God of Science and Astronomy
Relativism of a Straight Line
Consider a simple problem about centrifugal force. Imagine you stood at a pole of the earth, say the North Pole and constructed a wheel whose axis extended from the calculated axis of the earth. (This wheel would spin parallel to the plane of the equator.) Imagine that this wheel contained a precision force gauge whose output you could remotely read as the centrifugal force at the wheel’s rim.
You spin the wheel clockwise (from the top view) and recorded the force at the wheel’s rim. By spinning in the clockwise direction the wheel would be spinning opposite that of the earth’s rotation. Would the rotation of the earth, in effect, be subtracted from the spin of the wheel? Would the centrifugal force readout be higher if the earth did not rotate?
Now you stop the wheel and spin it in the opposite direction, i.e. counter clockwise at precisely the same speed (RPM) relative to you standing on the earth. Again you read the output of the force gauge and record it. In this direction would the earth’s rotation add to the wheel spin? Will the output of the second (counterclockwise) spin have an added centrifugal component that would show up on the force gauge? Or will the wheel produce the same centrifugal force? Does your effort, imparting a force in the wheel, somehow create it’s own frame of reference relative to you (the force) and the wheel? Or could the proximity of the wheel to the earth’s gravity somehow envelop and include the wheel in its rotational motion allowing the two opposite direction spins to produce an identical force output?
The speed of the wheel obviously depends on where you stand when you determine the wheel speed. If you float in space above the pole you will see the wheel spinning at different speeds. The counter clockwise wheel spin being 2 Revolutions per day (RPD) faster than the clockwise direction. And from that point of view you would expect the centrifugal force to be higher in the counterclockwise direction. If you took the remote readout of the force gauge in space above the pole, would the readout be different?
Centrifugal force is derived from the inertia of an object in motion (which prefers to travel in a straight line). Inertial resistance to that ever-changing circular motion produces the force. It is technically called angular momentum. Also, the velocity of that body in motion determines the amplitude of that force. So the question boils down to the immediate straight line moment of velocity of a point on the rim. However, this brings us back to the original problem. If you measured the moment of velocity at a point on the rim standing at the at the earth’s pole (or anywhere on the earth), it would again be the same in both directions. If you measured the moment of velocity from space, it would again be higher in the counter clockwise direction. It seems simple Newtonian motion is relative to the observer’s position and motion.
Our individual motion standing on the earth is far from simple. We are not only moving on a spinning earth but also orbit around the sun, which is moving through the galaxy. This galaxy is spinning around its center and moving relative to the local cluster. And this cluster is moving relative to the more distant background galaxies. So even the task of throwing a ball in space, which would appear to the thrower to go in a straight line, (producing no force of angular momentum) would not be moving in a Newtonian straight line if observed from, for instance, the moon.
So is the straight line motion of the ball solely determined by the force applied, from the point of applied force? If so the wheel would produce the same centrifugal force in both directions as the applied force is equal (though opposite). If the motion of a thrown ball is not a universal straight line but follows the curves and spins of an orbiting earth and moving sun, then the centrifugal force of the wheel will be different between a clockwise spin and a counter clockwise spin.
If the observer’s motion determines weather a line of motion is straight or curved, then consider an observer above the earth, watching a bullet fired from the equator to the north pole. It will naturally take the shortest path, (a straight line for us watching on earth). To eliminate any confusion about following the curvature of the earth I have will make the northern hemisphere a cone with the equator as the base and the north pole the apex and removed the attraction of gravity. From the firing position on the equator the bullet would describe a perfect straight line. From space above the rotating cone the path of the bullet would describe a tightening spiral. So the outside observer would see the bullet traveling a curved path and therefore assume that some outside force was causing the mass to travel a path other than a straight line. They would also assume that there was a side force on the projectile produced by the angular momentum. They would expect anyone traveling inside the bullet to experience this side force as one in a car when turning a corner.
So where lies this frame of reference for determining what is a straight line? The answer could come from the measurement of centrifugal force itself. It could be determined by performing our original experiment of spinning a wheel. If the centrifugal force is identical with both spins, the frame of reference is the wheel itself. If it is additive and subtractive by the earth’s rotation, the frame of reference then occurs in a larger context beyond the earth’s influence.
If the later was true, this experiment on a larger scale could determine the absolute frame of reference for all motion. It would be possible that the reference frame could be the universe and with a large enough wheel we could determine if the universe itself is in relative motion. We could measure this by a series of wheel spins (or tethered weight spins) in space with a precise force sensor. By changing the orientation and speed we could find the condition of zero angular momentum, when the wheel is at rest relative to the universe. The wheel speed and orientation would match the rotation and orientation of the universe. This would also mean that our universe not self contained but part of a larger framework possibly containing other multi-verses.
However, if the reference frame is that of the point of origin of the applied force, then every moving object in the universe determines its own straight line. And producing a universal straight line would be impossible. It would mean that straight line inertial motion is as relativistic as the speed of light. That any straight line motion is determined by the last applied motion changing force. Traveling in space (away from any influencing source of gravity) you would know that you were going in your own straight line but it would be impossible to prove it by observing outside motion.