I study pure mathematics. In pure mathematics, we begin from some axioms and obtain theorems. I am also interested in studying physics. I have some questions about the relationship between physical theory and mathematics. I apologize before asking if the questions are not appropriate. And I will be grateful to anyone who responds.
- Special relativity (SR) was originally proposed by Albert Einstein in a paper published in 1905. But Minkowski spacetime as a Mathematical structure for formulating SR introduced in 1908 (three years later)! I am confused about this. Did not Einstein himself state the mathematical framework of his theory? What is the difference between SR as Einstein himself formulated and SR in Minkowski's point of view? In fact, I always thought that every physical theory is formed at the same time as its mathematical formulation. Can we have a physical theory without any mathematical formulation?
- I read in some textbooks or internet pages (I do not remember which book or page) that in Quantum theories in physics there are some calculations that led to correct answers but we have no mathematical explanation for why. How is such a thing possible? Aren't our calculations based on mathematics?
- Is there any book to explain the difference between SR in Einstein's mind and Minkowski's? I heard that Einstein was a terrific intuitionist. Ok, but is intuition enough to form a physical theory? Thanks a lot.