Galilean Cutoff or the Beginning of Modern Physics

Image description: Aristotle's works describe an "intuitive" world, divided into two parts, the sublunary world (below the Moon, including the Earth) and the supralunary world (beyond the Moon, the rest of the Universe). The sublunary world is changing, imperfect, corruptible, the place of water, air, earth, and fire. The supralunary world is the place of ether, immutable, perfect, and incorruptible. Aristotle was a Greek logician, scientist, and philosopher, born in 384 BC and died in 322 BC in Chalcis. A student and disciple of Plato, Aristotle is one of the most influential thinkers in the Western world. His monumental writings encompass a large part of the philosophical and scientific knowledge of the time. The distinction between philosophy and science did not exist in Aristotle's time; it dates from the end of the 18th century. Image source: Astronoo.

History of the Galilean Cutoff

Science historians agree that the Galilean Cutoff marks the beginning of modern physics. From ancient Greece, around the 4th century BC until the end of the Middle Ages (15th century), the vision of the world was stable, that of the great Greek philosopher and scientist Aristotle (-384 -322 BC). His work, in the metaphysical and physical domains, is so considerable that it influenced many civilizations.

Aristotle's thought spread through the writings of many thinkers and various schools. Aristotle's works describe an "intuitive" world divided into two parts, the sublunary world (below the Moon, including the Earth) and the supralunary world (beyond the Moon, the rest of the Universe). The sublunary world is changing, imperfect, and corruptible, the place of fire, air, water, and earth. The supralunary world is the place of ether, immutable, perfect, and incorruptible.

The world is therefore geocentric, and the Earth is immobile in space; everyone accommodates this because it corresponds to the observations of the time. This vision of the world was propagated by all Aristotelian commentators (in Aristotle's time), the Neoplatonists (from about 300 to 540), the Arabs in the middle of the Middle Ages (from about 980 to 1200), the Jews (from about 1130 to 1200), the Byzantines (from about 1040 to 1140), and the Commentators of the Middle Ages (from about 1180 to 1280). Of course, some mathematicians, physicists, astronomers, philosophers, and science popularizers of the late Middle Ages were skeptical about this geocentric world, particularly Nicole Oresme (1320-1382) and Jean Buridan (1292-1363).

The Aristotelian world had reached its limits, but no one would question it because it perfectly suited the "Holy Scriptures" of the Middle Ages. With Nicolaus Copernicus (1473-1543), the world would change. The Polish canon, doctor, and astronomer developed a theory that placed the Sun at the center of the Universe (heliocentrism) around which the planets revolved. The Earth was no longer central and immobile but a planet like the others.

Deep Paradigm Shift

His 1543 book titled "De Revolutionibus Orbium Coelestium" was widely circulated. This deep paradigm shift, both philosophical and scientific, imposed by Copernicus is called the "Copernican Revolution," but it is Galileo (1564-1642) who would propel science into the modern world.

When we think of Galileo, we imagine him pointing his telescope at the uneven surfaces of the Moon, the stars of the Milky Way, the moons of Jupiter, the phases of Venus, or towards Saturn. But it is not the use of the telescope in astronomy that marks the beginning of modern physics.

The Galilean Cutoff is marked by the statement of the Law of Falling Bodies at the beginning of the 17th century, around 1604. It states: The acquired speed is proportional to the duration of the fall and is independent of the mass and nature of the body. This is the first time a physical law was expressed with the parameter "time"; according to the French physicist Etienne Klein (1958-), this is the Galilean Cutoff. Time becomes a mathematical variable and plays a decisive role in modern physics.

Galileo's law of falling bodies is revolutionary because it goes against our senses. Aristotle's intuitive theory seems more correct because it explains that heavy bodies fall faster than light bodies. But it is false.

Dialogue on the Two Chief World Systems

To better publicize his discoveries, Galileo wrote in 1632 "DIALOGO," a dialogue on the two chief world systems, that of Ptolemy (90-168) and that of Copernicus (1473-1543). He wrote this work in Italian to be better understood, and not in Latin, which was the language of publications at the time. He used three characters for this. For this book, Pope Urban VIII (1548-1644) condemned Galileo on June 22, 1633.

Excerpts from Galileo's book featuring three characters over 4 days, Simplicio defending Aristotle's theory, Sagredo, an honest, open, and cultivated man, and Salviati representing the ideas Galileo wanted to spread.

Simplicio: Aristotle demonstrated that, in the same medium, objects of different masses fall at different speeds and that these speeds are proportional to the masses of the objects. [...] You surely do not intend to prove to us that a cork ball falls at the same speed as a lead ball? [...]

Salviati: I strongly doubt that Aristotle based this on an experiment. [...]

Simplicio: His own words show that he observed the phenomenon, since he says "We see that the heavier... ". This "we see" refers to an experiment.

Sagredo: But I, who have actually tried it, Signor Simplicio, assure you that a cannonball of one hundred or two hundred pounds, or more, will not have advanced a palm's length upon reaching the ground compared to a half-pound musket ball, even if the height of the fall is one hundred cubits! [...]

Simplicio: I find it hard to believe that a drop of lead can fall as fast as a cannonball.

Salviati: [...] I would not want, Signor Simplicio, for you to focus on something I said that deviates from the truth by a hair's breadth to avoid seeing Aristotle's error as large as a hawser. Aristotle writes: "A one-hundred-pound iron ball falling from a height of one hundred cubits reaches the ground before a one-pound ball has descended a single cubit." I say that they arrive at the same time. You only need to do the experiment, and you will find that when the large ball touches the ground, the other is only two fingers away. And you would now want to hide Aristotle's ninety-nine cubits behind these two fingers and, pointing out my minor error, pass over his enormous error in silence.

Simplicio: Be that as it may, I cannot believe that in a vacuum, if movement were possible, a tuft of wool would fall as fast as a piece of lead.

Salviati: Gently, Signor Simplicio [...], listen rather to this reasoning that will enlighten you. We are seeking what would happen to objects of very different masses in a medium of zero resistance. [...] Only a space absolutely void of air would allow us to perceive an answer. As such a space does not exist, we will observe what happens in less resistant media compared to more resistant media; and if we find that different objects have speeds that are less and less different as the media become easier to traverse, [...] then we can admit with great probability, it seems to me, that in a vacuum the speeds would all be equal. [...] The experiment of taking two objects of very different masses and dropping them from a certain height to observe if their speeds are equal involves some difficulties. Indeed, if the height is significant, the medium will hinder the light object much more, and over a long distance, the light object will then lag behind. [...] However, if two objects of the same shape and made of the same material are taken, and the mass of one is reduced along with its surface area, there is no reduction in speed.[...] I therefore conclude that if the resistance of the medium were completely eliminated, all objects would fall at the same speed.

N.B.: Galileo imagined experiments with slowed falls so that they could be easily measured with the naked eye. For this, he slowed the fall of bodies by placing them on a smooth inclined plane. Thus, the effect of the force of gravity is reduced, and the perfectly polished and spherical bronze balls roll slowly, driven by their own weight. After numerous trials, Galileo was able to formulate the laws of falling bodies.