*Decades ago, Einstein concocted a theory in which space doesn’t just curve, but swirls like a cyclone. Now it is making a comeback because it could fix several of the biggest problems in cosmology.*

LONG ago, people thought that empty space was just what it sounds like: a
featureless void. But the more we have studied seeming emptiness, the more
we have shown that this is far from the truth. The air around us is full of
jostling gas molecules. In space proper, beyond our atmosphere, there are
quantum fields and particles of light. Even the emptiest corner of
interstellar wilderness isn’t devoid of character because space itself can
warp and curve.

But what if we still haven’t got to the bottom of what space is like? In the
middle of his career, Albert Einstein became convinced that general
relativity, his great theory of space and time, had missed a trick. Yes,
space did warp and curve – but not in the way he had thought. If the true
twistiness of space was accounted for, he reckoned, it might bring us closer
to a grand unified theory of physics.

Einstein never quite cracked the idea, and it has been largely left to
languish for almost a century. But now there is fresh cause to revive it.
Physicists are struggling with a raft of devilish problems in cosmology that
are forcing us to question the basics of even our most well-established
theories. Dark energy, the unidentified stuff that seems to be pushing the
universe apart at an ever accelerating rate, is just one example.

Some physicists are asking whether the answer to all these problems could be
to once again tweak our understanding of space itself. This time the goal
isn’t to unify all of physics. But if we give space the right kind of twist,
it is beginning to look like many of the most vexing problems in physics
could melt away.

The way we now understand space dates back to 1915, when Einstein published
his theory of general relativity. It is built upwards from his realisation
that the way objects respond to gravity and acceleration is
indistinguishable, which we now call the equivalence principle. The theory
tells us that space and time can’t be considered separately, but only as a
kind of four-dimensional canvas for reality.

As if that wasn’t enough, Einstein also showed that any object with mass
could warp and deform space-time, like a higher-dimensional version of a
bowling ball on a trampoline. It was these undulations in space-time that
gave rise to gravity. Objects falling from the sky were following invisible
contour lines in the fabric of space. It is a beautiful theory that has
stood the test of time. But for Einstein himself, trouble was already
brewing.

In the early 1920s, he and others were laying the foundations for the most
successful idea in all of physics: quantum theory. It explains the nature of
the subatomic world, including electromagnetism, the force that gives rise
to light and creates attractions and repulsions between charged particles.
From the start, this theory forced us to leave common sense at the door. It
works by predicting what will happen when an observer makes a measurement on
a quantum particle, and seems to suggest that before that measurement, the
particle exists in a nebulous cloud of indeterminacy. Einstein liked it not
one bit; he thought the chance and imprecision at the core of the theory was
a sign of our ignorance, not a true aspect of nature.

So he began work on an alternative theory of electromagnetism, one written
in similar mathematical language to general relativity. To understand how it
works, we need to know that mathematicians have two ways of talking about
how things curve. One is simply called curvature and it describes how lines
bend. Then there is a more sophisticated language called torsion, which is
used to describe how things twist. You could describe a piece of wiggly
spaghetti on a plate with curvature, but to define the corkscrew shape of
fusilli you would need torsion.

In general relativity, Einstein had found that using a 4D version of
curvature to describe space-time worked perfectly. His new plan was to
develop a version of the theory using torsion instead and see if this could
explain both gravity and electromagnetism in one neat package. It was a
delightful idea. In the new hypothesis, massive objects and charged objects
would cause space-time to twist up beneath them, like a cyclone in the
fabric of reality. They would do this in slightly different ways, one giving
rise to electromagnetism and the other gravity.

Einstein published this hypothesis in 1928. But he couldn’t get it to work
properly – the rewritten theory was really just general relativity expressed
in a new way and it couldn’t explain electromagnetism. It is known as
teleparallel gravity because of the way it was initially analysed by
examining parallel lines in space.

In the decades that followed, teleparallel gravity was worked on by the
occasional theorist. Meanwhile, general relativity scored success after
success and quantum theory matured and dominated fundamental physics.
Interest in Einstein’s attempt at unification waned.

Today, physics is in a wholly different place. General relativity and
quantum theory continue to be confirmed time after time. Yet it seems they
can’t be the complete description of reality because they are mutually
incompatible. There are also huge problems in cosmology that they can’t
answer (see “Four problems, one solution“).

