Physicists have a problem, and they will be the first to admit it. The two mathematical frameworks that govern modern physics, quantum mechanics and general relativity, just don’t play nicely together despite decades of attempts at unification. Eric Weinstein, a consultant at a New York City hedge fund with a background in mathematics and physics, says the solution is to find beauty before seeking truth.
Weinstein hit the headlines last week after mathematician Marcus du Sautoy at the University of Oxford invited him to give a lecture detailing his new theory of the universe, dubbed Geometric Unity. Du Sautoy also provided an overview of Weinstein’s theory on the website of The Guardian newspaper to “promote, perhaps, a new way of doing science”.
For a number of reasons, few physicists attended Weinstein’s initial lecture, and with no published equations to review, the highly public airing of his theory has generated heated controversy. Today, Weinstein attempted to rectify the situation by repeating his lecture at Oxford. This time a number of physicists were in the lecture hall. Most remain doubtful.
Space in 14 dimensions
Most physicists working on unification are trying to create a quantum version of general relativity, informed by the list of particles in the standard model of physics. Weinstein believes we should instead start with the basic geometric tools of general relativity and work at extending the equations in mathematically natural ways, without worrying whether they fit with the observable universe. Once you have such equations in hand, you can try to match them up with reality.
Weinstein says his approach follows in the footsteps of Albert Einstein, Paul Dirac and Chen Ning Yang, the physicists’ whose equations he is attempting to unify. “The principal authors of all three of our most basic equations subscribe to the aesthetic school, while the rest of the profession had chased the consequence of beauty with adherence to data,” he says.
For example, Dirac predicted the existence of the positron based on the symmetries of his equation describing the electron. He was led by the beauty of the mathematics, not the data at the time, which said such a thing did not exist, says Weinstein.
At the heart of Weinstein’s theory is the “observerse”, a 14-dimensional space that contains our familiar four-dimensional world (three dimensions of space plus one of time). The extra dimensions arise naturally by extending the mathematics of the original four, which appear in general relativity as the diagonal entries in a four-by-four matrix, he says.
The mathematical symmetries of the resulting equations predict three families, or generations, of particles, just as described by the standard model, though the third generation belongs in a different framework in Weinstein’s theory.
His work also predicts new, as yet undiscovered particles, along with mirror images of all of these particles. This group of particles could account for dark matter, the mysterious stuff thought to make up about 80 per cent of matter in the universe.
The trouble is that we should already have seen some of Weinstein’s new particles, if they exist, says physicist Joseph Conlon of the University of Oxford. Properties of some of the predicted particles mean that they should be linked to the strong force, one of the four fundamental forces and the one that binds protons and neutrons.
Experiments at the Large Hadron Collider at CERN near Geneva, Switzerland, have been smashing particles together at high enough energies to overcome the strong force, creating a spray of other more elusive particles, such as the Higgs boson. Weinstein’s new particles should therefore have been detected in the resulting particle shower.
In addition, any modification to the central equations of physics would have to give results that are only a slight correction to existing theories – just as Einstein’s equations offer very similar answers to the approximations of Newton’s equations, says John March-Russell. Right now, equations and experiments are agreeing to 1 part in 10 billion, so Weinstein’s theory would have to be a very small tweak indeed, and he has yet to reveal its size.
Back and forth
Perhaps more fundamental yet, it should be possible to perform a calculation called anomaly cancellation on Weinstein’s equations, says Conlon. This checks whether a list of particles is a consistent extension of the standard model, much like the digits of a credit card number can be added in a certain way to confirm their validity. If the predicted particles fail the test, the theory is wrong. “It would take an hour and a half,” Conlon said to Weinstein at the lecture.
“Can I ask you to do that?” countered Weinstein, who admitted that he did not have answers to these and other questions raised by his talk, but said he would like to discuss them further. He also has remained vague about when and where his equations will appear in print.
In some sense, though, it is a happy resolution to the media storm. Weinstein has found some physicists who are perhaps willing to listen and guide him, and his theory will face the scrutiny that should be applied to any good scientific idea. Geometric Unity could turn out to be a theory of everything – or just a nice bit of mathematics.
(Article by Jacob Aron)