14 SCIENCE NEWS | January 29, 2022
J. FANNEWS
MATTER & ENERGY
Physics requires imaginary numbers
Quantum theory based on only real numbers fails in new tests
BY EMILY CONOVER
Imaginary numbers might seem like
unicorns and goblins — interesting but
irrelevant to reality.
But for describing matter at its roots,
imaginary numbers turn out to be essen-
tial. They seem to be woven into the
fabric of quantum mechanics, the math
describing the realm of molecules, atoms
and subatomic particles. A theory obey-
ing the rules of quantum physics needs
imaginary numbers to describe the real
world, two experiments suggest.
Imaginary numbers result from tak-
ing the square root of a negative number.
They often pop up in equations as a math-
ematical tool to make calculations easier.
But everything we can actually measure
about the world is described by real
numbers, the normal figures we’re used
to. That’s true in quantum physics too.
Imaginary numbers appear in the inner
workings of the theory, but all possible
measurements generate real numbers.
Quantum theory’s prominent use of
complex numbers — sums of imaginary
and real numbers — was disconcerting
to its founders. “From the early days
of quantum theory, complex numbers
were treated more as a mathematical
convenience than a fundamental build-
ing block,” says physicist Jingyun Fan of
the Southern University of Science and
Technology in Shenzhen, China.
Some physicists have attempted to
build quantum theory using real numbers
only, avoiding the imaginary realm with
versions called “real quantum mechan-
ics.” But without an experimental test
of such theories, the question remained
whether imaginary numbers were neces-
sary or just a useful computational tool.
A type of experiment called a Bell test
resolved a different quantum quandary,
proving that quantum
mechanics requires entan-
glement, strange quantum
linkages between particles
(SN: 9/19/15, p. 12). “We
started thinking about
whether an experiment of
this sort could also refute
real quantum mechanics,”
says theoretical physicist
Miguel Navascués of the
Institute for Quantum
Optics and Quantum
Information–Vienna. He
and colleagues laid out a plan for an
experiment in the Dec. 23 Nature.
In this plan, researchers would send
pairs of entangled particles from two dif-
ferent sources to three different people,
named according to conventional phys-
ics lingo as Alice, Bob and Charlie. Alice
receives one particle and can measure it
using various experimental settings that
she chooses. Charlie does the same. Bob
receives two particles and performs a spe-
cial type of measurement to entangle theparticles that Alice and Charlie receive. A
real quantum theory, with no imaginary
numbers, would predict different results
than standard quantum physics, allowing
the test to discern which one is correct.
Fan and colleagues performed such an
experiment using photons, or particles of
light, they report in an upcoming paper
in Physical Review Letters. By studying
how Alice, Charlie and Bob’s results com-
pare across many measurements, Fan,
Navascués and colleagues show that the
data could be described only by a quan-
tum theory with complex numbers.
Another team of physi-
cists ran an experiment
based on the same concept
using a quantum computer
made with superconduc-
tors, materials that conduct
electricity without resis-
tance. That test also found
that quantum physics
requires complex numbers,
the team reports in another
upcoming paper in Physical
Review Letters.
But the results don’t
rule out all theories that eschew imagi-
nary numbers, says theoretical physicist
Jerry Finkelstein of Lawrence Berkeley
National Laboratory in California. The
research eliminated certain theories
based on real numbers, namely those that
still follow the conventions of quantum
mechanics. It’s still possible to explain
the results without imaginary numbers
by using a theory that breaks standard
quantum rules. But those theories run
into other conceptual issues, making
them “ugly,” he says. Still, “if you’re will-
ing to put up with the ugliness, then you
can have a real quantum theory.”
Despite the caveat, other physicists
agree that the quandary of imaginary
numbers remains compelling. “I find it
intriguing when you ask questions about
why is quantum mechanics the way it
is,” says Krister Shalm of the National
Institute of Standards and Technology in
Boulder, Colo. Asking whether quantum
theory could be simpler or if it contains
anything unnecessary “are very interest-
ing and thought-provoking questions.” s“From the early
days of quantum
theory, complex
numbers were
treated more as
a mathematical
convenience than
a fundamental
building block.”
JINGYUN FANTo explain the real world, imaginary
numbers are necessary, according to an
experiment performed by physicists
including Ya-Li Mao (shown with
the experiment) of the Southern
University of Science and
Technology in China.