Suppose that we are not allowed to use the notion of force to describe nature.

My understanding of general relativity says that won't be a problem because the Einstein field equation doesn't involve a gravity force. A freely falling particle follows the path of a geodesic in spacetime.

Also my understanding of quantum field theory shows that in particle physics when calculating the Feynman diagrams what is involved is the exchange of off mass shell particles in an interacting theory.

Now the first question is that if we can use these virtual particles not only in particle scale but also at the scale of two charged objects and therefore discard the notion of an electric "force" without much trouble.

The second question which is related is if we can learn and teach modern physics theories, in principle, without the notion of "force" at all?

Imagine pushing or pulling an object, for instance. Can we describe the motion without invoking "forces", in particular, in dynamics as opposed to kinematics.

If not and we need forces, what are the benefits involved, say simplifications, given the fact that underlying theories do not require it and they are not fundamental?


closed as primarily opinion-based by Kyle Kanos, John Rennie, CuriousOne, ACuriousMind, user36790 Mar 12 '16 at 19:27

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    $\begingroup$ It isn't obvious what answer we're supposed to give here. You're obviously familiar with the technical issues, so the question seems more whether physics could be effectively taught without mentioning forces. $\endgroup$ – John Rennie Mar 10 '16 at 17:35
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    $\begingroup$ Can we describe the motion of macroscopic objects without invoking "forces", in particular, in dynamics as opposed to kinematics? $\endgroup$ – user56963 Mar 10 '16 at 17:42
  • $\begingroup$ Why would you discard something that works so well? You have to be aware of the limitations and when it doesn't work, of course. $\endgroup$ – CuriousOne Mar 11 '16 at 0:16

Can we describe the motion of macroscopic objects without invoking "forces", in particular, in dynamics as opposed to kinematics?

Lagrangian and Hamiltonian mechanics do exactly that (getting everything the need by considering energy and (generalized) momentum). Indeed, if you want to get information about forces out of those frameworks you have to invoke more complicated versions of the frameworks.

But here is the thing: you can get information about forces out of them. Force hasn't gone away, it has just been tucked into a corner, so these theories don't say that force is somehow "not fundamental", they say it is simple one of several ways to understand physics.

  • $\begingroup$ Isn't this kinematics? But what about dynamics? Does it make sense without force? $\endgroup$ – user56963 Mar 10 '16 at 18:58
  • $\begingroup$ No. The three frameworks are equivalent to one another. Any thing you can get from Newtonian mechanics you can get from the other two as well. $\endgroup$ – dmckee Mar 10 '16 at 19:37
  • $\begingroup$ I think you should probably mention that not only do neither Lagrangian nor Hamiltonian mechanics discard forces but that there are plenty of problem classes for which neither Lagrangians nor Hamiltonians can even give the right answer. Classical mechanics is more than just those two frameworks and that's pretty much acknowledged in the theory books that I am aware of. Since most of those books are preliminaries to QM and relativity, though, they do not discuss non-Lagrangian and non-Hamiltonian scenarios in great detail, which, on some level, is a pity. $\endgroup$ – CuriousOne Mar 11 '16 at 0:19