The Anemometer Metaphor
"That which is looked upon by one generation as the apex of human knowledge is often considered an absurdity by the next, and that which is regarded as a superstition in one century, may form the basis of science for the following one."
As mentioned in Chapter 1, the version of the SR that Hafele and Keating used in their famous 1971 experiment is vastly different than the 1905 version. At the end of this chapter the differences between the original SR and the current or new SR will be better understood. But in order to accomplish that, it is critical that a metaphor be used to set the stage and establish important visualization concepts and terminology. This metaphor will be the bridge between the SR of 1905 and the "new SR" currently being used in physics. It will also aid immensely in an understanding of the H-K discussions in the next chapter.
The real purpose of this chapter, however, is that I want to make it perfectly clear that there must be a cause of the Hafele-Keating data. The fact that the SR changed from an "imaginary time" to an "actual time," but failed to make the transition from an "imaginary cause" to an "actual cause" must be clearly understood! This chapter will make it clear.
The Anemometer Metaphor
An "anemometer" is an object commonly used by meteorologists or weathermen to measure the speed or velocity of the wind. It consists of several cups (i.e. hollow hemispheres or hollow cones), placed on rods that are attached perpendicular to a vertical pole. The anemometer spins around as a function of the velocity of the wind (i.e. if the wind moves faster, the anemometer spins faster).
Now consider an automobile that has a long pole vertically attached to its roof and on top of this pole is an anemometer. Assuming there is no wind, suppose the automobile is driven across a large parking lot at 80 kph (kilometers per hour). Two teams of physics students, Team A and Team B, observe that as the car increases in velocity to its cruising speed, the anemometer spins ever faster and faster. Once the car reaches its cruising speed, they observe that the anemometer spins at a constant rate.
Note that whether the car is standing still and there is an 80 kph wind, or whether there is no wind and the car is moving at 80 kph, the anemometer will spin at exactly the same rate. Normally, anemometers are attached to building and thus they measure the velocity of the wind. But in this case it is assumed that there is no wind, but the anemometer is moving (i.e. the car it is attached to is moving).
Let us assume that two sets of physics students, Team A and Team B, are given the task of figuring out "why" (i.e. the "cause") the anemometer turns and to derive formulas to predict its spin velocity at different speeds of the car.
Let us assume the students in Team A have not yet been taught about small particles (i.e. air and wind) and they calculate the increasing spin on the basis of the "relative" velocity of two "coordinate systems." A "coordinate system" can be thought of as any object that has measurable motion, even if that motion is 0 kph. For example, the car (or the anemometer) will represent one coordinate system and an observer standing on the pavement will represent the second coordinate system. In this case the car accelerates to 80 kph, but the observer is standing still on the pavement and is thus traveling at 0 kph. When the car has reached its cruising speed of 80 kph, the "relative" velocity of the two coordinate systems is 80 kph because the car is traveling at 80 kph and the observer is traveling at 0 kph. To obtain the "relative" velocities it is simply necessary to subtract the velocities of the two coordinate systems in this simple example - 80 kph minus 0 kph equals 80 kph. Note that the "relative" velocity is actually the speed of the car, since one of the coordinate systems is not in motion and is always 0 kph.
Team B, on the other hand, believes that small particles called "air" are causing "resistance" to the cups. They had observed that if they stuck their hand out the window of a car when it is traveling 80 kph there is some invisible force that pushes against their hand much more strongly than if the car was traveling at 10 kph. They concluded that the same force that pushes against their hand was the same force pushing against the anemometer cups.
Team B derives their formulas based on resistance to predict the spin velocity of the anemometer, meaning based on the velocity of the anemometer to its ambient air stream. Thus Team A based their formulas on the relative velocity of the anemometer and the observer, but Team B based their formulas on the velocity of the anemometer and the ambient air or wind that surrounds it (i.e. the ambient velocity).
Both Team A and Team B derive exactly the same formulas. This is because in the case of Team A, the observer is stationary, thus the velocity of the car is also the relative velocity of the car and observer. Furthermore, there is no wind. Also, in the case of Team B, since there is no wind, the velocity of the car is also the relative velocity of the car and the air. Thus both teams generate exactly the same formulas.
The First Experiment
Because Team A and Team B have the same formulas, but not the same theories as to "why" the anemometer spins, two experiments are set up. In the first experiment the observer of Team A runs behind the car at a speed of 15 kph, and the car and wind act exactly as before, namely the car accelerates from 0 to 80 kph and there is no wind. In this experiment, it is noted that when the car reaches 80 kph, the "relative" velocity of the car and the observer is 65 kph (because the observer is running at 15 kph behind the car). However, it is noted that the anemometer spins at exactly the same velocity as it did in the original experiment. Thus Team A derives the wrong formula, but Team B continues to derive the correct formula.
