Chapter 20. Gedankenexperiments

Before showing that inertial force is a manifestation of gravitational force in the next chapter, we get into the proper frame of mind by performing two thought experiments or, as Einstein would have said, gedankenexperiments:

Suppose that an unpowered spaceship "floats" in space such that all of the masses of the universe--the sun, moon, earth, all of the other planets, moons, and asteroids, and all of the stars and galaxies, and so on--surround it. Each mass applies a gravitational pull on the spaceship such that all of the pulls vectorially add up to one effective gravitational force vector sum, which accelerates the spaceship at a particular magnitude and direction. So long as gravitational forces are the only ones applied to the spaceship, it and everything within it don't feel them--everything is "weightless."

Let us make an analogy, so that we can more-easily understand this thought experiment.

Let a corral at a ranch replace the universe, and, a maverick, the spaceship. Let wranglers' lassos be the pulls of gravity from the various masses in the universe. The wranglers surround the maverick with their lassos around its neck. These lassos are magic because they do not only apply their forces to the neck but equally to all parts of the maverick's body in proportion to each part's mass, mimicking the force of gravity. The wranglers pull on the maverick from many directions; however, the lasso force vector sum that they apply moves (accelerates) the maverick in one particular direction. So long as the maverick does not resist the pulls of the lassos, it does not feel them. Yet, should the maverick try to move in any direction, it must exert much force, which, if many wranglers exist, it might not possess. The maverick must overcome, not the lasso-force-vector sum, but the opposing pulls of all of the lassos.

Like the maverick, the spaceship detects no force. However, should the spaceship try to move, it--like the maverick--must overcome the forces created by all those surrounding celestial bodies. In other words, it must overcome inertia.

In another gedankenexperiment, we use a force that is just another form of inertial force--centrifugal force.

First, we set up the apparatus for the thought experiment: Suppose that you are weightless in a spaceship in the deepest reaches of space--the farthest that you can be from any mass--let us say, midway between the two superclusters of galaxies the most distant from each other.

All energy sources in your spaceship are turned off. You look out a porthole and see the infinite blackness of deep nothingness. With a powerful telescope, you barely see a faint white dot, which is one of the two superclusters. Likewise, from an opposing porthole, you barely discern the other supercluster. With your ultra-powerful telescope, you sweep the universe in all other directions, but the panorama yields no other points of light.

Periodically, you check the two points of light. They remain at the same locations relative to their respective portholes. You still float inside your spaceship in midair--weightless. We are ready to perform the gedankenexperiment.

You fire rockets that are tangential to the cross section of the spaceship, which begins to spin about its longitudinal axis. You know that it is spinning because the two points of light now appear to revolve about it. Faster and faster the spaceship spins until the two, white dots blur to create a faint circle of light around it. You shut off the rockets. Again, all power sources are off; all human-made forces, gone. Yet, the two points of light continue to blur in their rapid revolutions about the ship.

The question is: Are the items in your spaceship still weightless, or has centrifugal force pushed them against the hull of your spaceship?

Logically, from the point of view of an earthling, centrifugal force pushes them, but from where would the centrifugal force come? If the spaceship is, indeed, rotating, it rotates only in relation to other matter in the universe, and the closest is at one of those two points of light, billions of light years away.

Rotation relative to other masses creates centrifugal force, and your spaceship rotates only in relation to the distant superclusters, which, apparently, would be too far away to have much of an effect. So, the key question is: Does the magnitude of inertial force vary throughout the universe, and, if so, does the magnitude of the fine-structure constant indicate the magnitude of inertial force in our part of the universe relative to a basic magnitude elsewhere in the universe, where inertial force is 137 times less?