Einstein’s astonishing gravity theory is now easy to understand and prove, using our mobile phones. Finally see just how curved spacetime causes gravity — math optional.
This material, including the poster below, was presented in 2023 at The 3rd African Conference on Fundamental and Applied Physics.
This research demonstrates a little known fact: recent technology in many of our own pockets now offers clear and startling proof of Einstein’s theory of gravity. The truth may surprise you — since today, it’s not what many relativity students learn. It’s time for a bold new approach to teaching Einstein’s gravity.
Einstein’s general relativity theory considers the apparent downward pull of terrestrial gravity a fictitious force — the term physicists use for a mysterious apparent force seen by observers who don’t realize they’re accelerating. In the case of gravity, this means an apple in free fall does not accelerate downward toward the earth — the surface of the massive earth accelerates outward and upward toward the apple! Albert Einstein famously realized this while considering his weight change, and related thought experiments, on elevator rides in 1907. He realized, that’s why objects in free fall near earth’s surface all appear to accelerate downward at the same rate. Exhilarated, he would call it the “happiest thought” of his life.
Of course, it seems absurd and impossible that we on earth’s surface are accelerating upward. Until it’s explained, the simple non-Euclidean geometry behind it is far from obvious. So most people can’t quite accept it — and physicists aren’t immune. We naturally, unconsciously continue to believe and promote variations on Newton’s useful theory — confusing students, ourselves and one another. A relativity teacher or book might not mention the 4–pressure terms in Einstein’s field equation that describe how space is stretched by the matter contained in it. And most curricula miss simple new experiments that let students today easily prove Einstein’s theory of gravity is correct — while in a key sense, Newton’s gravity theory is wrong — beyond the gravitational lensing and time dilation confirmed in early proofs of the theory.
This short article lets readers easily understand Einstein’s stunning gravity theory, and even prove it — using their smart phones and the accelerometers inside them. Once we take those surprising measurements seriously, and focus on how spacetime curvature dynamically stretches space as well as time — we can both understand the geometry with very little math, and see why it’s been hard to present before.
While the ideas remain mind boggling, here they’re no longer hidden under reams of symbolic math. In fact we’ll see how the core math of Einstein’s gravity is so strikingly simple, we can derive Newton’s or Gauss’s classical formulas for gravity from Einstein’s in one short paragraph using middle school math and geometry.
I should stress that this article only covers how spacetime curvature results in everyday gravity — not the rest of general relativity, which includes electricity, magnetism, light, time dilation, Lorentz contraction and early hints of quantum theory. Nothing we discuss here applies precisely to objects moving near the speed of light or approaching the density of a black hole.
Rather, by following our accelerometer data, we’ll see that Einstein’s vision elegantly explains how the classical gravity of Newton, Gauss and Kepler results from spacetime curvature. And we’ll see why, because in many ways it’s the opposite of what Newton and the rest of us have always believed, this has been effectively hidden for over a century.
Einstein’s Gravity In Brief
It’s easier than one might think to picture how Einstein says gravity works, if we dare to accept this: When we toss a ball on earth, it travels in a straight line. To you, an observer standing on earth’s surface, it appears to curve downward only because you are actually being pushed upward by earth’s surface, at 1 g. (That’s 32 feet/sec/sec, or 9.81 meters/sec/sec, or 22 mph/sec — the acceleration of race car.) Pay attention and you can feel it — in your feet, against your butt when sitting, and even via motion sensors in your ears. But like Newton, we think of that as our weight — our body’s resistance to a real downward pull of gravity when we’re in contact with the earth. And Newton says, that same force pulls on an apple when it’s in free fall, accelerating it downward at 1 g.
Einstein says we on earth are really being pushed upward by its surface — that our weight is the reaction to that force. Absurdly, he insists the apple that looks like it’s accelerating downward at 1 g isn’t really accelerating at all — that the earth’s surface accelerates toward it. He says the downward pull of gravity is an illusion.
We can agree on the accelerating decrease in distance between the apple and the ground. But we’re intuitively certain that the better frame of reference for deciding which object is accelerating is on the ground, not in the falling apple.
Is there a simple way to say which is true? Actually, in Newton’s and Einstein’s day there wasn’t — and that has led to over a century of rampant confusion.
