"Newtons system was for a long time considered as final and the task... seemed simply to be an expansion.... The first difficulty arose in the discussion of the electromagnetic field in... Faraday and Maxwell. In Newtonian mechanics the gravitational force had been considered as given... In the work of Faraday and Maxwell... the field of force... became the object of the investigation... they tried to set up equations of motion for the fields, not primarily for the bodies... This change led back to a point of view...held... before Newton. An action could... be transferred... only when the two bodies touched... Newton had introduce a very new and strange hypothesis by assuming a force that acted over a long distance. Now in the theory of fields... action is transferred from one point to a neighboring point... in terms of differential equations. ...the description of the s... by Maxwells equations seemed a satisfactory solution of the problem of force. ...The axioms and definitions of Newton had referred to bodies and their motion; but with Maxwell the fields... seemed to have acquired the same degree of reality as the bodies in Newtons theory. This view... was not easily accepted.; and to avoid such a change in the concept of reality... many physicists believed that Maxwells equations actually referred to the deformations of an elastic medium... the ether... the medium was so light and thin that it could penetrate into other matter and could not be seen or felt. ...[H]owever ...it could not explain the complete absence of any longitudinal light waves."
In physics, a force field is a vector field corresponding with a non-contact force acting on a particle at various positions in space. Specifically, a force field is a vector field , where is the force that a particle would feel if it were at the position .
"The theory of relativity... showed in a conclusive way that the concept of the ether as a substance, to which Maxwells equations refer, had to be abandoned. ...the result was that the fields had to be considered as an independent reality."
"He was little interested mathematics or theory; for example, when his ideas on magnetic fields were extensively developed later by [James Clerk Maxwell] (1831-1879), Faraday was little concerned with the results. His own scientific career was characterized by simple ideas and simple experiments."
"We shall therefore assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system."
"The physicists definition of a field is the following. Its something that ... is spread everywhere throughout the universe. Its something that takes a particular value at every point in space. And whats more, that value can change in time."
"In order to appreciate the nature of Maxwells contributions, let us recall how matters stood in his day. ...Faradays law of induction ...states that a variable magnetic field generates an electric field. Maxwell, however, considered that this law, standing alone, lacked symmetry; so he formulated the hypothesis that conversely a variable electric field should generate a magnetic one, and proceeded to construct his theory... no experimental results could be claimed to have justified any such assumption... His celebrated equations of electromagnetics represented, therefore, the results of experiment, supplemented by this additional hypothetical assumption. The advisability of making this hypothesis was accentuated when it was found to ensure the law of conservation of electricity. ...In the particular case of free space in which only fields but no charges or currents are present, Maxwells equations of electromagnetics, termed field-equations (since they describe the state of the electromagnetic field), can be written:"
"I just want to explain what I mean when I say that we should try to hold on to physical reality. We are … all aware of the situation regarding what will turn out to be the basic foundational concepts in physics: the point-mass or the particle is surely not among them; the field, in the Faraday-Maxwell sense, might be, but not with certainty. But that which we conceive as existing ("real") should somehow be localized in time and space."