Irreducibility

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There are different types of representations that could be reducible and irreducible. It is particularly relevant in Group Theory[1][2][3][4], Quantum Mechanics. If this statement about quantum mechanics is a science of the irreducible observation or representation, then, the entanglement,superposition, and uncertainty as three separated ideas that describes quantum mechanics must be inter-connected and irreducibly combined to talk about the properties of systems being described by quantum mechanics.

In the video[5] by Gabriele Carcassi, the notion that all quantum systems are irreducible. It appears that this statement is directly tied to the idea of uncertainty principle, which should have been called:observable precision principe. This explanation can be related to the notion of commutator as explained by Brandon Sandoval[6].

the term "uncertainty principle" is not a perfect name for the principle, as it implies a fundamental limit to our ability to measure certain properties of a particle, when in reality the limit arises from the wave-like nature of particles and the relationship between position and momentum in quantum mechanics, "measurement disturbance principle" or "wave-particle duality principle" could be a better term to describe it.

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