Boscovich's Explanation Of Atomic Forces

A great example how a great deal of amazing insight can be gained from some very simple considerations is the explanation of atomic forces by the 18th century Jesuit polymath Roger Boscovich, who was born in Dubrovnik.

One of the great philosophical arguments at the time took place between the adherents of Descartes who—following Aristotle—thought that forces can only be the result of immediate contact and those who followed Newton and believed in his concept of force acting at a distance. Newton was the revolutionary here, but his opponents argued—with some justification—that "action at a distance" brought back into physics "occult" explanations that do not follow from the "clear and distinct" understanding that Descartes demanded. (In the following I am paraphrasing reference works.) Boscovich, a forceful advocate of the Newtonian point of view, turned the question around: Let's understand exactly what happens during the interaction that we would call immediate contact?

His arguments are very easy to understand and extremely convincing. Let's imagine two bodies, one of which is traveling at a speed of, say, 6 units, the other at a speed of 12 with the faster body catching up with the slower one along the same straight path. We imagine what transpires when the two bodies collide. By conservation of the "quantity of motion," both bodies should continue after collision along the same path, each with a speed of 9 units (in the case of inelastic collision, or in case of elastic collision for a brief period right after the collision)

But how did the velocity of the faster body come to be reduced from 12 to 9, and that of the slower body increased from 6 to 9? Clearly, the time interval for the change in velocities cannot be zero, for then, argued Boscovich, the instantaneous change in speed would violate the law of continuity. Furthermore, we would have to say that at the moment of impact, the speed of one body is simultaneously 12 and 9, which is patently absurd.

It is therefore necessary for the change in speed to take place in a small, yet finite, amount of time. But with this assumption, we arrive at yet another contradiction. Suppose, for example, that after a small interval of time, the speed of the faster body is 11, and that of the slower body is 7. But this would mean that they are not moving at the same velocity, and the front surface of the faster body would advance through the rear surface of the slower body, which is impossible because we have assumed that the bodies are impenetrable. It therefore becomes apparent that the interaction must take place immediately before the impact of the two bodies and that this interaction can only be a repulsive one because it is expressed in the slowing down of one body and the speeding up of the other.

Moreover, this argument is valid for arbitrary speeds, so one can no longer speak of definite dimensions for the particles that were until now thought of as impenetrable, namely, for the atoms. An atom should rather be viewed as a point source of force, with the force emanating from it acting in some complicated fashion that depends on distance.

According to Boscovich, when bodies are far apart, they act on each other through a force corresponding to the gravitational force, which is inversely proportional to the square of the distance. But with decreasing distance, this law must be modified because, in accordance with the above considerations, the force changes sign and must become a repulsive force. Boscovich even plotted fanciful traces of how the force should vary with distance in which the force changed sign several times, hinting to the existence of minima in the potential and the existence of stable bonds between the particles—the atoms.

With this idea Boscovich not only offered a new picture for interactions in place of the Aristotelian-Cartesian theory based on immediate contact, but also presaged our understanding of the structure of matter, especially that of solid bodies.