Physicist Carlo Rovelli wrote the article “Aristotle’s Physics: A Physicist’s Look” published in the Journal of the American Philosophical Association, Volume 1, Issue 1, Spring 2015, pp. 23-40 with a free version available here. Luke Barnes summarizes the article here. For more on limited domains see here and here.
Below are some excerpts from the free version:
Aristotelian physics is a correct and non-intuitive approximation of Newtonian physics in the suitable domain (motion in fluids), in the same technical sense in which Newton’s theory is an approximation of Einstein’s theory. Aristotelian physics lasted long not because it became dogma, but because it is a very good empirically grounded theory. The observation suggests some general considerations on inter-theoretical relations. p.1
… if we restrict Einstein’s theory to a certain domain of phenomena (small relative velocities, weak gravitational field…), we obtain the Newtonian theory in the appropriate approximation. … we already know, indeed, that Einstein’s theory, in turn, has limited domain of validity (it is invalid beyond the Planck scale). p.1
Here I compare the two theories of physics that have had the largest and the longest
success in the history of humanity, as a contemporary scientist would describe them: in modern technical terms. p.1
If we want to understand the past we must do so on its own terms, and disregard the future of that past, but if we want to understand the present we better not disregard the past steps that were essential for getting to the present. p.2
[Aristotle’s] theory is as follows. There are two kinds of motions
(a) Violent motion, or unnatural [Ph 254b10],
(b) Natural motion [He 300a20].
… Violent motion is of finite duration. That is:
(c) Once the effect of the agent causing a violent motion is exhausted, the violent motion ceases.
… Given [Aristotle’s] structure of the cosmos, we can now describe natural motion. This is of two different kinds, according to whether it is motion of the Ether, or motion of one of the four elements Earth, Water, Air and Fire.
(d) The natural motion of the Ether in the Heavens is circular around the center [He 26915].
(e) The natural motion of Earth, Water, Air and Fire is vertical, directed towards the natural place of the substance [He 300b25].
Since elements move naturally to their natural place, they are also found mostly at their natural place. This is the general scheme. More in detail, Aristotle discusses also the rate at which natural motion happens. He states that
(f) Heavier objects fall faster: their natural motion downwards happens faster [Ph 215a25, He 311a19-21];
(g) the same object falls faster in a less dense medium [Ph 215a25]. p.2-3
Rovelli infers the following relation from Aristotle:
v ∼ c (W / ρ)n,
with velocity v, weight W, density ρ of the medium, and constants c and n.
About the constant c, Aristotle says that
(i) The shape of the body […] accounts for their moving faster or slower [He 313a14];
that is, the constant c depends on the shape of the body. The context in which Aristotle refers to these relations is a discussion on the void. Aristotle argues that …
(j) In a vacuum with vanishing density a heavy body would fall with infinite velocity [Ph 216a].
In fact, it is mostly on the basis of this deduction that one can reconstruct [the equation above]. On the basis of this (and other) arguments, Aristotle concludes denying the possibility of void:
(k) “From what has been said it is evident that void does not exist […]” [Ph 217b20].
Two comments before proceeding. First, Aristotle’s choice of four elementary substances is strictly dependent on his theory of motion and is deduced from observation. If all things fell down, only one substance would be needed; but some things, like fire, move up. If there were only things moving upwards (like fire) or downward (like earth), two elementary substances would suffice: one with a natural tendency moving upward and one with a natural tendency moving downward. But observation teaches us that there are objects that move upwards in a medium but downward in another. Air bubbles up in water, but is pushed down by up going fire. Wood moves down in air and up in water. This requires a complex theory or relations between several elements [He 269b20-31 and 311a16-b26].
