# Differences in calculations should be due to differences in environment?

Lisa Randall in her book Warped Passages writes,

"A very reasonable thing to expect from physical laws is that they should be the same for everyone. No one could blame us for questioning their validity and utility if people in different countries or sitting on moving trains or flying on an airplane experienced different physical laws. Physical laws should be fundamental and hold true for any observer. Any differences in calculations should be due to differences in environment, not the physical laws."

What does she mean when she says "Any differences in calculations should be due to differences in environment, not the physical laws." Can one explain with an example?

She simply means that there needs to be a physical difference in the environment to have differences in the behaviour of phyiscal systems. For an example, supposed Newtonian mechanics was a fundamental theory of nature. Then the universal law is $$F = ma.$$ Suppose further the only thing in existence are charged particles moving in external electromagnetic fields (no backreaction of the moving charges on the fields), so the universal law is $$m\ddot{x} = q (E(x) + \dot{x}\times B(x)),$$ that is, the equation of motion under a Lorentz force. This law holds true for all observers in our hypothetical and very simple (and potentially inconsistent) universe. Different "calculations" arise from different values of $E(x)$ and $B(x)$ at different points, but the law itself never changes.