At first glance this model might appear to be similar to
String Theory because it involves an eight dimensional
manifold, but a deeper analysis reveals that it will lead to
physics quite unlike String Theory. Remember you read about
it here first.
E8 is known as the exceptional simple Lie group and is the
largest of this category possible. Anything larger has
infinite dimensions. Lie groups are continuous groups such as
the group of rotations of a sphere or a torus. It is possible
to represent the generators of these groups as a set of
matrices and in the case of E8 there are 248 of these if the
matrices are complex, or 496 if the matrices are real.
The group is thought of as being eight dimensional because
every Lie group is related by category theory to a group of
transformations to an underlying manifold, which in the case
of E8 has 248 complex dimensions, but there are only 8
degrees of freedom so the underlying space is of 8
dimensions. The full structure of E8 was only revealed in
March 2007 after hours of computation on a Super Computer.
As quoted in the New Scientist, Sabine Hossenfelder at the
Perimeter Institute argues that Lisi’s idea could be
complementary to String Theory because string theorists were
already looking at E8 in relation to the Calabi-Yau
manifolds. String theorists introduced these as a way of
explaining why the extra dimensions they required in their
string theory were not visible to us at macro scales.
Extending Quantum Field theory into the E8 structure
envisaged by Lisi would lead to a new physics very different
to string theory. For one thing a component of string theory
called super gravity hypothesized a set of super symmetric
partners for each known particle as a way of eliminating the
infinities that appear when extrapolating the theory to
smaller scales. Lisi’s model predicts there are just 20
undiscovered elementary particles. Also Lisi’s model predicts
the three generations of particles.
It seems to me that the reason why quantum waves appear to be
discrete or particle like at small scales can be explained by
the fact that these waves wrap around the underlying manifold
and so can only occur as superposition’s of a discreet
solutions. This is very different to vibrating strings.
It seems to me that the reason why quantum waves appear to be discrete or particle like at small scales can be explained by the fact that these waves wrap around the underlying manifold and so can only occur as superposition’s of a discreet solutions. This is very different to vibrating strings.
A colleague and I were working on this several years ago and we have devised a MUCH simpler version than one might expect it to be. I've started carrying the torch since my friend has since disappeared(if you read this Greg, get in touch with me) and I've gotten it to an almost workable theory at this point and as a matter of fact had a breakthrough just a couple weeks ago that I haven't written down yet.
Here's a basic rundown of it all:
Imagine a still pool of water. Now drop a pebble into it and you get ripples right? Now drop 2 pebbles at the same time and you get the pattern we know as wave interference. Look closely at that wave interference and you'll notice it matches perfectly the current model of the atom(in the case of 2 "pebbles" it'd be the hydrogen atom with an extra electron). If it were "pebbles" then atoms would have very short lifespans because the energy dissipates rather quickly so instead of pebbles, I have recently revised the metaphor to be two streams of water because it also further illustrates that there are two waves of energy(water) interfering with one another. Now if you want an electron to jump from one atom to another you only need to slightly move the "pebble" to create a new interference pattern. There's lots more to it than that but it's the best visual model that I've seen to date.
I have developed other hypotheses regarding this model and I think have devised how the model fits into E=mc^2 but haven't had anyone to discuss this with who is a)knowledgeable in quantum physics to some degree and b)willing to be open to the idea that something doesn't have to be "true" to be useful because I like to use metaphors and apply ideas across a broad range of topics.
Well, let's hear it; who thinks Lisi is a "crank"? I'm likely to think so given what I've read, although I'm definitely not qualified to accurately assess the situation (I leave that to the scientific community).
All that invective is only to be expected. Most of it though is somewhat irrelevant. Take for example the statement that E8 cannot lead to chiral forces. (The weak force is chiral meaning that its strength is depends on the spin state of the particle relative to the direction of the force.)
The latest thinking on chirality is that it indicates a prefered direction in space time. Recently one physicst described how this could be possible without breaking special relativity. The weak force is mediated by the z boson, which is a very massive particle. This relies on the notion that virtual particles unlike their real counterparts travel faster than light.
