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"We think in generalities, we live in details"
  
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Has a surfer discovered the theory of everything?
« on: 2007-12-02 12:51:46 » |
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[Blunderov] What is mathematics really? Is the universe made of it? It seems that information is "real". Does this mean mathematics is "real" too?
http://science.howstuffworks.com/theory-of-everything3.htm
Has a surfer discovered the theory of everything?
by Josh Clark
Inside This Article
1. Has a surfer discovered the theory of everything? 2. The Shape of Everything 3. Could E8 could be the theory of everything? 4. Criticism of Lisi's Theory 5. Lots More Information 6. See all Physical Science articles
When Albert Einstein published his paper on his special relativity theory in 1916, it seemed as though he had turned the physics of Isaac Newton on its ear, but in fact, he used Isaac Newton's physics as a base on which he could build his own theories. The universe is too complex for one person to understand alone, so physicists must rely on the aggregate findings of their peers to learn just what makes the universe tick. This includes the standard model of quantum physics, a theory began by Max Planck in 1900, which is arguably one of the most influential theories to date.
While many have contributed to the study of physics, not all theories have been proven correct, or even useful. Some theories are pared down, others are discarded entirely. Many researchers spend their life's work in pursuit of theories that later prove inaccurate. It is with this knowledge that A. Garrett Lisi submits his theory of everything to the world -- his "Exceptionally Simple Theory of Everything."
A. Garrett Lisi at the annual Burning Man festival.
Newtonian physics describes why a rolling ball eventually stops. Relativity explains why you don't fly right off the spinning Earth and into space. Quantum mechanics explains why the same force that keeps you firmly planted on Earth doesn't tear you to shreds. The only problem is, none of these physical theories fully -- entirely -- explains every single aspect of the universe. What's more, while we know that the universe is influenced by four forces -- gravity, electromagnetism, and strong and weak nuclear forces -- we don't know how gravity works in conjunction with the other three. But there must be one common thread that binds them all together: A theory of everything.
Physicists have searched for the thread that unites relativity and the standard model of quantum physics. If uncovered, this same thread is expected to reveal what constitutes the fabric from which our entire universe is woven. In the 1970s, physicist Michio Kaku postulated string theory. This theory of everything predicts that small, vibrating strings serve as the building blocks of all matter, and that their vibrations create all four of the forces in our universe.
But Kaku's theory requires the existence of 11 dimensions to work and, so far, we only know of four dimensions. Despite the fact that it can't be readily proven true, string theory has breathed life into the pursuit of the theory of everything, and the world of physics has invested deep inquiry into the theory.
Using yet-undiscovered aspects of physics to make scientific predictions is nothing new. The fact that scientists have yet to find tiny strings through scientific observation doesn't rule out string theory. And Einstein's special relativity mathematically predicted the existence of black holes, long before any evidence of them had been observed.
While academia has pursued its inquiry into the predictions of string theory, A. Garrett Lisi -- a Ph.D. in physics -- has lived in self-imposed exile from his field. He's spent his summers surfing in Hawaii and winters snowboarding in California. Perhaps while enjoying the snow and sea he found inspiration for what will prove to be the theory of everything.
The Shape of Everything
Mathematics is the language of the universe. Absolutely everything, from a plane crash to your skin pigment to the shape of a sphere can all be expressed using mathematical equations. This last example is most important to Lisi's pursuit of the theory of everything. It is using a description of a symmetrical geometric object that Lisi may have uncovered the relationship between the standard model of quantum physics and relativity.
In the 19th century, the mathematician Sophus Lie created algebraic formulas to describe the shape of symmetrical objects. These are called Lie fields. His work was built upon by succeeding mathematicians, and in the 1890s, Wilhelm Killing found a set of Lie fields that described perhaps the most complex shape in our universe, the E8 group. The E8 group, an interrelated 248-dimensional symmetrical object, is an extremely complex one.
Courtesy John Stembridge/Atlas of Lie Groups Project
The E8 Lie group, a perfectly symmetrical 248-dimensional object and possibly the structure that underlies everything in our universe.
This dense object is so complex, in fact, that it was plotted by computer for the first time in 2007. It took a team of 18 mathematicians -- the Atlas of Lie Groups project at the American Institute of Mathematics -- four years to calculate and plot the formula for E8. The group spent two years on the calculations, and two more dedicated to figuring out how to calculate the shape on the computers available today.
Ultimately, the Atlas project broke the E8 calculations into sections and assigned them to different computers. They took the incomplete answers from each section and pieced them together into the Sage supercomputer, which took 77 hours to complete the task. This is no comment on Sage's ability: Were the E8 formula and resulting answer written in small print on paper, the paper would cover a 7 square-mile area.
While the Atlas project was the first to actually plot E8, mathematicians have known about the existence of the symmetrical shape for years. So, too, have physicists. Some have even approached the E8 as a possible theory of everything, but none have come as close as Lisi.
So how can a symmetrical shape be the key to the universe? First remember that a geometrical shape is merely the graphic representation of mathematical formulae. This holds true for a rhombus you construct in high school math class or a racquetball. It is a pattern that is expressed in math and forms a shape when plotted. In this sense, the E8 could be the framework into which everything -- all forces and particles -- fits in our universe.
Confused? Consider yourself part of the club. Garrett Lisi, E8 and the theory of everything is pretty heady stuff. But Lisi actually used relatively basic math to use E8 as the possible key to the theory of everything. Read the next page
Could E8 could be the theory of everything?
