Galilean cutoff or beginning modern physics

Science historians agree that the Galilean Cutoff marks the beginning of modern physics. Since ancient Greece, about 4 centuries BC to the end of the Middle Ages (fifteenth century), the worldview is stable, that of the great Greek philosopher and scientist Aristotle (-384 -322 BC). His work, in the metaphysical and physical domain is so great that it will influence many civilizations. Indeed, the thought of Aristotle, Aristotelianism, will diffuse through the writings of many thinkers and various schools.
The works of Aristotle describes a world "intuitive", which is divided into two parts, the sublunary world (under the Moon, the Earth) and the supralunar world (beyond the Moon, the rest of the universe).
The sublunary world is changing, imperfect, corruptible, it is the place of fire, air, water and earth. The supralunary world is the place of the ether, immutable, perfect and incorruptible.
The world is geocentric and the Earth is immobile in space, everyone lives with it because it corresponds to the observations of the time. This worldview will be spread by all Aristotelian commentators (at the time of Aristotle), the Neoplatonists (from about 300 to 540), the Arabs in the Middle Ages (from about 980 to 1200), Jews (from about 1130 to 1200), the Byzantine (from about 1040 to 1140) and commentators of the Middle Age (from about 1180 to 1280). Of course some mathematicians, physicists, astronomers, philosophers and popularizer of sciences to the end of the middle age were skeptical about this geocentric world, especially Nicole Oresme (1320-1382) and Jean Buridan (1292-1363). This world has reached its limits, but no one will start it to question because it was appropriate perfectly the "scriptures" of the Middle Age.
With Nicolas Copernicus (1473-1543), the world will toggle. Copernicus, Polish astronomer and physician will develop a theory that places the Sun at the center of the universe (heliocentrism) around which turns the planets.

Earth was no longer central and immobile but a planet like the others.
His book of 1543, entitled "De revolutionibus Orbium Coelestium" will air "substantially". This profound paradigm shift in both philosophical and scientific, imposed by Copernicus, is called "Copernican revolution", but that's Galileo (1564-1642) that will toggle the science in the modern world.
When we think about Galilee, we imagine he, pointing his telescope to the uneven surfaces of the moon, the stars of the Milky Way, the moons of Jupiter, the phases of Venus, or to Saturn. But this is not the use of refracting telescope in astronomy, which marks the beginning of modern physics.
The Galilean Cutoff, is marked with the statement of the law of falling bodies by Galileo in the early 17th century, around 1604.
She said this: acquired speed is proportional to the duration of the fall and is independent of the mass and the nature of the body. This is the first time a physical law expressed with "time" parameter, according to the French physicist Etienne Klein, this is the Galilean Cutoff. Time becomes a mathematical variable and will play a decisive role in modern physics.
The law of falling bodies Galilee is revolutionary because it goes against our senses. Indeed intuitive theory of Aristotle seems to us more just because it explains that heavy bodies fall faster than light objects. But it is false.
To better make know his discoveries, Galileo wrote in 1632 "DIALOGO" a dialogue on the two major world systems, that of Ptolemy (90-168), and that of Copernicus (1473-1543). He wrote the book in Italian to be better understood, not in Latin which was the language of publications of the time.
To imagine falling bodies in a vacuum, Galileo went through a thought experiment, it will use for this, three people. For this book, Pope Urban VIII will condemn Galileo June 22, 1633 (see next chapter).

Image: The works of Aristotle describes a world "intuitive", which is divided into two parts, the sublunary world (under the Moon, i.e. the Earth) and the supralunar world (beyond the Moon, the rest of the universe). The sublunary world is changing, imperfect, corruptible, it is the place of water, air, earth and fire. The supralunar world is the place of the ether, immutable, perfect and incorruptible. Aristotle was a logician, scientific and Greek philosopher, born in 384 BC. and died in 322 BC. to Chalcis. Student and disciple of Plato, Aristotle is one of the most influential thinkers of the Western world. His monumental writings include much of the philosophical and scientific knowledge of the time. The distinction between philosophy and science does not exist at the time of Aristotle, it dates from the late eighteenth century. Credit image: astronoo.com

