The answer is that gravitation describes the property that lapse of time is just a choice of coordinates and, by itself, doesn’t have any intrinsic meaning. The details can be found in any textbook on general relativity.

To Preston: Please read my paper Orientation in Space

To Stam: Please read Curvilinear Cosmology.

See chapter 21 in MTW for ideas about the lapse function N. "The choice of N is to be made, not by nature, but by man."

Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald. Gravitation (p. 527). Princeton University Press. Kindle Edition.

Moreover, Big-bang is considered as the beginning of everything, including or especially the time. This relation need be continued in the further cosmic development.

9.8 meters (32 feet 2 inches) above the ground you are standing on the number of Planck times/second is 4.27x10^25 more than at ground level.

Why? Because 9.8 meters up is where time (age of the Universe) is already one-second into the future.

But wait a second! Now, the number of Planck times/second at the ground just caught up to that same number!

Swing a pendulum that is 9.8 meters long -- the period of that pendulum is 2π seconds (6.238 seconds).

Why? This length pendulum on Earth, in a sense, exchanges our perceptions of length in [meters] with our perception of the passage of time in [seconds].

Ready to be astonished? During each passing second the Earth's radius grows by 9.8 meters while the duration of a second grows by that 4.27x10^25 Planck times, meanwhile the circumference of the universe grows by 2*c. (Contrary to old school teachings, this means that every atom in and on the Earth is expanding along with the whole universe. In fact, this statement would have to be true about all atoms in the universe. Well, if that were true then conventional wisdom would say "You couldn't tell that this is happening -- scientists who did not know any better would conclude that "Galaxies do not expand, but the gaps between them do." Which is exactly what they have taught is for over a century.

Cosmological Relativity extends Einstein's General Relativity by giving us an awareness that our "emergent" metrics for length [meters] and for measuring time [seconds] grow in lockstep with each other so that the Speed of Light remains constant.

c = l_P/t_P = Ζο/μ_0.

Please see: TrueCosmology.info/cosmic-clock

Dear John Wsol

You wrote: "Contrary to old school teachings, this means that every atom in and on the Earth is expanding along with the whole universe. […] Well, if that were true then conventional wisdom would say "You couldn't tell that this is happening…".

That's correct. But in reality the universe doesn't expand with the same rate at all locations. The expansion rate of the whole universe ("edge") is exactly 1.5 times the rate at the observer. The effect can be observed from about 0,01R on. The reason is, that the universe earlier used to expand faster than nowadays. Please find the exact calculation in Preprint The Metric Universe

I tried to assimilate your document, but its 294 pages long. Then I tried to get help from an AI. It is 5.6 times too big to upload. After my meetings with Tony Robbins & Dean Graziosi (Sample here: https://youtu.be/muNil6QcIA8?t=10925)

I'll try to get one of our AI systems to read sections.

I see that your r_0/2*t_0 = c. Also, are you aware that H_0 is NOT constant, but its units simplfy to [/s] -- it is the reciprocal of the age of the universe in seconds.

What do you think about this Cosmic-Clock: TrueCosmology.info/cosmic-clock

Dear John Wsol You wrote: "I tried to assimilate your document, but it’s 294 pages long. Then I tried to get help from an AI. It is 5.6 times too big to upload." Nice idea, I had thought of something like that before, but since ChatGPT always chickened out on the third consecutive question (overloaded with too many questions from others), I haven't done it yet. But if 294 pages are too much, you may try it with Preprint The Electron and Weak Points of the Metric System

Preprint Expansion, Topology and Entropy

As that rigorously scientifically proven in the Shevchenko-Tokarevsky’s Planck scale informational physical model, Gravity fundamentally is nothing else than some fundamental Nature force, and – as any/every other fundamental Forces that act in Matter – fundamentally has no relation to fundamental phenomena/notions “Time” and “Space”, besides that, again as that all other Forces do, Gravity fundamentally obligatorily acts in space and time dimensions of Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct).

And any space and time dimensions fundamentally by no means can impact by any way on any, including Gravity, Force.

What is Gravity Force see SS&VT 2007 initial Planck scale informational physical model of this [and Electric] Force in

https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces

SS posts in

https://www.researchgate.net/post/How_many_fundamental_forces_exist_5_4_or_3/2 pages 2,3,7

https://www.researchgate.net/post/Ideas_for_Aether_Theory_of_Gravity/4

https://www.researchgate.net/post/NO36_Doubts_about_General_Relativity_1-Is_the_Geometry_Interpretation_of_Gravity_a_Paradox

.https://www.researchgate.net/post/Gravitation_and_Quantum_indeterminacy_contradict_each_other_something_is_not_right

https://www.researchgate.net/post/Gravity_and_Inertia

- are relevant to this thread question.

Cheers

This speculative discussion, founded on some formal concepts, does not concern at all my question: What may be the direct physical relation...

My thesis tries to explain gravitation as the fluid-dynamical force acting between parallel flows of matter along temporal axis.