The Dancing Wu Li Masters (18 page)

Frames of reference moving uniformly, relative to each other, are co-ordinate systems that move with a constant speed and direction. In other words, they are frames of reference that move with a constant velocity. For example, if, by accident, we drop a book while standing in line at the library, the book falls directly downward in accordance with Newton’s law of gravity, and strikes the ground directly beneath the place from which it was dropped. Our frame of reference is the earth. The earth is moving at a fantastic speed on its trip around the sun, but this speed is constant.
^*

If we drop the same book while we are traveling on an ideally smooth train which is moving at a constant speed, the same thing
happens. The book falls directly downward in accordance with Newton’s laws of gravitation, and strikes the floor of the train directly beneath the place from which it was dropped. This time, our frame of reference is the train. Because the train is moving uniformly, with no increases or decreases of speed, in relation to the earth, and because the earth is moving in a similar manner in relation to the train, the two frames of reference are moving uniformly relative to each other, and the laws of mechanics are valid in both of them. It does not matter in the least which of the frames of reference is “moving.” A person in either frame of reference can consider himself moving and the other frame of reference at rest (the earth is at rest and the train is moving) or the other way round (the train is at rest and the earth is moving). From the point of view of physics, there is no difference.

What happens if the engineer suddenly accelerates while we are doing our experiment? Then, of course, everything is upset. The falling book still will strike the floor of the train, but at a spot farther back since the floor of the train has moved forward beneath the book while it was falling. In this case, the train is not moving uniformly in relation to the earth, and the Galilean relativity principle does not apply.

Provided that all of the motion involved is uniformly relative, we can translate motion as perceived in one frame of reference into another frame of reference. For example, suppose that we are standing on the shore watching a ship move past us at thirty miles per hour. The ship is a frame of reference moving uniformly relative to us. There is a passenger, a man, standing on the deck of the ship, leaning against the railing. Since he is standing still, his velocity is the same as that of the ship, thirty miles per hour. (From his point of view, we are moving past
him
at thirty miles per hour).

Suppose now that the man begins to walk toward the front of the ship at three miles per hour. His velocity now, relative to us, is thirty-three miles per hour. The ship carries him forward at thirty miles per hour, and his walking adds three miles per hour to that. (You get to the top of an escalator faster if you walk.)

Suppose that the man turns around and walks back toward the
rear of the ship. His velocity relative to the ship is, again, three miles per hour, but his velocity relative to the shore is now twenty-seven miles per hour.

In other words, to calculate how fast this passenger moves relative to us, we add his velocity to the velocity of his co-ordinate system (the ship) if he is walking in the same direction that it is moving, and we subtract his velocity from the velocity of his co-ordinate system if he is walking in the opposite direction. This calculation is called a classical (Galilean) transformation. Knowing the uniform relative motion of our two frames of reference, we can transform the passenger’s velocity in reference to his own co-ordinate system (three miles per hour) into his velocity in reference to our co-ordinate system (thirty-three miles per hour).

The freeway provides abundant examples of classical transformations from one frame of reference to another. Suppose that we are driving at 75 miles per hour. We see a truck coming toward us. Its speedometer also reads 75 miles per hour. Making a classical transformation, we can say that, relative to us, the truck is approaching at 150 miles per hour, which explains why head-on collisions so often are fatal.

Suppose now that a car going in the same direction that we are going passes us. His speedometer reads 110 miles per hour (it’s a Ferrari). Again, making a classical transformation, we can say that, relative to us, the Ferrari is departing our location at 35 miles per hour.

The transformation laws of classical mechanics are common sense. They say that, even though we cannot determine whether a frame of reference is absolutely at rest or not, we can translate velocities (and positions) from one frame of reference into velocities (and positions) in other frames of reference, provided that the frames of reference are moving uniformly, relative to each other. Furthermore, the Galilean relativity principle, from which Galilean transformations come, says that if the laws of mechanics are valid in any one frame of reference, they also are valid in any other frame of reference moving uniformly relative to it.

Unfortunately, there is one catch in all this. No one yet has found a co-ordinate system in which the laws of mechanics are valid!
^*

“What! Impossible! Can’t be!” we cry, aghast. “What about the earth?”

Well, it is true that Galileo, who first probed the laws of classical mechanics, used the earth as a frame of reference, although not consciously. (The idea of co-ordinate systems did not come along until Descartes). However, our present measuring devices are more accurate than Galileo’s, who occasionally even used his pulse (which means that the more excited he got, the more inaccurate his measurements became!). Whenever we reconstruct Galileo’s falling body experiments, we always find discrepancies between the theoretical results that we should get and the experimental results that we actually do get. These discrepancies are due to the rotation of the earth. The bitter truth is that the laws of mechanics are not valid for a co-ordinate system rigidly attached to the earth. The earth is
not
an inertial frame of reference. Since their very inception, the poor laws of classical mechanics have been left, so to speak, without a home. No one has discovered a co-ordinate system in which they manifest themselves perfectly.

This leaves us, from a physicist’s point of view, in a pretty mess. On the one hand, we have the laws of classical mechanics, which are indispensable to physics, and, on the other hand, these same laws are predicated upon a co-ordinate system which may not even exist.

This problem is related to relativity, which is the problem of determining absolute nonmotion, in an intimate way. If such a thing as absolute nonmotion were detected, then a co-ordinate system attached to it would be the long-lost inertial frame of reference, the co-ordinate system in which the classical laws of mechanics are perfectly valid. Then everything would make sense again because, given a frame of reference in which the classical laws of mechanics are valid,
any
frame of reference, the classical laws of mechanics at last would have a permanent mailing address.

