The title about says it.
I have been thinking and reading a little about the electromagnetic potential and it gauge invariance lately. In simple, but absolutely correct terms, you can think of Gauge Invariance like this:
Electrons only respond to the slope of the voltage potential, and not the absolute value. So if you take any circuit, experiment, etc, planet, etc and add a million volts everywhere, no one will be able to tell, except people who look in from outside the circuit or planet.
This fact led physicists to renounce the potential as something real, and instead pronounce it as only a mathematical tool, useful for getting the field, which is the ‘real thing’. So in other words, ‘Voltage is not real’. Sure feels real to me when I get a shock from static or touching the wrong wire! But physics says its the potential difference that matters, and not the potential iteself. Point taken.
Then along comes the Aharonov-Bohm Effect (David Bohm is one of my heroes in physics). It describes an experiment where electrons can detect a change in the potential – where the changes result in no fields. In other words it seems that electrons can see this potential. To me, this is a sign that this potential is real. To others of course, its not.
Richard Feynman seemed to think more along the lines of the ‘potential is real’ camp.
So if its real, what gauge did nature choose? In other words what is the voltage of the universe? I of course don’t know, but if we assume that there is some real fixed gauge, then what could be the consequences?
1) No consequences for local experiments, etc.
2) Perhaps there are things on a larger scale that do arise from this permeating ‘potential’ everywhere. Could this potential (i.e. voltage) be real in the sense that it is made out of something? That is the crux. Its certainly not made of photons, like the electric field. My thinking of course is that it is made of gravity – standing wave patterns in space that make it possible for these varying mass electrons to communicate (feel force) from other electrons and particles operating at the same (super high 10^50Hz) frequencies.
Could this potential, if its real, be Dark Energy?
— Tom Andersen
Feynman, R. The Feynman Lectures on Physics 2. pp. 15–5. “knowledge of the classical electromagnetic field acting locally on a particle is not sufficient to predict its quantum-mechanical behavior. and …is the vector potential a “real” field? … a real field is a mathematical device for avoiding the idea of action at a distance. …. for a long time it was believed that A was not a “real” field. …. there are phenomena involving quantum mechanics which show that in fact A is a “real” field in the sense that we have defined it….. E and B are slowly disappearing from the modern expression of physical laws; they are being replaced by A [the vector potential] and [the scalar potential]“