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>Today we look upon electrons and other spin-1/2 particles as having an intrinsic angular momentum with no classical counterpart. This gave rise to the notion o

>Today we look upon electrons and other spin-1/2 particles as having an intrinsic angular momentum with no classical counterpart. This gave rise to the notion of such particles living in ‘‘spin space,’’ an abstract two-dimensional internal space that requires a description beyond that of scalars, vectors and tensors. Okay I admit it, this annoyed me. Electron spin doesn't require 2 dimensions to describe, its 1 dimensional, and even more, it requires 1 bit. Other spin values require slightly more space on a one dimensional line, but still. I like it better when maths people are meticulous.

cuspycode 6y ago
Terminology is not always unambiguous. The spin quantum number is discrete for electrons {-1/2,1/2}, but spin also means the physical entity that gives rise to the so-called intrinsic angular momentum, which is a vector.
- javajosh 6y ago
  I thought he was pretty unambiguous there. If we wants to talk about the underlying wave function before collapse, fine, its path in 2D space. But the measured spin only requires 1 bit. Note that the spin is NOT a 2D vector, but a path, which itself can described by a sequence of vectors. Yes yes, Bell's Theorem, EPR, collapse, and all, but I still think it was sloppy.
  - n4r9 6y ago
    Honestly I'm not sure what your complaint is here. Or at least you seem to be very adamant that some particular interpretation/ontology is obviously the right one. In standard quantum theory, electron spin can be modeled by a 2 dimensional complex vector. It's also possible to model the spin of an isolated system using 3 dimensional real vector (the "Bloch sphere").
chr1 6y ago
It would have been 1 bit if all measuring devices in the universe were oriented along the same axis. If you prepare electron in a device with one orientation, then measure it again with a different device you need the vector.

cuspycode 6y ago

Terminology is not always unambiguous. The spin quantum number is discrete for electrons {-1/2,1/2}, but spin also means the physical entity that gives rise to the so-called intrinsic angular momentum, which is a vector.

javajosh 6y ago
I thought he was pretty unambiguous there. If we wants to talk about the underlying wave function before collapse, fine, its path in 2D space. But the measured spin only requires 1 bit. Note that the spin is NOT a 2D vector, but a path, which itself can described by a sequence of vectors. Yes yes, Bell's Theorem, EPR, collapse, and all, but I still think it was sloppy.
- n4r9 6y ago
  Honestly I'm not sure what your complaint is here. Or at least you seem to be very adamant that some particular interpretation/ontology is obviously the right one. In standard quantum theory, electron spin can be modeled by a 2 dimensional complex vector. It's also possible to model the spin of an isolated system using 3 dimensional real vector (the "Bloch sphere").

chr1 6y ago

It would have been 1 bit if all measuring devices in the universe were oriented along the same axis. If you prepare electron in a device with one orientation, then measure it again with a different device you need the vector.