A couple of weeks ago Derrick Muller of the YouTube Channel Veritasium made a video asserting that the electrical energy in a circuit does not flow through the wires but through the fields. This is true and yet also a misleading misconception. This misconception in his problem arises because it deals with a circuit loop that reaches from the Earth to the Moon and back with a one-meter gap between the wires. He also uses a definition of the light being “on” which seems to be having any minuscule amount of current flow through the bulb. Then he justifies this will completely correct classical, non-relativistic electromagnetic theory. When in reality to address the problem, he asked fully would require Quantum Field Theory (QFT) or more specifically Quantum Electro Dynamics (QED).
What are QFT and QED
In Quantum Mechanics everything is a question of probability. We compute the probability of a given measurement being observed when a system we are studying is in a specified state.
In Special Relativity we compute the trajectory of a system given the postulates that the laws of physics must not change depending on your reference frame and that the speed of light must be constant in all reference frames. When the speed of light is relevant to a problem and cannot be ignored this is the framework that must be used. We can ignore gravity and General Relativity as its effects would be small in this problem.
Quantum Field theory unifies Quantum Mechanics with Special Relativity in such a way the idea of particles VS fields is nearly meaningless. Every particle is or can be a field and every field is or can be a particle. What we solve for in QFT are the probability amplitudes and cross-sections for various interactions between particles and fields. A simple way of thinking about this idea of a probability cross section would be to think of it as if each particle was a little sphere whose “size” varied depending on the interaction it was in. The bigger the cross section the more likely the particle/field will interact with another particle or field. (Clearly this is an oversimplification of the subject for the sake of simplicity.)
A clear, concise, and easy to understand example would be the concept of the bare charge VS the dressed charge. Every electron would be surrounded by many many virtual electron positron pairs which shield us from the full bare charge of the electron.
This effect would extend out, decreasing by a factor of 1/4 every time the distance is doubled or by a factor of 1/9 every time the distances is tripled. This is known as the inverse square law. Classically it would lead to the conclusion that there is no probability of energy transmission without the wires.
Let us consider placing a light bulb one meter away from a battery with no wires connected at all. Can the light bulb ever be “on” that is, can it ever have a single electron of current induced in it by the presence of that battery one meter away. The answer is yes, but the probability of this happening is very low. So why do we connect wires? A wire is nothing more than a set of particles/fields which are very close together. Molecular distances apart, nanometers apart. This makes the probability of an interaction being induced by a neighboring charge millions to billions of times more likely. So, it is not that energy flowing in the wire is a fluid like flow of electrons or waves of them moving back and forth. It is a field that propagates millions or billions of times more easily in the wire where the electrons are.
In short, this Veritasium video is mostly wrong since 99.9999999% of the energy will be transmitted through the wires, but it is right that it is fields which transmit the energy. Just not classical fields. The quantum scale fields in the wires are what transmit the vast majority of the energy. A tiny current a “leakage current” at best is what would be observed. Their video is correct in the sense that they have stimulated thought. Just do not change your basic introduction to E and M based on it.
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