User:LGUNN22/Theory of impetus

Aristotelian theory

Aristotelian physics is the form of natural science described in the works of the Greek philosopher Aristotle (384–322 BC). In his work Physics, Aristotle intended to establish general principles of change that govern all natural bodies, both living and inanimate, celestial and terrestrial – including all motion, quantitative change, qualitative change, and substantial change.

Aristotle describes two kinds of motion: "violent" or "unnatural motion", such as that of a thrown stone, in the Physics (254b10), and "natural motion", such as of a falling object, in On the Heavens (300a20). In violent motion, as soon as the agent stops causing it, the motion stops also: in other words, the natural state of an object is to be at rest, since Aristotle does not address friction.

Philoponan theory[edit]

In the 6th century, John Philoponus partly accepted Aristotle's theory that "continuation of motion depends on continued action of a force," but modified it to include his idea that the hurled body acquires a motive power or inclination for forced movement from the agent producing the initial motion and that this power secures the continuation of such motion. However, he argued that this impressed virtue was temporary: that it was a self-expending inclination, and thus the violent motion produced comes to an end, changing back into natural motion.

The tunnel experiment and oscillatory motion

The Buridan impetus theory developed one of the most important thought experiments in the history of science, the so-called 'tunnel-experiment'. This experiment was important because it incorporated oscillatory and pendulum motion into dynamical analysis and the science of motion for the very first time. It thereby also established one of the important principles of classical mechanics. The pendulum was crucially important to the development of mechanics in the 17th century. The tunnel experiment also gave rise to the more generally important axiomatic principle of Galilean, Huygenian and Leibnizian dynamics, namely that a body rises to the same height from which it has fallen, a principle of gravitational potential energy. As Galileo Galilei expressed this fundamental principle of his dynamics in his 1632 Dialogo:

The heavy falling body acquires sufficient impetus [in falling from a given height] to carry it back to an equal height.

This imaginary experiment predicted that a cannonball dropped down a tunnel going straight through the centre of the Earth and out the other side would go past the centre and rise on the opposite surface to the same height from which it had first fallen, driven upwards past the centre by the gravitationally created impetus it had continually accumulated while falling through the centre. This impetus would require a violent motion correspondingly rising to the same height past the centre for the now opposing force of gravity to destroy it all in the same distance which it had previously required to create it. At this turning point the ball would then descend again and oscillate back and forth between the two opposing surfaces about the centre infinitely in principle. Thus the tunnel experiment provided the first dynamical model of oscillatory motion, albeit a purely imaginary one, and specifically in terms of A-B impetus dynamics.

This thought-experiment was then applied to the dynamical explanation of a real world oscillatory motion, namely that of the pendulum, as follows. The oscillating motion of the cannonball was dynamically compared to that of a pendulum bob by imagining it to be attached to the end of an immensely cosmologically long cord suspended from the vault of the fixed stars centred on the Earth, whereby the relatively short arc of its path through the enormously distant Earth was practically a straight line along the tunnel. Real world pendula were then conceived of as just micro versions of this 'tunnel pendulum', the macro-cosmological dynamical model of the pendulum, but with far shorter cords and with their bobs oscillating above the Earth's surface in arcs corresponding to the tunnel inasmuch as their oscillatory midpoint was dynamically assimilated to the centre of the tunnel as the centre of the Earth.

By means of such 'lateral thinking', rather than the dynamics of pendulum motion being conceived of as the bob inexplicably somehow falling downwards compared to the vertical to a gravitationally lowest point and then inexplicably being pulled back up again on the same upper side of that point, its lateral horizontal motion that was conceived of as a case of gravitational free-fall followed by violent motion in a recurring cycle, with the bob repeatedly travelling through and beyond the motion's vertically lowest but horizontally middle point that substituted for the centre of the Earth in the tunnel pendulum. So on this imaginative lateral gravitational thinking outside the box the lateral motions of the bob first towards and then away from the normal in the downswing and upswing become lateral downward and upward motions in relation to the horizontal rather than to the vertical.

