## Eric Weinstein may have found the answer to physics’ biggest problems / Roll over Einstein: meet Weinstein

Eric Weinstein’s theory is the first major challenge to the validity of Albert Einstein’s Field Equations. Photograph: Keystone/Getty Images

##### Eric Weinstein may have found the answer to physics’ biggest problems

A physicist has formulated a mathematical theory that purports to explain why the universe works the way it does – and it feels like ‘the answer’

- guardian.co.uk, Thursday 23 May 2013

Two years ago, a mathematician and physicist whom I’ve known for more than 20 years arranged to meet me in a bar in New York. What he was about to show me, he explained, were ideas that he’d been working on for the past two decades. As he took me through the equations he had been formulating I began to see emerging before my eyes potential answers for many of the major problems in physics. It was an extremely exciting, daring proposal, but also mathematically so natural that one could not but feel that it smelled right.

He has spent the past two years taking me through the ins and outs of his theory and that initial feeling that I was looking at "the answer" has not waned. On Thursday in Oxford he will begin to outline his ideas to the rest of the mathematics and physics community. If he is right, his name will be an easy one to remember: Eric Weinstein.

One of the things that particularly appeals to me about the theory is that symmetry, my own field of research, is a key ingredient. Of course the idea that the fundamental particles of nature are intimately connected to questions of symmetry is not new. But despite the great successes of the Standard Model there remain some very strange questions that have intrigued physicists for some years.

The particles described by the Standard Model – the stuff of nature that is revealed in accelerators such as the Large Hadron Collider – fall into three "generations". In the first generation we see the electron, the electron neutrino, six quarks and their anti-particles, making 16 in total. But then rather bizarrely in the second generation we have another version of these particles which look exactly the same but are heavier than the first generation.

The heavier version of the electron is called the muon. The physicist Isadore Rabi famously quipped on hearing about the muon: "who ordered that?" It didn’t seem to make sense that you should have a heavier version of all the particles in the first generation. What was the logic in that? To compound things, there is a third generation heavier again than the second whose electron partner is called the tau particle.

One of the challenges facing fundamental physics has been to provide a natural explanation for these three generations. Weinstein’s theory does this by revealing the presence of a new geometric structure involving a much larger symmetry at work, inside which the symmetry of the Standard Model sits. What is so compelling about the geometry involving this larger symmetry group is that it explains why you get two copies of something with 16 particles but also that the third generation is something of an imposter. At high energies it will actually behave differently to the other two.

Not only that, it also predicts a slew of new particles that we can start looking for in our colliders. The particles in the Standard Model have a property called spin. The particles we see in the three generations we’ve seen to date all have spin 1/2. But Weinstein’s symmetry is predicting that we will see new particles with spin 3/2 exhibiting familiar responses to the nongravitational forces together with a slew of new exotic particles with familiar spin but unfamiliar responses to the forces of the standard model.

The mark of a good theory is that it makes unexpected predictions that can be put to the test. If the predictions are incorrect you throw out the theory. Supersymmetry, for example – one of the current proposals for how to go beyond the physics of the Standard Model – is beginning to look shaky because we aren’t seeing what the theory predicts we should see. It is interesting that, if Weinstein is correct, you would be hard-pushed to stumble on this stuff in the huge slew of data being generated by the LHC. You’d never find this from going from data to theory. Theory is needed to tell you where to look.

The geometry around the symmetry group that Weinstein is proposing also 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 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".

The beautiful thing for me is that Weinstein’s symmetry group doesn’t just appear out of nowhere. It very naturally emerges from his primary goal, which is to reconcile Einstein’s Field Equations with the Yang-Mills equations and the Dirac equation. The Field Equations control the curvature of space-time and represent our theory of gravity, whereas the Yang-Mills and Dirac equations represent our theory of particle interactions on a quantum level.

Both theories have been incredibly successful in describing the physical world, but they are not compatible with each other. The prevailing attempts to unify the two have been to try to "quantise geometry" – in other words move the geometry of Einstein into the quantum world. Weinstein’s ideas run counter to this trend and are more in line with Einstein’s belief in the power of mathematical geometry. Einstein talked about his belief that the universe was made of marble not wood. Weinstein’s proposal, which he calls Geometric Unity, realises Einstein’s dream.

Although a fan of Einstein, Weinstein’s theory is also the first major challenge to the validity of Einstein’s Field Equations. It requires some courage to challenge Einstein, but Weinstein’s theory reveals 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.

When Einstein produced his Field Equations it was believed 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 "the biggest blunder of my life".

But more recently we have discovered 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 perspective 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.

Another term that was added retrospectively to the Standard Model is the Higgs field. Without the Higgs mechanism, certain particles in the model would be massless. So this extra term is 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 programme is a mass term that doesn’t need to be added artificially. It emerges naturally from the theory.

