in Ad Astra, June 1991, page 14

Copyright © 1990, 1998, 1999, . All rights reserved.

The most fundamental difference between living on Earth and living anywhere else nearby is gravity. Most of us know that people weigh a lot less on the Moon or even on Mars than they do on Earth. In fact, a 100-kg* person would weigh 37 kg on Mars and only 18 kg on the Moon. (Instead of dieting in the future, people may simply opt to move!) The reason for the weight difference is gravity. But what many people don’t understand is what this property called gravity really is. As we move out into the universe it is very important to have a grasp of this most basic concept.

Think of the universe as a four-dimensional place in which three of the dimensions account for distances between things--just as in everyday geometry--and the fourth dimension is the perceptual distinction that accounts for time. This four-dimensional universe is called “spacetime.” There are three things to know about spacetime to understand gravity:

• Spacetime bends, or curves, in response to the presence of things in it.
• The path something occupies from one spacetime point to another is, if it is not affected by electromagnetic or nuclear forces, always the shortest path between the two points.
• A straight path in spacetime corresponds to three-dimensional motion at a constant velocity. A curved path in spacetime is three-dimensional motion with acceleration.

In deep space, where there is not a lot of stuff around, spacetime is almost flat, because of the first rule. If spacetime is flat, then the shortest path between two points is always a straight line, so the second rule means that spacetime paths will follow straight lines. The third rule says that these straight-line paths always show up in our three-dimensional perception as motion with a constant velocity. So, in deep space, far away from everything else, things move with constant velocity. This explains the law of inertia (objects in motion stay in motion; objects at rest stay at rest).

When a body is near a large object, like a planet or a star, spacetime is very curved. There are no straight paths in this region of spacetime, so all three-dimensional motion is accelerated. That acceleration is what we call gravity. It is what makes rain fall to the ground and keeps satellites in orbit around Earth.

The acceleration does not, by itself, cause weight. A falling object does not weigh anything until it comes to the ground. Imagine jumping from a tall building while standing on a bathroom scale. You and the scale would fall together, without exerting any force on each other.

When you walk around on the ground, the shortest path through spacetime would have you falling through the surface of Earth, but the structure of the planet holds you up and pushes you away from that path. It is that push that creates the phenomenon of weight.

Any curved surface looks flat when seen up close. The classic example is Earth, which looks flat until you get high enough above it to get a large scale view. In the same way, a small region of spacetime will always look flat, which is to say that no acceleration will be detectable from inside it. For example, while the curvature of spacetime around Earth keeps the Space Shuttle in orbit, on the scale of the interior of the Shuttle cabin that curvature is extremely tiny, and one sees no evidence of the gravitational acceleration.

To summarize, gravitational acceleration is the three-dimensional result of the curvature of spacetime paths in the vicinity of large objects. Weight is what happens when something pushes an object away from its natural, shortest path in spacetime. And, because curvature is only detectable on a large scale, there is no noticeable acceleration in small regions, such as inside an orbiting spacecraft.

So the reason a person weighs less on the Moon than on Earth is that the Moon’s smaller size means that spacetime is less curved there than it is here. Since the curvature is less, objects don’t accelerate as fast when they fall. And that means the Moon doesn’t have to push as hard to hold you up. Less push means less weight. Unfortunately, though, this won’t reduce your waist size!

It was not until 300 years ago that Isaac Newton figured out that falling apples and orbiting moons operate on the same principle. The explanation in terms of four-dimensional spacetime is only 73 years old. There are still many mysteries about the details of how gravity works, but we are privileged to live in an era that is beginning to develop an understanding of this phenomenon that governs every aspect of our lives.