Flat-moon theory

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Flat Moon Theory is a deliberately-perverse demonstration that it is possibel to star from a bad starting-point derive a bad theory, and still end up with the Lorentz relationships – the appearance of Lorentz relationships in a theory is therefore not proof that the theory is not a bad one (no matter how mathematically profound these relationships may appear to be).

Results of assuming a flat moon

Since the orbit of the Earth's Moon is tidally locked and always presents the same face to us, one can imagine a particularly obstinate computer program analysing the data and deciding that due to the statistical improbability of every picture of the moon showing exactly the same details, that it is simpler to assume that the moon is not a sphere, but a flat disc.

Examining photographs of the disc, we see that its surface features show an apparent distortion effect - while the surface craters appear almost perfectly circular near the disc's centre, craters closer to the rim appear progressively flattened into ellipses as their distance from the centre increases – they appear contracted along the disc's radii. If we analyse pictures of the Moon, we find that for a smallish crater placed at a radial distance [math]r[/math] from the disc centre, with the disc radius beind [math]R[/math], the radial contraction effect is

[math]{diameter}'/{diameter} = {\left( 1 - \frac{r^2}{R^2} \right)}^\frac{1}{2}[/math]

This is somewhat reminiscent of the Lorentz length-contraction or velocity-rescaling effect of special relativity,

[math]{value}'/{value} = {\left( 1 - \frac{v^2}{c^2} \right)}^\frac{1}{2}[/math]

, up to and including the existence of a horizon with attendant infinities at [math]r=R[/math]. Since events happening beyond the real spherical horizon could result in visible effects within the disc (an unseen astronaut over the horizon could throw a ball that could land in the visible area), it even includes a sort of counterpart to Hawking radiation.

The cautionary example of "flat moon" theory

In this case a physically-bad assumption (the "flat moon") generates SR-like Lorentz interrelationships that have similar mathematical profundity to those of the special theory.

No matter how deep these relationships appear, and how absorbing the implications might be for group theory or other fields of higher mathematics, the appearance of this relationship in a theory does not mean that the theory is not still fundamentally wrong in its founding assumptions, or that its ability to reproduce first-degree behaviour means that we "got it right". The appearance of the Lorentz relationship in a theory is no guarantee that the theory is "true". It might be, it might not be. To find out which, we need to apply different assesment criteria.

Notes

  • The aesthetics of the mathematician and that of the theoretical physicist can be very different. An operation that generates cascading series of correction factors (such as the infinite stream of digits that appears in Pi when we try to compare the diameter and circumference of a circle using integer math) is beautiful and magical, spawns new realms of mathematics and offers deep insights into the nature of the universe. To a physicist, it means that we probably just did something really stupid.
  • Where the mathematician is enthralled by mathematical sophistication, the physicist prefers systems and descriptions that are as mundane and uninteresting as possible. They ideally like things to equal "one" ... or perhaps, at a stretch, "two".