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"But when one thinks of the present as enduring, with the ideal past emerging in its wake, as an unreal thing about which records exist in the present, and the ideal future as something that's anticipated in the present,"
Jonathan, Daryl,
Sometimes the best mysteries are when the answer is hiding in plain sight. It's not that the present "moves" from past to future, but that what exists changes, creating current configurations out of constant interaction. Not the earth traveling a fourth narrative dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates. The present is simply what physically exists and its action. We think of it as a dimensionless point between past and future, but 1) There is no such thing as a dimensionless point. Anything multiplied by zero is zero. It is a mathematical convenience. A dimensionless point is as real as a dimensionless apple. 2) Also if you were to truly freeze time, then the very action causing it would cease to exist. It wouldn't be a snapshot of reality, but a state of absolute zero. It's just that light is very fast and we need to sense it in very brief frames in order to see clearly.
Duration isn't a timeline external to the present, but what is present between measured events.
Clock rates vary because levels of activity vary in different environments. Gravity and velocity slow and warp atomic activity and structure, which explains both time dilation and length contraction. This argues for space as an inertial state as evidenced by centrifugal force, which is the effect of inertia on spin. That is another topic though.
A faster clock isn't traveling into the future more quickly, but into the past, since it is aging faster.
We are not building up an immutable past, as George Ellis and Joy Christian have argued, because with every passing moment, prior events recede ever further into the past, altering any conscious or physical record of them. Remember reality is relativistic! There is no objective perspective, so the past is as much a construct of subjective perspective as any currently observed event! So adding events to the past doesn't push the present into the future. It pushes prior events further into the past!
This argument against simultaneity because perception is relative is nonsense. One might as well argue that since the people of Kansas City learned of Lincoln's death before the people of San Francisco, he must have died earlier from the perspective of KC. All observations are in the future of the event.
That damn cat is not both dead and alive, because it is the collapse of future probabilities which yields current actualities. It is only due to QM using an external timeline that a determined past is projected onto a probabilistic future. While the laws governing any outcome might well be exact(or they wouldn't be laws), the total input into any event cannot be known prior to the event, because the lightcone of input is only completed by the event.
As you read these words, you progress from prior to succeeding words. Much as the hands of a clock move from one mark to the next. That linear narrative is the basis of our intellect. From the dawn of life and mobile organisms, we move along a singular path, encountering sequences of events. Does that mean sequence is fundamental, or only fundamental to perception? Does yesterday cause today? Or is that as sensible as saying one rung on a ladder causes the next? Now my typing on these keys does cause letters to appear on the screen, because there is a definitive transfer of energy from the action to the consequence. Just as it is the energy of the sun shining on a rotating planet which causes the sequence of events called "days." The future is not where the information points, which is only referential to the point of perception, but where the energy goes.
We create knowledge inductively, future becoming past, but use it deductively, projecting the past onto the future.