In late May, mathematician Eric Weinstein gave a
talk at Oxford University about his ideas about “Geometric Unity,” a
mathematical theory that purports to explain why the universe works the way it
does. Weinstein He earned a 1992 Ph.D [in Mathematical Physics from Harvard
University and has since held a Lady Davis Fellowship in the Racah
Institute ofPhysics at Hebrew University, an NSF fellowship in the
mathematics Department of MIT.

The image illustrates dark matter particles in galaxy clusters. Dark matter is the invisible and unknown material that constitutes about 80% of the matter in the Universe. Credit: NASA/SAO/CXC |

As Marcus du Sautoy, the Simonyi Professor for the
Public Understanding of Science and a Professor of Mathematics at the
University of Oxford, reported in The Guardian, the geometry around the
symmetry that Weinstein is proposing "gives us an explanation of another
of the big mysteries of physics: what dark matter is and why we can't see it.
Our current theory of gravity predicts that there is a lot more matter in the
universe than the stuff we can see. This hidden matter has been dubbed dark
matter because none of the other forces of nature seem to interact with
it."

When the symmetry in Weinstein's model breaks into
pieces, du Sautoy adds, "there is one half that gets separated in the
mathematics from the piece we interact with. The particles corresponding to
this bit of the symmetry-breaking might account for a piece that has an impact
on gravity but mathematically can't interact with the other fields, such as
electromagnetism, making it 'dark'."

But Weinstein's symmetry group doesn't just appear
out of nowhere according to dy Sautoy, rather it naturally emerges from his
primary goal, which is to reconcile Einstein's Field Equations with the Yang-Millsequations and
the Dirac equation. The Field Equations control the curvature of space-time and
represent our theory of gravity, while the Yang-Mills and Dirac equations
represent the theory of particle interactions on a quantum level.

Weinstein's theory is also the first major challenge
to the validity of Einstein's Field Equations, revealing that "just as
Newton's equations were an approximation to nature so too are Einstein's. One
of the intriguing things to emerge from the mathematics that Weinstein weaves
while combining these theories is a solution to one of the other enduring
mysteries of physics: dark energy and the cosmological constant."

Du Sautoy reports that When Einstein produced his
Field Equations, the prevailing wisdom was that "the universe was
stationary – neither expanding nor contracting. To make his equations work he
arbitrarily had to stick in an extra term called the cosmological constant to
ensure the universe stood still. When it was later discovered that in fact the
universe was expanding he removed the term and dubbed it 'biggest blunder of my
life'."

But we have recently discovered, du Sautoy reports
that "not only is the universe expanding, that expansion is accelerating,
being pushed by some unknown source we have dubbed dark energy. One proposal
for the source of this push involves reintroducing the cosmological constant
into Einstein's Field Equations. But this cosmological constant has always
seemed very arbitrary and a retrospective fix. Weinstein's new theory gives
rise to equations that provide a coherent mathematical justification for why
this extra term should be there. And contrary to what people have thought, it
is not constant. Rather, it varies with the curvature of the universe. We are
in a relatively flat piece of the universe, which explains why the cosmological
constant is so small."

Additionally according to du Sautoy, without the
Higgs field boson, certain particles in the Standrad Model would be massless.
So this the Higgs boson "was added to fix the fact that we know that
particles like the W and Z particles that control the weak force do have mass.
Again, one of the beautiful insights to emerge from Weinstein's unification
theory is a mass term that doesn't need to be added artificially. It emerges
naturally from the theory."

Du Sautoy concludes his Guardian report observing
that Weinstein's radical theory is a major project spanning huge stretches of
mathematics and physics that "just as Einstein's general theory of
relativity took some years to stabilise there are likely to be modifications to
the theory before it is complete. But for me what is so appealing about
Weinstein's ideas is the naturalness of the story, the way things aren't
arbitrarily inserted to make the theory fit the data but instead emerge as a
necessary part of the mathematics."

But, as Columbia University mathematician, Peter
Woit writes in this blog, Not Even Wrong, that if Weinstein "wants to be
taken seriously, Eric needs to disseminate the details of his ideas about this,
as a paper, slides of a talk, multimedia web-site, or whatever. As one
physicist put it here succinctly: 'Paper, or it didn’t happen."

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