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Symmetries of things

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“Symmetries of things” is my specialist subject, and has been for 49.5 years. One of the first things one learns in this subject is to distinguish between studying different symmetries of the same thing, and studying different things with the same symmetries. The former subject is called “group theory”, the latter is called “representation theory”.

As you know, there is a symmetry group in the theory of relativity, called the Lorentz group. There is also a symmetry group in quantum mechanics, called the Lorentz group. In physics, it is assumed that these are the same group, acting as the same symmetries of different things. This assumption leads to a contradiction, which physicists have struggled unsuccessfully to deal with for 96 years.

For 9 years, I have tried to explain that they are in fact different groups of symmetries of the same thing. I have tried to explain, in other words, that physicists are doing representation theory when they should be doing group theory. They refuse to listen to my expertise. Therefore they are still stuck in the same hole they’ve been stuck in for 96 years. Sod ’em.


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