There have already been feelings within the physics community that the Higgs boson we are seeing in the LHC might not be quite what we think it is. Weinstein’s perspective might help us articulate what it is we are actually seeing.

It has been a privilege to be one of the first to see the ideas that Weinstein is proposing. This is such a major project spanning huge stretches of mathematics and physics that it will take some time to realise the full implications of the ideas. And 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.

Weinstein begins the paper in which he explains his proposal with a quote from Einstein: "What really interests me is whether God had any choice in the creation of the world." Weinstein’s theory answers this in spades. Very little in the universe is arbitrary. The mathematics explains why it should work the way it does. If this isn’t a description of how our universe works then frankly I’d prefer to move to the universe where it does!

*You can respond to Weinstein’s new theory **by leaving a comment under the accompanying blogpost by Alok Jha*

##### Roll over Einstein: meet Weinstein

What are we to make of a man who left academia more than two decades ago but claims to have solved some of the most intractable problems in physics?

In Eric Weinstein’s mathematical universe there is no missing dark matter. Photograph: AP

There are a lot of open questions in modern physics.

Most of the universe is missing, for example. The atoms we know about account for less than 5% of the mass of the observable universe – the rest is dark matter (around 25% of the mass of the universe) and dark energy (a whopping 70%). No one knows what either of these things actually is.

At the subatomic scale, we know there are three families of fundamental particles – called "generations" – and each one contains two quarks, a neutrino and a negatively charged particle (the lightest being the electron). But why are there three generations in the first place?

And the big one: why do the two pillars of 20th century physics, quantum mechanics and Albert Einstein‘s general theory of relativity, not agree with each other?

Solving these problems, the last one in particular, has been the goal of many generations of scientists. A final theory of nature would have to explain all of the outstanding questions and, though many (including Albert Einstein himself) have tried, no one has come close to an answer.

At 4pm on Thursday at the University of Oxford, the latest attempt to fill the biggest holes in physics will be presented in a lecture at the prestigious Clarendon Laboratory. The man behind the ideas, Eric Weinstein, is not someone you might normally expect to be probing the very edge of theoretical physics. After a PhD in mathematical physics at Harvard University, he left academia more than two decades ago (via stints at the Massachusetts Institute of Technology and the Hebrew University of Jerusalem) and is now an economist and consultant at the Natron Group, a New York hedge fund.

He may have an impressive CV, but Weinstein is in no way part of the academic physics community. He will speak in Oxford at the invitation ofMarcus du Sautoy, one of the university’s most famous and accomplished mathematicians who also holds Richard Dawkins’s former academic position as the Simonyi professor of the public understanding of science. Weinstein and du Sautoy met as postdoctoral mathematics students at the Hebrew University in the 1990s.

Weinstein has been working on his ideas to unify physics for more than two decades, but he only shared them two years ago with du Sautoy, who since then has been keenly studying the mathematics. "I get so many letters and emails to me explaining big theories of the universe and I don’t take them all so seriously," says du Sautoy. "Eric’s been telling me the story of his ideas and what I immediately found appealing about them was the naturalness of them. You don’t have to put in extraneous things. There’s a beauty about it that gives you a feeling that there’s a truth about it."

In Weinstein’s theory, called Geometric Unity, he proposes a 14-dimensional "observerse" that has our familiar four-dimensional space-time continuum embedded within it. The interaction between the two is something like the relationship between the people in the stands and those on the pitch at a football stadium – the spectators (limited to their four-dimensional space) can see and are affected by the action on the pitch (representing all 14 dimensions) but are somewhat removed from it and cannot detect every detail.

In the mathematics of the observerse there is no missing dark matter. Weinstein explains that the mass only seems to be missing because of the "handedness" of our current understanding of the universe, the Standard Model of particle physics. This is the most complete mathematical description physicists have of the universe at the quantum level and describes 12 particles of matter (called fermions) and 12 force-carrying particles (called bosons), in addition to their antimatter partners.

"The Standard Model relies on a fundamental asymmetry between left-handedness and right-handedness in order to keep the observed particles very light in the mass scale of the universe," says Weinstein.

He says his theory does not have the asymmetry associated with the Standard Model. The reason we cannot easily detect the dark matter is that, in the observerse, when space is relatively flat, the left-handed and right-handed spaces would become disconnected and the two sides would not be aware of each other.

"Imagine a neurological patient whose left and right hand sides were not aware of each other," he says. "You’d have a situation where each side felt itself to be asymmetric, even though anyone looking at both halves together would see a symmetric individual whose left hand counterbalanced the right."

He proposes that dark energy is a type of fundamental force that could sit alongside gravity, electromagnetism, the strong and weak nuclear forces. This force pushes space apart and its strength is variable throughout the universe. Furthermore, Weinstein’s theory predicts the existence of more than 150 new subatomic particles, most of them with exotic properties (such as electric charges that are greater than one, which is the maximum seen in nature at present).

