What’s the underlying principle on why you can’t know the position and momentum of a particle at the same time? Is there an explanation? I don’t have any knowledge of calculus or the math behind anything so I’m asking here, thanks!
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There are 6 postulates in quantum mechanics. These are the baseline principles upon which all of quantum mechanics is built on. The uncertainty principle is a logical conclusion that can be made from those postulates
1. The entire state of a system can be described with a wave function.
2. Any observable value has something called a “Hermitian operator” associated with it.
3. When you apply those “Hermitian operators” to a state, it gives some constant multiplied by that state.
4. A normalized wave function has an average value.
5. The Schrodinger equation describes time evolution.
6. The Pauli exclusion principle applies to fermions (protons, electrons, and some others)
The Heisenberg uncertainty principle is these applied, along with mathematics to reach the conclusions that position and momentum are mutually exclusive. It takes about 3 months of undergrad work to get to the point where you can do that “proof”
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