21st Century Proof of Einstein’s Gravity
Today it’s easy. In 2007 — exactly a century after Einstein’s elevator rides — mobile phones, tablets and other devices like the iPhone began to include tiny 3D accelerometers, along with gyroscopes to track orientation and rotation, and displays. Some apps specifically function as accelerometers, while a million common apps rely on the sensors to do things like keep their screen images and text upright when used on earth. Rather than measure distances between objects, accelerometers directly measure the proper acceleration of the sensor in its own frame of reference, independent of any external reference point.
Experiment: Toss a Mobile Device
Run any 3D accelerometer app with a display. Hold the mobile device vertically, carefully toss it up vertically in the air, and catch it. While predictably the device appears to slow down, reach a maximum height, reverse direction, and fall faster and faster downward toward the ground, the device’s accelerometers will read 0.0 in every direction throughout its flight — showing that in fact, it’s moving at a constant velocity in a straight line — until it lands or you catch it.
But hold the device in your hand, or set it on a table or the ground, and you’ll measure a constant upward acceleration of 1 g. That’s why the device appears to change direction and fall — we and the surface of the earth are accelerating upward, catching up with the device we tossed, and outpacing it. Since these are 3D accelerometers, we can confirm this in many different ways by looking at the X, Y and Z acceleration values as we turn or toss the device.
In the figure Red, Green and Blue represent the phone’s acceleration along X, Y and Z axes respectively. Green is the vertical acceleration, with positive Y going down the screen like text — so a green value of -1.0 is upward, away from earth’s center. Yellow is the acceleration magnitude — which is 0.0 when the device is falling, NOT 1 g as Newton’s theory predicted.
So when an apple or an iPhone is evidently falling faster and faster down toward the ground, it is not accelerating at all. And when it’s lying on a table or the ground, it’s accelerating upward, away from earth’s center, at 1 g.
This reality is a predicted and well-documented result of Einstein’s spacetime curvature theory. We can read about it in Wikipedia. It is increasingly understood by engineers and mobile software developers.
But for the most part, relativity textbooks and curricula have not caught up. Even the simplest modern accelerometer experiments are often missed or avoided in relativity classes, and we’ll see, the very language of the real gravitational forces and accelerations remains practically alien to students.
The Real Forces Behind the Illusion of Gravity
Many relativity students have never heard that the real gravitational force on an object resting on the ground is called the proper force on it — and that it’s the same magnitude as the fictitious force we call its weight, but is in the exact opposite direction — upward. And while many students learning relativity concepts like time dilation know the term proper time from their assignments, most have never heard of proper acceleration — which is now easily measured by accelerometers Einstein never had. They clearly show the ground is accelerating upward toward the apple, pushing up against objects on its surface. Likewise, relativity textbooks often neglect the space-scaling pressure terms in the metric tensor of Einstein’s field equation, which describe how rigid objects, ordinary rulers, and lengths themselnves continuously stretch in the vicinity of matter. Some textbooks even avoid the term fictitious force entirely. But you can follow the links in this paragraph and meet the real forces and accelerations behind the illusion of gravity — already hiding in plain sight in Wikipedia.
Of course, this peculiar outward acceleration would be impossible in ordinary geometry unless the earth was getting bigger — another absurd idea. But in Einstein’s non-Euclidean geometry, earth’s surface accelerates outward without its diameter in meters increasing. In Einstein’s spacetime curvature, positive pressure coefficients in the core metric tensor diagonal say that in a volume containing matter, meters are getting longer.
Professors Thorne and Feynman on Einstein’s Gravity
Nobel laureate Kip S. Thorne created an illuminating storyboard (Thorne, pp. 97–99) explaining gravity from the point of view of an inertial observer like a cliff diver, who sees that a cannonball fired on earth’s surface follows a straight line trajectory. This is contrasted with a dog or person on the ground, who sees the ball move in a parabola relative to the earth’s surface — which we tacitly, incorrectly treat as an unaccelerated frame of reference.
Prof Thorne shared the storyboard above in 1994, describing the dynamic stretching of space in terms of warpage, as Einstein often did. But like many 20th century relativity books, he doesn’t explicitly mention fictitious force, proper force or proper acceleration — the real forces behind gravity — or how accelerometers might measure them. So he doesn’t anticipate the accelerometer experiments that today confirm a tossed ball travels in a straight line while while observers on the surface accelerate upward.
Completing Feynman’s Lecture on Gravity
Nobel laureate Prof Richard Feynman raises gravity as a fictitious (or pseudo) force in his renowned lectures and books, such as Six (Not So) Easy Pieces in the 1960s. His lectures touch on the gravity ideas raised in this article — though he often frames them cautiously, as possibilities.
