Force That ClicksBonus: The Speed of Force ③ (closing the trilogy)

Speed ①: change travels at c ／ Speed ②: why c → Speed ③: the true nature of a force that looks "instantaneous"

A Quiet Force
Carries No News The force of a source moving at constant velocity seems to point at its current position, as if instantaneous (faster than light?).
But it carries no information. Only acceleration sends the real news (a wave) at \(c\).

Tools you'll need: Speed ①②, radiation from Wave ②, virtual particles from Episode 6 Only acceleration puts out news

The homework set in Speed ① ── "the force of a source moving at constant velocity seems, at first glance, to instantly track its current position" ── we finally solve it here. This is not faster-than-light, and it does not break causality. The key is whether information (news) is being carried. Constant-velocity motion is predictable, so there is no news; even though the force points at the current position, nothing is being transmitted. What truly puts out news and carries it at \(c\) is ── acceleration alone. We close the speed trilogy on this one point. And the honest line about "virtual particles" from Episode 6 gets picked up right here.

01A constant-velocity source ── the force points at the "current position" (but not instantly)

Suppose a charge is flying straight ahead at constant velocity. The electric force felt by a distant partner, surprisingly, does not point at the delayed position (the one lagging by the time light takes to arrive) but seems to act toward the current position. It's as if the force instantly knows "where the charge is right now" ── it looks faster than light. But it isn't. Constant-velocity motion is completely predictable, so the partner's field was arranged in advance as "if it keeps going like this, it's here now." No new information has arrived. So causality is not broken, and you cannot use this to send a signal.

The crux this time ── apparent instantaneity carries zero information

The force of a constant-velocity source points at the "current position" because the field has been set up ahead of time, exactly by the amount of the predictable motion.
Even if it looks faster than light, the news (new information) is zero. No signal can be sent, and causality is not broken.
"Looks instantaneous" and "information travels instantaneously" are entirely different things.

02The real news comes from acceleration ── a kink flies at c

So how does truly new information ── "the source's motion changed!" ── get transmitted? The moment you accelerate the source, a fold (a kink) forms in the field's pattern, and it spreads outward at \(c\). This very fold is the radiation (electromagnetic waves, light) we saw in Wave ②. Only an unpredictable change (acceleration) creates news, and it can only travel at \(c\). In the figure below, watch how, when a charge that was at rest is set in motion (accelerated) at t=0, a "shell" of updated information spreads out at \(c\).

Figure: A charge that was at rest is set moving (accelerated) at t=0. Inside the shell (red, radius c·t) the field is already updated (from the new position); outside it is still old information (from the original position). Shell = kink = radiation (news, at c)

03Virtual vs. real particles ── the quiet force vs. radiation

In Episode 6 we drew an honest line: "a force is an exchange of carriers (photons), but the carrier of a static force is a virtual particle ── it isn't a little ball flying across." Here it all connects ── the static force (a constant-velocity source) = an exchange of virtual (off-shell) photons, which is a term in a calculation, not "something real flying at \(c\)." That's why an apparent instantaneity, "pointing at the current position," shows up. On the other hand, the radiation put out by acceleration = real (on-shell) photons = genuine light, which really does fly at \(c\) and carries news. The word "flying" in "a force is photons flying across" has meaning only for the latter (radiation).

Sorting out the quiet force and radiation

Static / constant-velocity force (near field)

Virtual photons (off-shell). A term in the calculation; it has no "speed." It looks like it points at the current position, but the news is zero and no signal is possible.

Radiation from acceleration (far field = light)

Real photons (on-shell). A wave that genuinely flies at \(c\). It carries an unpredictable change (news). It is the very light of Wave ②.

