Unified theory of everything that might actually work.

[Mr. Tea]

No, I'm not a field-theorist, but I have a reasonable grasp of at least the basic concepts involved, and other people were taking part in the discussion too. It's interesting for a number of reasons: it doesn't involved any more dimensions than the familiar 3+1, which is almost unheard of in attempts at unifying field theories over the past 20 or 30 years; the use of an obscure symmetry group discovered 120 years ago; and the possibility of empirically testable results. Plus there's the science-sociology aspect of the 'outsider' character (potentially) taking the establishment by storm with his 'wacky' ideas (which, in the topsy-turvy world of modern theoretical physics, are unusual because of how unwacky they are).
So I can't necessarily say "Oh dear, his treatment of the Cartan subalgebra looks well dodgy, it's all a load of old toot", but we can nonetheless have an interesting and enlightening discussion about it. Or you can carry on bitching about Alan Sokal, it's up to you.

Edit: the new PBF is serendipitously germane:

Edit edit: Nicholas Gurewitch gets mad props for using algebra from special relativity, although I'm not sure why mathematicians would need to wear lab coats.

 

[Eric]

I found this a bit shocking, from the blog Bruno linked:

>What about next, I would be thinking. Would cranks with their "theories of everything" who know less than 1% what I do and whose IQ is 45 below mine - literally an inferior species - would be placed upon us or even dictate what we can think about physics? Well, this epoch just here. It has become politically incorrect to say that what surfers like Garrett Lisi are doing are light years away from what theoretical physics is. The closer one is to the top of the real physics, the most impossible it is for him or her to declare any opinions. With a realistic idea about psychology and social science, where do you think that the society will be going if the relative influences are arranged in this way?

What a bastard! `literally an inferior species' indeed.

I havent read the paper and I am no field theorist, but reactions like this one indicate to me a massive insecurity. Not sure about the math. So a Z_2 algebra means what in this context? Does it mean that incommensurable measures don't sum, but just `run in parallel' or something?

I have to say I found the thread more interesting before it devolved into yet another thread on continental philosophy (or whatever one calls it). It is a little amusing/ironic how people complain when MrTea says stuff on `their' criticism threads, and then blithely hijack one of the rare science ones where he is the expert.

 

[Mr. Tea]

Cheers Eric, although as I said upthread, it'd be pushing it a bit to call me the 'expert' here, I just have a basic grounding in the stuff he's going on about.

I have no idea who this Lubos guy is (the bloke you quoted from the blog). Maybe he knows what he's talking about in cutting-edge field theory, but with phrases like "more impossible" he's clearly not a professor of language, at any rate.

Edit: hahah, this is quite good: http://uncyclopedia.org/wiki/UnNews:Surfer_dude_stuns_physicists_with_theory_of_everything (nice Time cube reference!)
Also, Lubos Motl is described as being 'critical of alarmism over global warming' and apparently calls himself a "Christian atheist". :slanted: http://en.wikipedia.org/wiki/Lubos_motl

 

[gek-opel]

Mr Tea: Re: String theory- why all the problems in empirically testing it?

 

[Mr. Tea]

Mr Tea: Re: String theory- why all the problems in empirically testing it?

It's because superstrings exist on the theoretically smallest possible length scale, called the Planck scale, about 10^-35m. To probe physical phenomena at a given scale, you need a certain energy; the two are in inverse proportion, so small scales correspond to high energies. Trouble is, the LHC (due to start next year) will be able to probe physics on a scale of around 10^-19 or 10^-20m, so there is a BIG gap between the superstring scale and the energy reach of even the next generation of colliders. Some wag even calculated that using conventional collider technology, you'd need a machine with roughly the same radius as the observable universe to reach the Planck scale. :slanted: So classic string theory will certainly never be directly testable in this way.

However, there are some claims that the dimensions in which strings exist needn't be on the Planck scale, or that residual stringy phenomena could be measured at more down-to-earth energies, and that the theories might therefore be testable in the near future. In fact, a pretty serious theoretician named Michio Kaku has placed a large bet that a Nobel Prize (which cannot be given for theoretical work without empirical verification) will be awarded for string theory before 2015 or thereabouts.