Second, contrary to what sometimes stated, the distinction between natural and violent motion survives in later theories of motion. For instance, the first two laws of Newton clearly reproduce this distinction: in Newton theory, the natural motion of a body is rectilinear and uniform (constant speed and straight): this is how a body moves if nothing acts on it. While violent motion is the accelerated motion of an object subject to a force. The two theories differ in the identification of the “natural” motion (rectilinear uniform in Newton, vertical and ending at the natural place in Aristotle), but also in the effect caused by an agent: an external agent causes an acceleration in Newton’s theory, while it causes a displacement in Aristotle’s theory. p.3
The fact that Aristotelian physics (unlike that of most of his commentators) is to be properly understood as the physics of objects immersed in a fluid, air or water, has been emphasized by Monica Ugaglia and in my opinion is the key to understand Aristotle’s physics in modern terms. p.4
For a student who has learned physics in a modern school it may sound strange to start physics by studying objects in a fluid. But for somebody who hasn’t it may sound strange not to: everything around us is immersed in a fluid. Aristotle’s physics is a highly nontrivial correct description of these phenomena, without mistakes, and consistent with Newtonian physics, in the same manner in which Newtonian physics is consistent with Einstein physics in its domain of validity. p.4
The body will immediately start moving up or down, according to whether its density is higher or lower than the density of the fluid in which it is immersed. Therefore Earth will move down in any case. Water will move down in Air. Air will move up in water. Objects that have a specific weight intermediate between water and air (like wood), in Aristotelian terms mixtures including Air as well as Water, will move up in Water and down in Air, and so on. This is precisely the content of (e) above. Furthermore, if a body is immersed in a substance of the same kind, as Water in Water, then it can stay at rest: it is at its natural place. In other words, the theory of natural motion is the correct description of the vertical motion of bodies immersed in spherical layers of increasingly dense fluids as are the bodies in the domain of validity of Aristotelian theory. p.4
The existence of these two phases [transient, then steady] is important for understanding the common confusion about Aristotle’s theory of falling. Let me explain this key point for the readers less at ease with equations. A piece of metal falling in water reaches very rapidly a constant velocity. Similarly, a stone left at high altitude by a bird reaches rapidly a constant velocity. This true fact of nature is commonly disregarded by most critics of Aristotle’s. p.5
[In the steady phase n = 1/2 and] c is a constant that depends on the shape and the dimension of the body, which is not easy to predict with elementary tools.
This shows that a heavier body falls faster than a lighter body, precisely as Aristotle states in (f) and that equal bodies fall faster in a less dense medium, as Aristotle states in (g). p.5
Let us now consider violent motion, for terrestrial objects. … The slowing logarithmic growth of x(t) has the consequence that the natural motion brings the object downward before much path can be covered. This has the effect that any violent motion comes effectively to an end in a finite time, as Aristotle states in (c). p.5-6
The terrestrial physics of Aristotle matches perfectly the Newtonian one in the appropriate regime. It is definitely not true that objects with different weight fall at the same speed, in any reasonable terrestrial regime. p.6
Aristotle’s detailed theory however, as well as … Aristotle’s detailed observations leading to it, refer mostly to the steady regime of falling where observation is easier. It disregards the initial transient phase. This phase is either too short (in water) or too rapid (for very heavy objects in air) for any careful observation. This phase, on the other hand, is relevant for the short fall of heavy objects, which is the regime on which Galileo (fruitfully) concentrated, circumventing the difficulty of observation by the ingenious trick of the incline. p.6
In summary, Aristotle’s physics of motion can be seen, after translation into the language of classical physics, to yield a highly non trivial, but correct empirical approximation to the actual physical behavior of objects in motion in the circumscribed terrestrial domain for which the theory was created. p.7
Aristotelian physics is often presented as the dogma that slowed the development of science. I think that this is very incorrect. The scientists after Aristotle had no hesitation in modifying, violating, or ignoring Aristotle’s physics. p.8
It was not a dogmatic view of Aristotle’s theory that kept it alive: it was the difficulty to find something better. In a similar way, Newton theory did not remain the fundamental paradigm for three centuries because it was a dogma, but because it was difficult to find something better. The reason Aristotelian physics lasted so long is not because it became dogma: it is because it is a very good theory. p.9
Advanced theories build heavily on past theories, rebuilding continuously on their conceptual structure and rearranging continuously this conceptual structure. p.9
Galileo, master of propaganda and grand master in the use of words, did his best to ridicule Aristotelian
ideas, in the effort to win a difficult battle against a giant. From this, much of the bad press suffered by Aristotle’s physics followed. But Galileo himself, from which so much of the present attitude against Aristotle’s physics derives, recognizes the value of the theory of his opponent: he repeatedly opines that Aristotle was enough of an empiricist to modify his view in the light of the new experimental evidence. p.10
Galileo’s struggle with Aristotle is similar to that of Copernicus with Ptolemy, Newton with Descartes, Einstein with Newton or Dirac with Hamilton. p.10
Aristotle never claimed that bodies fall at different speed “if we take away the air”. He was interested in the speed of real bodies falling in our real world, where air or water is present. It is curious to read everywhere “Why didn’t Aristotle do the actual experiment?” I would retort: “Those writing this, why don’t they do the actual experiment?”. They would find Aristotle right. p.10