I have an instinct that I have not yet framed into some sort of theory… I feel that our notions of “force” and “acceleration” are not quite calibrated correctly, philosophically speaking. Their math works out, and that’s fine for that level of thinking, but when it comes to how we THINK about Force and Acceleration… I’m not sure we know what we’re really talking about.
For one thing, Newton, who first quantitized our modern concept of Force, originally said it was momentum-per-time-unit, which we today formulate as mass-times-acceleration…
[here’s how the two statements above are equivalent for my fellow nerds: momentum (call it “p“) is mass-times-velocity. So, Newton’s formulation of Force would be F = m*v/ t where the “v” (velocity) equals change-in-distance-per-time, making the entire v/t term equal to… change-in-distance-per-time-PER TIME…which IS acceleration… thus F=p/t as well as F=m*a).]
However, I’ve also seen Force defined as… [avg acceleration] * time, with no mass included in the formula (although, this could have been an erroneous formulation).
And in his book, The Science Of Mechanics, Ernst Mach defines Force thusly… “Force is any circumstance of which the consequence is motion.” –– and yet– he, himself, points out that forces “may be so conjoined that in the result there shall be no motion.” (This is basically the science of “Statics.”)
When we move to the “fields” (haha) of Magnetism and Gravity, we begin hearing Force spoken of as if it’s some sort of Cloud Of Energy which travels through Space (with or without need of a medium) in so-called Lines Of Force.
And if one defines Force as “that which changes velocity” or “that which counteracts inertia”… uhm, where precisely is the “that” at?
I’m always relieved to bump into other doubters of orthodoxy along my lonely path… and while reading my Mach, I discovered that Hertz also did not have much truck with this notion of “Force,” saying that the several Forces proposed by physicists were no more than “empty-running wheels.” Hertz was convinced that masses are only affected by other masses. There is no “Force” moving magically through Void-Space without need of a medium. Where we do not discern the affecting masses, they are simply hidden to our perception. Furthermore, when we find a mass behaving as if being acted upon by a “Force,” you can bet that whatever is happening, the mass in question is attempting to alter its course as little as possible.
Neumann theorized that if we could have direct knowledge of the true relationships of masses, we could account for their complex multiplicity of interactions by using powerful “integral laws” and that “the concept of ‘Force’ will have become superfluous.”