Radical ideas that claim to solve all the problems of physics – so-called final theories of everything – have come and gone countless times in the history of physics and many are notable for emerging from outside the traditional world of university physics departments. In 2007, physicist and surfer Garrett Lisi made headlines when he claimed to have found a way to unify physics. Lisi’s ideas never took off, because his theories did not make enough predictions that could be tested in experiments, the hallmark of a good scientific idea.

Weinstein has not shared his ideas too widely yet. Scientists who have seen some of the details similarly agree that there is some elegant mathematics in his 14-dimensional observerse. But it takes more than elegant mathematics to make a good scientific theory.

The current leading candidate to unify the fundamental forces of nature is M theory (also known as superstring theory), which proposes that all the particles we know of are actually, at the tiniest scale, vibrating loops of energy. Despite decades of effort from the cream of the theoretical physics community, however, M theory struggles to make any experimentally testable predictions.

David Kaplan, a particle theorist at Johns Hopkins University in Baltimore, has seen and discussed some of Weinstein’s ideas with him. On the plus side, Kaplan says it is "phenomenal" that someone coming from outside academia could put together something so coherent. "There are many people who come from the outside with crazy theories, but they are not serious. Eric is serious."

But he says the theory is incomplete and should have spent more time being critiqued by academics before receiving any wider public attention. "What I would encourage him to do is modest things and take steps and commit to a physical manifestation of his theory – to say ‘here is a set of instructions and a set of equations, do this calculation and you can make the following predictions.’ And then see if his theory matches with the real world or not. He doesn’t have enough of a case. What I’d like him to do is to keep working."

Edward Frenkel, a mathematician at the University of California, Berkeley, has been discussing Weinstein’s ideas with him for the past year. "I think that both mathematicians and physicists should take Eric’s ideas very seriously," he says. "Even independently of their physical implications, I believe that Eric’s insights will be useful to mathematicians, because he points to some structures which have not been studied before, as far as I know. As for the physical implications, it is quite possible that this new framework will lead to new answers to the big questions, after necessary work is done to make precise predictions which can be tested experimentally."

Jim al-Khalili, a nuclear physicist at the University of Surrey who has seen a summary of Weinstein’s ideas (but not the maths) is sceptical. He says Weinstein will need to do a "heck of a lot of convincing" if he wants physicists to take his ideas seriously. "My main concern with Weinstein’s claims is that they are simply too grand – too sweeping. It would be one thing if he argued for some modest prediction that his theory was making, and importantly one that could be tested experimentally, or that it explained a phenomenon or mechanism that other theories have failed to do, but he makes the mistake of claiming too much for it."

Until Weinstein produces a paper, physicists will remain unconvinced and, crucially, unable to properly assess the claims he is making. His lecture at Oxford today will give more mathematical details and Weinstein plans to put a manuscript on the Arxiv preprint server – a website where scientists often publish early drafts of their work, many of which subsequently get published in peer-reviewed journals.

Du Sautoy defends the unorthodox way that Weinstein’s ideas have filtered into the world and expects corrections and updates to become apparent. "We live in an age where everything has to be sealed and delivered and complete when it’s delivered and complete when it meets a journal and, in fact, that’s not how science is done," he says.

Einstein’s theory of general relativity, he added, was not a finished product when first presented, taking a decade of evolution and discussion to get into its final form.

"I’m trying to promote, perhaps, a new way of doing science. Let’s start with really big ideas, let’s be brave and let’s have a discussion," says du Sautoy. "Science is very much an evolutionary process and [Weinstein’s] is such a wide-ranging theory and involves such a wide area of mathematics and physics, this is an invitation to say, ‘This is speculative and it’s claiming a lot so let’s see where it can go.’"

Whatever happens, says Frenkel, Weinstein is an example of how science might change in future. "I find it remarkable that Eric was able to come up with such beautiful and original ideas even though he has been out of academia for so long (doing wonderful things in other areas, such as economics and finance). In the past week we have learned about an outstanding result about prime numbers proved by a mathematician who had been virtually unknown, and now comes Eric’s lecture at Oxford.

"I think this represents a new trend. It used to be that one had to be part of an academic hub, such as Harvard or Oxford, to produce cutting-edge research. But not any more. Part of the reason is the wide availability of scientific information on the internet. And I think this is a wonderful development, which should be supported.

"I also see two lessons coming from this. The first is for the young generation: with passion and perseverance there is no limit to what you can do, even in high-end theoretical science. The other lesson is for me and my colleagues in academia – and I say this as someone who on most days takes an elevator to his office in an Ivory Tower, as it were – we should be more inclusive and more open to ideas which come from outside the standard channels of academia, and we’ll be better off for it."

Alok Jha, science correspondent

Thursday 23 May 2013 guardian.co.uk

## Πρόσφατα σχόλια