Physicists do not enjoy theories with loose ends. Before Einstein, the problem of detecting absolute motion (or absolute non-motion—if we find one, we find the other), and the problem of finding an inertial co-ordinate system were, to say the least, loose ends. The entire structure of classical mechanics was based on the fact that somewhere, somehow, there must be a frame of reference in which the laws of classical mechanics are valid. The inability of physicists to find it made classical mechanics appear exactly like a huge castle built on sand.

Although no one, including Einstein, discovered absolute non-motion, the inability to detect it was a major concern of Einstein’s day. The second major controversy of Einstein’s day (not counting Planck’s discovery of the quantum) was an incomprehensible, logic-defying characteristic of light.

In the course of their experiments with the speed of light, physicists discovered something very strange. The speed of light disregards the transformation laws of classical mechanics. Of course, that’s impossible, but nevertheless, experiment after experiment proved just the opposite. The speed of light just happens to be the most nonsensical thing ever discovered. That is because it never changes.

“So light always travels at the same speed,” we ask, “what’s so strange about that?”

“Oh my, oh my,” says a distraught physicist, circa 1887, “you simply don’t understand the problem. The problem is that no matter what the circumstances of the measurement, no matter what the motion of the observer, the speed of light
always
measures 186,000 miles per second.”
^*

“Is this bad?” we say, beginning to sense that something
is
strange here.

“Worse,” says the physicist. “It’s impossible. Look,” he tells us, trying to calm himself, “suppose that we are standing still and that somewhere in front of us is a light bulb that also is standing still. The light bulb flashes on and off and we measure the velocity of the light that comes from it. What do you suppose that velocity will be?”

“186,000 miles per second,” we answer, “the speed of light.”

“Correct!” says the physicist, with a knowing look that makes us uncomfortable. “Now, suppose the light bulb still is standing still, but we are moving toward it at 100,000 miles per second. Now what will we measure the speed of the light to be?”

“286,000 miles per second,” we answer, “the speed of light (186,000 miles per second) plus our speed (100,000 miles per second).” (This is a typical example of a classical transformation.)

“Wrong!” shouts the physicist. “That’s just the point.
The speed of the light is still 186,000 miles per second
.”

“Wait a minute,” we say. “That can’t be. You say that if the light bulb is at rest and we are at rest, the speed of photons emitted from it will measure the same to us as the speed of photons emitted from it when we are rushing toward the light bulb? That doesn’t make sense. When the photons are emitted, they are traveling at 186,000 miles per second. If we also are moving, and moving toward them, their velocity should measure that much faster. In fact, they should appear to be traveling with the speed at which they were emitted
plus
our speed. Their velocity should measure 186,000 miles per second plus 100,000 miles per second.”

“True,” says our friend, “but it doesn’t. It measures 186,000 miles per second, just as if we still were standing still.”

Pausing for that to sink in, he continues, “Now consider the opposite situation. Suppose that the light bulb still is standing still, and this time we are moving
away
from it at 100,000 miles per second. What will the velocity of the photons measure now?”

“86,000 miles per second?” we say, hopefully, “the speed of light minus our speed as we move away from the approaching photons?”

“Wrong, again!” exclaims our friend again. “It should, but it
doesn’t. The speed of the photons still measures 186,000 miles per second.”

“This is very hard to believe. Do you mean that if a light bulb is at rest and we measure the speed of the photons emitted from it while we also are at rest, and if we then measure the speed of the photons from it while we are moving toward it, and lastly, if we measure the speed of the photons emitted from it while we are moving away from it, we get
the same result
in all three cases?”

“Exactly!” says the physicist. “186,000 miles per second.”
^*

“Do you have any evidence?” we ask him.

“Unfortunately,” he says, “I do. Two American physicists, Albert Michelson and Edward Morley, have just completed an experiment which seems to show that the speed of light is constant, regardless of the state of motion of the observer.

“This can’t happen,” he sighs, “but it
is
happening. It just doesn’t make sense.”

The problem of absolute nonmotion and the problem of the constancy of the speed of light converged in the Michelson-Morley experiment. The Michelson-Morley experiment (1887) was a crucial experiment. A crucial experiment is an experiment which determines
the life or death of a scientific theory. The theory that was tested by the Michelson-Morley experiment was the theory of the ether.

The theory of the ether was that the entire universe lies in and is permeated by an invisible, tasteless, odorless substance that has no properties at all, and exists simply because it has to exist so that light waves can have something to propagate in. For light to travel as waves, according to the theory, something has to be waving. That something was the ether. The theory of the ether was the last attempt to explain the universe by explaining some
thing
. Interpreting the universe in terms of things (like the Great Machine idea) was the distinguishing characteristic of the mechanical view, which means all of physics from Newton until the middle 1800s.

The ether, according to the theory, is everywhere and in everything. We live and perform our experiments in a sea of ether. To the ether, the hardest substance is as porous as a sponge to water. There are no doors to the ether. Although we move in the ether sea, the ether sea does not move. It is absolutely, unequivocally not moving.

Therefore, although the primary reason for the existence of the ether was to give light something to propagate through, its existence also solved the old problem of locating the original inertial coordinate system, that frame of reference in which the laws of mechanics are completely valid. If the ether existed (and it
had
to exist), the co-ordinate system attached to it was
the
co-ordinate system against which all others could be compared to see if they were moving or not.

The findings of Michelson and Morley gave a verdict of death to the theory of the ether.
^*
Equally important, they led to the mathematical foundations of Einstein’s revolutionary new theory.

The idea of the Michelson-Morley experiment was to determine the motion of the earth through the ether sea. The problem was how to do this. Two ships at sea can determine their motion relative to one another, but if only one ship moves through a smooth sea, it has no
reference point against which to measure its progress. In the old days, seamen would throw a log overboard and measure their progress relative to it. Michelson and Morley did the same thing, except that the log that they threw overboard was a beam of light.