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I have been reading Galileo's Two New Sciences recently. Galileo explicitly disproved most of the Aristotelian ideas, except for the one regarding vacuum. He seemed to support the idea that nature abhors a vacuum. Here is the detailed description of the experiment that Galileo demonstrated in his book:

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To summarize this experiment, Galileo set up a device that contains nothing but water between the cylinder CAB and the stopper EFGH. A limited amount of weight (K) can be applied to the stopper without having the stopper fallen out of the cylinder. My question is: what is this force that holds the stopper back in place? Is it really the “repugnance which nature exhibits towards a vacuum” as Galileo hypothesized?

Here is the detailed procedure of the experiment if you are interested (from the book):

“Let CABD represent the cross section of a cylinder either of metal or, preferably, of glass, hollow inside and accurately turned. Into this is introduced a perfectly fitting cylinder of wood, represented in cross section by EGHF, and capable of up-and-down motion. Through the middle of this cylinder is bored a hole to receive an iron wire, carrying a hook at the end K, while the upper end of the wire, I, is provided with a conical head. The wooden cylinder is countersunk at the top so as to receive, with a perfect fit, the conical head I of the wire, IK, when pulled down by the end K.

Now insert the wooden cylinder EH in the hollow cylinder AD, so as not to touch the upper end of the latter but to leave free a space of two or three finger-breadths; this space is to be filled with water by holding the vessel with the mouth CD upwards, pushing down on the stopper EH, and at the same time keeping the conical head of the wire, I, away from the hollow portion of the wooden cylinder. The air is thus allowed to escape alongside the iron wire (which does not make a close fit) as soon as one presses down on the wooden stopper. The air having been allowed to escape and the iron wire having been drawn back so that it fits snugly against the conical depression in the wood, invert the vessel, bringing it mouth downwards, and hang on the hook K a vessel which can be filled with sand or any heavy material in quantity sufficient to finally separate the upper surface of the stopper, EF, from the lower surface of the water to which it was attached only by the resistance of the vacuum. Next weigh the stopper and wire together with the attached vessel and its contents; we shall then have the force of the vacuum [forza del vacuo].”

Excerpt From: Galileo Galilei. “Dialogues Concerning Two New Sciences.” Apple Books. https://books.apple.com/us/book/dialogues-concerning-two-new-sciences/id451931970

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The force is air pressure. A force equal to the weight of all the air above a horizontal area equal to the cross-sectional area of the piston is pushing in all directions except that one which is at a lower pressure.

There’s nothing implicitly wrong with setting pressure at sea level equal to zero and allowing pressures to range from -1 atm to infinity instead of from 0 to infinity, which is how Galileo has set it up in describing the force of the vacuum. Our way just makes the math easier and the conceptual connection to reality less arbitrary. In much the same way, coincidentally, as heliocentrism isn’t strictly more correct than geocentrism, just conducive of easier math and more logical physics.

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  • $\begingroup$ But there is no air left inside that piston according to the procedure though (hypothetically). I have thought of that too but in this situation it is just water alone, which makes it a bit tricky. $\endgroup$
    – Cam
    Dec 1, 2021 at 2:23
  • $\begingroup$ There is air outside the piston, where the piston is extending into. If you did this experiment on the moon, pressure inside the cavity from boiling water would eject the piston without any weight applied at all. $\endgroup$
    – g s
    Dec 1, 2021 at 2:42
  • $\begingroup$ Ohh. Now I can understand what you are saying. So in the environment where the only force acting on the stopper is its own weight (and of the water too), it would have fallen out. $\endgroup$
    – Cam
    Dec 1, 2021 at 20:07
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The modern physics explanation would be that the weight of the vessel causes a downward force that is transmitted to the stopper, which in turn produces a negative pressure in the fluid. As the force is increased from zero the pressure decreases until it exactly balances the force. There is no horror vacui going on, but rather something similar to how a pulled spring reaches an equilibrium of tension with the force pulling on it.

Pull strongly enough and the water will give away (since the partial pressure of vapour is exceeded and vapour bubbles show up, expanding the volume and causing a breakdown).

One way of "explaining" horror vacui in this kind of case is to note that gases try to spread out evenly, and tend to exert a normal force on all surfaces due to the molecules randomly bumping around (with a pressure dependent on temperature, amount of gas etc.) Any hole is quickly (speed of sound) filled in unless there is some force keeping the gas out. Fluids behave the same, although in a more complex way due to surface tension and the possibility of free surfaces (where the fluid is stable because the outside pressure is above the vapour pressure; when it isn't the fluid boils). So it is not so much that there is a deliberate attempt at filling holes as that local gas or fluid parcels are propelled inward into the hole by the pressure of the rest of the gas or fluid.

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  • $\begingroup$ Note the pressure is not negative, but the pressure inside minus the pressure outside is. Negative absolute pressure would imply molecules with negative kinetic energy, hence negative mass, which isn’t real. $\endgroup$
    – g s
    Dec 1, 2021 at 6:59

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