1

**Physics, Astronomy & Cosmology / Re: Theoretical information**

« **on:**11/11/2024 18:56:16 »

...which is still an approximation to the analytic statement.There is something a bit weird about analytic continuation. If you expand a unitary "space" by functionalising it, that is, you map a pair of complex matrix exponentials, along with their inverses such that their product is 1, but you still have a Taylor series.

Because of continuity you can show that you still get Euler's formula, even with just the first three terms of the Taylor polynomial. Unitarity is a real thing though. It also has something to do with normalisation and measurement.

One way I think about the Taylor expansion is, how many dots do I need to see a pattern that isn't random? The dots, their positions, are the "polynomial expression", it has to be unitary in that, I need a large enough volume for all the individual probabilities to add up to "a pattern".

If that's no help at all, yeah, I guess. I've been watching Sir Roger Penrose on Youtube, talk about Schrodinger and how that man was sure he had it wrong, even though it works.

That stuff about expanding matrix exponentials was part of an online MIT course by Seth Lloyd, the goal was to show that for electrons, or charged particles generally, an external magnetic field can rotate some abstract angle. I recall the three normalised real unit vectors were in there, this was meant to be something that fermions do in real 3-space, or as physicists like to call it, a lab.