Last night I heard a wonderful lecture by Dr Harald Fox from Lancaster University. He was explaining the need for the Higgs Boson. He started with Noether's Theorem. Emmy Noether was a brilliant mathematician who proved that if you have a symmetry in nature, then you will have a conservation law. I'm beginning to get my head round this so there will be a some posts about it to help me to understand it. One example of a symmetry is that of electromagnetic potential. He described it as a "bird-on-a-wire" potential so I was very pleased to spot this bird this morning. Normally they perch on the very top wire, which is the earth wire and has no current or potential. This bird was perched on one of the lower wires. Judging by the number of insulators, I'd say the lines would be at least 10,000V. So why isn't the bird hurt? The answer is because both legs are at 10,000V. You need a potential DIFFERENCE to get a current to flow. As long as the bird only touches wires at that potential, there is no difference and the bird is safe. If we transferred the bird to a higher voltage line, say 425,000V, then the same thing would apply and the bird would still be safe. Provided there is no difference in the voltage (potential) for each leg, then the bird will be safe wherever. That's what we call a SYMMETRY. You can change the condition but get the same result. The overall situation looks the same although we have changed one condition. So we have a symmetry with electromagnetic potential (voltage). There must be a conservation law connected with it. In this case, it is conservation of CHARGE. And that's what we check when we are looking at particle interaction equations to see if they will work.
