other explanations prove to be false whereas all phenomena agree with this one…
Just a word of the modernity of it all: the idea translates directly into defining force(s) with changes of distance between geodesics (in differential manifold theory).
Buridan states that impetus = weight x velocity (modern momentum). All the predecessors of Buridan thought one needed a force to keep on moving, but Buridan did not. Famous predecessors such as Hibat Allah Abu’l-Barakat al-Baghdaadi, who modified Avicenna’s theory, which followed John Philoponus believed in inertia NOT. They all followed Aristotle, who believed all and any motion died away, if no force was applied. (Not to say no Muslim ever invented anything scientific: the Uzbek ibn-Musa al-Khowarizmi crucially put the finishing touch on the zero, which he partly got from India, in the Ninth Century.)
Buridan’s pupil Dominicus de Clavasio in his 1357 De Caelo, pointed out that this extended to gravity:
“When something moves a stone by violence, in addition to imposing on it an actual force, it impresses in it a certain impetus. In the same way gravity not only gives motion itself to a moving body, but also gives it a motive power and an impetus, …”.
Buridan knew celestial bodies were moving from inertia: “God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them he impressed in them impetuses which moved them without his having to move them any more…And those impetuses which he impressed in the celestial bodies were not decreased or corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus.”
By definition, inertial mass is what resists an applied force. The greater the resistance to a force, the greater the inertial mass of what it is applied to.
Buridan introduced p = mv, called it “impetus” and stated that it did not change if no force was applied. Thus Buridan buried the complete idiocy known as Aristotle’s physics. (That Aristotle could be a complete idiot at the mental retard level is philosophically, and historically capital, as Aristotle set in place the leadership system through celebrities, which we enjoy to this day).
Buridan’s Inertia Law is known as Newton’s First Law (because Buridan was from Paris, while Newton demonstrates the superiority of the English born three centuries later by attributing to him what Isaac did not discover).
More generally Newton asserted clearly his Second Law: dp/dt = F (where F is the Force, by definition). It’s an axiom. (Weirdly the Second Law implies the First…)
Force = Deviation From Trajectory:
This is Buridan’s idea. It was taken over again by Bernhard Riemann, in the early 1860s (five centuries after Buridan’s death). In modern mathematical parlance, force is depicted by geodesic deviation. It’s this idea which is at the triple core of Einstein’s theory (with the idea that gravitation/spacetime is a field, and that it’s Newton’s theory, in first order).
So this is ultramodern: the idea got carried over in “Gauge Theories”, and, because there are several forces, there are many dimensions.
Thought Experiment Often Precedes Experiment:
Yesterday I bought a (2015) book by a (British academic) historian of science. In it, the honorably paid professional asserted modern science started with Tycho in 1572. Tycho, a Count set his student Kepler onto the refined study of the orbit of Mars. Both Tycho and Kepler were 5 star scientists (differently from, say Copernicus or Einstein, both of whom too little inclined to quote their sources). So they were, because, differently from, say, Obama, they had strong personalities. Great ideas come from great emotions. Tycho believed the Ancients had lied. And he was right, they had lied about the orbits of the planets: observations with the same instruments gave different results from the ones the Ancients had claimed.
The preceding shows that this trite notion is profoundly false; the scientific revolution was launched by Buridan and his students (among them Oresme, Albert of Saxony), contemporaries and predecessors (including Gerard de Bruxelles and the Oxford Calculators). Some of their work on basic kinematics, the exponential and the mean theorem of calculus was erroneously attributed to Galileo or Newton, centuries later.
To believe everything got invented around the seventeenth century is not to understand how the human mind works. Experience has to be preceded by thought-experiment (even Einstein understood that). Buridan and his contemporaries did the preliminary thinking (while others were making clocks and hydraulic presses). All of this would become immensely easier after the invention of algebra and Descartes’ analytic geometry, true.
So let’s have a loving and admirative thought for Buridan, the main author of the scientific revolution, whose reputation was destroyed by the CATHOLIC STATE: Buridan’s astronomical reputation was destroyed by the Catho-fascists, more than a century after his death. That’s why the heliocentric system is attributed to an abbot from a rich family (Copernicus), instead of the master physicist said abbot was forced to read as a student.
Studying the history of science, and mathematics uncovers the fundamental axioms, in the natural order given by their obviousness.
Determining which ideas came first, and why is not about determining who is the brightest child, or most impressive bully in the courtyard. In 1907, Einstein made a big deal that he, Albert, was the discoverer of Energy = Mass (“E = mc2”). A careful inspection shows that this either reflects dishonesty, or misunderstanding on his part. Or both. I will address this soon, as I keep on studying mass and momentum.
Buridan put momentum at the core of physics, and thought-measured if dynamically. Momentum is still at the core: photons have momentum, but not mass.
It’s important to realize that many of the latest ideas in physics (all of “Gauge Theories”) rest on an idea invented in Paris seven centuries ago. Not to slight it, or to heap contempt on all the noble Nobels. But, surely, the time has come for really new ideas!