Team A thinks they have the answer to the fact their formulas don't work. They claim that their formulas are based on the "apparent" or "relative" perspective of the observer. They claim that because the observer is running, he "thought" that the anemometer is rotating at a velocity based on a 65 kph speed of the car. In other words, they claim that the observer, since he would be in motion, observes the spin velocity of the anemometer differently than he would if he were "at rest," meaning standing still on the pavement and moving at 0 kph. Under this assumption, the formulas of Team A work.
The leader of Team B asks the question: "suppose there are two observers, one standing still on the pavement and one running behind the car at 15 kph, then how fast is the anemometer rotating?" Team A answers that the "at rest" observer will "see" the anemometer rotating at an 80 kph spin velocity and that the running observer will simultaneously "see" the anemometer rotating at a 65 kph spin velocity. Team A thinks they have proven that "air" doesn't exist.
The Second Experiment
Now a second experiment is designed. In this experiment everyone waits until the wind is blowing at exactly 15 kph in the same direction the car will be headed. At this point the car is accelerated exactly as it originally did and the observer is stationary. In this case, the "ambient velocity" of the wind and the anemometer becomes 65 kph, however, the "relative velocity" of the observer (who is standing still in this experiment) and car is 80 kph. In this case the anemometer is actually spinning more slowly than it did in the original experiment.
Because the observer is not running in this case, the formulas of Team A do not "work" (i.e. they do not correctly predict the spin velocity of the anemometer), because they predict the spin velocity based on 80 kph. But the formulas of Team B do work when the wind is moving at 15 kph in the same direction as the car. Remember Team B is comparing the anemometer to the ambient velocity of the wind that surrounds it. Team A has no answer for their failure in this case because they do not believe in "air," and to adjust their formulas for "wind" would be to admit that they believe in air.
Formulas Versus Theories
One of the most common errors made in physics is not thinking independently about a formula (or raw data) and a theory. Note that the "formulas" of Team A are valid (if there is no wind and the observer is stationary) and can be verified by anyone. The data that leads to the formulas (ditto) is also verifiable and replicable. However, the "theories" of Team A are false, even though their formulas are correct, and therefore their formulas at times do not work and at other times Team A has to give some strange and paradoxical explanations to justify their results. Their "theories" are that it is the relative motion of the observer and anemometer that cause the anemometer to rotate, but in fact it is the relationship between the ambient air and the anemometer that causes the anemometer to rotate. In fact a person could argue that Team A doesn't even have a "theory" since they make no explanation for a cause of why it is the relative difference between the observer and the anemometer that causes the anemometer to rotate. More will be said about this in a future chapter.
What it takes for Team A to Look Good
Now let us take this example a little further. How can Team A get their formulas to work in every case and thus have a chance of always being right? Ponder that question before reading on.
The answer is for Team A to require that the observer is always standing still and that there be no wind during the contest. Thus they only allow one observer coordinate system, one that is not moving, and is always "at rest," meaning standing still, and they require that there be no wind. In this case their formulas will always work.
There is another way to look at this. Team A must make sure the observer is moving in the correct direction and velocity relative to the anemometer when they build their mathematical model. In other words, they must pick the correct "at rest" motion of the observer. In this case the correct direction and velocity is 0 kph (of course, assuming no wind). But suppose they had incorrectly concluded that the correct direction and velocity for the observer was to run behind the car at 15 kph because on the day they made this calculation there happened to be a 15 kph wind moving in the same direction as the car. They would have picked the wrong "at rest" motion of the observer and their formulas would not have worked on days when the wind was not moving or was moving at a different speed or in a different direction. In summary, with the right restrictions (no wind), and the correct choice of the "at rest" reference frame, Team A will always get the right answer from their formulas even though their theory is totally wrong.
There are several things to learn from the Anemometer Metaphor:
1) The "formulas" of Team A can be perfectly valid, but their theories can be totally false (this is "bifurcating" a formula [or data] and a theory).
2) Team A's formulas are dependent on choosing the correct direction and velocity of the observer (and that there is no wind).
3) Team A offers no physical cause as to why the cups rotate, they only offer a formula that works if the correct direction and velocity of the observer is used and there is no wind.
4) Note that if the direction and velocity of the observer changes (i.e. he starts running when he is supposed to be standing still), it will have no affect on the spin velocity of the anemometer.
5) Since the formulas of Team A involve the "relative" velocity of the anemometer and the observer, the observer is part of the formula (i.e. a factor must be in the formula for the direction and velocity of the observer in order to calculate the "relative" velocity of the two coordinate systems). Because the observer is part of the formula, it is only natural and logical that the observer would have some affect on the spin velocity of the anemometer. In other words, because the observer's direction and velocity are built into the formulas of Team A, then the observer's direction and velocity should affect the actual spin velocity of the anemometer. Or to put it yet another way, since the direction and velocity of the observer is part of the formula, if the observer changes direction and velocity, the rotation velocity of the anemometer should change. But it doesn't. So why is the observer's direction and velocity part of the formula?
Based on the first chapter, the reader should already see why the Anemometer Metaphor is so similar to the SR. However, there is much yet to be said about the SR.