379(3): General Counter Gravitational Equations

This note gives the solution (7) of the ECE wave equation (1), and shows that the Euler Bernoulli resonance equation (16) is true for the time independent wave (15). The theory is illustrated with the resonant absorption of electromagnetic radiation by an electron beam. The electron wavefunction (26) has the same format as the electron scalar potential (15). Therefore resonant absorption in electrons, atoms and molecules can be thought of as Euler Bernoulli resonance (Marion and Thornton, “Classical Dynamics”, chapter three). In Eq. (31), an electromagnetic driving potential is applied to the gravitational solution of the ECE gravitational wave equation. Resonance occurs when the electromagnetic driving force is tuned as in Eq. (38). At resonance the gravitational potential approaches positive infinity, and an object m is repelled by an object M. This is a simple example of resonance induced counter gravitation. This experiment is also a simple test for the existence of a gravitational wave. In ECE2 theory such waves exist from the ECE2 gravitational field equations, and have the same propoerties as electromagnetic waves. However they are twenty three orders of magnitude weaker, so resonance is needed for effective countre gravitation. This is possible in theory.


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