I backed out of the garage and to the right onto the parking area, then turned left onto the driveway. At the end of the driveway I turned left onto the road heading south. That is a mental depiction as if I were an outside observer. What I visually observed could have been captured by a camcorder facing out the windshield. That observation would be the garage receding from the car, the driveway turning perpendicular to the car, then turning in alignment with the car opposite to the car’s original orientation, the road approaching as the driveway moved past, the road turning in alignment with the car and finally, along with other scenery, the road passing the car from south to north.
Notice that in playing such a recording, the recorder is necessarily a stationary reference frame for the motion displayed, which motion is by something other than the observing recorder. Yet, no one would offer the actually observed motion as truly depicting the motion, though not denying it. What is offered as the true depiction of the motion is a logical analysis as if by a virtual, outside observer.
If I said, “She walked from the dining room into the kitchen,” I would be relating a visual observation. If I said, “I walked from the dining room into the kitchen,” I would be relating an interpretative depiction of what I did not observe based on the visual observation of the dining room’s passing my point of observation, and the kitchen’s surrounding my point of observation. Yet, I would always state the interpretative depiction and never what I directly observed.
It should be apparent that the virtual depiction of motion can only be ‘true’ if the actually observed motion is true. I can affirm the truth of the unobserved, virtual depiction that the car backed out of the garage, only if I affirm the truth of what I actually observed, namely that the garage receded from the car.
Notice that the two depictions of motion, the virtual, unobserved and the actually observed are not either or. They are not mutually exclusive. For either to be true, both must be true. They are necessarily interdependent. Unless the receding of the garage captured by the camcorder is a true observation of the motion, it would not be true that the car backed out of the garage.
In stating that something is in motion, one must at least implicitly affirm something else not to be in motion. That something else is the reference frame. In the common range of motion that we experience, a reference frame is an arbitrary choice. The choice of one reference frame does not classify a different choice as false. Reference frames are compatible, as we know from analytical geometry. A choice is typically one of convenience. A choice may be viewed as affording greater utility or greater simplicity than another, but a choice isn’t between a true and a false reference frame.
Reference frames are typically in conjunction with a virtual observer. This is because the depiction of motion is commonly analytical in which the narrator indulges in the luxury of imagining himself outside his own skin. This luxury is affordable in the range of motion, which we commonly experience.
The freedom of choice is evident in this sentence: The flight attendant walked to the rear of the aircraft as it circled the airport prior to landing at sunset. For the first motion, the aircraft is the stationary reference frame to the motion of the attendant. For the second and third, the airport is stationary to the motion of the aircraft. For the fourth, the earth is stationary to the motion of the sun. For all four, the observer is implicitly virtual.
Everyone recognizes the three reference frames as convenient. Yet, if there were an absolute reference frame, at least two of these three frames would be false.
In the 5th century, St. Augustine recognized that the topic of Scripture was Divine revelation, the relationship between God and men. It was not any mundane topic, which would include analytical geometry. In the 17th century, Galileo claimed that there is an absolute reference frame in analytical geometry and that Scripture was in error in misidentifying it.
In the 19th century, in accord with the choice of a reference frame in analytical geometry, the Michelson-Morley experiment demonstrated that the speed of light does not depend on direction, which it would if the earth were moving with respect to an absolute reference frame. Yet, Galileo’s claim of an absolute reference frame in analytical geometry has persisted.
Karl Keating recently authored, The New Geocentrists, who, today, concur in the error that there is an absolute reference frame. However, they do not entirely agree with Galileo. They claim that scripture has accurately identified the absolute reference frame of analytical geometry. Like Galileo, they don’t realize that the choice of a reference frame for the depiction of motion, within the scope of common observation, is trivial.
Galileo, a man of his time, had an excuse. Copernicus’ analytical depiction of planetary motion was so stunning in its simplicity and lucidity, its reference frame appeared to be absolute. It appeared to be a natural discovery rather than a mental construct, a mere choice within the logic of analytical geometry.
The equivalence of reference frames is customarily noted in that any frame can be linearly expressed as another. Consequently, an equation is of the same power, no matter the reference frame chosen for its expression.
I would like to see a computer simulation of the relative motion of solid balls in two dimensions. There would be nine balls, B1 through B9. The animation would begin with ball 1, (B1) at the center of the computer screen with the other 8 orbiting it in 8 concentric circles. Sometime after each ball moved through its period, B2 would become stationary and the other eight balls would move relative to it. This would put B1 in motion with respect to B2 and the computer screen. Each successive ball, B3 through B9, would become stationary with the other eight in motion.
The second phase of the program would alternate between B1 and B4 as stationary. In analogy, this would furnish a visual display of the simplicity and beauty of the Copernican depiction of planetary motion about the sun, rather than the earth, the third planet from the sun.
I suspect that the relative motion with B4 as stationary would be esthetically beautiful. However, it would not appear as simple to the human mind, as the motion of B2 through B9 orbiting B1 as stationary. To judge the depiction with B1 as stationary to be objectively more orderly than with B4 as stationary, would be to conflate the limits of human mental acuity with less order. Both depictions are of one and the same motion.