> Is there any real physical evidence that an electron can be both states at the same time, outside the mathematical framework of QM?
Another way to respond to your question is to consider that the transistors inside the machine you used to post your comment were designed based on QM models of the electron that essentially follow from the Schrodinger Equation (e.g. via Fermi-Dirac statistics [0]).
As far as has been known since 1947, without QM it is extremely unlikely humans would ever have discovered how to build solid state semiconductor devices like the transistor. A key intrinsic feature of QM is superposition.
The double-slit experiment is a famous experiment that provides "tangible" evidence for superposition. [1]
Another way to respond to your question is to consider that the transistors inside the machine you used to post your comment were designed based on QM models of the electron that essentially follow from the Schrodinger Equation (e.g. via Fermi-Dirac statistics [0]).
As far as has been known since 1947, without QM it is extremely unlikely humans would ever have discovered how to build solid state semiconductor devices like the transistor. A key intrinsic feature of QM is superposition.
The double-slit experiment is a famous experiment that provides "tangible" evidence for superposition. [1]
[0] https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_statistics [1] https://en.wikipedia.org/wiki/Double-slit_experiment