Extracts from Galileo's book staging for 4 days, three people, Simplicio supporter of the theory of Aristotle, Sagredo, open, honest and cultivated man, Salviati representing ideas that Galileo wants to diffuse.
Simplicio: Aristotle has shown that, in the same medium, objects of different mass fall at different speeds and these speeds are proportional to the masses of the objects. [...] You do not still intend to prove to us that a cork ball falls at the same speed as a lead ball? [...]
Salviati: I doubt that Aristotle relies on an experiment to confirm this. [...]
Simplicio: Yet his words show that he observed the phenomenon, since he says "We see that the heaviest...". This "we see" alludes to an experience.
Sagredo: But I, which makes the test, Signor Simplicio, I assure you that a cannonball, a hundred or two hundred pounds, or more, will not take advance of a palm on his arrival the ground, on a musket ball of half a pound, even if the drop height was a hundred cubits! [...]
Simplicio: I find it hard to believe that lead tear can fall as fast as a cannonball.
Salviati: [...] I would not, Signor Simplicio, that, like many others, you can concentrate on such a thing that I said and which deviates from the truth of the thickness of a hair, to avoid to see the error as big as a mooring line, that Aristotle committed. Aristotle writes: "An iron ball of one hundred pounds falling from a height of one hundred cubits reaches the ground before a ball of a pound, descended a single cubit". I tell myself, they come together. You only have to experience, and you will find that when the big ball touches the ground, the other is far from just two fingers. And you would now behind these two fingers, hide ninety nine cubits of Aristotle, and raising my small error, ignore his huge mistake.
Simplicio: Anyway, I do not believe in a vacuum, if the movement was possible there, a ball of wool fall as fast as a piece of lead.

Salviati: Slowly, Signor Simplicio [...], rather listen to reasoning will enlighten you. We seek what would happen to objects of very different masses in a zero resistance medium. [...] Only a completely empty air space would allow us to perceive a reply. As such a space does not exist, we will see what happens in very resistant environments, compared with more resistant backgrounds; and if we find that different objects have less and less different speeds when the media are increasingly easy to cross, [...] then we can assume with high probability, to me it seems that in vacuum speeds are equal. [...] The experience of taking two objects of very different masses, and let go of a certain height to observe if their speeds are equal, has some difficulties. Indeed, if the height is important, the middle interfere much the light object and a long distance the light object will then remain behind. [...] However, if one takes the two objects of the same shape and of the same material, and that it reduces the mass of one simultaneously its surface, there occurs no reduction in speed. [... ] This brings me to the conclusion that if we completely eliminated the resistance of the medium, all objects fall at the same speed.

NB: Galileo imagined experiences of falls slowed down, so that they are easily measured with the naked eye. For that it slows the body fall by placing them on an inclined smooth plane. Thus the effect of gravity is reduced and bronze balls, perfectly polished spherical roll slowly entrained by their own weight. After extensive testing, Galileo was able to formulate the laws of falling bodies.

Image: To better make know his discoveries, Galileo wrote in 1632 "DIALOGO" a dialogue on the two major world systems, that of Ptolemy (90-168), and that of Copernicus (1473-1543). He wrote the book in Italian to be better understood, not in Latin which was the language of publications of the time. En italian: Doue ne i congressi di quattro giornate si discorre sopra i due massimi sistemi del mundo tolemaico, e copernicano;
Galilee ends his book "DIALOGO" in 1629 but publishes it in Florence than 1632. Galileo stages for 4 days, three people, Simplicio supporter of the theory of Aristotle, Sagredo, open, honest and cultivated man and Salviati representing Galileo's ideas. Simplicios is the name of the sixth century philosopher and commentator of Aristotle, Salviati and Sagredo are the names of two friends of Galilee. Pope Urban VIII, trapped by Galileo, will try to prohibit this book is a plea for the Copernican system, and therefore against the Scriptures, but Galileo published in Florence, not Rome as desired by the pope. Pope Urban VIII, for geopolitical reasons, has to show his power and is condemned Galileo a slight Assent on June 22, 1633, Galileo must recant his errors, his work is prohibited and will be under house arrest until the end of his life, January 8, 1642.