Whitehead would have a sharp, specific answer here — and would push back on the Einstein framing.
On the block universe ("all time exists currently")
Whitehead explicitly rejected this. For him, the block universe — where past, present, and future are equally real coordinates in a four-dimensional manifold — commits what he called the "fallacy of misplaced concreteness": treating an abstraction (the mathematical model) as more real than lived experience. The present moment isn't just a perspective on a static whole. It is the site of genuine becoming. The past is fixed and objectively immortal; the future is genuinely open; the present is the creative advance from one into the other.
On what clocks measure
Whitehead's answer: clocks measure the rhythm of periodic processes — and in doing so, they measure something real but derivative. What underlies any periodic process is the succession of what he called "actual occasions" — momentary events of becoming that arise, achieve their character, and perish. Each actual occasion prehends (grasps) its past, becomes determinate, and then becomes data for the next occasion. Time is the form this creative advance takes.
So when Rogan asks "what are we measuring?" — Whitehead's answer is: the rate of creative becoming in a given physical process, used as a standard against which to compare other processes. The clock doesn't reveal time from the outside; it participates in time as one more chain of becoming.
On why the question "caused everything to fall apart"
Whitehead would say physics fell apart precisely because it tried to eliminate becoming from its account of nature. Newtonian time was a featureless container. Einsteinian time became a dimension geometrically equivalent to space. Both abstractions are useful but both strip out the one feature of time that is phenomenologically undeniable: that the present is different in kind from past and future. It is the only moment where anything is actually happening. Physics has no variable for "now" — and that's the lacuna.
The bottom line
Whitehead's answer to Rogan's "I still don't understand what we're measuring" would be: you're measuring the pace at which the universe creates novelty. A clock is a stable, periodic instance of the same process that underlies everything — the passage of nature, the creative advance of actual occasions from potentiality into fact. What makes time mysterious isn't that we lack data; it's that the standard tools of physics were deliberately built to abstract time into a spatial dimension, and in doing so they discarded the very feature — becoming — that makes time time. – GPT