I often see when an article or text describes a "field of force" (for this question lets use the electric field) that they say that its a "forces at a distance". Whats going on here? How does a field interact with an object in such field? (Positive test charge in an electric field of a much bigger positive charge or negative charge, etc) I'm having a hard time visually understanding whats going on...any clarification would be much appreciated, cheers!
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A field, such as the electric field, is an hypothesized entity.
The type of phenomenon that is observable is motion.
For example, an analog oscilloscope.
(Nowadays the display of an oscilloscope is a display screen like the display screen of a computer. An analog oscilloscope is the historical design, with an actual electron emitter, and deflector plates to create the electric field that deflects the electrons.)
What is observable is where the electrons strike the fluorescent screen.
Another example is a cloud chamber From the condensation trail the trajectory of the particle can be inferred, and from that properties of the particle such as mass can be inferred.
No experiment exists that can directly show something about the electric field. The effect is always indirect: motion of charged particles is being affected.
There are compelling reasons to hypothesize the Coulomb field.
The theory of the electromagnetic field describes the electromagnetic field as mediator of electromagnetic interaction.
A change of a source of electromagnetic interaction is not felt immediately at distance. Any change takes a finite time to propagate. As we know, the speed of this propagation is equal to the speed of light.
My understanding is:
It is mathematically possible to formulate a theory of electromagnetic interaction without introducing a mediator of the interaction. Then each interaction is described as occuring directly from particle to particle. But such a mediator-free theory still has to accommodate that a change at a source propagates at finite speed.
Also: We know that is is possible to emit electromagnetic waves, and these waves keep propagating after the original source has gone away. How to accommodate that when trying to formulate a theory of electromagnetic interaction that does not use the concept of a field?
So the general concensus in the physics community is that the existance of the electromagnetic field must be granted.
What is known about the properties of the electromagnetic field is known through inferring. When you hypothesize something, you want to be minimal about it. You hypothesize the minimum that is sufficient to formulate the theory that you need.
What if physicists would have insisted on first being able to understand fields visually, and only then start to use it in theories?
If they would have done that they would only have bogged themselves down.
In physics, in order to make progress it often happens that something must be granted. Occasionally it happens that after many years something that was initially granted is explained, but there is never a guarantee that will happen.
