Published in astro.philica.com
The inverse square law and its associated uses in force equations is claimed to “break down” as radial distance approaches zero. But from another point of view, the resulting zero-point infinity makes sense.
Consider an observer riding an imaginary coherent wave front of vectors F, all pointing inwards towards a singularity (div F negative). As the observer on this wave nears a Planck zero point (much as light rays converge into, then emerge the focal point of a magnifying glass or lens) the vectors will pass through then emerge the zero point in an inverted state. An observer riding the front of this incoming then outgoing measurement wave would see forces that approach infinity because of the compression of all vectors into a zero volume. However, another way of looking at the problem reveals that, just at the point of emergence out to the “other side” of the singularity, where the radius just turns negative, (div F switching positive) the observer would be peering outwards from this 4-geometry “peep hole” at the entire universe, whose forces would indeed integrate as infinite, as this new observed volume of the universe would encompass all existence. It would then seem to be more than just a mathematical anomaly.
Result of pondering the dilemma that, nature abhors a discontinuity or an infinity…
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This Observation was published on 22nd February, 2010 at 14:22:14 and has been viewed 5829 times.