May 18 2024

## 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 in a push and peel process, in pairs, backward, laterally at an acute angle. 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.

The H field, just like in electrodynamics, is a magnetic field.

“ h_{–} + n(I) = dim H ≤ a(I) = i(I) + n(I), so h_{–} ≤ i(I) “ ([1], pg. 233)

“ h_{–} “ is centripetal force from a magnetic field, producing a corkscrew, and n(I) is the antenna.

**24.10.** THEOREM. “*If n ≡ 0 mod 4, then π _{n} (R_{n+1}) contains a cyclic group of order 2 whose non-zero element is represented by T_{n+2}*.” ([2], pg. 130)

The electrons in the antenna produce 4 corkscrews for each signal. Electrons tend to congregate at the outside of the antenna, so it may be 4 electrons to a signal. Outside the antenna they quickly spread. What is meant by augmented index, a(I), is that the cosine waves, as they are emitted, go out in all directions from the antenna.

[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

[2] Steenrod, Norman, “The Topolgy of Fibre Bundles”, Princeton University Press, c. 1951