@rosborne979,
gage theory comes from functions as a different form of each other, like 2 versions of X (x and X'). In effect hes saying that the math of the measure shows that there must be "something" there to mesure the differences as defined in the equation,(no matter how the coordinates are translated, because gage theory states that all physical equations are the same no matter how their coordinates are screwed with.)
My understanding is admittedly, imperfect because everything Ive done with particles is in the fields of isotope age dating and sensing of particle decay.