TODO are there experiments, or just theoretical?
Why are complex numbers used in the Schrodinger equation? by 
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01This useless video doesn't really explain anything, he just says "it's needed because the equation has an in it".
The real explanation is: they are not needed, they just allow us to write the equation in a shorter form, which is always a win: physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600
Ciro Santilli's hardware House 2018-01 Toilet sink by Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-05-09 +Created 1970-01-012021-04 clogged
The Equation "Definition of the elliptic curves" and definitions on elliptic curve point addition both hold directly.
The idea the the wave function of a small observed system collapses "obviously" cannot be the full physical truth, only a very useful approximation of reality.
Because then are are hard pressed to determine the boundary between what collapses and what doesn't, and there isn't such a boundary, as everything is interacting, including the observer.
The many-worlds interpretation is an elegant explanation for this. Though it does feel a bit sad and superfluous.
Quantum version of the Hall effect.
As you increase the magnetic field, you can see the Hall resistance increase, but it does so in discrete steps.
Gotta understand this because the name sounds cool. Maybe also because it is used to define the fucking ampere in the 2019 redefinition of the SI base units.
At least the experiment description itself is easy to understand. The hard part is the physical theory behind.
The effect can be separated into two modes:
- Integer quantum Hall effect: easier to explain from first principles
- Fractional quantum Hall effect: harder to explain from first principles
- Fractional quantum Hall effect for : 1998 Nobel Prize in Physics
- Fractional quantum Hall effect for : one of the most important unsolved physics problems as of 2023
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