Sunday, February 10, 2019


Time warp

As I’ve noted before,1 I am neither a mathematician nor a physicist. I’m an English major by education and a writer of both technical documentation and science fiction by profession. I’m not equipped to analyze a claim mathematically, but I know a good story when I hear it. And I can pick apart a story line when I detect a subtle falsehood.

For a long time I thought of gravity as a “force,” similar to an electromagnetic field or the strong or weak forces in atomic nuclei. In this I was not alone. After all, the mathematical and physical definition of a force is mass times acceleration, F=ma. That is, the force needed to throw a baseball equals the mass of the ball times the acceleration of the pitcher’s arm from the start of the pitch until the release of the ball. Mass times acceleration. Once the ball leaves the pitcher’s fingertips, it is no longer accelerating but just traveling at its final—and perhaps slowly decreasing, due to air resistance—velocity toward home plate.

Similarly, the force exerted by gravity, at least on the surface of planet Earth, is whatever mass is involved—say, a person weighing 150 pounds—times the acceleration of gravity, which in this particular place is 9.8 meters (or, if you like, 32 feet) per second per second, g=9.8m/s2. A thousand kilometers above the surface, and so farther away from the planet’s center of mass, that value drops to 7.33 meters per second squared. And the farther out you go, the slower the acceleration becomes.2

The one thing that physicists could not figure out, however, was how the Earth or any other large body exerted this force to pull people, houses, cars, plants, water, dirt, and everything else downward. Since most forces in physics are represented by a field—the electromagnetic force, for example—with an accompanying particle—in the case of electromagnetism, the photon—quantum mechanics comforts itself by representing gravity with the graviton. And, presumably, the force of gravity is achieved by an exchange of gravitons, from my body to the Earth, and from the Earth to my body.

But for a particle we’ve never seen, touched, or even detected, that’s a lot of gravitons. The Earth is supposedly exchanging these particles back and forth all the time and with every person, car, seed, grain of sand, and even with parts of its own mass like the planet’s layers of atmosphere, lithosphere, mantle, and outer iron core. At the same time, the Earth is also exchanging gravitons with the Moon to hold her in orbit, and with the Sun to stay in its own orbit around the star. You might as well say that tiny pixies grab your feet and hold you down.

Long before I became concerned with this matter of force, Albert Einstein resolved the issue of gravity in another way. The masses of the Earth, the other planets and moons, our Sun and the stars don’t exert a force per se. Instead, they shape or bend both space and time in their immediate neighborhoods. You and I shape space and time with our own masses, too, but the deflection is so small as to pass unnoticed in even the densest of crowds.

To show that this bending of space and time is equivalent to the pull of gravity, Einstein conducted a thought experiment. He mentally placed a person in a room far out in space, away from any stars or planets, and attached a long cable to the room. He then began drawing the room upward, in a direction opposite to the room’s floor, at an acceleration of 9.8 meters per second squared. To the person inside the room, that acceleration was identical to the apparent “force” with which gravity holds him to the floor at the surface of the Earth. The person is allowed to perform whatever experiments within the room that he pleases: throw baseballs, drop coins, pour out pitchers of water, and so on. So long as the pull of that long cable remained at a constant acceleration of 9.8 meters per second per second, the person could not tell he was anywhere but on the home planet.

This, as I understand it, was Einstein’s proof of equivalence, that gravity and acceleration were the same thing.

I don’t doubt that they are equivalent, at least conceptually and mathematically. But I detect a hitch in the story: the equivalence is purely subjective. From the viewpoint of the person in the room, and only so long as he doesn’t look out a window, the acceleration of the room and the acceleration of gravity on the Earth’s surface are the same. But objectively, they are different.

Objectively, a person standing in a room on Earth isn’t going anywhere, at least relative to the center of the planet’s mass. He may be traveling eastward at a thousand miles an hour if the room is at the equator, or around a little circle with a circumference of only a few feet during a whole day spent at the North Pole. He may be moving with the planet along its orbit around the Sun, and with the Sun in its orbit around the galaxy. But relative to the center of the Earth, he moves not one millimeter, so long as the floor holds.

Meanwhile, objectively, a person in a room being hauled along at an acceleration of 9.8 meters per second squared is traveling through space at an ever-increasing speed. Within a finite amount of time, something on the order of ten years, at that acceleration—initially about 22 miles per hour, but speeding up all the while—the room and the person would achieve about ten percent of light speed. Within a hundred years or so, if the physics of spacetime allowed it, the person would be traveling at and then exceeding light speed. Of course, according to Einstein, the person’s mass would then increase toward infinity while his perception of time would stop. But otherwise, the person would have no sense of any difference from being quietly positioned on Earth—except that if he had a window, he would see the stars outside blur their colors into the bluer part of the spectrum ahead of him and to red behind him. And if he made a radio call to a friend on Earth, his own voice would be getting lower and slower, while his friend would start sounding more and more like a chipmunk.

Objectively, traveling in a long-haul elevator or on a runaway rocket is not the same as standing on the Earth. The fact of physical acceleration matters. In one case, on the planet’s surface, the acceleration is merely conceptual, the equivalent of increasing speed time over time, but without the actual effects of acceleration. In the other, in the elevator or the rocket, the acceleration is a real motion and has predictable consequences.

The fact is, each of us is accelerating toward the center of mass of the planet from the day we’re born to the day we die and our atoms disperse, and then they keep accelerating in some other form. Conceptually and mathematically, we are all going faster and faster, eventually exceeding theoretical light speed, and yet going nowhere. This is the conundrum I find with any current definition of gravity. And it is associated in the posts referenced at the beginning of this piece as well, which deal with our definitions and conceptions of space and time—the two key components of either gravity-as-force or gravity-as-distortion of that slippery thing called “spacetime.”

We can measure gravity, space, and time. We can envision them as forces or dimensions or other real things. We can write equations about them and manipulate them mathematically. But we don’t really know what they are. And until we do—or meet up the people who have solved this conundrum—our notions of the physical world will remain those of a child.

1. See previous posts in this vein, starting with Fun with Numbers (I) from September 19, 2010, and (II) from September 26, 2010.

2. Need I say here that when orbiting at a comfortable near-Earth distance—say, the Space Shuttle’s maximum service ceiling of 643 kilometers—the apparent weightlessness of people and things is not at all due to this drop-off in, or any kind of final disappearance of, the accelerations of gravity? Instead, in order to achieve a stable orbit, the ship moves fast enough that its fall toward the planet, due to gravity, is countered by its forward momentum, so that the ship is still falling but its point of impact is forever over the horizon.
    In the same way, if you jump out of an airplane and fall toward the planet’s surface, you will apparently become weightless for the time you are still falling. If you take, say, a coin from your pocket and release it from your hand, it will appear to be weightless, too, while falling beside you—except for any difference in wind resistance which may allow the thin coin to fall somewhat faster than your large and obstructive body. Above the atmosphere, however, with no resistance you and the coin would drop in perfect synchrony.

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