Imaginary numbers are crucial if traditional quantum theory remains true.
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Two new
research claim that imaginary numbers are required to adequately depict
reality.
When you
square the square root of a negative number, you get imaginary numbers, which
have long been utilised in the most essential equations of quantum mechanics,
the branch of physics that deals with the realm of the very small. Complex
numbers are formed when imaginary and real numbers are added together, allowing
physicists to state quantum equations in simple terms. However, it has long
been debatable whether quantum theory requires these mathematical chimaeras or
just exploits them as useful shortcuts.
In fact,
even the pioneers of quantum mechanics were concerned about the consequences of
using complex numbers in their equations. Physicist Erwin Schrödinger — the
first to introduce complex numbers into quantum theory with his quantum wave
function (ψ) — remarked in a letter to his friend Hendrik Lorentz, "The
use of complex numbers is unappealing, and it is directly to be opposed to. is
unquestionably a genuine function."
Later
scientists have done the same with other sections of quantum theory.
Schrödinger did develop ways to represent his equation using only real numbers,
along with an additional set of rules for how to utilise the equation. However,
given the absence of clear experimental data to decide on the predictions of
these "all real" equations, a debate has lingered: Are imaginary
numbers an optional simplification, or does working without them render quantum
theory incapable of describing reality?
Now, two
studies published in the journals Nature and Physical Review Letters on
December 15 have disproved Schrödinger's theory. They demonstrate that, if
quantum physics is right, imaginary numbers are a necessary feature of our
universe's mathematics through a relatively easy experiment.
Lead
author Marc-Olivier Renou, a theoretical physicist at the Institute of Photonic
Sciences in Spain, said, "The early founders of quantum mechanics couldn't
discover any method to understand the complex numbers emerging in the
theory." "Having them [complex numbers] works well, but there is no
clear way to identify complex numbers with a realistic element."
The
authors of the first study created a variation on the famous quantum experiment
known as the Bell test to see if complex numbers were genuinely important. The
test was first proposed by physicist John Bell in 1964 as a technique to show
that quantum theory needed quantum entanglement — the strange connection
between two far-apart particles that Albert Einstein derided as "spooky
activity at a distance."
The
physicists created an experiment in which two independent sources (named S and
R) would be put between three detectors (A, B, and C) in an elementary quantum
network in an updated version of the original Bell test. The source S would
then emit two light particles, or photons, in an entangled form, one to A and
the other to B. The source R would also emit two entangled photons, which would
be sent to nodes B and C. The photons arriving at detectors A and C would not
need to be entangled if the universe were characterized by a typical quantum
mechanics based on complex numbers, but they would in a quantum theory based on
real numbers.
The
researchers of the second study conducted an experiment in which they beamed
laser beams onto a crystal to evaluate this configuration. Some of the
crystals' atoms received energy from the laser, which was later released as
entangled photons. By examining the states of photons arriving at their three
detectors, the researchers discovered that the states of photons arriving at
detectors A and C were not entangled, implying that their data could only be
explained using a quantum theory based on complex numbers.
The
finding makes logical sense: photons must physically interact to become
entangled, thus those arriving at detectors A and C shouldn't be. However, the
researchers highlighted that their experiment only rules out theories that do
not use imaginary numbers assuming the current quantum mechanics norms are
valid. Despite the fact that most scientists are certain that this is the case,
this is a crucial caution to remember.
According
to Renou, the conclusion shows that the mathematical ways we may represent the
cosmos are far more confined than we might have anticipated.
"We
can rule out many alternative descriptions just by watching what comes out of
particular trials," Renou added, "without making any assumptions [on
the] dependability of the physical instruments employed in the
experiment." In the future, this could mean that physicists will only need
a minimal number of experiments to arrive at a comprehensive quantum theory
based on fundamental principles.
The
researchers also stated that their experimental setup, which consisted of a
basic quantum network, could be beneficial in laying down the principles on
which a future quantum internet would be based.
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