Whereas the orthodox Aristotelians could only see pendulum motion as a dynamical anomaly, as inexplicably somehow 'falling to rest with difficulty' as historian and philosopher of science Thomas Kuhn put it in his 1962 The Structure of Scientific Revolutions, on the impetus theory's novel analysis it was not falling with any dynamical difficulty at all in principle, but was rather falling in repeated and potentially endless cycles of alternating downward gravitationally natural motion and upward gravitationally violent motion. Hence, for example, Galileo eventually appealed to pendulum motion to demonstrate that the speed of gravitational free-fall is the same for all unequal weights precisely by virtue of dynamically modelling pendulum motion in this manner as a case of cyclically repeated gravitational free-fall along the horizontal in principle.

The tunnel experiment was a crucial experiment in favour of impetus dynamics against both orthodox Aristotelian dynamics without any auxiliary impetus theory and Aristotelian dynamics with its H-P variant. For according to the latter two theories the bob cannot possibly pass beyond the normal. In orthodox Aristotelian dynamics there is no force to carry the bob upwards beyond the centre in violent motion against its own gravity that carries it to the centre, where it stops. When conjoined with the Philoponus auxiliary theory, in the case where the cannonball is released from rest, again there is no such force because either all the initial upward force of impetus originally impressed within it to hold it in static dynamical equilibrium has been exhausted, or else if any remained it would be acting in the opposite direction and combine with gravity to prevent motion through and beyond the centre. Nor were the cannonball to be positively hurled downwards, and thus with a downward initial impetus, could it possibly result in an oscillatory motion. For although it could then possibly pass beyond the centre, it could never return to pass through it and rise back up again. For dynamically in this case although it would be logically possible for it to pass beyond the centre if when it reached it some of the constantly decaying downward impetus remained and still sufficiently much to be stronger than gravity to push it beyond the centre and upwards again, nevertheless when it eventually then became weaker than gravity, whereupon the ball would then be pulled back towards the centre by its gravity, it could not then pass beyond the centre to rise up again, because it would have no force directed against gravity to overcome it. For any possibly remaining impetus would be directed 'downwards' towards the centre, that is, in the same direction in which it was originally created.

Thus pendulum motion was dynamically impossible for both orthodox Aristotelian dynamics and also for H-P impetus dynamics on this 'tunnel model' analogical reasoning. It was predicted by the impetus theory's tunnel prediction precisely because that theory posited that a continually accumulating downwards force of impetus directed towards the centre is acquired in natural motion, sufficient to then carry it upwards beyond the centre against gravity, and rather than only having an initially upwards force of impetus away from the centre as in the theory of natural motion. So the tunnel experiment constituted a crucial experiment between three alternative theories of natural motion.

On this analysis then impetus dynamics was to be preferred if the Aristotelian science of motion was to incorporate a dynamical explanation of pendulum motion. It was also to be preferred more generally if it was to explain other oscillatory motions, such as the to and fro vibrations around the normal of musical strings in tension, such as those of a zither, lute or guitar. For here the analogy made with the gravitational tunnel experiment was that the tension in the string pulling it towards the normal played the role of gravity, and thus when plucked (i.e. pulled away from the normal) and then released, this was the equivalent of pulling the cannonball to the Earth's surface and then releasing it. Thus the musical string vibrated in a continual cycle of the alternating creation of impetus towards the normal and its destruction after passing through the normal until this process starts again with the creation of fresh 'downward' impetus once all the 'upward' impetus has been destroyed.

This positing of a dynamical family resemblance of the motions of pendula and vibrating strings with the paradigmatic tunnel-experiment, the original mother of all oscillations in the history of dynamics, was one of the greatest imaginative developments of medieval Aristotelian dynamics in its increasing repertoire of dynamical models of different kinds of motion.

Shortly before Galileo's theory of impetus, Giambattista Benedetti modified the growing theory of impetus to involve linear motion alone:

"…[Any] portion of corporeal matter which moves by itself when an impetus has been impressed on it by any external motive force has a natural tendency to move on a rectilinear, not a curved, path."

Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion.