Chapter 17 Poincaré and Susy 17 . 1 Poincaré Invariance

A great advance in physics came when it was realized that it was better to think about motion in empty space rather than starting with what happen in the “real world” with gravity pulling things downwards, friction slowing things down, etc. First, that the laws of physics should be the same at one point as at another, i.e. that they are translation invariant, and also from one day to another, i.e. that they are invariant under translations in time as well. Also they are direction independent space is isotropic. Another great breakthrough was Galileo’s recognition that two reference systems in relative motion at constant velocity have the same physics, so there is an underlying galilean invariance under spatial and time translations, rotations, and boosts. Thus we have a 10 parameter Lie group of symmetry transformations. Of course Einstein corrected some details, finding that the boosts affected time as well as space, in such a way as to leave invariant