70 Science & technology The EconomistOctober 17th 2020
2W
hen it comesto cosmic speed limits,
light gets all the attention. Its velocity
in a vacuum, a tad below 300m metres per
second, is an absolute upper bound on how
fast anything in the universe can travel.
This value, called “c” by physicists, is some-
how baked into the fabric of reality as what
is known as a fundamental constant.
The speed of sound, by contrast, has no
obvious upper limit of its own. Find the
right material, it has always been assumed,
and you could make sound travel arbitrari-
ly fast—so long as you did not break the
speed of light.
Kostya Trachenko of Queen Mary Uni-
versity of London, however, disputes
this—at least when the sound in question
is travelling through a solid or a liquid. He
proposes that in these circumstances
sound, too, has a maximum possible veloc-
ity. Intriguingly, he also proposes that this
is likewise baked into reality’s fabric by be-
ing composed solely of fundamental con-
stants. In a paper just published in Science
Advances, he lays out the reasons why.
Sound travels by making things vibrate.
In solids and liquids—known collectively
to physicists as the condensed phases of
matter—molecules are bound to one an-
other tightly. When one moves, its neigh-
bours follow suit, and a wave of sound is
thus transmitted. Allowing for differences
in properties such as density and inter-
atomic bond strength, Dr Trachenko and
his colleagues calculated that the speed of
sound in condensed matter obeys a simple
trend. The lighter the particle doing the vi-
brating, the faster it transmits sound.Sound’s highest speed in such matter, they
therefore predict, will be through a solid
made of the lightest atoms: hydrogen.
Unfortunately hydrogen, which gener-
ally exists as a gas, is notoriously difficult
to squeeze into a solid form, so measuring
the speed of sound within its solid phase is
tricky. But Dr Trachenko’s analysis predicts
that if and when this is done, the result will
be about 36,000 metres per second. That
testable prediction of his theory is twice
the current measured record for con-
densed-matter sound waves, which is held
by diamond—ie, crystallised carbon.
Part of what makes Dr Trachenko’s work
so surprising is the way he arrived at this
figure. His formula depends only on four
fundamental constants of nature. One is c.
The others are the mass of an electron, the
mass of a proton and something called the
fine-structure constant. This last is a pa-
rameter from quantum theory, the branch
of physics which describes the universe on
its smallest scales.
Dr Trachenko’s insights do not apply to
uncondensed matter—namely gases and
the state of matter called plasma, in which
electrons break free from their parent at-
oms. In gases, the speed of sound increases
with temperature, so the newly described
speed limit might be exceeded were a gas
hot enough. It would, though, need to be at
well over 1m degrees for this to happen, and
at that temperature it would have turned to
plasma. The acoustic physics of plasma are
not well understood, so what the speed of
sound would be then is anyone’s guess.
The other place to look for sound travel-
ling at supersonic speeds, as it were, would
be a form of matter where the word “con-
densed” barely begins to describe what is
happening. Neutron stars, composed, as
their name suggests, almost entirely of
those particular subatomic particles, are
the densest objects known of outside a
black hole. That density might overcome
Dr Trachenko’s new limit. But finding out
would be the stuff of Nobel prizes. 7Just how fast can sound travel?PhysicsMax machs
cause such surveys have used satellite pho-
tographs that have insufficient resolution
to spot individual trees’ canopies. Instead,
they have looked for contiguous patches of
green that represent woods and forests.
Dr Brandt and Dr Tucker thought this
approach old-fashioned. Many high-reso-
lution satellite photographs of Earth’s sur-
face now exist. Some—in the hands of
armed forces and intelligence agencies—
are secret. But others, owned by private
Earth-observation firms, can be inspected
at a price. As it happened, that price had al-
ready been paid by the American govern-
ment for a set of appropriate images. This
gave the researchers access to shots with a
resolution as small as 50cm, rather than
the 10-30 metres of those used in the past.
It is one thing, though, to have adequate
resolving power. It is quite another to be
able to use it. For that, Dr Brandt and Dr
Tucker had to apply some artificial intelli-
gence to the problem. This involved hand-
labelling 89,899 individual trees in a set of
training images, in order for the search al-
gorithm to be able to learn what a tree looks
like at different times of day, when covered
by cloud, when shrouded by dust and when
viewed from different angles. And, of
course, individual trees themselves look
different from one another.
Once it had digested these images, the
algorithm was let loose on high-resolution
photographs covering 1.3m square kilo-
metres of the Sahara and the Sahel. In con-
trast to the previous negative results, it re-
ported that there are 1.8bn trees in the area.
In the global scheme of things, 1.8bn is
still a tiny number. People debate how
many trees Earth supports, but it is proba-
bly in the low trillions. Locally, however,
even sparse tree cover is important. Trees
provide shade for people and animals, and
their roots hold the soil together. On top of
this, being able to monitor these loners will
help to monitor a region’s ecological
health. Crucially, the price of high-resolu-
tion images is expected to fall as more
firms enter the market, and satellites get
smaller and cheaper to launch. Dr Brandt
and Dr Tucker therefore suggest using their
approach to analyse other parts of the
world currently listed as having few trees.
Something similar, but more sophisti-
cated, might have still wider applications,
like permitting different species to be re-
cognised or allowing individual trees to be
distinguished within forests. At the limit of
the imagination lies the possibility of map-
ping every sizeable tree in the world. Ecol-
ogists would love this level of detail—pro-
vided that they did not have to hug them all
asa result. 7AwardOliver Morton, The Economist’s Briefings
editor, has been named British Science Journalist of
the Year by the Association of British Science
Writers for pieces he has written on climate change
and synthetic biology