The opening of the classic song “The Sound of Silence” greets darkness as an old friend who has returned. If we take that greeting literally, darkness seems to have traveled from somewhere to reach the narrator, which suggests that it has a speed.
We know that light has a measurable speed, so what happens when the light stops coming? That gives us a physics question behind the greeting: what is the speed of dark?
It depends on whether we mean darkness following a beam or sweeping across a surface, because these involve different kinds of motion.
When a lamp is on, it continually emits light that travels outward. Switching it off stops further emission, but the light already traveling away does not disappear.
At a nearby wall, illumination therefore continues until the last light emitted before switch-off arrives. The wall then becomes darker, so the delay is determined by the distance from the lamp and the speed of light.
For an idealized lamp and a wall 3.0 m away, taking the speed in air as approximately the vacuum value:
\( t = \frac{3.0}{3.00 \times 10^{8}} = 1.0 \times 10^{-8} \text { s} = 10 \text { ns}\)That is ten billionths of a second, which explains why the change seems immediate to us. The delay is real, but it is much shorter than we can notice directly. Calling this the “speed of dark” is essentially saying that the trailing edge of a light beam is travelling at the speed of light.
As just noted, the delay is too short to notice across a room, but the Sun’s distance lets us visualize the same process over several minutes.
In a similar fashion, if the Sun disappeared , light already on their way to Earth would continue traveling toward us. Earth would therefore remain illuminated until the last sunlight arrived, even though its source was no longer there.
Using the approximate Sun–Earth distance of 150 million kilometers, it would take the trailing edge this much time to reach the earth.
\(t=\frac {1.5 \times 10^{11}}{3.0 \times 10^{8}} = 500 \text { s}\)This means that if the Sun suddenly disappears, we would only know about it about eight minutes and twenty seconds after. The trailing edge of its light travels at c, just like the trailing edge of the beam from the lamp; increasing the distance simply makes the delay longer.
Extra thought: the Sun disappearing would not only be seen 8 minutes after the fact, but would also be felt at the same time. Einstein’s theory of general relativity has shown that gravity, like light, travels at speed c. However, this needs to be discussed at another time.
Here’s a video where a camera operating at two billion frames per second records a light pulse traveling through a garage.
At that two billion frames per second, the interval represented by consecutive frames is:
\( Δt = \frac {1}{2 × 10^{9}} = 0.5 \text{ ns} \)During that interval, light travels approximately 15 cm. This gives a useful scale: light travels about 30 cm in a nanosecond. Remember though; the position of the trailing end of the laser beam must shift by 15 cm across the recorded image.
Yes, some of the light beam must scatter toward the camera to be recorded. The camera therefore receives light only after two stages: the beam reaches a scattering location, and scattered light then travels from that location to the camera.
For two locations along the beam, the difference in arrival times is:
\(Δt_\text{arrival} = Δt_\text{beam} + \frac{Δd_{\text{camera}}}{c}\)
Here, \(Δt_\text{beam}\) is the time between the beam reaching those locations, while \(Δd_{\text{camera}}\) is the change in distance from them to the camera.
If the beam moves toward the camera, later scattering locations are closer to it. Their shorter travel distance reduces the separation between arrival times, so the recorded motion can appear faster.
But if the beam moves away from the camera, later scattering locations are farther away. The additional travel time increases the separation between arrivals, so the recorded motion can appear slower.
This explains why changing the viewing angle can make the outward and returning parts of a light pulse appear to move differently, as shown in the video. The light’s local speed has not changed; the camera is recording a combination of beam travel and travel toward the camera.
To separate photon speed from sweep speed, consider an idealized narrow beam that sends individual photons toward a distant screen. Each photon travels from the source to the screen at c in vacuum, but changing the beam’s direction changes where successive photons arrive.
A photon sent in one direction reaches point A, while a later photon sent in a slightly different direction reaches point B. The second photon does not travel from A to B; it takes its own path from the source to B.
The illuminated position therefore changes from A to B without either photon traveling sideways between those points. Sweep speed describes how quickly that position changes, while photon speed describes how quickly each photon travels along its own path.
For a small angular sweep across a screen approximately perpendicular to the beam, the separation between arrival positions is:
\(Δx ≈ RΔθ\)Here, R is the distance to the screen and Δθ is the change in beam direction in radians. Dividing by the interval between the photons’ arrivals gives:
\(v_\text{sweep} ≈ \frac {RΔθ}{Δt_\text{arrival}}\)If the screen is much farther away than the separation between the illuminated points, the two photon paths have approximately equal lengths. Their travel times are then approximately equal, so the interval between arrivals is approximately the interval between emissions.
Keeping the same angular change and timing, we can compare two screen distances:
\(\frac {v_2}{v_1} ≈ \frac {R_2}{R_1}\)A screen a thousand times farther away therefore gives approximately a thousand times the sweep speed. But each photon still travels at c; the greater distance makes the arrival positions farther apart without requiring a photon to move between them.
The Moon is approximately \(R = 3.8 × 10⁸ m\) away from the Earth. If two photons are shot to the Moon 0.010 s apart at an angle between their paths as 0.010 rad (~ 0.6 degrees), and their path lengths are approximately equal:
This gives a sweep speed that is greater than the speed of light. Specifically, the two illuminated positions appear to travel at about 1.3c in this model. But both photons travel from the source to the screen at c, and neither crosses the screen at that calculated sweep speed.
The photon arriving at B carries information from the source, not from A. If someone at A wants to send a new message to B, that message needs its own physical signal, which cannot travel between them faster than c in vacuum.
A sweeping shadow follows the same reasoning through missing illumination. Point A becomes dark because photons heading toward A are blocked, while point B becomes dark because photons heading toward B are blocked; no particle of darkness needs to travel from A to B.
The boundary between illuminated and dark regions can therefore sweep faster than light. But the changes at each location still depend on light traveling from the source and interacting with the obstruction.
An astronomical light echo provides another example. Light from a stellar outburst reaches surrounding dust and scatters toward us, so different dust regions become visible at different times.
The arrival time depends on the entire path from the star to the dust and then to the observer. As different paths contribute to the image, the visible illumination pattern can form a ring that appears to expand faster than light.
But the dust does not need to move outward with that ring. Observations of the light echo around V838 Monocerotis show how successive illumination of existing dust can create apparent faster-than-light expansion.
The distinction is the same as for the moving spot: a pattern changes position without matter traveling along the pattern’s path. We must therefore identify what the measured “speed” belongs to before interpreting it.
A simple classroom demonstration can use a lamp and an opaque object to move a shadow across a wall. Changing the distances reveals how geometry affects the shadow’s movement, although an ordinary classroom setup will not produce measurable faster-than-light motion.
This went deeper than I expected, as there were several points that needed to be clarified on each step. I think this can still be further explained, but for now, I hope this was an interesting read.
