Hawking Forum Post 35099
| Subject: | A Result of GR, Schwarzchild Two-Sphere Geometry, SRT, and Observed Flat, Euclidean Space in the Construction of the Particulate, 4D World We Inhabit |
| Date: | November 16, 2002 |
| Poster: | Samuel A. (Sam) Cox |
Authors comments following this note from a reader of the site: hi sam... just read your posting of smolin's work. i recently read his latest "three roads to quantum gravity" and dropped him an e-mail. i know he's a busy guy. its imperative that you look at bucky fuller if you haven't. the common rhombic dodecahedron has the exact toplogy of a 4-cube and is an all-space filler (no interstitial vacancies), and is apparently the most common crystallographic lattice in nature. its dual-reciprocal negative-space complement is the cubeoctahedron ( your observer perspective) which is stunning. do you know about it? best jonathan Authors Comments: This note is very perceptive, and points out the very important relationship in geometry between circles and spheres (as in GR and Schwarzschilds Two Sphere) and "flat sided" Euclidean figures and objects in 2,3 and 4 dimensions (as in SRT and Euclidean Geometry).Without going into the exact derivations of formulae for 3D objects (of all shapes) from formulae for 2D figures (of all shapes), the studied reader will remember that Euclidean and Spherical Geometry are conceptually linked. Some important linking concepts are straight vs curved lines and their nomenclature, global as opposed to local, coordinates, angles and observing frames. Continuing, we need to recognize and understand what happens when a higher dimensional object is projected onto a lower dimensional surface to understand this world of ours. To use one simple illustration, (and bypass many other important principles), a 3D cone projected onto a two dimensional surface can be observed in two ways, but only one way at the same time. Likewise, a universe in extra large dimensions, as the Schwarzschild two/ sphere when projected and observed on 4D surfaces, can also be observed in two ways, but only one way at a time.Speaking in terms of degrees, when we observe a 7 dimensional, two/ sphere universe at 360 degrees, we only observe 1/2 of the entire reality. Walk around a friend and observe them front and back...from every possible direction at 360 degrees. You are only seeing one half of your friend. The other half is "on the other side". Just as you cannot see landmasses over the horizon of the Earth, this other half of your friend is just as real, just as massive, just as particulate and just as observable; but not from our present coordinates. The way nature is organized reflects the basic principles of its construction, both at the local, 4D SRT, flat, Euclidean level and at the macroscopic 7D GR, Two/ Sphere level. Everything is linked and related. This fact makes the above post and the observations noted therein, highly significant. Best Wishes, Sam Cox |
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