This video (https://www.youtube.com/watch?v=gWTnpy7sw2g), together with my recent preprint on RG that's mentioned in this discussion, makes me think my ideas about the universe being composed of topology aren't a wild fantasy after all.
17 minutes into the video, Sabine says "light doesn't interact with itself". It does. Electrical engineer Hong Tang and his team at Yale demonstrated that, on nano-scales, light (electromagnetism) can attract and repel itself like electric charges or magnets.
(Mo Li, W. H. P. Pernice & H. X. Tang, “Tunable bipolar optical interactions between guided lightwaves”, Nature Photonics 3, 464 - 468 [2009])
This is the Optical Bonding Force. An article I wrote (Alternating Current, Superconductivity, And Stellar Quantum Entanglement) proposes that light can attract itself because a photon, the quantum of electromagnetism, is composed of trillions of Mobius strips (a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist).
In attraction, a pair of them can fit together and form a Klein bottle (another example of mathematics’ topology or “rubber-sheet geometry” which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down). The Klein bottle is a two-dimensional manifold mathematically immersed – not embedded – in the third dimension (an immersion may have self-intersections; embeddings have no self-intersections).
Trillions of bottles form a graviton, the quantum of gravity (when a graviton dissociates or separates into Mobius strips, the building blocks of photons adopting different paths, light repels itself).
If this explanation of a science experiment's results is correct, the shared topology making up photons and gravitons would indicate electromagnetic-gravitational unification. If the pressure of interacting photons and gravitons produces mass, the explanation suggests a supersymmetrical correspondence between matter's fermions and energy's bosons.
Einstein's equations say gravitational fields carry enough information about electromagnetism to allow Maxwell's equations to be restated in terms of these gravitational fields. This was discovered by the mathematical physicist George Yuri Rainich. (Rainich, G.Y., Transactions of the American Mathematical Society, 27, 106. [1925]) Therefore, gravitational waves might also be capable of attracting and repelling. Suppose all the gravitational and electromagnetic waves composing space-time between a spaceship and a distant galaxy were compressed by attraction or repulsion into a vertically flat plane. Then there'd be no distance between astronauts and, say, the Andromeda galaxy and they could travel there instantly (instead of making a journey that takes more than 2 million years at the speed of light).
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