- #1

physwiz222

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- TL;DR Summary
- What does Position and Momentum not commuting have to do with particles not being allowed to simultaneously have defined position and momenta. I want a conceptual explanation.

In Quantum Mechanics a particle cannot have both a defined position and momentum due to the uncertainty principle we all know that. A reason for this is because the Position and Momentum Operators dont commute but it can be demonstrated with Fourier Transforms.

I know how to mathematically derive the generalized uncertainty principle and what uncertainty principle physically means. What I want to know is what is the connection between Position and Momentum not commuting the order mattering and a particle not being able to have simultaneously defined x and p. Like how are these 2 things connected physically.

I want to emphasize I am not looking for a mathematical derivation I know how the Generalized Uncertainty Principle is derived for any pair of observables and how Uncertainty related to Fourier Transforms. What I want is a conceptual explanation for why the fact that x and p operators dont commute means the particle cant have both simultaneously defined. I know the Math and how its derived I want a conceptual reason.

I know how to mathematically derive the generalized uncertainty principle and what uncertainty principle physically means. What I want to know is what is the connection between Position and Momentum not commuting the order mattering and a particle not being able to have simultaneously defined x and p. Like how are these 2 things connected physically.

I want to emphasize I am not looking for a mathematical derivation I know how the Generalized Uncertainty Principle is derived for any pair of observables and how Uncertainty related to Fourier Transforms. What I want is a conceptual explanation for why the fact that x and p operators dont commute means the particle cant have both simultaneously defined. I know the Math and how its derived I want a conceptual reason.