◇ ◇ ◇

04What peeling it back revealed ── the speed trilogy closes

The conclusion of The Speed of Force ③. A quiet (constant-velocity) force carries no news. The apparent instantaneity of pointing at the current position is nothing but the field getting a head start on predictable motion ── zero information, no violation of causality. The real news is born from acceleration and flies at \(c\) as a kink = radiation (real photons = light). Bundle the speed trilogy together ── ① a change in force travels at \(c\); ② it is exactly \(c\) because the carrier has zero mass (range ≠ speed); ③ a quiet force carries no news, and news comes from acceleration at \(c\). "Looks instantaneous" and "information travels instantaneously" are different ── causality was preserved everywhere, all along.

The honest line

"The force of a constant-velocity source points at the current position" is a property of uniform straight-line motion; when the source is accelerating, the direction it points shifts a little (strictly, the Liénard–Wiechert potential). The point is that "the predictable part (constant velocity) can be gotten ahead of, but an unpredictable change (acceleration) can only travel at \(c\)." Virtual photons are internal lines in a perturbative calculation, not observed particles; "off-shell" and "having no speed" are plain-language restatements in that sense.

The figure is a schematic reproducing the key points ── "updated inside / old outside / shell = kink" ── (a simplified version of a Purcell-type explanatory diagram); it is not a rigorous calculation of the actual field-line shapes.

Practice problems
  1. Even though the force of a constant-velocity charge points at its "current position," why is it not faster than light?
    See the answer
    Because constant-velocity motion is predictable, and the field has been set up ahead of time by exactly that amount. No new information (news) has arrived, so you cannot send a signal with it. "Looks instantaneous" and "information travels instantaneously" are different.
  2. The real news (new information) ── what does it come from, and how does it travel?
    See the answer
    From the source's acceleration. A fold (a kink) forms in the field and travels outward at c as radiation (real photons = light, from Wave ②). Only an unpredictable change carries news.
  3. Distinguish a static force from radiation using the language of virtual/real.
    See the answer
    Static / constant-velocity force = virtual photons (off-shell, a term in the calculation, no speed, an appearance of pointing at the current position). Radiation from acceleration = real photons (on-shell, genuine light, flying at c and carrying news).

SummaryApparent instantaneity carries no information

The force of a source moving at constant velocity points at its current position and looks, at first glance, "instantaneous," but that is merely the field getting a head start on predictable motion ── the news is zero ── neither faster-than-light nor a violation of causality. The real news is born from acceleration and flies at \(c\) as a kink in the field = radiation (real photons = light). Static force = virtual photons (a calculational term with no speed); radiation = real photons (genuine light flying at c) ── the honest line from Episode 6 gets sorted out right here.

The speed trilogy: ① change travels at \(c\); ② it is exactly \(c\) because of zero mass, and range ≠ speed; ③ a quiet force carries no news, and news comes from acceleration at \(c\). "Looks instantaneous" and "information is instantaneous" are different things, and causality was preserved everywhere. A force is a relation, and at the same time, the "update" of that relation always travels no faster than \(c\) ── the thread running through the main series and the bonuses closes on the side of time as well. Next: the final bonus, "AI and Force."

This document is "The Speed of Force" ③ of the bonus edition of the "Force That Clicks" series, a reading piece for high-school and university students who love physics. That the electric field of a charge in uniform straight-line motion points toward the instantaneous position (not the retarded position), that this is not information transfer and cannot send a signal, and that an accelerating charge produces radiation as a kink in the field (a transverse component) that propagates at the speed of light (corresponding to Purcell's explanatory diagram) are all established content. The distinction between the virtual-photon (off-shell) description of static / constant-velocity interactions and the real-photon (on-shell) description of radiation is also standard. Strictly, it is described by the Liénard–Wiechert potential, and the property of pointing at the instantaneous position is a consequence of the constant-velocity case. Virtual particles are internal lines of perturbation theory and are not observed particles. The figure is a simplified conceptual schematic. ── To print, use your browser's "Print" and "Save as PDF" (in the print version the slider and answers are frozen or hidden).

Print / save as PDF: ⌘+P (Ctrl+P on Windows). On screen, the slider lets you watch the shell of updates spread out at c. "See the answer" opens each solution.