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.
Best Answer
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.