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?
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...
Why do the laws of nature have to be second order diff. equations in order to be invariant ?
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?