Difference between revisions of "Irreducibility"
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There are different types of representations that could be reducible and irreducible. It is particularly relevant in [[Group Theory]]<ref>{{:Video/How to use Group Theory in Physics ?}}</ref><ref>{{:Video/Reducible and irreducible representation}}</ref><ref>{{:Video/What are...representations?}}</ref><ref>{{:Video/Symmetry and Group Theory: Systematic Reduction of a Reducible Representation}}</ref>, [[Quantum Mechanics]], and [[ | There are different types of representations that could be reducible and irreducible. It is particularly relevant in [[Group Theory]]<ref>{{:Video/How to use Group Theory in Physics ?}}</ref><ref>{{:Video/Reducible and irreducible representation}}</ref><ref>{{:Video/What are...representations?}}</ref><ref>{{:Video/Symmetry and Group Theory: Systematic Reduction of a Reducible Representation}}</ref>, [[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<ref>{{:Video/What is a quantum system (Quantum Essentials)}}</ref> 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:[[ | In the video<ref>{{:Video/What is a quantum system (Quantum Essentials)}}</ref> 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]]<ref>{{:Video/Ch 10: What's the commutator and the uncertainty principle?}}</ref>. | ||
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Latest revision as of 14:54, 28 January 2023
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.
— ChatGPT
References
- ↑ Vector7, ed. (Aug 23, 2021). How to use Group Theory in Physics ?. local page: Vector7.
- ↑ Physics Learning With Dr. Shaw, ed. (Sep 24, 2020). What is group? - Examples of Group - Uniqueness of Identity and Inverse - Group Theory - Part 1. local page: Physics Learning With Dr. Shaw.
- ↑ Tubbenhauer, Daniel (Mar 30, 2022). What are...representations?. local page: VisualMath.
- ↑ Tye, Jesse (Apr 13, 2020). Symmetry and Group Theory: Systematic Reduction of a Reducible Representation. local page: Jesse Tye.
- ↑ Carcassi, Gabriele (Oct 19, 2021). What is a quantum system (Quantum Essentials). local page: Gabriele Carcassi.
- ↑ Sandoval, Brandon (Jan 24, 2023). Quantum Sense, ed. Ch 10: What's the commutator and the uncertainty principle?. local page: Quantum Sense.
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