Gauge Symmetry

Gauge symmetry starts simply with the conservation of electric charge–the sign of the charge (positive/negative) is arbitrary. Therefore, we could change the sign of every electric charge in nature and the world would carry on in exactly the same way as if nothing had changed. Those are the basics; but, the essence of gauge symmetry is much more complex. It expresses a much deeper symmetry in which the equivalence of two things can be defined by measuring other associated quantities to obtain identical information. In order for such principles to be applied successfully, it is essential that the symmetry be continuous; meaning, the parameters used to measure the associated quantities can be varied continuously and the transformation can be indiscriminately close to the original without altering the system. In short, the laws of nature are always in operation and are inherently discrete or otherwise unnoticeable. [1]

Lawrence Kraus does an excellent job of explaining this concept in his book, The Greatest Story Ever Told–So Far, by using a chess board example. He recaps the details of the example in an interview with the Scientific American:

So, imagine the universe as a big chessboard. I could change every white square on a chessboard to a black square and every black square to a white square and the game would be exactly the same. That’s the simple kind of symmetry. Now I can turn it into a gauge symmetry by making it much trickier. I can say, “Let me just change locally, whenever I want, a white square to a black square or a black square to a white square. Not everywhere but place to place.” Now the chessboard doesn’t look the same at all, so the game can’t be the same unless I also have a rule book—a coordinate system for what happens at every point—containing rules for the pieces of the chessboard to follow to keep the game the same, rules that account for everywhere I have changed the color of a square. That becomes a very weird symmetry. [2]

To put it another way, what science can tell us will continue to change as civilization continues to progress. As we develop new understandings of the universe and how it works we will continue to update the laws of physics but, the laws of nature will stay consistent. Nature will continue to function as it always has regardless of how we understand it. Nature explains science, not the other way around…

Seen in Dalston, London, U.K. | Artist: Banksy

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