One of them first appeared about 20 years ago, when astronomers noticed that
the rate of expansion of the universe is accelerating. We have no good
explanation for this apart from to invoke an unknown substance called dark
energy. The past few years have thrown up an even more embarrassing problem.
We measure the rate of expansion of the universe using two different
methods, one based on exploding stars and one based on the cosmic microwave
background, a sea of radiation emitted shortly after the big bang. These two
methods give us two quite different answers. It is still just possible that
this trouble, known as the Hubble tension, could be down to a measurement
error. But it is fair to say that cosmologists are in crisis mode.

One resolution might lie in accepting that general relativity doesn’t
provide a perfect description of reality. In this reading, there is no dark
energy – it is just that gravity itself doesn’t work quite how we thought it
does.

Theorists have been producing modifications to general relativity for
decades. Most focus on adding new ingredients to the formula, allowing the
curvature of space-time to respond to more than the presence of matter and
energy. But with so many flavours on offer, how do you discern if any are
correct?

One way to judge involves gravitational waves, fluctuations in space-time
that result from collisions between stars, black holes and the like. General
relativity says that these waves should propagate at the speed of light. But
modified theories of gravity almost always predict a slightly slower speed.

In 2017, we managed to
observe the gravitational waves caused by the smashing together of two
neutron stars
– and the light that this produced. The flash of light and the gravitational
waves arrived at Earth within seconds of each other. There was no slowing,
and this result was enough to wipe almost every theory of modified gravity
off the table.

### Last one standing

But not teleparallel gravity. The theory doesn’t predict any change to the
speed of gravitational waves. This means that, for those who think the
Hubble tension can be resolved by overhauling gravity, there are few options
left except teleparallel gravity.

It is this kind of logic that motivates people like Jackson Said at the
University of Malta, a leading figure in teleparallel research. “These are
very exciting times, with a new synergy in the community in getting
teleparallel gravity to help solve some of the big problems in modern
cosmology,” says Said.

He isn’t alone in his enthusiasm. “As a cosmologist, I find teleparallel
gravity very intriguing,” says Celia Escamilla-Rivera at the National
Autonomous University of Mexico. “We are excited that it can shed some light
on the questions that have been problems for several years in cosmology,
like the nature of the dark sector.”

We have known for a long time that the equations of general relativity can
be written down using the language of torsion as well as curvature, and the
two work out as equivalent. This was proved back in 1976. It means that if
Einstein had chosen to use torsion to write out his equations from the very
start, his theory would still have worked just as well.

The audacious hope is that teleparallel gravity is actually better than
general relativity. The mathematical language of torsion is more malleable
than curvature, so researchers can fit terms into the equations that make
matter and energy more responsive to the twistiness of space-time. In almost
all circumstances, including the ordinary space in our solar system, these
modifications make no noticeable difference to anything. But they would kick
into gear in extreme situations, like at the big bang or on the epic scales
of the entire universe – exactly where we encounter the biggest problems.

In 2018, astrophysicist Rafael Nunes at the National Institute for Space
Research in Sao Paulo, Brazil, used teleparallel gravity to explore the
Hubble tension. He tried a simple modification to basic teleparallel gravity
and used this framework to calculate the rate of the universe’s expansion
from data on the cosmic microwave background.
It came out the same as the rate given by supernovae. The Hubble tension had melted away.

There are now published models of teleparallel gravity that can explain away
three other big problems in cosmology too. But these each use different
modifications – there is no single theory of teleparallel gravity.

Recently, however, there has been a finding that boosted the case for
teleparallel gravity, one that circles back to Einstein’s original vision.
One of the leading candidates for a unified theory of physics today is
string theory, which says that all forces and energy in the universe arise
from the vibrations of invisible strings. The theory is much maligned for
its lack of testable predictions and intractable mathematics. But with a
dearth of strong competitors, it still commands plenty of interest as a
possible theory of everything. If it is, then a new theory of gravity should
be derivable from string theory.

Earlier this year, a team of theorists led by Sebastian Bahamonde at the
University of Tartu in Estonia found that
teleparallel gravity is contained within string theory. They used mathematical language borrowed from string theory to derive a
teleparallel-based history of the universe, and found that it mimicked many
key features of our cosmological past. It is far from a closed case, but is
another hint. “We do not expect that general relativity is the final theory
of gravity,” says Bahamonde.

