Why are so many of the important equations of physics first or second order differential equations (schrodinger etc).Why are there few third or fourth order differential equations that describe the physical world?
Why do the laws of nature have to be second order diff. equations in order to be invariant ?I can only second that !
But as the question *why* does spacetime have these symmetries, the answer is then that these leave the laws of nature invariant, which are... second order diff. equations...
No, it is the other way around (hence why this is begging the OP's question). BECAUSE we find that the laws of nature are second-order, we NOTICE that they are invariant under certain transformations, and hence we call these invariance laws, the invariance of spacetime.Why do the laws of nature have to be second order diff. equations in order to be invariant ?
Given a solution to Newton's equation:But if there is a non-zero jerk over time then surely there has to be a non-zero d^4x/dt^4 and a d^5x/dt^5, etc. Why are these not considered?