What is symmetry in physics?
A symmetry is a change in how the world is written down that leaves a named quantity alone, which makes it a claim that part of the description was never physical. Longitude shows it. Latitude has a zero the planet supplies, the equator. Longitude has none, because turning the whole Earth about its axis changes no measurable relation between places. So in October 1884 delegates from twenty-six nations met in Washington and voted for a zero, and Greenwich won twenty-two to one. Distances came through the vote unchanged. Physics runs the same operation on bigger descriptions. The laws are the same here and elsewhere, today and in the Cretaceous, and Emmy Noether proved in 1918 that those two symmetries give conservation of momentum and of energy. Scale is no symmetry. Atoms have a definite size.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 5: Why Do You and I See the Same Table?watch a universe make its own particles