“If we distort the geometry sufficiently it is possible that all gravitation is related in some way to pseudo forces; that is the general idea of the Einsteinian theory of gravitation.”
“One very important feature of pseudo forces is that they are always proportional to the masses. The same is true of gravity. The possibility exists therefore, that gravity itself is a pseudo force. Is it not possible that perhaps gravitation is due simply to the fact we do not have the right coordinate system?”
“Einstein found that gravity could be considered a pseudo force … and was led by his considerations to suggest that the geometry of the world is more complicated than ordinary Euclidean geometry.”
And after discussing gravitational time-dilation, Feynman emphasizes the necessity of meters changing length in the presence of matter: “Just as time scales change from place to place in a gravitational field, so do the length scales. … It is impossible with space and time so intimately mixed to have something happen with time that isn’t in some way reflected in space.” (Feynman p. 225)
Thus we find Feynman speaking very generally, even pulling his punches as he points out that Einstein’s gravity theory is founded on fictitious force, meters that stretch, and non-Euclidean geometry. Perhaps he’s humbly confessing he isn’t certain enough of the details to fully explain it — or perhaps there just wasn’t sufficient time in his wide ranging physics lecture.
Six decades later, this article aims to fill in the details by speaking more definitely. What we call gravity is a fictitious force. Defying Euclid and Newton, meters and rigid objects do stretch continuously and geometrically in the vicinity of matter — with Newton’s G as a key scale factor. Viewed from a continuously expanding coordinate system, the math is quite simple. Modern accelerometers Feynman didn’t have let us easily demonstrate and prove the theory. And concepts like volume acceleration derived directly from G let us explain it all in one brief lecture or article. Now the main barrier to understanding Einstein’s gravity is denial.
Math and Misdirection
When we hold and then release an apple or ball near the surface of the earth, why does it appear to fall at 1 g? A 20th century physics student might answer: “because it follows a geodesic curve”. In fact, a geodesic path is a straight line through stretching 4D spacetime, as Prof Thorne’s inertial cliff diver can see. But unless one is reminded about the acceleration of the earth’s surface instead of the apple, the fictitious force illusion, and how meters stretch, one can’t really understand the lesson. In fact, characterizing the ball’s path as any curve tends to obscure Thorne’s elegant point; mask the local changes in scale that govern the acceleration of a massive body’s surface; and obscure Einstein’s fundamental insight into how space stretches.
So when a student steeped in 4D symbolic math answers “the apple falls because it’s following a geodesic” instead of “it appears to fall because you, the observer, are being pushed upward,” those hard-earned 4D math lessons are leading away from the real answer.
Thus, whereas physics students may assume complex math is the route to understanding relativity, in fact it can be a key barrier to comprehending Einstein’s simple but rather counterintuitive and implausible theory. Students may imagine If only I was more fluent in the math, I’d truly master general relativity. They don’t suspect the gap is, There’s a much simpler but weirder explanation that our textbooks are leaving out.
It’s almost as if complex 4D symbolic math serves partly as an intellectual poultice — a salve to soothe and distract from the painful, embarrassing cognitive dissonance of accepting Einstein’s nutty, stretchy, inside-out theory. And that can obscure the startling ways Einstein’s gravity idea is practically the opposite of Newton’s — with potentially major scientific ramifications we can hardly think about. For example, in Einstein’s geometry matter effectively creates local space, which is not conserved.
To be clear, in general relativity, a focus on geodesics is valuable in calculations for time dilation, gravitational lensing, the motion of light and more. But the speed of light is so large compared to that of any material objects around us, time stretching has no practical effect on our everyday gravity or accelerometer readings. That’s exactly why Newton’s laws worked so well. Focusing on that added dimension has been a leading distraction from understanding how space stretching results in everyday gravity.
Metric Stretching in the Metric Tensor
The space stretching responsible for gravity, and the math for it, actually aren’t complicated. Very succinctly (here’s the only paragraph with jargon, arriving at a very simple result): in Einstein’s field equation, the relevant terms appear in diagonal 4-pressure coefficients of the stress-energy tensor. Their magnitude ρκ/2 is proportional to the mass (and energy) density ρ and Einstein’s Constant κ, which is in turn proportional to Newton’s G. We use Einstein’s e=Mc² to calculate the energy from mass, and Einstein’s Constant κ is 8πG/c². Bottom line: the stretching term is (Mc² * 8πG/c²)/2, which is an outward volume acceleration of 4πGM — which we’ll return to in a moment. What matters is, the 3D acceleration is simply proportional to both the mass M and Newton’s G.
