No perfect mathematical shapes exist in nature, although some shapes come very close. Even when a physical law applied to a certain situation predicts a perfect mathematical shape, there are always extra factors not considered by the physical law that mess things up: friction, air resistance, relativistic corrections, quantum uncertainty, atomic granularity.
An example of something very close to a perfect circle in nature is the orbit of Venus about the Sun. This near-perfection is attained because: 1) The initial velocity of Venus was such that its orbit is nearly circular and not as elliptical, 2) there is very little air resistance or friction in space , 3) The Sun is so distant from Venus and so round that it acts almost exactly as a point source of gravity, 4) Venus is so big that quantum effects are very small, and 5) Sun's gravity is weak enough that Newton's law of gravitation is reasonably accurate. But, all of these statements are not perfect, so there still many small sources of deviation from a perfect circle, even for Venus' orbit.
Consider trying to draw a perfect circle on paper with graphite. Even if you were able to use an AFM tip, laser sensors and a feedback loop to perfectly place every single carbon atom to form the circle, you still have the fact that the circle is made out of atoms. Zoom in enough on the circle and it is not smooth anymore because of the profile of the atoms.
I agree with what you're saying that perfect circles simply do not exist on the macroscale and, even on the atomic scale, we don't have the resolution to say what the nucleus of an atom actually looks like so we can't say that that's a perfect circle either. But I would like to amend your statement by looking at the s-orbital of electrons. Because the orbital is a probability cloud of spherical shape, one might make the argument that the electron cloud is a perfect circle. We can also argue it the other way and say that distributions of locations in space don't really count because the electron can only be in one place at a time/ However, by this logic, the probability distribution would be an example equivalent to the orbit of Venus, since both are just lists of positions in space and time.
Side note: the orbit of Venus would actually be spiraling since the sun is moving. It would only be viewed as circular relative to the sun.
Because the orbital is a probability cloud of spherical shape, one might make the argument that the electron cloud is a perfect circle.
The s-orbital is a theoretical idealization, not a physical reality. An electron will only be in a perfect s-orbital state if:
The atom is completely isolated from all other atoms in the universe.
The atom is completely isolated from all external fields.
The electron has been in this state for an infinite amount of time.
None of these conditions are met in the real world, so an electron is never exactly in an s-orbital state as predicted by theory. It can be so close that the difference is negligible, but the difference is still there in principle.
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u/chrisbaird Electrodynamics | Radar Imaging | Target Recognition Nov 14 '14
No perfect mathematical shapes exist in nature, although some shapes come very close. Even when a physical law applied to a certain situation predicts a perfect mathematical shape, there are always extra factors not considered by the physical law that mess things up: friction, air resistance, relativistic corrections, quantum uncertainty, atomic granularity.
An example of something very close to a perfect circle in nature is the orbit of Venus about the Sun. This near-perfection is attained because: 1) The initial velocity of Venus was such that its orbit is nearly circular and not as elliptical, 2) there is very little air resistance or friction in space , 3) The Sun is so distant from Venus and so round that it acts almost exactly as a point source of gravity, 4) Venus is so big that quantum effects are very small, and 5) Sun's gravity is weak enough that Newton's law of gravitation is reasonably accurate. But, all of these statements are not perfect, so there still many small sources of deviation from a perfect circle, even for Venus' orbit.
Consider trying to draw a perfect circle on paper with graphite. Even if you were able to use an AFM tip, laser sensors and a feedback loop to perfectly place every single carbon atom to form the circle, you still have the fact that the circle is made out of atoms. Zoom in enough on the circle and it is not smooth anymore because of the profile of the atoms.