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I'm limiting my question to this field because it is the only one I know of with a certain degree of knowledge.

I doubt they really exist because of the following reasoning:

Coulombs law was stated because it makes mathematical sense (think of "force directly proportional to the charges and inversely proportional to the radius squared"). Then, someone created this mathematical field be dividing by the force by the test charge and said the electric field is kq/r^2. But I see this only as a mathematical tool, I just can't see how why it is a fact that the electric field exists.

Is there any proof that it exists? I can only think of proving it after measuring a force caused by it, but I don't think that would be proving the electric field exists.

What bothers me most is this jargon of "energy stored in the field". I just can't believe energy is stored in the field, it seems way too magical for me. The way I'm thinking of "energy stored in a field" is as if it were some type of hypothetical case. Like "how much would be released if all the charges creating the field in the system released all their potential energy".

I hope someone can demystify this for me.

Edit: I can see this question might seem like philosophical babble. But it really is not!

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    $\begingroup$ Do you agree that light has energy? Because light is just oscillating electric and magnetic fields. $\endgroup$
    – johnpaton
    Commented Sep 24, 2014 at 17:48
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    $\begingroup$ Related physics.stackexchange.com/q/80912 $\endgroup$
    – Shivam Sarodia
    Commented Sep 24, 2014 at 17:50
  • $\begingroup$ David, you are not going to get a real answer, because mainstream physics doesn't know what electromagnetism really is. We are only given pluses and minuses, backed up with equations and virtual particles, but no real mechanics. None ever explained how attraction might work. We are told that it is mediated by messenger photons. The name tells it all. Yes, physics has become (applied) mathematics. $\endgroup$
    – bright magus
    Commented Sep 24, 2014 at 18:03
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    $\begingroup$ I am sorry that physics does not describe the world according to your satisfaction! However, I could just as easily ask whether charge was just a fundamental tool, since it is used only to make the math work, and, yeah, some measurements can be done that seem to indicate it exists, but I don't believe in them, so tell me how they can be so. Mathematical tools are used by physicists to help concretely describe phenomena that we observe. Whether that description is the actual reality or not is a philosophy question, and not a very useful one at that. $\endgroup$
    – Jon Custer
    Commented Sep 24, 2014 at 18:06
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    $\begingroup$ The first part of the question is basically philosophy, as it depends on what "exist" means. The second half is "I can not believe the widely confirmed fact that EM fields have energy". $\endgroup$
    – fqq
    Commented Sep 24, 2014 at 20:27

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Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. So, if there is force acting on a unit charge, then electric field does exist. It is the way by which we can prove the existence of electric field (as per definition demands). I don't know why you don't believe in it.

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