This essay continues from the previous one in this series, “Five-minute Explainer: Why Is Mass Equivalent to Energy?”
An old story relates that Newton figured out gravity when an apple fell on his head. Newton himself doesn’t mention the apple falling on his head—this appears to be a later embellishment—but he does mention the apple anecdote a couple of times in his dotage. John Conduitt remembered,1
In the year 1666 [Newton] retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from Earth, but that this power must extend much further than was usually thought.
Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her orbit, whereupon he fell a calculating what would be the effect of that supposition.
This anecdote describes a key quality of gravity as understood then: its nature as an occult force—something working mysteriously and unseen across space.
Before Newton, it was known that the planets moved according to well known laws (Kepler’s laws) which allowed their motions to be predictable. It was not understood, however, why they should move in that way. Kepler’s laws merely came from generalizations after many observations.
Philosophers at the time were troubled that the planets appeared to have no reason to move as they did. Aristotelian thought required that something must drive the planets in their motions. If concentric spheres of quintessence did not, what could this be? For a while, we believed space might be full of a kind of fluid which moved in vortices which propelled the planets like clockwork. This explanation was unexpectedly successful for decades precisely because it did not require belief in occult forces—which is to say, it didn’t require something invisible to reach magically over distances and cause a thing to happen without touching it. It pushed instead of pulled.
Newton had looked at the apple and realized nothing had pushed it to the ground. It seemed to have fallen of its own accord. Newton then extrapolated this idea out beyond the garden into the stars. Once he did, a compact set of laws allowed him to explain all the motions of the heavens very tidily. His explanation, eventually known as the Principia, laid the groundwork for fundamental physics for centuries to come. It was a feat on par with Euclid’s Elements and fully completed the Scientific Revolution which Galileo had inaugurated.
In the second edition of the Principia, Newton tacked on some notes by popular demand. In this General Scholium, he explained that he was in no position to explain what gravity could tangibly be. Famously, he said, “Hypotheses non fingo” (“I do not feign hypotheses [of what gravity could be]”). He described nature as he found it, and the explanation worked. That’s how the matter lay for centuries.
One problem is that, over time, we observed that Newton’s explanations were not perfect after all. There were subtle but galling errors which cropped up in very rare circumstances (such as predicting where Mercury would be over time). Another problem was more metaphysical—Newton’s laws only explained how gravity worked, not what it was.
Einstein solved both problems in a single stroke with general relativity. His theory of general relativity followed in the decade after special relativity as a consequence of the latter. The general theory extended the special one to more situations and provided a more fundamental explanation of universal phenomena, particularly gravity.
If you’ve made it this far, you’ve read how energy is an impetus to change over time. Motion can be a form of energy because it can impart motion on another object, accelerating it. Energy is also equivalent to mass, and mass to energy—even at rest. Finally, you’ve seen how motion itself changes energy, space, and time relative to someone observing the motion.
Now we add a new equivalence—one so incredible in its implications that Einstein called it his “happiest thought.”2 It’s now simply known as the equivalence principle, special enough to stand alone by that name. It states that it’s impossible to distinguish between acceleration and gravity in any real, physical way.
That is to say, if you were trapped in some enclosed box and unable to see outside, you could not devise any instrument which would be able to tell you whether that box were accelerating in some direction steadily (and therefore drawing you toward the floor) or within a gravitational field (which would accomplish the same effect). Therefore, experiencing acceleration is equivalent to experiencing a gravitational field.
Einstein realized this in November 1907.3 From that point, he realized that energy, mass, space, time, and gravity were all inseparably linked, and he spent the next several years feverishly working toward a general theory of relativity to explain how it all works. The explanation he came up with in 1915 works so well that its predictive power overturned Newton and has held up even to this day.
As a result of special relativity, we saw that motion warps space and time. We also know that motion relative to an observer represents kinetic energy, which is equivalent to any other form of energy. Finally, we know that energy is equivalent to mass and vice versa. The final piece of the puzzle to put into place here is that, since motion—and therefore energy—warps time and space, so does mass.
Think of mass as bottled motion. Mass–energy equivalence lets us treat mass as energy which has congealed, more or less, into one place. As I said in the last essay, it’s not enough to think of mass and energy as distinct things sharing some properties—they are a single substance. Therefore, all the same properties and consequences which apply to one form also apply to the other. That means that all the warping effects which apply to energy—to motion—also apply to mass.
So mass warps time and space, but what does this actually mean in reality? The result is gravity! Gravity is an emergent consequence of how mass warps time and space, exactly the same way motion warps time and space due to special relativity. Gravity is in fact not a force reaching mysteriously across distances but instead a bending of space and time which changes the paths of objects traveling through that space and time, leading them inexorably closer to one another.
Let’s dispense with the tired bowling-ball-on-a-rubber-sheet imagery and talk about what that last paragraph actually means. We can begin with the classic assumptions about how objects behave. Newton’s laws state that objects in motion tend to stay in motion, or at rest, unless acted on. They also state that there’s always an opposite and equal reaction for every action.
These are, at their heart, conservation laws. For things to behave otherwise would mean creating or destroying energy. An action must impart an opposite and equal reaction, or energy would go missing. An object at rest must stay at rest, or energy would spontaneously appear. An object in motion must stay in motion, or energy would vanish.
In flat space, therefore, moving objects tend to stay the course in order to conserve energy. You can trace the line of how the object moves geometrically as a straight line. Now if we introduce a mass nearby, space and time contract and stretch, respectively, in the vicinity of that mass. The object’s path still needs to conserve energy, and in order to do so, the line we trace now curves closer to the mass. It appears as if the object “falls” inwards toward the mass—exactly as you’d expect from a gravitational field.
We no longer need an “occult force” to explain the mechanism of gravity. General relativity—which geometrically describes space and time as it bends under the influence of mass and energy—provides the complete picture.
As it turns out, gravity is not a force at all in the ordinary sense. It only appears to exert a force in the way that a merry-go-round in motion appears to make a ball curve through the air when you throw it from one side to the other.4 Gravity plays a similar trick on us: we’re constantly on a path through time and space which, were it not for the gigantic rock beneath us, would cause us to curve inexorably toward the center of the Earth. Since the Earth itself interrupts our course, we press against it, and it against us, which imparts the force we’re familiar with.
By uniting conservation laws and a handful of postulates, we can fully explain the substance and behavior of gravity. When we combine this knowledge with the speed limit of the universe, we see that even gravity takes time to travel, which means that changes in gravity take time to travel. This allows gravity to ripple across space and time. We’ll now be prepared to look at these waves in the next explainer.