How do forces work

Question

Is there a mechanistic-type explanation for how forces work? For example, two electrons repel each other. How does that happen? Other than saying that there are force fields that exert forces, how does the electromagnetic force accomplish its effects. What is the interface/link/connection between the force (field) and the objects on which it acts. Or is all we can say is that it just happens: it's a physics primitive?

A similar question was asked here, but I'd like something more intuitive if possible.

Answer 1

Quantum Mechanics says force is not physics primitive. It shows the undelying mechanism for them.

What is a force? It is something that changes the velocity of a particle, with the Newton's second law: $$\vec{F}=m\dfrac{d\vec{v}}{dt}$$ Any other appearances of forces can be reduced to this. For example, when we measure the force with a dynamometer, it is actually two forces aplied to the same particle, and they cancel each other when the particle reaches the offset equilibrium position.

Without any force, the particle would move with the same velocity $\vec{v}=\mathrm{const}$. But the Quantum Mechanics shows a more complicated picture: the particle is distributed in space, and depicted as a wave packet. Its evolution (motion and change) without a force is governed by the Schrödinger wave equation $$i\hbar\dfrac{\partial\Psi}{\partial t}=\dfrac{-\hbar^2}{2m}\nabla^2\Psi\qquad\left[=\dfrac{-\hbar^2}{2m}\dfrac{\partial^2\Psi}{\partial x^2}\quad\text{(in 1D space)}\right]$$ That does say the same thing, $\vec{v}=\mathrm{const}$, but in a sense that all velocity components of the wave packet (that is, its Fourier coefficients) evolve constantly in time, and independently on each other. But that's the mathematical abstraction. Physically, it tells some different story: the wave function oscillates and flows. The rate of oscillations is what we call enegry, and the flow is kept up by the gradient of the phase.

Then, what happens when a force appears on the scene? We should add the potential energy of that force to the Schrödinger equation: $$i\hbar\dfrac{\partial\Psi}{\partial t}=\dfrac{-\hbar^2}{2m}\nabla^2\Psi+U\Psi\qquad\left[=\dfrac{-\hbar^2}{2m}\dfrac{\partial^2\Psi}{\partial x^2}+U\Psi\quad\text{(in 1D space)}\right]$$ What happens to the wave funtion then? It starts to oscillate with higher rate in some points (where $U>0$), while with the same rate in some others (where $U=0$). Because of that, the phase in the first points would outrun the phase the second points. And the gradient of phase tells the wave function to flow away in the direction of the retarding phase. So the particle would run away from the place where the potential energy is high! That's how forces work.

Answer 2

The interface between the force(field) and the objects is what we call "charge". Electromagnetism, for example, does not excert any force on an electrically neutral object.

In a very crude way, you could imagine charge as the hooks, on which the springs that mediate the force are hung.

One has to be careful with Newton's graviation, however. It works fine for everyday applications such as falling bodies etc. to picture the graviational charge as "mass". A massless object is weightless from this point of view. This is not true in general relativity! There, mass bends space itself and photons, too, are subject to it, albeit not having any (rest) mass.

The similarities between Newtonian gravitation and electromagnetism go quite far. You could imagine the electromagnetic potential as a mountain at the position of one electron from the point of view of another. The repelling force then acts like a ball rolling up a slope and down again.

Answer 3

A force is the name given to a physical measurement that isn't a physical property of an accelerated mass, but still allows us to predict a value for its acceleration, given the numerical value of a force present.

The only interpretation of force which physically matters is how you assign a number to it.