In one reference frame, the virtual z particle that mediates the weak force transaction is travelling close to infinite velocity, has near zero energy and finite momentum. The strength of this momentum depends on the direction of its spin relative to the direction of its momentum, it is not symetric and hence is chiral. Any Lorentz transformation always yields a consistent view of the way these virtual bosons behave. We may not be completely comfortable with prefered directions, it still seems to imply some form of symetry breaking, but then so also does the notion that particles only gain rest mass via a symetry breaking higs field.
Chirality does not invalidate E8 as a basis for describing the set of elementary particles and their interactions.
It's probably not a "Theory of Everything" but then again such a theory might not be possible. What we really want here is a model that takes us one step past the Standard Model and makes easily verifiable predictions.
I'd say the jury is still out. Everything the Ars article complained of is at least equally true of String Theory.
Many have commented that String Theory has so many degrees of freedom to twiddle that it could describe just about anything at all and so has practically no predictive power. It could even be argued that String Theory can't really be considered a theory so much as a metatheory.
That dosn't make string theory wrong or Lisi's theory right, it just makes it a bit early to start throwing stones. The good news for Lisi's theory is that it will likely come to a point where it can be tested a lot sooner. He will work on the missing parts to nail down the properties of the predicted particles. Then LHC will find them or it will not.
I frequently get the funny feeling that modern physics is doing the same thing the classical astronomers did. They presumed that planets moved in circles. When observations stubbornly didn't match up, they added epicycles to compensate. Of course the epicycles needed epicycles as well and so on until the calculations were approaching impossible but were also approaching a match with observation. Then this outa the box kind of guy suggested simple elliptical orbits and it all into place. Interestingly, an eliptical path CAN be described as an infinite series of epicycles, it's just not the best approach.
I don't know about all the crazy 60gb math formulas but it does have a bit of synchronicity to it that fits in with every thing I've ever observed about the natural world.
That statement should be: "Remember, if you don't look at Reddit, Digg, Slashdot, or the dozens of other more popular sites that carried this story a couple of days ago, that you read about it here first". :-)
I have a very deep respect for all those physicists who have dedicated their superior minds to a life time in accademia. Sometimes I guess they must wish that they had gone into investment banking. Believe me though, it's no fun when you wake up one day and the firm has lost a billion dollars trying to start a hedge fund.
The accademic world has its downside too. They form golden citation circles and survival depends on joining such a group and being cited. Like in all that spay in that blog, they hammer on you if you don't pay homage to all that legacy bagage.
Not very often a new golden circle starts up taking a fresh approach, and it could very well be that this is one of those occassions.
For a long time now there has been an undercurrent of discontent with the String theory. For example Roger Penrose expresses doubts in his "The Road to Reality". Once you finally create an equation that describes your particular theory, you have a much bigger problem to solve, the equations that describe the space in which the branes and strings inhabit. Hardly a theory of everything! Then again there may be no such thing!
I have long believed that string theory lost direction very early on in its origins. It does not for example increase our understanding of the wave particle duality and quantum entanglement. It digs a hole way too deep. With origins in super gravity and the renormalisation group, it was able to unify all the forces except for gravity, so at a very fine magnfication the music stops and particles become strings and branes or quantised space-time. Surely what happens at such a deep level is almost irrelevant.
I think that E8 offers great hope simply because it is the most complex simple Lie group possible (with finite dimension) and particle interactions are described by Lie groups. The renormaliation and the non-linear aspects that lead to quantisation can come later.
The science is way over my head, so I'll just comment on the personalities :-)
Like in all that spay in that blog, they hammer on you if you don't pay homage to all that legacy baggage.
I guess Garrett's theory, if right, makes String theory redundant and wrong, so the string-theorists feel threatened. They maybe in danger of becoming like these scientists The Onion reported on. The (most) hostile guy in the thread is the one that the Ars Technica article mentioned in a comment above refers to as part of its "crank" labeling. Go ahead and point out the falsities in a paper, but when you start labeling the author a "crank", "crackpot", and his paper "nonsense" it says more about you than it does him. The labels say nothing about his theory. It seems to me that some of these guys are treating their scientific beliefs like a religion.
Does this theory - or does any aspect, of such theories - say anything about why the speed of light "is what it is?"
I know (we all know) it's 186-thousand-blah-blah miles per second, and independent of the reference frame of the observer, and all that. But does anything, yet, tell "why 186-thousand-blah-blah, instead of, you know, 203-thousand-blah-blah ?". What's it *contingent* on? Does _that_ fall out of these theories, anywhere?
