Nitpick: the atoms are accelerating at 9.81 m/s[SUP]2[/SUP]. That means that, starting from rest, the velocity of the body is 9.81 m/s (down) after one second, 19.6 m/s (down) after two seconds, 29.4 m/s (down) after three seconds, et cetera, until it comes to a sudden and complete stop upon hitting the pavement.
The “rubber sheet analogy” is, like all analogies, a comparison between the phenomenon in question and something that is more familiar to the student for the purposes of illustration. Analogy doesn’t “explain” anything, and it is a mistake to think that the insight and intuition which may be gained by consideration of an analogy is equivalent to fundamentally understanding the phenomenon in question any more than you can genuinely comprehend a Japanese text by running it through a Babelfish filter and reading the Engrish result.
Electromagnetic fields are very well and thoroughly explained at both the macroscopic level of classical electrodynamics, including (with a few modest modifications to the so-called Maxwell’s equations) behavior in a relativistic regime, and at a discrete level via quantum electrodynamics (QED), which brings in the direct interaction of charged matter and light at a fundamental level. QED is widely regarded as the “crown jewel” in physical theories because of the extreme precision of results that have been predicted by the model. As much as we can say to have fundamental understanding of any physical phenomena, we have an absolute understanding of electrodynamics (including magnetic fields) at a fundamental level. The challenge of QED is taking what we know about interactions between individual particles, which are really “pretty simple” e.g. only requires about three or four years of dedicated study to understand, and building it into an understanding of the behavior of large groups of particles, which is something we’ve been working on for somewhat over a century and are still struggling to develop into a useful predictive model for even “simple” phenomena.
Getting back to the question of the o.p. we can be said to have a rather good understanding of gravitation (to the tune of 1215 pages of dense equations and examples) down to a a certain level, and that level is what we call the space-time continuum, which is the level at which gravitational interactions, as we currently understand them, fundamentally occur. Why do we give it such a weird label? Well, because all the terms are reduced to parameters measured in distance (space) and duration (time) which are equivalenced (hence, why they are hyphenated) and are assumed to occur over a continuous metric (continuum). This body of knowledge is collectively referred to as general relativity and described by the Einstein field equations, which describe the topology (shape) of space-time in terms of momentum and local energy and the actions that it has upon other fields of mass and energy. It also happens to say that space and time are two components of the same metric, and that mass and energy are the same thing in different wrappers. Now, this may bother you that “space-time” isn’t made of real stuff that we can hold and measure, and that “mass-energy” seems like a marriage between Joan Baez and Dick Cheney, but all we can say about that is that this is the way the world works.
The problem with general relativity is that while it works well in making predictions that have been verified to pretty good precision (not as good as QED, but somebody has to be in the lead) the ability to make predictions where space-time is no longer continuous or at a level where mass-energy is measured in discrete measures rather than distributed fields breaks down completely. So when you start looking at black holes or quantum interactions, general relativity is suddenly and almost completely worthless, which is really distressing to a lot of people, some of whom have gone completely nuts and have taken to standing on street corners screaming random gibberish in frustration, or else making up crazy and totally unsubstantiated clams about vibrating strings, twistors, quantum loops, or Roger Penrose’s interpretation which is so batshit beyond belief that it doesn’t even get a proper name. Unfortunately, no one has really come up with a genuinely plausible hypothesis that can be falsified by experiment and observation, and it is possible that any one of these theories is at least partially correct, or at least not entirely wrong (even nutty Roger Penrose). What we can say is that there is clearly some underlying plenum below this “space-time” textile business at which more fundamental interactions occur, and we would like it to be in the same type of mechanics as the quantum particle/field business (e.g. a quantum theory that can be renormalized to give useful predictions) and hopefully describe interactions combining electrodynamics and gravity but there is no clear avenue to that end.
By the way, not to confuse the issue further, but there is also a counterpart to QED called quantum chromodynamics (QCD) which describes interactions at the nuclear level. Since we don’t see these on an everyday level there is no need to have a macroscopic simplification of it, and because QCD interactions are much more complex the theory isn’t as complete or well-verified as QED, but from everything we know about nuclear interactions it seems to be viable, and in fact we (well, Sheldon Glashow, Steven Weinberg, and Abdus Salam) have managed to unify much of the two individual models into something called electroweak interaction. Combining the nuclear ‘strong’ force to get to a grand unified theory (GUT) has still eluded us, but there is hope for achieving a useful model in the foreseeable future.
Stranger