We all know that objects create fields and force is about what happens when an alien object is influenced by fields. Why is it necessary to use the concept of a field influencing objects to explain the force between two or more objects?

  • $\begingroup$ It is not necessary. Fields are not observable. They are a part of phenomenology (language, so to say). You can come up with any alternative way of describing forces if you want. $\endgroup$ – MsTais Aug 1 '17 at 15:59
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    $\begingroup$ How did Faraday and other people find fields as a good way or good language to describe forces? That's what I tried to convey, actually. $\endgroup$ – Sashank Sriram Aug 1 '17 at 16:28
  • $\begingroup$ I think a lot of that grow from E&M actually. They had to describe force at a distance without direct interaction. They had to accept that energy in the form of potentials has to have a way to be passed over from one object to another through empty space. The precursor of the modern Field was 1) the idea of potential 2) Ether theory. $\endgroup$ – MsTais Aug 2 '17 at 2:08

It's not absolutely necessary, but it is useful.

Fields turn forces into radiation

Just to take a step back to the idea's first unambiguous victory, James Clerk Maxwell published the paper On Physical Lines of Force in which he imagined that all of space was somehow filled with field lines and little fluid vortices and such; he devotes a lot of thought to the "tension" in the ether, which is an idea that we would find much more difficult today.

Some of the background to this paper is covered in this reference[pdf], but to cut the long story short there appear to have been three other key figures working on electromagnetism at the time: Weber, Kohlrausch, and Ludwig Lorenz. (There are multiple Lorentz/Lorenz names that figure into early electrodynamics.) Weber's theory was about the forces between moving charges and contained a speed which related electrically-measured charge and magnetically-measured charge, this factor was apparently also named $c$ but we would now regard as $c_W = c \sqrt{2},$ off by a constant factor. Kohlrausch had observed that one prediction of Weber's theory was that electrical signals propagating in conductors should propagate with speed $c_W/\sqrt{2}.$

Maxwell's huge win, also apparently discovered by Lorenz independently, was that now that he had this theory of an aether, a field permeating all of space, he could use these ideas of tension in the lines and vortices and whatnot to think about what the transverse excitations of this medium would look like: and he indeed also discovered that those transverse excitations would propagate with speed $c_W/\sqrt{2}.$ Calculating out this number, Maxwell says:

The velocity of transverse undulations in our hypothetical medium, calculated from the electro-magnetic experiments of MM. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau, that we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.

This is now essentially our mainstream account of light. We sometimes revert to a particle picture to talk about photons, but those are today understood to be excitations in an underlying quantum field.

This is really a broader feature of fields in general: classical or quantum. Imagining forces as coming from a field permeating space, one can immediately test this by understanding whether there are vibrations in that field which can be picked up by very sensitive force-detectors for that force. We don't know how to properly quantize gravity, but we do know from general relativity that its force-effects are described as tensor fields over space, and this has led to a prediction of gravitational waves. Creating observatories which can measure these gravitational waves has been a mammoth undertaking, but we now are reasonably sure that we've been able to see them.

Fields also allow more structured mathematics

In addition to the above purely physics reason, there is also a pure-laziness reason as well. A lot of where science goes is driven by the great virtue of laziness; lazy grad students allow great conceptual simplifications because the mathematics is easier to work with.

Fields are very similar. If you are dealing with point charges then you have an annoying problem: each particle exerts forces on all the other particles but not on itself. It's usually the same with any "stuff" even if it's not charge: you have this annoying problem of calculating how each bit of stuff interacts with the others. But if you smear that stuff out over space a little bit you get a scalar "density field" and with a little bit of motion you get a vector "current density field" too. Now instead of dealing with a lot of individual items, you get to use theory-tools for vector and scalar fields, in particular multivariable calculus like divergences and curls and Laplace operators. Other questions like "is this expression acceptable according to the principles of special relativity" can often be done by inspection at these field levels. Very often a field is described nicely by a Lagrangian density, which is a nice bit of mathematics that lets us quickly prove that certain values are conserved and quickly switch to new coordinates to let us more easily solve problems. In one celebrated victory, the Aharonov-Bohm effect was predicted very easily from our electromagnetic field theory and the (non-field) Lagrangian that it implies.

So if you're lazy -- and laziness is often a good thing for science -- then you will just be saying "yeah, yeah, let's suppose the fields are real, whatever -- does that give me the answer easily and quickly?" and the fact is, it does. So that's why we get great scientific value from supposing that the world is filled with these fields, even though it's not absolutely necessary.

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The use of fields to explain forces is bascially optional, however fields become well nigh essential is in dealing with energy and momentum conservation in at-a-distance interactions.

Energy and momentum can leave one object and only later be transferred to another object. This would present a problem if you try to do without fields because the energy and momentum wouldn't be anywhere in the mean time—our conservation rules would fall apart.

But in the conventional picture fields carry energy and momentum, so those quantities are present in the fields en route and the books balance at all times.

We can also test this notion that fields carry energy and momentum with tools like radiant heaters (for energy) and light sails (for momentum). The former is such a common experience that you've done it yourself. The latter is a little more esoteric, but has also been put to the test.

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