But that action at a distance is not instantaneous. If you played with fast voltage rise times applied to the self capacitance of an electrode (as I have done) and examined the Coulomb field you would find that any change of field travels at velocity c. This is not EM radiation as it is not a tranverse wave, it is a longitudinal wave along the Coulomb field direction. So I ask myself the question, when I charge a sphere I establish a radial electric field emanating from the sphere, and apart from a small loss due to radiation (that can be minimized by doing it slowly) the energy I supplied is contained in that field that goes out to infinity. I recover most of that energy when I discharge the capacitance. How does the energy in areas away from the sphere travel backwards?
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There is another way of looking at it. The field around each charge is always present, extends to infinity, it is an intrinsic part of the charge. And a charge is conserved. So you can never change the field of a charge, you can't take any energy from it or give it any energy.
Since positive and negative charges are equal in number in the universe, in the general case their fields cancel each other out.
To obtain a field, we must separate the positive charges from the negative charges, and therefore perform work, work that is reflected in the energy that can be withdrawn from the field. The fields of positive and negative charges are effectively superimposed, even when their resultant is zero, since the fields do not interact.
So when you say that by charging a sphere you generate a radial field, this is a partial way of looking at things. By charging a sphere, you shift the field of negative charges from that of positive charges in all the surrounding space, making a non-zero resultant appear. This shift is propagated from near to near at the speed c as you said.
When you get it back, you ask yourself: "How does the energy in areas away from the sphere travel backwards?"
The answer is simple, the energy doesn't travel, unlike the field. The energy of the field is only potential. Such and such a field in such and such a place allows you to recover energy, but the only physical reality is the field, not the energy.
The best proof of this is the interference of two radio transmitters of the same frequency, spaced far enough apart not to influence each other. If we draw a straight line from the antenna of one of them, it will cross areas where the field is double, and others where it is zero, depending on the interference. It is therefore clear that the energy did not follow this straight line, otherwise we would not have a null zone, and that if it had zigzagged from one zone of constructive interference to another in order to pass, it would have had to go at a speed >c because the path would no longer be a straight line.
Once we understand that energy is only the potentiality of a physical condition, we also understand that it does not have to propagate. Energy is a condition created locally by the configuration of the elements of reality in it, such as the field, and this condition, the recoverable energy, depends on the frame of reference and therefore on the observer. Energy is not an intrinsic property of the field.
You ask the question in the context of electromagnetism, but why not ask it for other forms of energy as well? Why don't you ask yourself where kinetic energy is or how it travels? Because again, this is not an element of reality. The car will have kinetic energy if you are on the side of the road, but if you are in the car, its kinetic energy will be zero compared to you. As you can see, the question of the "travel" of energy is nonsense, energy is only a potentiality of local conditions as seen by the observer.
In the near field, you change the superposition configuration of the positive and negative charge fields, so you create distant conditions where energy can be recovered locally, but no more than your charge displacement operation, such as charging a capacitor, will have required.
PS - I may be a little less present in the next few days, I'm off on holiday to visit Cornwall and Wales
. But I'm not giving up on this interesting discussion.
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Topic: Energy from electron spin (Read 12013 times)