Einstein’s Theory Explains Classical Gravity
Now we will see how easy it is for Einstein’s spacetime curvature theory to explain Newton’s gravity: Matter continuously stretches rigid objects in the space that contains it.
You might be surprised how few relativity textbooks present a simple mapping between Einstein’s field equation and classical gravity laws. In relativity courses there’s a natural tendency to focus on features like time dilation that weren’t understood before Einstein, or on the differences that emerge when matter or energy travels near the speed of light — while implicitly assuming the rest of gravity follows Newton’s theory. In one popular textbook, a section that offers to derive Newton’s law from Einstein’s spans ten strained pages of dense symbolic math full of geodesics and 4D symbols, but never mentions fictitious force or proper force — and in the end naturally doesn’t get the sign correct!
But really Einstein’s gravity theory is so simple and elegant, once we accept the continuous stretching of space by matter, we can understand the classical laws of Newton, Gauss and Kepler in just a few simple formulas.
Newton’s Gravitational Constant G and Spacetime Curvature
First, here’s a helpful but little-discussed fact about Newton’s gravitational constant G: dimensional analysis of its physical units qualitatively reveals just how Einstein’s spacetime curvature works!
Physics students first learn of Newton’s G as the constant that lets us calculate the attractive force between two masses in kilograms, separated by a known distance in meters. To obtain the force, multiply G by the masses and divide by the square of the distance. So G is in units of (force/kilogram²)/meter². But since force itself is really mass*acceleration in units of kilogram*meters/second², we can substitute, units cancel, and we can simplify much further.
G is simply in units of (m³/s²) / kg . That’s volume acceleration (cubic meters per second per second) in direct proportion to mass (per kilogram) — presenting a universal relationship between mass (or equivalent energy) and the stretching of space over time. Einstein’s metric tensor says: a point mass M stretches the space containing it outward at a volume acceleration of 4πGM m³/s². (Of course multiplying by 4π doesn’t affect the units.)
How Space Accelerates
It’s a challenge to picture how space dynamically stretches. Volume acceleration can be a key to understanding Einstein’s theory of gravity. Remember, ever since his first special relativity discoveries, Einstein insisted — in contrast to Newton — that meters and seconds vary in length depending on local context. Now his general relativity formula applies that to explain gravity.
It’s reasonable to be suspicious. Space itself can’t actually move — rather, it defines how we measure distances. So a volume of space can’t vary in position, or have a velocity in any direction. Moreover, acceleration ordinarily expresses a change in velocity or direction. So how can a volume of space accelerate?
In the neat 4D math of Einstein’s field equation, the scale of a volume of space can accelerate over time. Einstein and Thorne refer to this as warpage.
In fact, the math doesn’t let us consider a snapshot or the static scale of a meter. So of course, it’s silly to ask “How long is a meter here on earth right now?” But volume acceleration helps us express how fast the length of a meter is changing at some location.
Matter accelerates the scale of meters (rigid objects) in the space containing it. The length of a meter accelerates faster near the mass than further away. We don’t see it directly because:
• the increase is continuous over time;
• the rate is continuous in space around us, with the scale of meters growing at the same rate equally out to the horizon; and
• the scale of our own point of view accelerates at that same rate.
Combine this with our strong Newtonian biases, and we’re utterly, profoundly certain that meters and rigid objects are constant in length — even if we’ve been studying relativity and should know better! This is naturally the biggest cognitive hurdle in accepting spacetime curvature.
It can be helpful to picture: a volume of space that contains matter takes up more and more space over time — encroaching on nearby objects so they appear to accelerate toward it; while any rigid surface containing a mass really does accelerate outward. In both cases, it causes what we call gravity.
Einstein’s Theory Explains Newton’s Law of Gravity
Now it’s easy to calculate the acceleration of earth’s surface and see why Einstein’s theory predicts so many of Newton’s results.
Picture space as an expanding uncompressible liquid, flowing outward from a mass M faster and faster at 4πGM through a closed surface. How fast will the liquid flow out of the surface? Simply divide the volume acceleration by the surface area. So if it’s say, a spherical planet of radius R, its surface area is 4πR², and the rate of outward acceleration a at its surface will be:
a = 4πGM / 4πR² = ̶4̶π̶GM / ̶4̶π̶R²
a = GM/R²
That’s Newton’s gravity law, including his Inverse Square relation, derived from Einstein’s field equation. For earth’s mass and radius, that comes out to 1 g.
