What is it? Ultimately, Unity Root Matrix Theory (URMT) is about a discrete formulation of the laws of nature, i.e. 'Physics in Integers'.


Why? It is believed that the laws of nature are not as complicated as currently formulated, and that we are taking the wrong approach by formulating a theory of nature that assumes it is continuous, even at the Planck level, i.e. we cannot keep applying our differential equations at all scales. Instead, we need to start from the bottom-up with a discrete, all -integer theory that, to all intents and purposes, looks like our macroscopic world when the numbers get very large. This is not the same as approximating continuous functions by discrete forms, URMT starts with discrete forms, which only give the same results as their continuous forms at large scales.


Justification? "too many similarities to concepts in mathematical physics to ignore"


Having originated as a study of some simple congruences in number theory, URMT's methods and results started to look very similar to those of modern mathematical physics. Eight years, and five books later, this claim remains more valid than ever. URMT starts with a conservation equation, applies an invariance principle, and produces physically recognisable equations - all in integers.


Is this just another "all physics is wrong" rant? An emphatic no! We would not have got this far if current physical theories were entirely wrong. Relativity is a triumph, the Standard model is very successful, you would be a fool to deny these theories. It is believed these theories are successful precisely because their fundamental principles are, indeed, those of nature. Neither does URMT really deviate from this path - the concepts of invariance and symmetry are just as paramount to URMT as they are to modern field theories.


If the Standard Model and Relativity are so good, then why URMT? Having come so far, gravity still stands apart from the other three other forces of nature, i.e. the Weak and Strong forces, and Electromagnetism. Neither do we seem to be getting any closer to merging all four. Most current research interest is focused on String theory and its M-theory derivative, but this has not resulted in any real success, even after 40 or so years. Sadly this also goes for other candidates.


This inability to unify is believed not so much due to erroneous principles or ideas, but rather due to a mistaken formulation of the physical laws as continuous differential equations that, ultimately, are really just a good approximation of a discrete universe, and only truly valid at macroscopic scales.


Difficult though it is, we may have to accept that we are not getting there, and one final big push will not resolve the problem. Something radical is required. That something may or may not be URMT, but whatever it is, it will have to be radical nonetheless.


Unity Root Matrix Theory
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