About category theory and physics Could the ideas of category theory be applied to Physics, maybe simplifying how algebraic topology and sheaf theory and other hard-to-explain subjects are used in physics?
Do Category Theory and/or Quantum Logic add value in physics? I know they have their adherents, but do more or less esoteric branches of mathematics such as Category Theory and/or Quantum Logic provide powerful tools for new theory development or are they just occasionally-useful presentational frameworks?  More particularly, is it worth investing the time to study these formalisms?
What are the mechanics by which Time Dilation and Length Contraction occur? What are the mechanics of time dilation and length contraction? Going beyond the mathematical equations involving light and the "speed limit of the universe", what is observed is merely a phenomenon and not a true explanation of why time dilates or length contracts.  It has been proven to work out, but do we know why?  Is it something that happens at a subatomic level?