The Speed of Dark
“Light thinks it travels faster than anything but it is wrong. No matter how fast light travels, it finds the darkness has always got there first, and is waiting for it.”
-
By Terry Pratchett in : “Reaper man” [1]
This reminds me of the graffiti that I came
across recently: Nothing can replace a bikini.
Terry Pratchett’s remark seems to be just a wisecrack. But
is it?
Let us rephrase it: No thing can travel faster than light.
Exactly: darkness isn’t a thing. So it can travel faster
than light, as Terry Pratchett said.
The speed of light is well-defined. The speed of dark? Not
so much.
Firstly, there’s no such thing as really dark [2] as George
Musser points out:
” is there even such a thing as
darkness? If you did switch off the sun, Earth wouldn’t
go completely dark. Light from stars, nebulae, and the big bang would fill the
sky. The planet and everything on it, including our bodies, would blaze in
the infrared. Depending on how, exactly, you’d managed to switch the sun
off, it would keep on glowing for eons. As long as we were able to see, we’d
see something. No light detector can register total darkness, because, if
nothing else, quantum fluctuations produce tiny flashes of light. Even a black
hole, the darkest conceivable object, emits some light.”
This follows from Planck’s law: any object with a
temperature above absolute zero emits radiation. By the Third Law of
thermodynamics, we cannot cool any object down to absolute zero (even a black
hole!), so in the vicinity of matter, there is no such thing as absolute
dark. So, one may retrieve the question by speaking about some kind of
subjective feeling of dark: there may be a few photons of some wavelength or
the other around (and our eyes don’t respond to the infrared, anyway), but we
do not consciously respond to them and we think it is dark.
Even after we get that out of the way, there
is some ambiguity. One author [3] denies that darkness has a speed, because it
is just the absence of light and not a thing in itself. If it isn’t a thing,
how can you define a speed?
”Since darkness doesn’t actually exist, it cannot
move and therefore cannot have a speed. However, since the level of
illumination of a given area cannot change at a different rate than the speed
of light, you could also equate it as having the speed of light, though less
correctly.”
Actually, the astronomer Neil de Grasse Tyson argues exactly
that [2]:
“The speed
of dark... Consider dark getting erased by light. The light erases it at the
speed of light so the speed of dark would be negative the speed of light. If
light is a vector, it has magnitude and direction, so… to call it negative
means it’s in a negative direction. The dark is receding rather than
advancing. I’d call it negative the speed of light.”
So that’s it, then? Not quite. The physicists
Sarah Caudill and David Reitze considers [2] what happens if you fall into a
black hole:
“Because the
black hole has such strong gravity, time dilation will affect observations from
outside the strong gravitational field.
For example,
a distant observer watching a glowing object fall into a black hole will see it
slow down and fade, eventually becoming so dim it cannot be seen. This observer
won’t ever see the object cross the event horizon.
We can also
take the perspective of stuff falling into the black hole, instead of a distant
observer.”
“If you
happen to be the unlucky matter falling in, the speed is potentially very
large, in principle approaching the speed of light.
If you’re
the observer and you’re far enough away, the speed with which matter is
consumed is dramatically slowed down due to an effect known as gravitational
time dilation—clocks run slower in gravitational fields, and much slower in the
immense gravitational fields near the event horizon of the black hole. In
fact, to the far away person it will take an infinite amount of time for
something to travel to the event horizon of the black hole.”
Clear as mud, that is!
So, if that weren’t enough there is the
lighthouse effect to worry about.
There is a difference between the speed of
propagation and, um, the speed of scanning. Here goes [2]:
“For starters, what we commonly call
the “speed of light” is the speed of propagation, and that’s not always
the deciding factor. A shadow swoops across the landscape at a speed governed
by the object that casts it. For instance, as a lighthouse beacon rotates, it
lights up the surroundings at regular intervals. The ground speed of its
shadow increases with distance from the lighthouse.
Go far
enough away and the shadow will wash over you faster than the propagation speed
of light.”
According to Reuben Westmaas [4], the same
point is made, a bit differently:
“Imagine you have a light that's powerful enough to reach
the planet Jupiter. Imagine also that it casts that beam in a cone that's broad
enough to cover the entire diameter of the planet. When you pass your finger
over the lens, the shadow will cross the entire diameter of the planet — a
distance of 139,821 kms. The speed of light is 299,338 km/sec. So if it takes
you less than half a second to move your hand that distance, then that shadow
will have "broken" the speed of light.
Since there's nothing that's actually traveling the
distance, the only thing that's "moving" is an area where
photons aren't. There's no information that's being transmitted
faster than light, only a blockage of information.”