Cosmologist Eleonora Di Valentino at Durham University, UK, is paying close
attention to teleparallelism. “My point of view is that at this stage all
the possibilities are welcomed,” she says. “Teleparallel gravity is a
quickly growing, but still very theoretical, field.”

Testing teleparallel gravity is the only way we will find out if it is
correct. But that won’t be easy. The idea comes in so many flavours that no
single test would prove it right or wrong. Instead, progress is more likely
to come from tests that push general relativity past its breaking point. So
far, Einstein’s theory has proved singularly resilient, even describing
extreme scenarios like the collisions of black holes to perfection.

### Mysterious equivalence

There may be one way to directly test teleparallel gravity and that is
through the equivalence principle, the bedrock idea on which general
relativity is built. The principle says that an object’s gravitational mass,
which responds to the warping of space-time, is the same as its inertial
mass, which resists acceleration.

In general relativity, the equivalence principle has to be true, or the
theory collapses. But there has never been an obvious reason this is so. All
we know is that, empirically, the principle is sound – at least in all
measurements we have made so far.

One manifestation of the principle is that all objects fall to Earth with
the same acceleration regardless of their mass, as long as things like air
resistance don’t interfere. We already know this is true to an accuracy of
one part in a trillion. But if we found even the tiniest difference, that
would show that general relativity is wrong and point strongly towards
teleparallel gravity.

There is one proposed experiment that might just be capable of checking
this. The
Satellite Test of the Equivalence Principle project aims to put eight
different test masses into orbit, shield them from drag and measure how they respond to Earth’s gravity in
minute detail. If any difference appears between the behaviour of the
masses, that would be a violation of equivalence – and teleparallelism will
be right there waiting to explain the results.

Einstein himself never gave up on finding an alternative to quantum theory
until his death in 1955. His forgotten theory isn’t what he once hoped it
could be. But it is possible that his twisted vision of space wasn’t
entirely wrong. For now, at least, Einstein’s dream is still alive.

**Four problems, one solution**

Cosmology is facing four huge, interrelated problems. A resurgent theory
called teleparallel gravity might provide answers to them all

Problem 1:

**Dark matter**
Beginning in the 1970s, astronomers began to realise that many galaxies are
rotating so fast that they ought to spin themselves apart – unless, that is,
they contain extra, invisible matter. Further evidence has led us to believe
that this dark matter makes up more than 80 per cent of all matter in the
universe – but we don’t know what it is.

Problem 2:

**Inflation**
In order to explain how uniform the universe is on the largest scales,
cosmologists think it ballooned at incredible speed soon after the big bang.
But what triggered this period of inflation and what switched it off? One
hypothesis involves a quantum field that has since disappeared for
unexplained reasons.

Problem 3:

**Dark energy**
In 1998, we discovered that the universe’s rate of expansion is
accelerating. So far, all cosmologists have been able to do is give this
phenomenon a name: dark energy. We have very little idea what it actually
is.

Problem 4:

**The Hubble tension**
We can measure the present-day expansion rate of the universe – known as the
Hubble constant – in two ways, one based on nearby supernovae and another
based on radiation left over from soon after the big bang, called the cosmic
microwave background (CMB). The latter method gives a number that is about
10 per cent smaller than that given by the former.

Solution:

Under teleparallel gravity, there is no need to invoke dark matter or dark
energy. Instead we have a different picture of how ordinary matter responds
to gravity. Inflation still happens, but it is a natural consequence of the
state of the early universe. The Hubble tension also disappears. If gravity
operates differently to how we think on the largest scales, then we would
need to tweak the way we analyse the CMB. Indeed a version of teleparallel
gravity has already been shown to resolve the Hubble tension in principle
(see main story).

What one can agree with after reading this article (in which there is not a word about the Holographic Principle) is that cosmology, like all physics, is in a state of deep crisis. As a consumer, I have the right to judge that the architect and builders built a bad foundation, spent a lot of money, but if the foundation does not work, then instead of a strong building we get construction waste.

ReplyDeleteYou are making such a brave statement about others' work (obviously including Einstein's, Hubble's, DeBroigle's and Hoking's among others). You must be a great scientist or indeed a very successful person of global significance to judge what people like those have achieved. Could you share some of your latest articles or any signiticant scientific achievement of yours, pleaae? I am really curious about how you suggest resolving the crisis.

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