In a Weyl geometry, two identical clocks separated and moved along different world lines between the same two events will differ not only in elapsed time but also in their rate of ticking (unit of time) at the destination event.
The amount of time that actually passes as measured by a clock moving through space—how much time the clock actually records.
Events (in spacetime)(as used in physics and philosophy of spacetime)
Specific points in space and time, like 'a clock at this location at this exact moment'—the basic building blocks for describing what happens in the universe.
Unit of time(as used in physics and philosophy of measurement)
The standard measure you use to count time intervals, like a second—but in Weyl geometry, this standard can change depending on where you are.
Weyl geometry(Infinitesimal geometry)
A geometric structure determined by a conformal structure together with a length connection or gauge field A_j(x), which together uniquely determine a Weyl connection
world lines(Used in the plasticine analogy to illustrate the structure of the four-dimensional world.)
Individual fibers traversing the four-dimensional world, representing the trajectories of material particles through spacetime.
Suppose physical spacetime corresponds to a Weyl geometry. Then two identical clocks \(A\) and \(B\) at an event \(p\) with a common unit of time, that is, a timelike vector of given length \(l_{p}\), which are separated and moved along different world lines to an event \(q\), will not only differ with respect to the elapsed time (first clock effect (i.e., relativistic effect)), but in general the clocks will differ with respect to their common unit of time (rate of ticking) at \(q\) (secon
Extraction notes
Validity: Extracted via Max plan + API grounding/validity checks