Does the unpredictability in the “micro world” means that everything is if we can look at it close enough imperfect?

Does the unpredictability in the "micro world" means that everything is if we can look at it close enough imperfect?

I mean, there is a saying "You will never stand in the same river again" or something like that. So, if nothing in our makro world is the same, if we look close enough (no two people or flowers are the same; and if they seem, it just means you are not looking carefully or cose enough ;)

Is this also true in the micro world?

If yes, does that mean that e.g no two atoms of hydrogen are the same and the sign $H$ is only some kind of reference for "from-to" or "plus-minus-something-like-that" tolerance?

And the same principle can be applied for smaller particles or even strings etc.?

Does that mean that there is no such thing as two identical proto particles and everything is slighty different?

And my final concern is... Do we live in "The Imperfect Universe"? ;)

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You are probably talking about the unpredictability in the micro world as dictated by quantum mechanics (?) If this is how you mean it, it is an interesting question, and here are some thoughts about it.

Being unpredictable is not necessarily equivalent to being imperfect. On the contrary, unpredictability is the source of all beauty we witness in nature. By being unpredictable, through quantum mechanics, nature achieves the creation and manufacturing of perfect structures. It is not hard to see this if you look at the right places, a couple of which are briefly discussed below:

(i) The crystalline structure of matter. Perfect crystal symmetry, from the simplest to the most complex symmetry groups (from mathematics point of view,) lead to the perfect crystal structures we admire in nature. The laws of quantum mechanics that conspire for the organisation of matter in such perfect ways are totally probabilistic, and yet, the outcome is awesome.

(ii) The beautiful interference coloured patterns we observe on a thin film of oil floating on the water, or on the feathers of a peacock, is the result of the probabilistic properties of light in the form of photons.

Are two electrons or photons different? To answer this question you need to examine the way electrons or photons respond to various conditions we put them through. If for example we shoot two electrons perpendicularly into a uniform magnetic field, both at speed v, they will both follow circular paths of the same radius and they will move in the same direction around the circle.

When photons of red light fall at right angles to the surface of glass, they will all reflect with the same probability, no photon will have more or less chance that 4%, say.

If electrons were really different, then, when they are captured by the protons to make hydrogen atoms, they would move in different orbit sizes and they would have different energies.

However, there is no experimental evidence of such differences.

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At the level of quantum mechanics, the only thing that distinguishes particles from each other are their intrinsic quantum numbers as encapsulated in the standard model. The standard model is a shorthand for practically all the experimental data we have gathered about elementary particles and their interactions.

The particles may have different energies but there are no characteristics that can distinguish one from the other except their intrinsic quantum numbers.

This carries over to the nuclear and atomic world. One hydrogen atom is the same as another hydrogen atom in its intrinsic properties. It is when the complexity rises that the need and possibility for identification becomes important, as for example DNA molecules where still quantum mechanics is important but identity differences can be assigned.

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