Another way to visualize it: although the radius of the sphere/planet is constant, at a distance R from a mass M, the acceleration of the surface is what we’d feel if the scale of the rigid sphere was growing geometrically — as if it’s radius was continuously doubling with a period T = sqrt(R³/GM). Kepler’s Law of Orbits is easily derived from this observation.
Einstein’s Theory Explains Gauss’s Law of Gravity
Next, let’s take a moment to also derive Gauss’s Law for Gravity, from the same classical era of physics. It’s just as simple and illuminating as Newton’s. The integral form is:
Gauss called the left hand side the gravitational flux, a function of a gravitational field g . But what units is the flux in? We know, because it’s equal to the right side — which is almost identical to our expression for relativistic volume acceleration: cubic meters per second per second, proportional to mass.
Why did Gauss express this using the term flux instead? Partly because he was using similar terms to think about electricity and magnetism. But mainly because before Einstein, no one believed that rulers can locally change length and space itself can stretch! Einstein’s spacetime curvature made Gauss’s gravitational flux idea more understandable — and in a way, obsolete.
And finally, what about the minus sign in Gauss’s -4πGM — which isn’t in our relativity formula? The difference proves Einstein’s point. Since Gauss didn’t realize gravity is a fictitious force, he has it pulling instead of pushing. Otherwise his formula for gravity tracks Einstein’s space stretching formula perfectly.
That’s it! We’re done. In just a few pages we’ve seen how simple Einstein’s gravity and spacetime curvature theory can be, and how it accounts for classical gravity theories — while making distinct experimental predictions that easily confirm Einstein’s theory is the correct one.
To review: the apparent downward pull of gravity on earth is a classical fictitious force — an illusion seen by observers that are, unwittingly, accelerating. Still, we find it difficult to accept Einstein’s idea that on earth’s surface, we are all being continuously pushed upward, away from earth’s center. It’s ludicrous to imagine earth’s surface expands towards a “falling” apple or a dropped bowling ball. Yet, that explains our accelerometer measurements, as well as the fact that all matter in free fall near earth’s surface appears to accelerate downward at 1 g.
We likewise have trouble believing Einstein’s non-Newtonian, non-Euclidean idea that the rulers we use to measure distances should not be considered fixed in length — that lengths are local, with meters and ‘rigid’ objects varying in length over time — specifically, in the vicinity of matter. But it’s right there in the aptly named metric tensor of the field equation.
So although this is central to Einstein’s field equation for spacetime curvature, we rarely teach that aspect, dwell on it, or acknowledge its central role in gravitational forces. We eagerly (and often unconsciously) adopt more acceptable theories: ‘Einstein’s gravity is just like Newton’s except for time dilation and gravitational lensing.’ But today, easily repeated accelerometer experiments prove otherwise.
Once we let go of our presumption of fixed-length rulers, we can embrace a deeper intuition to clearly see just how simple Einstein’s spacetime curvature theory is, and how it results in gravity. Earth’s surface accelerates outward exactly as if: whereas its diameter in meters is fixed, here on earth’s surface, the lengths of meters themselves geometrically increase. The metric tensor in the field equation says, at a distance R from a mass, meters themselves have gradually doubled in length during the past sqrt(R³/GM) seconds, pushing earth’s surface away from earth’s center — without affecting the relative scale of objects on the surface. The stretching factor is in units of Newton’s gravitational constant G: cubic meters per second per second, per kilogram. Specifically, a mass of M kilograms expands the space that contains it at a volume acceleration of 4πGM m³/s². And we’ve seen how space itself accelerates — not by moving, but by changing scale.
So for gravity, the math in Einstein’s field equation isn’t complicated. It’s just very difficult to believe that earth’s surface accelerates outward or that, in the vicinity of matter, the scale of rigid objects increases over time.
This is the core gravitational part of the civilization’s most renowned physical theory, proven again and again for over a century. Throughout, scientists like Feynman and Thorne have tried to clarify the gravity theory Einstein first conceived in his thought experiments around an elevator. A century later we see it proven again in simple, repeatable 21st century experiments with accelerometers.
Addendum: Why Isn’t This More Widely Understood?
Students typically encounter Einstein’s elevator epiphany and fictitious force idea in an early overview of general relativity — and then barely hear of it again. No one continues talking about the push that causes gravity. Many students never even learn the term for it — the proper force behind the fictitious force we call our weight. Thus without a sustained connection or campaign, they grow to view Einstein’s time in the elevator as a cool anecdote — without asking just where his fictitious force idea manifests in the field equation they might learn later. Typical relativity curricula wind up expressing the situation indirectly, as an aspect of general relativity’s principle of equivalence of gravitational and inertial mass. All but forgetting the illusion, some students grow confident that Einstein’s gravity is almost exactly like Newton’s, except in details like the light speed limit and time dilation.
