V12·Act III · Time
Each observer's own modular clock
A wall of clocks, one per observer, ticking at its own rate and visibly drifting out of step.
The relation on screen
With no external clock, the state's own modular flow is the only intrinsic notion of time evolution.
Symbols
- modular operator of the state on the observer's algebra
- modular automorphism group, the flow
- modular Hamiltonian
loading observers
what to look for · Different observers tick at different rates. Time here belongs to a state on an algebra and no background clock is available to compare them.
Consensus to physics
- 01an observer is a patch cluster that reads its own records
- 02modular flow on its support algebra generates a one-parameter automorphism
- 03the flow parameter is the only ordering the observer can build internally
- 04that parameter is the observer's proper time
In standard physics
Tomita-Takesaki modular flow as thermal time
Proper time is personal and there is no master clock on the wall behind the observers. Different observers carry different modular depths, which is what makes time observer-relative.
boundary · Modular depth orders events for one observer. Converting it to seconds needs a rate this run does not fix.