Manuscript X-K-ST@1 · X-K-ST.tex · proposition · 93c39c0f

Proposition: Finite CCR limitation

External time and Problem 8 › The composition law does not imply relational dynamics · lines 1693–1705 · proof included or linked

X-K-ST@1#prop:CCR

Finite matrices $T_{C}, H_{C}$ cannot satisfy

[T_{C}, H_{C}] = i ℏ I when ℏ \neq = 0.

Proof. A finite matrix commutator has trace zero, whereas the right side has trace $i ℏ dim H_{C} \neq = 0$ .

Displayed formulas in this passage