A few months ago Dialect published this: https://www.youtube.com/watch?v=PjT85AxTmI0 in which they reported themselves to be very much put out at the widely promulgated assertion that time dilation is the cause of gravitational attraction in common circumstances (the apple that falls on Newton’s head). Since the offending assertion is essentially a restatement of the identity of the metric and gravitational fields - their position seems overwrought. But the weirdest part was the difficulty they were having as to where the idea came from (Albert Einstein). They were apparently convinced it must have come from the world wide web.
Here was my response:
The videos you attack are correct. As other respondents have indicated and as emphasized by Thorne, Schutz, and other leaders in the field, curved spacetime has a time component which dominates in certain conditions - weak gravitational field and viewed at low velocity. (Like an apple falling from a tree, as opposed to starlight bending around the sun.) It is called the Newtonian limit. The Einstein equation reduces to Newtonian gravity in everyday life situations where only time curvature (otherwise known as the time dilation gradient) applies. The curvature of space in these conditions is de minimis.
Narrowly defined, the Newtonian limit is uncontroversial. It is explicit in the math and in Einstein's explanations of general relativity and universally recognized. The dispute among experts and groupies alike is about physical intuition and is due to systemic pedagogy failure and a philosophical prejudice that both go back to Einstein. When Minkowski introduced spacetime, Einstein famously quipped that since the mathematicians got a hold of it, he no longer understood his own theory. His reputation for abstract thought notwithstanding, Einstein was most at home with imagined concrete events and bridled at the ontological weight Minkowski attributed to the most ethereal of abstractions: spacetime. At this time, Einstein was just starting to work on gravity and it took him several years before he reluctantly conceded the power of a modified version of Minkowski's scheme ( a pseudo-Riemannian manifold) to get him to his destination.
But way before the curved spacetime breakthrough, Einstein did develop a picture of a gravitational time gradient causing the bending of starlight around the sun. Your presentation indicated that you pursued the provenance of the ideas in the target videos and the trail goes cold a few years ago. Please. That's off by about a century. The real source is a 1907 breakthrough memorialized in Einstein's 1911 "On the Influence of Gravitation on the Propagation of Light". According to this paper, the range of differences in time dilation at different points on the radial axis causes gravitational attraction. This is what we now call time curvature.
When he later nailed the new theory of gravity at the end of 1915, this model of time curvature was subsumed into a more complete model of curved spacetime - a phrase he himself assiduously avoided, even though it would have elegantly explained why his earlier deflection prediction was short by half. Here was his unfortunate description of the separate elements involved: "...half of this deflection is produced by the Newtonian field of the sun, and the other half by the geometrical modification ("curvature") of space caused by the sun." This startling quote exposes the gulf between his reliable spacetime math and his resistance to embracing the intuitions implicit therein. It's as if he is propounding a system of mere curved space (not spacetime) and then attempts to coax an exhausted Newton into what should have been an unnecessary assist.