Taking a grid of 'evenly-spaced' space-time points. e.g. at integer values of (x,y,z,t). Now do a Lorentz boost on this grid. We end up with a grid of points which are much closer together.
It is bothering me that the grid of points only looks evenly distributed in certain frames (related by spacial rotations) but looks different under Lorentz boosts. The points that looked like neighbours no longer look like neighbours.
When working out results in lattice QCD, does this mean that the results you get don't exhibit Lorentz symmetry. And how can we be sure in the limit the Lorentz symmetry is conserved?
Edit: I just came across this animation from John Baez on time crystals.
Which seems to suggest that for certain lattices like a triangular lattice, the Lorentz transformation can preserve the Lattice form. Although looking at the middle point, it's neighbours are continually changing. And Lattice QCD is based on calculations of nearest neighbours (discrete derivative). I guess one could reformulate the calculations to all neighbours a unit Minkowski-distance away. But this would increase the number of neighbours a lot for large volumes of space-time. (and does this obey the concept of `locality'??)