Hidden assumptions

One of the most important tasks of mathematics is the examination of assumptions. Mathematics enables us to see which assumptions are necessary, and which are sufficient, and if any of the assumptions contradicts one of the others.

Theoretical physics makes many assumptions, and it is well-known that not all these assumptions are consistent with each other. Most of the time, this does not matter, because they are simplifying assumptions that only apply in restricted circumstances, and they permit practical calculations without bothering about irrelevant details.

But if you want to build, say, a fundamental theory of everything, then you need to get rid of the inconsistencies in the assumptions. The standard theory of atomic structure, and sub-atomic particles more generally, is known to be inconsistent with the standard theory of galactic structure, and gravity in general.

This blog is largely devoted to a discussion of the mathematical issues raised by this contradiction, and to proposals for possible ways to modify the assumptions to remove the contradiction. As such, it discusses the assumptions in minute detail, and examines a range of experimental evidence, but largely avoids discussing the existing mathematical models, since it is mathematically, logically, physically and philosophically obvious that the existing models are wrong in important ways, and therefore misleading.

 

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