Both of
these arguments are characterized as the ‘lighthouse paradox’ and it has been
discussed by several authors [5] and in a couple of online forums [6]. The
point that no photons are going faster than light speeds is made in a video
[6b] about scanning a laser across the Moon:
“In
truth, nothing here is really travelling faster than the speed of light. The
individual particles coming out of my laser, the photons, are still travelling
to the moon at the speed of light. It’s just that they’re landing side by side
in such quick succession that they form a spot that moves faster than the speed
of light, but really, it’s just an illusion.”
Specifically,
the apparent superliminal speed is purely geometric; the only motion of photons
is along the beam direction, and there is no transverse motion of
photons.
However,
Neil de Grasse Tyson also said [7]:
“…the
idea of a speed of darkness is no more than a poetic metaphor, but has no place
in legitimate scientific discussion. ”
He also
said [7]:
“Strictly speaking, dark is simply the
absence of light, and thus has no speed at all.”
Joanne
Kendall [8] quotes someone who summarizes these different arguments:
“In
principle, shadows can move faster than the speed of light. “Strictly
speaking dark cannot have a speed,” says Pete Edwards of Durham University. “It
does not move or travel in any way. However, if we think of dark as the absence
of light, dark is chased away by light and so it disappears at the same speed
as light arrives. In this sense the speed of dark is equivalent to the speed of
light.”
Along
some distance, a shadow can become larger than the object creating it.
When a shadow is bigger than the object casting it, it moves at a greater
distance but in the same amount of time. If the shadow is large enough,
it could move across the surface faster than light.
This
is an illusion that darkness travels faster than the speed of light, and it is
still agreed that no physical object can travel faster — since darkness has no
mass.”
I think
the idea propagated by Reuben Westmaas, of an apparent ‘scanning speed’, may be
correct - but it doesn’t accord with our normal idea of a speed of propagation.
This is addressed by Christopher Baird [9]:
“… consider that you are in distant space, far from all light
sources such as the sun, and you have a light bulb on the nose of your space
ship. The light from the light bulb is spreading out in all directions through
space at the speed of light. If you briefly turn off your light bulb and then
turn it back on, there is light traveling out in all directions from before you
dimmed the bulb, and behind it there is light traveling in all directions from
after you dimmed the bulb. But between the two spheres of light there is no
light, because no light was created when the blub was briefly off. And no light
means darkness. So there is a band of darkness in between the two spheres of
light. Since both spheres of light are expanding outwards in all directions at
the speed of light, the band of darkness between them must also be traveling at
the speed of light. You can think of darkness as what you get right after the
last bit of light arrives. Since the last bit of light travels at the speed of
light, the state right after must also travel at the speed of light.”
I would go with this logic, but I would add a
small wrinkle. One has to take into account the turn-off time Dt0:
if you switch off a light it takes some finite time for the photons to all
disappear, leaving darkness (inasmuch as any darkness exists at all!):
The intensity of light going down to zero is shown for
simplicity as linear, but it could have any arbitrary time-dependence. Assume
the light source is at the centre of the circle (light is emitted in all
directions).
Speed of dark d £ c speed of light because:
The thickness of the annular space – where the intensity of
light is falling to zero - is: (c)(Dt0)
This means the speed of dark d can approach c in the limit,
as Dt0 ® 0.
This is just a minor add-on to the argument given by Baird
[9].
But let’s get back to Terry Pratchett [10] about the speed
of dark:
“As
yet unmeasured, but believed to be faster than light owing to its ability to
move so quickly out of light’s way.”
The ancients conceived of an eternal struggle between Light
and Dark. Well, as Terry Pratchett says, Dark is a lot faster. If it’s a race,
Dark wins.
So does Terry Pratchett get the Last Word? Nah! The last word is quantum mechanics. The shoe is on the other foot [2]: there's no such thing as dark, not really.
Except that, it is light - but we just can't see it...
References:
1.
Monica Grady https://www.interaliamag.org/articles/can-the-laws-of-physics-disprove-god/
2.
Sophie Weiner https://gizmodo.com/whats-the-speed-of-dark-1791292842
3.
https://futurism.com/the-speed-of-darkness
(14th March 2014)
4.
Reuben Westmaas https://www.discovery.com/science/darkness-is-faster-than-the-speed-of-light 1st
Aug.2019
5.
https://science.howstuffworks.com/dictionary/astronomy-terms/speed-of-darkness.htm
16th
Feb.2021
6.
a) https://en.m.wikipedia.org/wiki/Lighthouse_paradox
7.
https://www.physicsforums.com/threads/lighthouse-paradox-revisited.267258/
8.
http://thescienceexplorer.com/universe/4-ways-travel-faster-speed-light Joanne
Kendall 26th Nov.2015
9.
https://wtamu.edu/~cbaird/sq/2013/06/20/what-is-the-speed-of-dark/ 20th
June 2013
10.
https://everything2.com/title/The+speed+of+dark
