Having finished Waves and Force → "just how fast does force actually travel?"
In the Waves and Force trilogy we saw that "what carries force is the field, and that field, when shaken, is a wave (light)." So a naive question ── how fast does that force (or wave) travel? There is a lot of confusion around "the speed of force," so across these three bonus pieces we untangle it carefully. The conclusion of part one is clear ── force does not travel instantly. Force (a change in the field) chases after you at the speed of light \(c\). The "two distant parties attract each other instantly (action at a distance)" that Newton drew was in fact an approximation that works because the speed of light is so very fast.
A thought experiment. If the Sun vanished without a trace at this very moment, when would Earth notice? With Newton's action at a distance (force is instantaneous), Earth would lose its tether and fly off at that very instant. But reality is different. As we saw in Episode 6, force is carried by way of a field. The "news" that the Sun has vanished ── the change in the gravitational field ── travels through space at the speed of light. The Sun is about 8 light-minutes away. So ── for 8 minutes, knowing nothing, Earth keeps orbiting the vanished Sun. The light going out and the gravity going out both arrive together, 8 minutes later.
It is not force itself but a change in force (the news) whose speed of travel is \(c\).
Whatever happens at the source, a partner a distance \(r\) away notices only \(r/c\) later.
Newton's "instantaneous" was an approximation that works because \(c\) is so overwhelmingly fast.
There is a deeper reason why "force is instantaneous" fails. In relativity, sending information faster than \(c\) makes the order of cause and effect flip depending on the observer. A world where the effect comes before the cause breaks causality. So, force or anything else, whatever carries information cannot exceed \(c\). Force is a means of telling a partner "the source has moved," so its transmission, too, is naturally at most \(c\). Instantaneous action at a distance is incompatible with causality.
"Gravity also travels at the speed of light" was long a theoretical prediction, but by now it has been confirmed by observation. In 2017, far away, two neutron stars merged and simultaneously emitted gravitational waves and gamma rays (light) (GW170817). Both traveled about 130 million light-years to reach Earth, and the difference in their arrival times was a mere 1.7 seconds. That they arrived nearly together after such an enormous journey means ── the speed at which gravity travels matches the speed of light to staggering precision. "The change in a force-carrying field = a wave," seen in Episode 6 and Waves ②, was proven to fly at the speed of light for gravity, too.
The conclusion of The Speed of Force ①. Force does not travel instantly. A change in force travels, by way of a field, at the speed of light \(c\). Newton's action at a distance (attracting instantly) was merely an excellent approximation that works because \(c\) is so fast that, over everyday distances, it seems like an instant. Relativity and causality force \(c\) as the ceiling, and the observation of gravitational waves backed up "the speed of gravity = the speed of light." To Episode 6's "force acts through a field," we've added a layer of time: "the change in that field travels at \(c\)."
What travels at \(c\) is a change in force (new information). In fact, for a source moving in a straight line at constant velocity, the direction of the force a partner feels appears to point at the source's "current position", so at first glance it can seem to "track it instantly (faster than light?)." But that carries no information and breaks no causality ── we'll properly resolve this subtle point in The Speed of Force ③. The key point this time is: "when a real change (acceleration, disappearance) occurs at the source, that news can travel only at \(c\)."
"The Sun vanishing" is an unrealistic setup that breaks causality and could not actually happen (energy conservation and so on), but it is valid as a thought experiment for thinking about the speed of transmission. The distances and times in the figure are schematic (Earth ≈ 8 light-minutes), and the orbital motion is simplified.
Force does not travel instantly. Even if the Sun vanished, Earth wouldn't notice for about 8 minutes ── because a change in force (the news) travels, by way of a field, at the speed of light \(c\). Newton's action at a distance (instantaneous) is an approximation that works because \(c\) is so overwhelmingly fast. Relativity and causality force \(c\) as the ceiling, and the 2017 gravitational-wave observation (GW170817) backed up "the speed of gravity = the speed of light" to a precision of 1.7 seconds.
It converges here with Waves ②'s "shake a force-carrying field and a wave flies off, at speed \(c\)" ── change in force = wave in the field = speed of light. To Episode 6's "force acts through a field," a layer of time (it takes \(c\) to travel) was added. Next time: "why exactly the speed of light" ── the carrier's mass and speed, and untangling the mix-up that "range and speed are the same thing."
Print / Save as PDF: ⌘+P (Ctrl+P on Windows). On screen, use the slider to watch the ring of change spread out and reach Earth. Click "See the answer" to open each solution.