Thank you for your comments and elucidation so far.
The speed of light depends on the units of length and time you are using. Sometimes physicists simply use units that make c=1. Some physicists have proposed a variable speed of light therory as an alternative to the hyperinflation. In this model the speed of light is proposed to have been much faster in the past.
Of course, since you can always choose units that make c=1, this is equivalent to making some other constant vary over time, specifically they are refering to the fine structure constant, a dimensionless number that combines the charge on the electron and planks constant.
None of this has anything to do with using E8 to describe the set of elementary particles and their interations. As I said before, if Garret succeeds, it is unlikely to be a theory of everything, but it just might kick start a new boom of activity in related areas like cosmology.
>>>The speed of light depends on the units of length and time you are using.<<<
Oh ... well, of course it depends on the units, but I meant, "with the units being what they are ..."
Hmm. So, I suppose my question is essentially equivalent to asking "why is the fine structure constant what it is?" (Good article at wikipedia, by the way ... thank you for suggesting it. Feynman's quote was essentially _my_ question, except with 'the speed of light' instead of 'the fine structure constant'.)
I looked into the variable speed of light theory years ago. To me it seems to imply plank's constant changing over time rather than C. The effects of this change are quite unlike those of GR where close to a massive object clocks slow down and space in the radial direction stretches. VSL implies back in the past clocks slow down but space is compressed. The framework of GR can represent this as warped space time, but I guess it's easier to think of it as quantum temperature thing. The quantum temperature was lower so correlation lengths in both the space and time directions were longer.
Albert Einstein was a patent clerk with no university affiliation when he formulated his theory of relativity. Universities do not hold the monopoly on creative reasoning. I do not have the necessary physics background to critique this paper effectively, but to label this individual a "crank" because of his non-affiliation definately falls outside of the realm of scientific reasoning.
Much more important than whether he is a crank or not is whether there are any testable predictions - he claims there will be before LHC starts producing data.
Go for it.
Right now physics is in a funk because the Standard Model is both very good and crap. Very good at predicting numbers and crap without gravity and an explanation of how to get the 17 arbitrary parametes from first principles.
If someone goes off and shows that this E8 is crap by fixing the standard model we have all won.
Breakthrough on the theory of everything, is Garrett Lisi another Einstein?
News this week that a complete unknown not affiliated with any University has produced a model based on the E8 Lie Group that seems to extend the standard model of nuclear physics to include gravity. See Surfer makes waves with scientific 'theory of everything and Is mathematical pattern the theory of everything.
At first glance this model might appear to be similar to String Theory because it involves an eight dimensional manifold, but a deeper analysis reveals that it will lead to physics quite unlike String Theory. Remember you read about it here first.
E8 is known as the exceptional simple Lie group and is the largest of this category possible. Anything larger has infinite dimensions. Lie groups are continuous groups such as the group of rotations of a sphere or a torus. It is possible to represent the generators of these groups as a set of matrices and in the case of E8 there are 248 of these if the matrices are complex, or 496 if the matrices are real.
The group is thought of as being eight dimensional because every Lie group is related by category theory to a group of transformations to an underlying manifold, which in the case of E8 has 248 complex dimensions, but there are only 8 degrees of freedom so the underlying space is of 8 dimensions. The full structure of E8 was only revealed in March 2007 after hours of computation on a Super Computer.
As quoted in the New Scientist, Sabine Hossenfelder at the Perimeter Institute argues that Lisi’s idea could be complementary to String Theory because string theorists were already looking at E8 in relation to the Calabi-Yau manifolds. String theorists introduced these as a way of explaining why the extra dimensions they required in their string theory were not visible to us at macro scales.
Extending Quantum Field theory into the E8 structure envisaged by Lisi would lead to a new physics very different to string theory. For one thing a component of string theory called super gravity hypothesized a set of super symmetric partners for each known particle as a way of eliminating the infinities that appear when extrapolating the theory to smaller scales. Lisi’s model predicts there are just 20 undiscovered elementary particles. Also Lisi’s model predicts the three generations of particles.
It seems to me that the reason why quantum waves appear to be discrete or particle like at small scales can be explained by the fact that these waves wrap around the underlying manifold and so can only occur as superposition’s of a discreet solutions. This is very different to vibrating strings.