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David Kahana
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physicist unhingedUpdated 4y
What is 'gauge' in physics in layman's terms?

Imagine that you can measure something using a gauge, such as a pressure gauge, or a gauge or a meter which determines the electric potential of some conductor.

Further, imagine that the physics of a given situation, what actually happens, depends only on the difference in electric potential between two conductors, not at all on the absolute value of either potential. It may sound very unusual, but it is in fact pretty generally the case, when those conductors are isolated from everything else.

Then you have a gauge invariance of the physics, since if you measure 500 volts on the first conductor, say with respect to the electric potential of the Earth, and 1000 volts on the second conductor, with respect to the potential of Earth, and these conductors are both completely isolated from the Earth, in vacuum say, it will not matter to anything that happens between the two conductors, what the absolute value of the potential is. They could be at 9500 volts and 10000 volts instead.

All that matters locally and to the physics, is what the difference between the potentials is. The potentials must be measured with respect to some reference. But if it doesn’t matter what that reference is, then there is a gauge freedom in the description.

The absolute value of the potential has no direct effect. So the choice of it is quite free - the physics is independent of it. If so, then such a choice, such a freedom of choice is called a choice of “gauge” in physics.

Electromagnetism is the first example of a theory with such a gauge invariance that was constructed.

What it means is that many different fields may be chosen that describe the same basic underlying physical situation, and these fields are called gauge fields. Electromagnetism has on the face of it six fields that describe the state of the electromagnetic field everywhere in space. These fields are the three components of the electric field, and the three components of the magnetic field.

But some of the equations of electromagnetism amount to constraints among those six fields that always must be satisfied among those six fields, and so less fields actually matter than six. In fact, four potentials are enough to describe all possible situations, and there is a freedom in the choice of those potentials. That freedom is called a gauge freedom or a choice of gauge.

Interestingly when it comes to making a quantum theory involving the electromagnetic field and its sources it turns out that the four potentials are actually the more basic fields, and that they directly influence the physical predictions, quite independently of whether there are any electric or magnetic fields present in a given region.
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