[“Quantum foundations” series]
Force-less physics? No, I do NOT mean that the language of forces (electromagnetism, strong, weak, gravity) does not apply to our everyday experience or to physical descriptions. But only to a point, yes, as maybe counterproductive to deeper understanding. To getting beyond the Standard Model . To understanding how the wave function is an approximation. And taking quantum field theory (QFT) really seriously.
QFT is hard, a combination of the hardest and most important physics. Lots of infinite quantities. Hilbert spaces. Normalizing. Best way to describe nature at its deepest level. – my note from Sean Carroll’s YouTube video The Biggest Ideas in the Universe | 9. Fields
It’s really all about energy. And how that contoured energy emerges in terms of forces. 
So, if the best analogies (or metaphors) for explaining “forces” are tossing objects back & forth, then something’s still “fishy” about quantum theory.
Subatomic forces at the quantum level are best understood as a cloud of force-carrying particles jumping from one object to another. – Don Lincoln 
In one case, for repulsion, analogies use scenarios of standard objects thrown back & forth between “agents” (people, automata, etc.) on a slippery surface. Thrown = emitted. Caught = absorbed. The actions and reactions cause the agents to move apart. Throwing pushes the thrower away; catching pushes the catcher away. So, the agents move away from each other. [Find a video of an actual demonstration?]
In the other case, for attraction, analogies use scenarios of peculiar objects thrown back & forth. Objects that carry momentum in a contrary direction. Objects like boomerangs. For example, agent #1 throws a boomerang in the opposite direction to agent #2, but it loops back toward and around agent #2, who catches the boomerang as it’s going back toward agent #1. Throwing pushes the thrower toward; catching pushes the catcher toward. So, the agents move toward each other.
Moving up a level of understanding, Feynman’s sum over all (possible) paths of exchanged (virtual) particles results in a net metaphorical hill or valley of action/reaction energy between the agents. Hill = repulsion. Valley = attraction. At least in this case, for the electromagnetic (EM) force, there’s only one type of photon rather than standard and boomerang types. [Find a visualization of that?]
Can we do without swarms of force-carrying particles?
Can’t we at least imagine some visualizations involving fluids and pressure gradient differences?
Sure, there are limits to any analogy. A point where any metaphor becomes a counterproductive rabbit hole. But can’t we do better? There’s just something so lacking in analogies presented by physicists. (Perhaps that’s why quantum theory is incomplete as well?)
I’m surprised that veteran physicists and seasoned science communicators can’t do better. I expected more in the last 50 years. Perhaps there’s just no practical reason to pursue better visualizations. After all, in practice everything works just fine. Calculations to 12 decimal places! Technology advances. Career-wise, not much incentive to speculate, more motivation to compute or advance exotic mathematical frameworks.
But there’re problems. Nags that quantum theory is incomplete. Unsolved problems in physics.
So, in quantum electrodynamics (QED) and quantum chromodynamics (QCD), there’re so-called matter particles and “force carrying” particles (bosons). Feyman diagrams are visual ways of organizing the complex math. Physicists recognize that particle exchange really is about field interactions. But visualization goes no further.
Interaction between vacuum energy (of so-called empty space) and field energy is left as “the dance of quantum activity that includes virtual quarks … in the hubbub of virtual activity that surrounds all particles.” 
Feynman diagrams are shorthand accounting. Virtual “force particle” exchange is just a visual way of accounting for a more complex way in which energy density – field potential, is shaped. And contoured energy density sort of sounds like fluid dynamics, eh.
But when I think of sum over all paths, I think of interactions of expansive, extended vibrations in spacetime, not particle paths. Like waves moving in all directions (vs. moving along paths). As Carroll says in his YouTube video The Biggest Ideas in the Universe | 8. Entanglement: “Some smushy spherical disturbance, going off in all different directions.”
And when I think of (matter) fields, I think of interacting excitations. Extended in space and time. Superimposed excitations. Entangled excitations. And the energy in spacetime contoured by “charge.” Contoured so that net gradients between excitations may be characterized as repulsive or attractive.
 In the sense that we tend to identify forces with the (spatial) derivatives of (field) potential.
As I’ve written elsewhere:
Metaphorically, consider a stream or pond with an outflow point in the bed or bottom. That point does not (symmetrically) pull or push water. What it does is create localized [pressure] gradients in the flow of water. An object caught in those gradients is moved, as if a force is pulling / pushing it. The outflow point does not have a property of attraction (or repulsion).
Or, as Wilczek wrote: “… charge … creates a disturbance in the Grid” – a space-filling medium aboil with virtual particles – what we normally perceive as empty space.
Ordinary matter is a secondary manifestation of the Grid, tracing its level of excitation.
In Wilczek’s view, mass arises because the Grid is permeated with a not-yet-understood property that “slows down” some of the interactions in the field, just as electrons are slowed down in a superconducting medium. In the medium known as the Grid, we perceive that slowed-down quality as mass.
 Regarding analogies (vs. impenetrable math) on how “force” particles cause attraction and repulsion, this Fermilab video probably has the clearest visualizations you’ll find.
YouTube > Fermilab > Don Lincoln > “Subatomic Stories: Forces the Feynman way” (May 6, 2020).
Subatomic forces at the quantum level are best understood as a cloud of force-carrying particles jumping from one object to another. In Episode 5 of Subatomic Stories, Fermilab’s Dr. Don Lincoln gives a brief explanation of this phenomenon, including two analogies for how this complicated mathematics can be understood.
 Or imagine in electromagnetism (EM) that somehow an opposite charge causes the virtual photon to behave as if it (the exchanged particle) has negative mass.
 So, mass might be considered some type of “charge.” In a metric field. Then EM and gravity are about charge. Or, “charge” is some type of energy; and then EM and gravity are about energy density.
 Also, if an electron and positron share the same (electron) field and are reverse excitations in some sense; and “collisions” typically result in annihilation with emission of photons … it may be simpler to visualize wave forms being flipped / nulled (and kinetic surplus carried off as real photons) than swarms of (virtual) photons disappearing. In any case, an interesting experiment might be to detect any time-lag between proximty and emission of radiation.
And as to why there are only two types of EM charge … symmetry?
But the metric field is really the (spacetime) vacuum and effectively neutral. Paired virtual particles of opposite charge may emerge into fields, but the vacuum itself is not characterized by contrary excitations. So, as to whether spacetime geometry can be “reversed” …
 Quanta Magazine > “What Goes On in a Proton? Quark Math Still Conflicts With Experiments” by Charlie Wood (May 6, 2020).
A humble electron, for instance, can briefly emit and then absorb a photon. During that photon’s short life, it can split into a pair of matter-antimatter particles, each of which can engage in further acrobatics, ad infinitum. As long as each individual event ends quickly, quantum mechanics allows the combined flurry of “virtual” activity to continue indefinitely.
 The “Physics preamble” of this “LHC the Guide: faq” CERN Brochure (January 2008) contains a helpful recap of the Standard Model.
Please note that when speaking about particle collisions in the accelerator, the word ‘interaction’ is a synonym of ‘collision’.