Thus we come to the Gestalt picture I referred to at the beginning:

Newton said that a falling apple is accelerating. Since acceleration requires a force, Newton had to invent the idea of a gravitational force that tugs on the apple while it is falling, making it fall faster and faster. Einstein said that it is precisely when the apple is falling that it is not accelerating (straight line trajectory in our space station example), and there is no need to introduce a mysterious gravitational force.

Newton said that an apple in your hand is not accelerating. No acceleration means no force. To arrive at no force, Newton imagined two exactly counterbalancing forces at work: gravity pulling the apple down and our hand pushing it up. Einstein said there is only one force at work: our hand pushing it up. This “unbalancing” force causes the apple to veer off its natural trajectory (and move instead on the circular trajectory in our space station example).

In short, what Newton got backwards was when the apple is accelerating and when it is not. This false starting point, although it is the common sense one, led him astray and required him to invent the idea of a gravitational force. Einstein took the diametrically opposite perspective, which showed “gravitational force” to be a red herring. What we have been discussing is an aspect of Einstein’s “equivalence principle”, which in this example amounts to the inability for Alice to distinguish in any way between the following two situations:

1. She is inside a rotating space station, holding an apple in her hand. The force she is applying to the apple is required to counter the apple’s inertia (natural tendency to move in a straight line) and make it move in a circle.
2. She is inside a non-rotating space station, holding an apple in her hand. The force she is applying to the apple is required to counter the apple’s weight (the “gravitational force” exerted on it by other masses, which she presumes exist somewhere outside the space station).

But there’s still a crucial piece of the puzzle missing. While Einstein’s position makes sense in our little rotating space station example, how is it supposed to make sense for real gravity? Remember, what Einstein is saying is that when you are standing on the Earth holding an apple in your hand, the force applied by your hand is causing the apple to continually accelerate. And yet it appears to be very much at rest! It is easy to see how this is not a paradox in our rotating space station example: from Alice’s perspective the apple is, indeed, at rest—she is holding it in her hand—and yet it is actually continually accelerating since it is moving in a circle. But it is not so easy to see what’s going on when we transplant Alice and her apple to the real gravity situation on the surface of the Earth. The “at rest” part is easy to see, but the “continually accelerating” part is not. It took the genius of Einstein to make sense of this—to see that what is involved is a warping of space and time. How Einstein realized that gravity is likely associated with a warping of space and time is the subject of this essay (Part I). In Part II we will see how the idea of warped space and time resolves the puzzle of “apparently at rest and yet continually accelerating”. So let’s now return to Einstein’s rotating disk [rotating space station] thought experiment to learn how he arrived at the idea of warped space and time.

[Incidentally, I invite the reader to imagine other experiments Alice could perform that might distinguish her experience of this “artificial” gravity from “real” gravity on Earth. For example, will a balance scale work the same in this artificial gravity as it does on Earth? What about a weigh scale? From Alice’s perspective, will a pitched baseball travel along a parabolic trajectory? What about the beam of light from a flashlight? These are all interesting questions worth pondering if you wish to get a better feel for Einstein’s perspective on gravity.]

The Warping of Time

Einstein started with two simple facts about the nature of space and time (in the absence of gravity) that he had discovered through his development of the theory of special relativity. The two facts are “time dilation” and “length contraction”, which led him to warped time and warped space, respectively. These are fascinating effects in their own right, but I will not attempt to explain them in any detail since there are plenty of excellent references on special relativity. I will simply describe what these effects are, and move on to the more interesting discussion of their consequences for the nature of gravity.

Let’s begin with time dilation. Imagine that Alice and her friend Bob have identical watches. Standing next to each other, they synchronize the pair of watches to read exactly the same time. As a double check that everything is in order, they hold the watches side by side and observe that they are ticking at exactly the same rate. Then, at exactly 12 noon according to both watches, Alice leaves and goes for a walk around the block. When she returns and they compare watches, the time showing on Alice’s watch will be a fraction of a second behind the time showing on Bob’s watch. They are surprised! So they check again, and sure enough both watches are ticking at exactly the same rate, just as before, but Alice’s watch reading is now slightly behind Bob’s. How is this possible? It must have something to do with her motion relative to Bob. It is important to realize that her motion is not in any way affecting the mechanical mechanism inside her watch. Rather, because of her motion, time itself is moving more slowly for Alice during her walk relative to the rate at which time is moving for Bob.