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I am basically talking in terms of Newtonian mechanics. The Newton's laws started with a good and easy assumption of particles as point masses. This assumption clearly reformed physics and a great series of scientific experiments and observations on macroscopic objects reveal that the assumption is magnificent.

I do not want to go through all details in this single question only. I will post some of my thoughts and would love to discuss about this great assumption with all the interested users in a sequence of questions on this website.

A speculation of particles as point masses leads to a great simplification of mathematics used in Newtonian mechanics. The question I am going to ask may seem suitable for a mathematics forum but what I think it is well suited for physics as physicists may predict better than mathematicians.

It is very non intuitive for me if Nothing makes everything. This sentence is quite analogous to the assumption of particles as point masses. Euclidean geometry tells us that points are dimensionless. How these dimensionless points arranged close to each other can make a whole body? How dimensionless things can make an extended body?

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  • $\begingroup$ Extended just means distributed in space. Are asking why extended collections of point particles can appear to be a solid object? $\endgroup$
    – G. Smith
    Jul 4, 2019 at 19:32
  • $\begingroup$ Why do you think a point particle is “nothing”? $\endgroup$
    – G. Smith
    Jul 4, 2019 at 19:34
  • $\begingroup$ The point particle approximation has known errors. It's mostly fields that take up space. Things interact to keep them closer together or farther apart. Someone else could probably give a more detailed explanation. $\endgroup$
    – user234190
    Jul 4, 2019 at 20:02
  • $\begingroup$ @G. Smith I am saying that dimensionless seems nothing to me $\endgroup$ Nov 15, 2019 at 6:36

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There are three principles to consider here (sorry, I almost wrote three points).

The first is that most of what you perceive to be the volume occupied by solid day to day objects is indeed empty space. The typical lattice spacing in a regular crystalline solid is a few Angstroms, which is a few thousand times larger than the diameters of the nuclei of the constituent atoms- so the space between the nuclei is vast compared with the physical volume of the electrons occupying it. The tiny particles create the effect of solidity because they are held together by a combination of forces that prevents them from collapsing together more closely under day to day conditions. The optical properties of the crystalline arrangement typically make a solid opaque, so you can't see the space between the particles, but with glass, for example, you can naively interpret its transparency as illustrating the fact that its constituent particles are not shoulder to shoulder.

The second is that there is a difference between very small and infinitely small. Experiments suggest that physical particles are very small, rather than having zero spatial extent. That might be a distinction better discussed in a maths forum.

The third principle is that Newtonian mechanics, as with quantum mechanics, is just a model of reality. You can get into all sorts of confusion if you try to query the implications of a model in areas in which you shouldn't necessarily expect it to match reality.

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