Von Neumann Rewrote Quantum Mechanics as a Geometry of Pure Possibility
In Hilbert space, all things are quantumly possible
Quantum mechanics doesn't track objects moving through ordinary space; it tracks arrows pointing through Hilbert space, a realm whose axes mark every possible future. In 1927, 23-year-old John von Neumann showed that Heisenberg's matrices and Schrödinger's waves were two views of the same vector, and defined the space that holds it. Quanta traces how that abstraction became physics' fundamental arena — and why some researchers now suspect it isn't the final word.
I would like to make a confession which may seem immoral: I do not believe in Hilbert space anymore.
- djsjajah
Not all things are possible, only potentially possible ones.
If you take all the numbers between zero and one, you will find an endless supply of distinct numbers but none of them are 3.
- librasteve
Sean Carroll (name checked in the article) has an excellent podcast “Mindscape” (https://preposterousuniverse.com/podcast/)
I particularly like the one with David Wallace.
- dbvdh
It’s not ‘all’ things that are possible, just things that are allowed within the laws of physics :)
Subtle difference, but energy conservation for example has to be adhered to.
- rozgo
"I would like to make a confession which may seem immoral: I do not believe absolutely in Hilbert space anymore." - John von Neumann
- rootedbox
Just a reminder.. Hilbert space is just a tool/abstraction/map... and the map is not the territory..