Waves ①: a wave is born from force → Waves ②: force itself was a wave
In Waves ① we saw "a wave is born from force" (a chain of restoring force + inertia). This time we step one further into the story that "force itself was a wave." In Episode 6 we saw that force is transmitted through a field. That field ── the electromagnetic field ── appears, when still, as a "force" that pulls/pushes charges toward or away from each other. But shake that same field and ripples rise and fly far away. That is light. The field that carries force, and the true nature of light, turned out to be one and the same thing. We look, from the side of force, at the substance of Maxwell's discovery ── the one that bundled electricity, magnetism, and light into one.
A charge creates an electromagnetic field in the surrounding space (Episodes 2 & 6). When it sits still, this field stretches out radially and acts as a force pulling or pushing another nearby charge. This is the everyday electric force, and the force that binds atoms together (Episode 2). It's the state in which the field wears the face of "force."
Now shake the charge. The field's "stretch" wobbles, and that wobble travels outward like ripples. The traveling wobble ── that is the electromagnetic wave, i.e., light. Maxwell, pushing the laws of electricity and magnetism to their limit, derived that the speed of this wave is \(c=1/\sqrt{\varepsilon_0\mu_0}\), and because that matched the speed of light he saw through to it: "light is an electromagnetic wave." It's exactly the same skeleton as \(v=\sqrt{\text{restoring force}/\text{inertia}}\) from Waves ① (the ratio of the vacuum's electric and magnetic "stiffness").
A still electromagnetic field → force (pulls/pushes what's near; the near field).
A shaken electromagnetic field → a wave (light) (radiation flying far away).
The two are not separate; they're the still and moving faces of one and the same electromagnetic field. Force itself, when shaken, becomes a wave.
In the figure below, try changing how the charge is shaken. Don't shake it, and the field stays a straight-stretched "force." The more you shake, the more a wave (light) rides on the field and flies far away. One and the same field is both force and wave.
In Episode 6 we saw "force is an exchange of carriers (photons)." The true nature of that photon connects now ── a photon is a "particle" of this electromagnetic field's wave. In other words, the carrier that transmits force (the photon) and light (the electromagnetic wave) are the same thing. There is no distinction between the thing that transmits force and light. "Force itself was a wave" meant that the field that carries force can, just as it is, fly off as a wave. Episode 6 (the exchange) and Waves ① (force → wave) converge here to a single point.
The conclusion of Waves ②. Force and wave are not separate phenomena; they're the "still" and "moving" faces of one field. A still field exerts a force nearby; a wobbling field becomes a wave and flies far away. For electromagnetism, force (the pull of electricity) and light (the electromagnetic wave) are the same electromagnetic field. That's why "force itself was a wave." Onto the main series' backbone, "force is a relationship mediated by a field," we've laid a further sheet: "and that field, when shaken, becomes a wave."
The static force (near field) and the wave that flies off (radiation field) are, strictly, different components of the field, and radiation is emitted only when the charge accelerates (not at constant velocity ── the story of the bonus "The Speed of Force ③"). "Force and wave are the two faces of the same field" is correct, but a "still force" does not simply turn into a wave; more precisely, shaking (accelerating) it produces a wave.
Writing the static Coulomb force as "an exchange of virtual photons" is a calculational description and is not identical to real light (real photons) (the honest line of Episode 6). The figure simplifies the field's behavior into a single line; it is not a rigorous depiction of an actual electromagnetic wave in which the electric and magnetic fields propagate at right angles.
The electromagnetic field around a charge is, when still, a "force" pulling/pushing what's near (the near field). Shake that same field (accelerate the charge) and ripples rise and it becomes a "wave (light)" flying far away. Maxwell saw through to "light is an electromagnetic wave" from the fact that the electromagnetic wave's speed matches the speed of light ── the same skeleton as v=√(restoring force/inertia) from Waves ①. Force and light were the still and moving faces of one electromagnetic field.
The carrier of Episode 6 (the photon) is a particle of this field's wave. So the thing that transmits force and light are the same ── "force itself was a wave." Gravity is the same: shake spacetime and a gravitational wave flies. Every force is a force when still and a wave when moving. Next time (Waves ③) we head to the wave conversely exerting a force (radiation pressure), and to the deepest "force that looks like a wave" of all, where in the quantum world "a particle is a wave and force is phase."
Print / PDF: ⌘+P (Ctrl+P on Windows). On screen, the slider lets you see the field become a wave (light) and fly off as you shake it. "See the answer" opens each solution.