A simple way to understand global phase in terms of the Bloch sphere is that when the angle θ is 0° or 180° then the angle φ is irrelevant.

Exactly the way longitude is irrelevant at the North and South poles.

]]>And given that the Schrödinger equation *derives*, in good part, from de Broglie’s matter-wave duality, I wonder all the more to what extent matter waves, specifically their wavelengths, are significant.

I’m not sure I’d go that far, but I do think his faith in the MWI is kinda stupid.

I used to have a lot of regard for the guy, but over the years that declined, and I most see him now as I do Michio Kaku — as someone who sold his integrity (or lost his mind) to being a “popular” science writer. I have zero regard for Kaku, and I’m increasingly seeing Carroll likewise.

]]>Also… a 3D version!

]]>It was a fun mini project. I may blog about it someday, but here’s a sample for now:

There’s still a bug if you look closely. Sometimes balls that pass too closely fall into each other’s orbits and spiral in on each other. A consequence of a virtual reality where the balls have no actual substance and coincidence is only prevented in software.

]]>The coefficients α and β are complex numbers with a phase. They interact to control the “longitude” of the state vector in the Bloch sphere (and, of course, its latitude, but it’s the longitude that’s the phase of the state).

A measurement reduces the vector to **|0⟩** or **|1⟩** and the latitude is lost. It’s only when combined with another qubit, or a “gate” operation, that the phase matters.