I teach Physical Science 101 on an adjunct basis, so I’m familiar with the basics (Newton’s laws of motion, F = ma, vector addition, etc.). No problems there. But I often ask myself, “What is a force?” It seems so abstract compared to things like length and mass. The best definition I can come up with is, “Force is an odorless, colorless… thing that causes a mass to accelerate.” Or put slightly differently, “If a mass is accelerating, there is a mysterious, invisible thing we call ‘force’ that is causing the mass to accelerate.”

I guess what I’m asking is this: is force a real, objective entity? Or is it an invention to make it easier for the human brain to conceptualize and make the math easier?

That is a question that has been long, and hotly, debated in the philosophy of science.

That being so, this is much more of a GD than a GQ question.

The last time I was paying attention to the professional, academic debate, the realists, who hold force to be a real, objective thing, were in the ascendant (although far from unchallenged), but that was quite some time ago, and things may well have gone the other way since then. It is quite possible that force-instrumentalism has made a comeback.

It is also possible that some forces (e.g., gravity or electrical attraction) are real things, whereas others, such as a resultant force calculated via the parallelogram of forces, are not, but are mere mathematical conveniences.

Leaving aside the metaphysics, it’s a big question for which there isn’t entirely satisfactory answer. You can define force as dp/dt or ma, but then why do we talk about forces in statics where there is always no change in momentum/acceleration?

Missed edit window: I have also heard the opposite argued: that a resultant force is real, because it actually accelerates something, whereas the components that comprise it are not.

The point, however, is that there are lots of positions apart from “all force is real” and “all ‘forces’ are just mathematical fictions”, and not much consensus.

There’s gravity, electro-magnetism; forces which act through distances using fields (or distortion of space time?)
imparted momentum by contact; I suppose even radiation (force of sunlight) can be momentum transferred from photons?

Force in a stretched spring is basically the pull of stretched electromagnetic crystal/molecular bonds to return to the point of equilibrium?

At the middle school level, the definition is simply “A force is a push or a pull”. Which usually satisfies students, but if you think too hard about it, it shouldn’t. What is a push or a pull? They’re both kinds of forces. We’re used to pushes and pulls, and so we think we understand them.

I agree with Chronos. But then, after wrestling with the “what is a push or a pull?” for a while and debating with myself throughout my physics career on what a force is or isn’t, I’ve gone back to being perfectly happy with a force being a “push or a pull” and I try not to think about it too hard anymore after that!

Don’t even get me started on what Energy is though, please!

In most cases, it’s easier to call force the derivative of a potential and worry about what “potential” means. I’m not sure how to define that other than a wishy-washy description like “something that causes changes in a system” or a purely formal description like “a particular term that appears in Newton’s laws / Euler-Lagrange equations / action principle / Schroedinger’s equation / etc.” In any case, you have to start with some first principles; that’s what separates physics from math. I can’t argue that “a push or a pull” is anything besides an utterly awful and unhelpful description, though.

Actually, this one’s easier: Physics is invariant under time, so Noether’s theorem gives a conserved current that we call (total) energy. (By ‘invariant under time’, I don’t mean that every system is independent of time; I mean that you’d get the same results if you put t = 0 now versus putting it at midnight yesterday. Also, you want your potential to be time-invariant, blah blah blah. There are also other things called energy as well.)

Is it, though? Weighing things is concrete enough, but that’s begging the question; you’re considering weight (a force), not mass, and you’re implicitly assuming that the m in F = ma (inertial mass) is the same m that appears in the gravitational mass. Which it is— but it’s a bit disingenuous to claim that mass is completely concrete and intuitive. The mass of a neutron is two orders of magnitude greater than the sum of the masses of its constituent quarks. Again, that’s not problematic or inexplicable, but it does suggest that mass isn’t as simple as ordinary experience would suggest. Length gets complicated in relativity, and even ordinary, completely Newtonians ideas of length implicitly assume that we live in a flat universe where scaling and translation make perfect sense.

The content of Newton’s law isn’t just that given a series of forces, we can compute the resulting acceleration on a particle. The point is that forces universally act that way: they accelerate things inversely proportional to mass, which you can (rather circularly) take as a definition of a force. You have to start with some background (or else you’re just rambling about philosophy, and nothing ever gets done), and Newton’s laws are the start of physics; forces are as good a place to start as any.

The idea of force doesn’t generalize nicely to further physics, though; the usual formalism there is in terms of Lagrangians, which are built up around potentials rather than forces. I find the former nicer conceptually than forces themselves; your mileage may vary.

I have a related question I’ve been meaning to ask for a while: when analyzing units, division is pretty intuitive. It’s the “per”, or to rephrase it “for every”. So m/s is “for every second, there is a meter”. For multiplication, multiplying with the same unit is pretty intuitive. M^2 is just a grid of meters. However, I could never get my head around any intuitive sense of what multiplying unlike units meant.

This ties into this question in that 1Newton = 1 kgm/(s^2). What does it mean to multiply a kilogram by a unit of acceleration. Or take Nm (Newton-meters), what does it mean to have force times meters? N/m would be self-explanatory, for each meter, a unit of force is applied. Yet N*m isn’t that self explanatory, despite being a Joule (or, if you prefer, the unit for torque).

To a certain extent, I think this question can be answered only in quantum mechanics. A while back, I have attempted to do so, mostly via analogy and pretty pictures, rooting force ultimately in the quantum phenomenon of interference. Of course, this opens up other questions, such as why quantum mechanics works the way it does, but I think this simply goes to show that we haven’t arrived at a complete answer of this question yet.