This makes intuitive sense to me, but isn't the issue that relativity states that time is intrinsically coupled with space? Ones experience of time relative to another's is directly related to the topological features of the space they're in. If it's more curved, time also "curves" and slows down relative to another observer in flatter space.
How does this notion of time become decoupled from space?
One way I imagine it is that "time" as a concept encapsulates at least two properties:
1) The degree of freedom (i.e., dimension) through which things can change; and 2) The unidirectional flow of causal events
Relativity seems more concerned with defining time in terms of casual events (e.g., event horizons) than its dimensionality. If we define "fundamental time" as a dimension that allows for change can it then be decoupled from space?