Theoretical implications


In the previous pages I showed that Newton was right all along, so there is really no need to 'save' his theory by introducing 'dark matter' in our galaxy, nor is there a need to modify his theory in any way (at least not in the realm of low speed - relativity is another thing). It's hard to assess where, how or why things went wrong, but once you accept that one defining feature of Newtonian gravity is, that the volume of an enclosed mass diminishes in a very predictable way, the conclusion that a ~ 1/r for the mass distribution of our galaxy is inevitable.

We could leave it at that, but I think we'd miss the opportunity te have a fresh look at the basics of his theory.

In my line of thinking 'Volume' is the central concept.
7)    ΔVol = -2πMGΔt2
As noted before: when a volume contains no mass, that volume will not change when accelerated by gravity (though the shape might). I'd call that 'conservation of empty space volume'. If a volume contains mass, it changes linearly with the mass contained, and squared with the time interval involved. Starting from this expression you'd find Newtonian gravity and vice verca - they are equivalent and interchangable. In fact, I myself started with the idea of 'empty space' not changing volume when attracted by gravity, and in no time I derived Newtonian gravity.

I think the volume-way of thinking is the more fundamental, because it explains (in geometrical terms) why in Newtons original expression we find an 1/r2. In the original theory there is no reason for this square, it could have been a third power, or there could have been an extra (smaller) term. The only reason is, that this appears to be the best description of reality.
Starting of with volumes it is immediately clear why things could not have been any other way - at least not in Euclidean space.
This also severely limits the possibility to tinker with the theory. We do not only want a theory that fits the data, we also prefer to understand why things are the way they are. With a principle of conservation of empty volume I think we do, at least more so than in the original theory.

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