We can be grateful to professors who teach relativity by emphasizing the view that gravity is a fictitious force, from the outset and throughout. Nobel laureate H. David Politzer, who wrote about fictitious force in Scientific American, demonstrates it to students on the first day of his relativity class with a projectile that hits a falling monkey. Prof Brian Cox likes to show that Newton’s apple, a bowling ball and (in a vacuum) even a feather all seem to be pulled with the same acceleration, because really earth’s surface is accelerating outward. And recently, Veritasium’s video Why Gravity is Not A Force addressed many of these issues. But none of these accounts offer clear accelerometer data, or account for how the massive object’s surface acceleration is reflected in Einstein’s field equation.
Otherwise, students and professors who were pretty sure they understood relativity may find these aspects of Einstein’s theory alien, highly suspicious, ridiculous, outrageous or even humiliating. It’s a cognitive crisis: no one warned us that Einstein’s spacetime curvature would show how earth’s surface can accelerate outward without the planet getting any bigger!
It’s partly a demonstration that, even in science, people fear believing implausible things — it’s too embarrassing — and will do almost anything to escape the cognitive dissonance. We think in narratives and routinely filter evidence. We often overlook inconsistencies, and politely avoid interrogating or contradicting our professors and our peers. And often, we believe what we expect and want to believe.
Einstein Struggled to Understand This
For years after his 1907 elevator epiphany, Einstein struggled to reconcile his intuitive fictitious force idea with the light speed limit and other elements of his previous special relativity theory. Bogged down in symbolic math for so long, he mourned that his simple, elegant insight was being buried under abstractions. What happened to the fun and magic of proving how gravity works in an elevator?
And he worried that the emerging math of general relativity might be misleading us all. He fumed, “Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.” (Schilpp p. 102)
His team eventually mastered that math, and in 1915 he made new predictions — in particular, that light would not only appear to be gravitationally pulled by nearby matter, but would be deflected more than matter, since seconds are longer where it gets close. In 1919, a telescope experiment during a solar eclipse in Africa confirmed his prediction and made him world famous.
But his worry was prescient. If the math for relativity was so inscrutable that at times Einstein did “not understand it myself anymore,” what hope was there that a new generation of professors and students would follow it? Today, many still don’t. But now, 21st century accelerometer experiments can help clarify it.
It’s worth remembering that Newton himself was overtly suspicious of his own implausible new gravity theory! He worried: “That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it.”(Cohen and Westfall, p.337) Newton rightly questioned a force that acts on distant objects without physical contact!
In Einstein’s version, terrestrial ‘gravity’ is really a reaction to proper force exerted by contact with the earth, and the gradual stretching of the space around it. Newton would celebrate.
While this article aims to capture the essential ideas, a truly persuasive explanation requires more of a book, with animation, an app for experiments, and recorded video. 3D animation can play a key role in clarifying the theory. A short book The Secret Truth About Gravity from a leading publisher will include all of those in 2024.
In conversation, Prof Thorne mentions he has yet to see animation of his simple storyboard. I’ve created draft 3D animation to help viewers better visualize volume acceleration, by showing the difference between ordinary and expanding points of view — something we ordinarily can’t see — while drawing dynamic 3D rulers in the stretching space. Even a very rough model shows how acceleration of space appears to result in an attractive force.
In a modern world of ubiquitous mobile laboratories, space satellites, and vast resources for 3D animation, we should expect our understanding of relativity and gravity to far exceed that of Newton, Einstein, Feynman, Thorne and the others whose shoulders we stand on.
Schilpp, Paul Arthur, Editor. Albert Einstein, Philosopher-Scientist: The Library of Living Philosophers Volume VII.
Open Court, 1998.
Einstein, Albert. Relativity — The Special & the General Theory.
Crown Publishers, 1961.
Feynman, Richard P. Six Not-So-Easy Pieces: Einstein’s Relativity, Symmetry and Space-Time.
Basic Books, 1996.
Thorne, Kip S. Black Holes & Time Warps: Einstein’s Outrageous Legacy.
W. W. Norton & Company, 1994.
Cohen, I. Bernard and Westfall, Richard S., Editors. Newton.
W. W. Norton & Company, 1995.