Gravity/Energy Paradox

To illustrate a paradox that occurs in both Newton’s and Einstein’s theories of gravitation, let’s consider a simple thought experiment in which Max drops two identical, one kilogram metal balls from different points on a building.

Max drops the first ball from the top of the building, then runs down to the next floor and drops the second ball from a point 5 meters lower than the first, exactly one second later. At the instant that Max releases the second ball, both will be at exactly the same height above the ground. At this point in time, the first ball will have a velocity of approximately 10 meters per second (10m/s) and a kinetic energy of 50 joules. The second ball will have zero velocity and zero kinetic energy. Then at the end of the 2nd second Max catches both balls to measure their velocity and kinetic energy. He finds that the first ball has a velocity of 20m/s and a kinetic energy of 200 joules, and that the second ball has a velocity of 10m/s and a kinetic energy of 50 joules.

The paradox here is that these two identical balls each acquired greatly differing amounts of energy in the same last second of fall. If gravity is an attraction between the earth and the balls, in which kinetic energy is constantly being added to the falling balls, then how is it possible for the earth to add three times as much energy to the first ball as the second ball even though both balls began their last second of fall at exactly the same distance from the earth? How does the earth “know” that it must apply 3 times as much energy to the first ball as it does to the second ball during the same one second interval? How is it possible that the magnitude and the direction of a body’s motion can have such a large effect on the amount of energy that the earth’s gravity exerts on that body?

In Absolute Motion Theory, there is no paradox because there is no transfer of force between bodies unless they are in physical contact with one another. In the experiment, neither ball gains any energy after being dropped by Max. They undergo no change in absolute motion between the time they are released and the time they are caught. The energy released when Max catches the balls comes not from the motionless balls, but from the upward motion of the earth’s surface on which Max stands. The first ball releases more energy than the second ball because the second ball was accelerated upward for one second after the first ball became motionless. When the second ball was released it possessed an upward velocity of 10m/s away from the first ball. It is this Absolute Motion away from each other that allows the balls to produce different amounts of energy when they impact Max’s upward moving hands.

To understand this experiment in terms of Absolute Motion Theory, we must use the first ball’s position in space as our inertial frame of reference, instead of earth’s surface. In the drawings to the right, the experiment is shown against a grid of squares which represents the inertial reference frame of the first ball. Within this frame of reference the first ball remains motionless from the moment it is released until Max catches it two seconds later. An accelerometer attached to this ball would register no change in motion between these points in time. An accelerometer attached to the second ball would show that during the first second it was accelerated upward with Max and the building at a rate of 10m/s2 up and away from the first ball’s inertial frame of reference. This acceleration ceased when the second ball was released but its upward velocity carried it 10 meters away from the first ball during this last second. At the moment that Max catches the balls, the second ball is motionless within its own inertial reference frame but is moving 10m/s upward within the first ball’s reference frame and is moving 10m/s downward in the earth’s reference frame.

The apparent kinetic energy of a “falling” body is contained completely within the upward moving surface of the earth.

1 Kilogram Ball
1st second
2nd second
Velocity of Fall (V) 10 m/s 20 m/s
Energy of Fall (E) 50 J 200 J
Distance of Fall (D) 5 m 20 m

Gravitational Attraction

Gravitational Expansion

Our perception:


Earth's surfact as the inertial frame of reference. First balls's position as the inertial frame of reference.

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