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Wikipedia says

A point particle is an idealization of particles heavily used in physics.

Also

In philosophy of science, idealization is the process by which scientific models assume facts about the phenomenon being modeled that are strictly false but make models easier to understand or solve.

However many Pop-Science books and videos claim particles are just points. Also if particles are not really point, will we be able to discover their size eventually? Does it mean they have specific shape?

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A particle is a point from the perspective of us in the same way that the Earth is a point from the perspective of galaxies.

The Earth is not really a point, because it obviously does extend into space with non-zero size. But it is so tiny in comparison to anything relevant that it can be considered a point without losing relevant detail in analyses made at galactic scales. In other words, the Earth is modelled as a point. This is an idealisation that simplifies the calculations by ignoring unnecessary detail and information.

A particle such as the electron, the photon, the phonon, the quantum bosons etc. at the quantum scale is - depending on the particle - typically considered a probability cloud, a concentration of energy, a vibration chunk or the like. These also do extend into space with non-zero size. But they are so, so tiny in comparison to anything else which is not also close to the same particle-scale.

In theory there does not exist any object in our world which is not in 3D. Everything has some size, however small. No 0D point-particles exist. Only point-like particle because we choose to consider them as were they just points.

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    $\begingroup$ Here is an interesting article on the "size" of an electron: How big is an electron? $\endgroup$
    – Philip
    Commented Aug 20, 2021 at 16:18
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    $\begingroup$ "In theory there does not exist any object in our world which is not in 3D", this is classical mechanics . The theory of the standard model assumes axiomatically that elementary particles are point particles. en.wikipedia.org/wiki/Elementary_particle $\endgroup$
    – anna v
    Commented Aug 21, 2021 at 2:48

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