Lisi is not the first physicist to look to the E8 -- an interrelated 248-dimensional symmetrical object -- as the possible key to the theory of everything. But he's come up with a clever method that may overcome the tricky problem of adding gravity to the mix. Prior to his attempt, physicists generally held that gravity couldn't be expressed mathematically in the same way as electromagnetism and strong and weak nuclear forces could. It's somewhat like combining paragraphs of Mandarin Chinese and Spanish and attempting to translate the resulting document into English using only an English-Spanish dictionary.
But Lisi had heard about a mathematical way of expressing gravity uncovered in 1977, called MacDowell-Mansouri gravity. He used this method to add an English-Mandarin appendix to the dictionary. Using this expression, Lisi can use mathematical expressions to plug gravity into E8, along with electromagnetism, and weak and strong nuclear forces.
All four of the forces in the universe create a distinct effect on all of the most basic subatomic forms of matter -- called elementary particles. When these particles interact with force carriers (called bosons), they become different particles. For example, when one of the most basic quantum particles -- the lepton -- encounters a weak-force boson, it becomes a neutrino. A lepton interacting with a photon (a boson that carries an electromagnetic charge) becomes an electron. So while there are limited numbers of the most basic particles, when they encounter the different forces, they change to become other, distinct particles. What's more, for every particle, there is an equally distinct anti-particle, for example an anti-quark or anti-neutrino. In total, these make up the elementary particles, and there are 28 of them.
Each of these distinct elementary particles has eight quantum numbers assigned to it, based on the charges each particle has. This brings the number of distinct particles to 224. These numbers helped Lisi make the particles fit into the E8 model. While the E8 is expressed as a 248-dimensional object in one way, it can also be expressed as an eight-dimensional object with 248 symmetries. Lisi used E8 within eight dimensions for his calculations. For the remaining 24 places unfilled by distinct known particles, Lisi used theoretical particles which are yet to be observed.
Take another look at E8, and notice how the lines radiate from each point:
Courtesy John Stembridge/Atlas of Lie Groups Project
Lisi assigned each of these 248 points to a particle, using the eight numbers based on their charges as coordinates within the eight dimensions. What he found was that, like the symmetries in the E8 group, quantum particles share the same relationship within the symmetrical object. He has hope that he has figured out a way to crack the theory of everything, because when he rotated the E8 filled with the force-influenced (including gravity) quantum particles, he found patterns emerging between particles and forces -- photons interacting with leptons, for example, created electrons. The connections shown within points on the E8 match up to real, known connections between particles in our physical world.
If Lisi's method is proven correct, then evaluating the E8 could show physicists how macro-scale gravity interacts with the other, highly-localized three forces.
But does it really work, and how can a 248-dimensional object be the theory of everything? Read the next page to find out what some critics are saying
Criticism of Lisi's Theory
Lisi's theory that E8 could be the answer to how gravity and the other forces work together does have some problems. Lisi himself explains that it's in the most infant of stages. "I'm the first to admit that it's a long shot," Lisi tells the magazine New Scientist.
One of the key hypotheses that may prove or disprove Lisi's theory of everything could actually be substantiated by 2008. Like Kaku's string theory, Lisi's method predicts and requires the existence of presently undiscovered matter. He has used theoretical particles to fill in the gaps left after he used all of the elementary particles. It's possible that the existence of these particles could be detected when the Large Hadron Collider, the most powerful particle accelerator in the world, is completed and put into use at CERN, a particle physics laboratory in Switzerland. The existence of these particles would go a long way toward showing that Lisi's idea may be the one that points the way to the theory of everything.
But there are other, more prickly problems with using the E8 as the basis for the theory of everything. Some physicists dismiss Lisi's method outright, simply because he used an expression of gravity in the same terms of as electromagnetism and strong and weak nuclear forces. The laws of physics state that, because it works on a macro, or cosmic scale, gravity simply doesn't exist in the manner that the other three forces do, since they work on a much smaller scale. These scientists insist that gravity isn't capable of being expressed in the same way as the other three forces. This has been the sticking point for many physicists in search of the theory of everything, and some find it dubious that Lisi has been able to accurately meld gravity and the other three on a mathematical level.
Lisi has also been criticized for adding values that, to this point, haven't been able to be added, specifically fermions and bosons. Fermions are particles that don't spin in whole integers (theirs are stated in fractions, such as 3/2), and bosons -- the force-carrying particles -- have spins stated in whole numbers, like 1 or 2. By adding these two particles together, Lisi has attracted the ire of some of his fellow physicists. One astrophysicist who wrote on Lisi's discovery said that adding bosons and fermions isn't even like adding apples and oranges, but more like adding an apple and a lightning bolt [source: Sigurdsson].
That doesn't mean Lisi's idea for overcoming the disparate nature of gravity and the other forces is wrong. It's important to remember that Lisi is not the first to try using E8 as a way of looking how the forces and particles in our universe interact. But he may be the person who has come upon a clever way which no one else has thought of, and uncovered the first glimpse at the basic function of the universe. But how can a symmetrical object be the theory of everything?
Lisi himself doesn't address this. If his idea proves correct, it could be that the E8 structure provides the infinitely small and unobservable framework for all matter and forces in the universe. It is also possible that the E8 is an image of what our universe as a whole looks like. But before investigation into what E8 represents, it must first be proven that the E8 is really what Lisi suspects it might be.
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