Theories of the Universe: Thank God, the Ground Broke My Fall!
Thank God, the Ground Broke My Fall!
Newton's law of universal gravitation works wonders. It allows us to send men to the moon and probes to Mars, know the position of any celestial body and a lot more. There's just one small problem. It doesn't work with the special theory of relativity. Einstein recognized this, which is why he developed his theory of general relativity.
We all know by now that there is nothing that can travel faster than the speed of light. This applies to information, signals, and influences as well. Newton's theory of gravitation explains that one body exerts a gravitational pull on another body with a strength determined only by the mass of the objects involved and the degree of their separation. (If you need to, go back and review the definition.) What this means is that if their mass or separation should suddenly change, based on Newton's theory, they would immediately experience a change in their mutual gravitational pull.
Let's look at an example. If for some reason the Sun were to explode, normally it would take eight minutes for the impact of that event to reach us. That's because that's how fast it takes light to reach us. Under Newton's theory of gravity, the explosion would register instantaneously and the gravitational effect would be transmitted to earth with no time going by. Well, according to special relativity, that's just not possible.
Einstein recognized this conflict and set out to devise a new theory of gravity. Our understanding of time and space was about to go through yet another alteration.
A common question to ask is, “If there are these three or four problems that have been discovered in classical physics, why is it still used and taught?” Well, there is nothing inherently wrong with classical physics. Yes, there are problems that it can't deal with (extreme speeds, the quantum world, gravity), but in our everyday world it works just fine. Skyscrapers and bridges are built, the speed of baseballs is measured, and shuttles orbit the earth, using the physics of Newton and Maxwell.
Einstein's Happiest Thought
There are two main aspects of general relativity. The first, which I'll be discussing shortly, has to do with something called the principle of equivalence. The second aspect, which I'll get to as well, has to do with the shape of space. Einstein realized that he had to extend his special theory of relativity to resolve the conflict of “action at a distance,” which was another phrase for the instantaneous transmission of gravity through space previously discussed. He also knew that his special theory didn't account for accelerated motion, only constant velocity motion. The following is a quote from Einstein revealing what he was about to discover:
The theory of relativity resembles a building consisting of two separate stories, the special theory and the general theory. The special theory, on which the general theory rests, applies to all physical phenomena with the exception of gravitation, the general theory provides the law of gravitation and its relation to the other forces in nature.
So to summarize the main difference between the two we could say:
- The special theory deals with frames of reference that are moving in a straight line, toward or away from each other, and are not accelerating, but instead are moving at constant or uniform speed.
- The general theory defines the relationships between objects throughout all of space, moving in any direction, with or without acceleration.
The principle of equivalence simply states that you can't tell the difference between gravity and accelerated motion without a frame of reference. Gravity is equivalent to acceleration. It is one of the two main ideas found in Einstein's theory of general relativity.
Out of his search to find the extension of his special theory, Einstein one day had what he considered “the happiest thought of my life.” This thought was the realization that without a frame of reference you would not be able to tell the difference between gravity and accelerated motion. Let's do a few thought experiments so you can experience his happiest thought for yourself.
Centrifugal force is what you feel on a spinning amusement park ride. It's what keeps you pinned to the sides of that ride whose floor drops out from underneath you, while you remain stuck to the inside of the rotating walls. You can also experience it whenever you spin an object on the end of a string over your head. The outward force is what keeps it spinning instead of hitting you in the head.
Let's begin with a ride in our rocket ship to a distant planet. The ship is accelerating to achieve top speed. All of a sudden you drop your cell phone. Now if you were simply drifting around in orbit, your cell phone would also be floating next to you in space. But because the ship is accelerating, the floor soon overtakes the cell phone and it appears to “fall” to the floor. From the point of view of someone, let's say on a passing planet, they would see the cell phone remain stationary while the accelerating ship moved to catch up to it. (Yes, you have a transparent ship so all the extraterrestrials can see everything that you do.) But to you inside the ship, it would appear as though some outside force, like gravity, was attracting the cell phone to the floor. Get the idea?
Sometimes trying to understand general relativity isn't easy. It's a lot like the story of the engineer who tried to explain to a peasant how a steam engine works. After he described where the steam goes and how it moves through the engine and moves the piston, the peasant replied, “I understand all of that, but where's the horse?” (Output is measured in horsepower.) And that's how some people feel about general relativity. They get the details, but still don't know where the horse is.
Here's another example. Imagine that you're on a return journey from a distant planet to earth. The controls are on automatic pilot and the ship is accelerating to get home in a hurry. You fall asleep, having complete trust in the ship's ability to get you home and even land without your help. You wake up and can't tell if you landed on earth or if you're still in outer space. You bounce a couple balls, pour yourself a drink, and get ready to disembark, because it seems that you've landed. However, just before you open the door, you happen to look out the portal window and see that you're still flying through space. As before, inside Galileo's ship, you have no way of knowing what is influencing your perspective. In this case it's gravity; in Galileo's ship it was motion. This was Einstein's happiest thought. He had the realization that you can't tell the difference between gravity and accelerated motion without a frame of reference. This is known as the principle of equivalence.
Gravity Is Relative, Too
Equivalence can be easy to get used to. When astronauts accelerate from the launching pad in a rocket toward outer space, they measure the force of acceleration in so many Gs. A “G” is the designation for the force of one unit of earth's gravity. Two Gs would equal twice the force of the Earth's gravity, and so on. The ideas we have about space stations orbiting the Earth substitute another kind of acceleration for gravity, centrifugal force. Huge circular rings of the space station swirl around in space, throwing people and objects outward like stones twirled on strings. If the ground is built on the outer edge of the circular space station, then the centrifugal acceleration will be exactly equivalent to gravity.
Interesting enough, Newton believed that accelerating motion created by centrifugal force was absolute, not relative. He said that while steady motion was relative, as shown by Galileo, accelerating motion was not. If you spun a bucket of water, the centrifugal force would make the water rise at the sides, very much in the same way that the spin of the earth causes it to bulge outward at the equator. This bulge was clear evidence that these things were moving and not at rest. However, around 1900, Ernst Mach (one of Einstein's revered mentors) explained that if you spun the whole universe and kept the bucket or the Earth at rest, you still couldn't tell whether you were at rest or accelerating.
The idea that a force like gravity can be relative can be a difficult idea to get used to. When you push something to make it go, or throw a ball, there doesn't seem to be anything relative about it. If you push something with a large force and it goes farther than when you push it with a small force, there's nothing relative about that either. But if motions are relative and motions are the result of forces, then it's easy to see that forces have relative qualities as well.
Excerpted from The Complete Idiot's Guide to Theories of the Universe © 2001 by Gary F. Moring. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books, a member of Penguin Group (USA) Inc.
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