Mar 06 2023
Emitting Cell Phone, Radio, and Television EM Waves
Let us say there is an imaginary horizontal disk centered on a vertical, unshielded emitting antenna. Cosine waves of various frequencies and amplitudes go out in all directions centered on the disk. As a cosine wave travels away from the disk, it imbues EM waves of the same frequency perpendicular outward to the electric part of the cosine wave in a push. As the cosine wave comes back toward the disk, there is no push, preventing double signals. Each torus grows continually until it runs out of momentum, and in a complex set of signals there are many interspersed tori.
The amplitude of each cosine signal, as it multiplies, may not be constant throughout the torus, though frequency is. For a given location of a receiving antenna, the amplitude ratios of all the signals are the same.
By the 80:20 rule, 80% of a cell phone, radio, or television EM wave travels through the h field, and 20% travels by using the g field. According to Morse Theory, 100% travels through the h field:
“ h– + n(I) = dim H ≤ a(I) = i(I) + n(I), so h– ≤ i(I) “ ([1], pg. 233)
This is from the proof of Theorem 6, and in the next section it is written: “the Morse index theorem says that the inequality of theorem 6 is an equation.” ([1], pg. 233) With the torus action: “t passes from 0 to b” ([1], pg. 234) in the positive and negative directions. What is meant by augmented index, a(I), is that the cosine waves, as they are emitted, go out horizontally in all directions from the antenna.
In outer space, the way signals can travel long distances, the Morse index theorem comes very close to reality. In earth’s atmosphere the tori run out of momentum faster.
[1] Bishop, Richard L. and Crittenden, Richard J., “Geometry of Manifolds”, AMS CHELSEA PUBLISHING, Copyright 1964 held by the American Mathematical Society. Reprinted with corrections by the American Mathematical Society, 2001