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Is the concept of a field just a mathematical construct? Is there any way to realize its existence? For instance, the fact that moving a charge affects other charges in the surrounding not instantaneously is explained in terms of the existence of an electric field. Is there no other approach to this problem?

innisfree
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Adrian Joseph Alva
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  • A field is something that has a value at every point in your coordinate system. Temperature is a field, for example. The fact that moving charges don't affect other charges instantaneously is explained by the speed of light, not by the electric field – Jim Jul 09 '15 at 15:20
  • This is more a philosophy question than one of physics. Physics is the attempt to describe nature using models. It's nonsense in physics to ask for the "meaning" of a piece of the model. Fields, like everything else in physics, are mathematical constructs that describe certain interactions in nature. Mathematically, they are useful due to the principle of locality (two bodies can only interact at the same point in spacetime). All we can say about fields is how this [mathematical object] evolves in time and how it affects the time evolution of other [mathematical objects] in physics. – Ultima Jul 09 '15 at 15:24
  • Adrian, can you clarify what you're asking? A pressure field or temperature field has an obvious physical relevance, though these are properties of a medium. I wonder if you really asking about the physical reality (whatever that means) of fields that don't require a medium, for example the electrostatic field or gravitational field. – John Rennie Jul 09 '15 at 16:02
  • Yes, my question is pertaining to fields that do not require a medium. – Adrian Joseph Alva Jul 09 '15 at 16:09
  • Yes, my question is pertaining to fields that do not require a medium. @JohnRennie – Adrian Joseph Alva Jul 09 '15 at 16:18
  • About the reality of electric and magnetic fields see my paper. – HolgerFiedler Jul 09 '15 at 19:48

2 Answers2

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Does a field have any physical meaning or significance?

Yes. See Einstein talking about field theory in 1929 and note this: "The two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric". This is Einstein saying a field is a state of space. When you play around with a couple of magnets feeling attraction and repulsion, it's because of the space between those magnets has a different state to the space between my two hands. It's similar for a gravitational field. The state of space in the room you're in is different to the state of space way away from any stars or planets.

Is the concept of a field just a mathematical construct?

No. See above.

Is there any way to realize its existence?

Yes, you let go of your electron, or your pencil. If it stays put you tend to say there's no field there.

For instance, the fact that moving a charge affects other charges in the surrounding not instantaneously is explained in terms of the existence of an electric field. Is there no other approach to this problem?

Yes and no. See the Wikipedia Coulomb Law article and note this: "An electric field is a vector field that associates to each point in space the Coulomb force experienced by a test charge". Also see the Wikipedia electromagnetic field article: "Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole — the electromagnetic field". The electric field describes the force between two (or more) charged particles. It doesn't describe the state of space where one particle is. The electromagnetic field does that, and the force is the result of the interaction of two electromagnetic fields. Remember this: a single charged particles doesn't feel any force at all, because it takes two to tango.

John Duffield
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Field is a mathematical notion. It is possible to formulate electromagnetic theory with particles in such a way that the field is not needed. This is due to Fokker and Tetrode, I think. More accessible reference is the paper (the part about the absorber is additional, not needed for the theory to work without fields):

J. A. Wheeler, R. P. Feynman, Classical Electrodynamics in Terms of Direct Interparticle Interaction, Rev. Mod. Phys., 21, 3, (1949), p. 425-433. http://dx.doi.org/10.1103/RevModPhys.21.425

Ján Lalinský
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