User:Constant314/Physical fields

This essay is an attempt to urge editors to use a consistent notion of a physical field, especially the electromagnetic field.

Real field

Every time I read the intro of electric field, I cringe. It is pretty much 19th century physics. Now, 19th century physics is useful and widely taught, especially to non-physicists. It is great for engineering. Yet it contains misconceptions that hinder and cause frustration for folks trying to “get it” on a deeper level. Let me quote Feynman, which you can read here The Vector Potential. In section 15-4, Feynman says.

"A real field is a mathematical function we use for avoiding the idea of action at a distance."

And

"A “real” field is then a set of numbers we specify in such a way that what happens at a point depends only on the numbers at that point."

The chapter is about the vector potential, but Feynman isn't limiting himself to only the vector potential. He is addressing all real fields, including the electric field.

So, this is my elaboration. The field is made of nothing but numbers. The numbers are not unique. Your numbers may be different from my numbers. Thankfully we have the theory of relativity that allows us to understand each other's numbers. The numbers at each point in the field are useful for computing the forces on particles at that point. The field exists only because we humans find it useful. The field is not physical. It is not fundamental. It doesn't move. It doesn't do anything. It is not attached to charge particles. There is only one field of a given type, therefore the proper article is "the", as in "the electric field." A charged particle does not have "an electric field." Electric fields do not interact because there is only one electric field. Electric fields do not propagate. However, we do say, write, and repeat those things. We can find plenty of examples in reliable sources. It is not wrong; it is a type of jargon. It allows to say things using fewer words. If we were writing carefully what we would say is that a charged particle influences the value of the field in its vicinity. The values of the field change dynamically over space and time in accordance with a wave equation. The electric field is such a useful and reliable artifice for computing outcomes, that we sometimes tend to think of it as a physical thing. It is not. It is nothing but imagination. The electric force is real. It does things. The electric field is a purely human construct. Once you embrace that, you can stop wasting time by asking unanswerable questions.

I am not proposing to rewrite the entire article, but only the first few sentences.

Quotes

• Richard Feynman The Vector Potential. In section 15-4,

• "A real field is a mathematical function we use for avoiding the idea of action at a distance."
• "A “real” field is then a set of numbers we specify in such a way that what happens at a point depends only on the numbers at that point."

Comment: Feynman does not say that a real field is something that can be represented by numbers. He says that a real field is numbers.

• John David Jackson

"It [the electric field] is a vector function of position, denoted by E."

Comment: A vector function is just an ordered set of numbers. This is all Jackson says.

• Edward M. Purcell

"Is it [the electric field] something real or is it merely a name for a factor in an equation ... since it works, it doesn't make any difference."

Comment: You can assume that the electric field is something real and I can assume that it is nothing, but numbers attached to points in space, and we will both get the right answer. If you assume that the field acts in anyway different from numbers attached to points in space, you will get a wrong answer.

• David J. Griffiths

"I encourage you to think of the field as a real physical entity ... I can't tell you, then, what a real field is -- only how to calculate it and what it can do for you once you've got it."

Comment: Griffiths likes to think of the field as physical. Many people also think that. But he is not going to tell you that it is physical, because he cannot. He cannot give you any reason to believe that the field is anything other than numbers attached to points in space. But notice the words he uses. He can tell you what the numbers that you calculate can be used for, but he does not say that he can tell you what the field does. Numbers cannot do anything. If Griffiths could tell you anything that the field does, that numbers attached to points in space cannot do, then he would have evidence of the field being physical.