Edit: I should also say that if string theory (or one of the string theories, or a more general class of theories call M-theory, to which string theories belong) is indeed a 'theory of everythging', it ought to be possible to use it to calculate ab initio the properties of the known consitiuents of particle physics: why there are three 'generations' of matter particles, their masses, quantum numbers (spin, electric charge etc.) and the nature of the interactions between them. So far, nobody has succeeded in doing this, so string theory as it stands has neither predictions to make that can be tested, nor can it postdict the properties of the already well-known Standard Model particles.

 

[Eric]

Here is another basic question. What kind of mathematics forms the basics of this kind physics? Newtonian physics is based on calculus (well maybe this is more chicken-eggy than this way of putting things makes it seem). Presumably it's an applied area of some kind of abstract math right? (You see I have no idea ...)

 

[hundredmillionlifetimes]

I have to say I found the thread more interesting before it devolved into yet another thread on continental philosophy (or whatever one calls it). It is a little amusing/ironic how people complain when MrTea says stuff on `their' criticism threads, and then blithely hijack one of the rare science ones where he is the expert.

No, you still fail to appreciate the irony [or rather the deadlock]: The 'stuff' [very appropriate description, though 'spam' also comes to mind] Tea blurts out on countless posts here is based entirely on ignorance and a constitutive, knee-jerk contempt for the subjects being discussed, irrespective of the knowledge of those contributing or being cited [in science, homologously, its the equivalent of someone spouting "all physics is an irrelevant jerk-off, populated by maladjusted nerds who can't get it up" etc], or rather, such contempt being directly proportional to such knowledge. And given his general absence of posts, the poverty of any posts on conventional science topics, his preference for one-line adolescent sound-bite cliches (school-yard 'jokes' and putdowns), it is clear that he posts on this forum to completely escape from the very area in which he is claiming - simply by announcing it - 'expertise'. He has yet to demonstrate or 'prove' his self-announced credentials here; and what little he has contributed on science is considerably less enlightening than even such popular 'layperson' texts as those of Roger Penrose, Stephen Hawkins, or, indeed, Richard Dawkins, with which many posters here of whatever ilk are already familiar.

And even in THIS thread, he preempts all judgement, as Gek already stated, by confessing to not "actually understanding the intricacies of field theory sufficiently to actually be able to discuss the merits (or otherwise) of this paper."

If you fail to see the mind-numbing, chronic - and sad - irony in all of this, well ...

HMLT: Is it possible that the disjunct between these fields is such that neither are actually legitimised to comment upon the other with any authority? (altho the cross-disciplinary Phil/science stuff in Collapse was much more along the right lines... the arche-fossil explored from an anti-correlationist AND dark matter astrophysics/cosmological PoV...)

For sure. I've always been amazed by this incredible deadlock, partly because I'm just as interested in developments in science as in social theory and philosophy [I once had the very same problem trying to teach maths and stats to eng-lit students as I later did trying to teach political economy to engineers. The antinomy is extraordinary, and not just ideological]

 

[Eric]

Fair enough: trying to engage vs not trying to engage. It also makes some sense that people would turn things so they can be viewed through their favored lens ...

 

[Eric]

Oh blimey, it's hard to say. I work in experimental particle physics and this is hardcore field theory, which is a related but in practice quite distinct discipline. Accusations that his algebra doesn't stand up to dimensional analysis (loosely, that he adds things that in principle can't be added, like masses and distances) are pretty serious, but when you get into this very rarefied kind of mathematical physics, intuitions you may have from more 'down to earth' physics can't necessarily be trusted.

So I guess I'm not really expert enough in this subject to make pronouncements on it myself, and there may be some legitimate criticism but then it may just be jealously from people who can't handle the idea that he's produced this all on his own outsided the mainstream scientific community.

But also hmlt, this doesn't say `I cannot talk about this subject intellligently and am unwilling to say anything further' but `I cnnot make pronouncements' which is quite a different deal isnt it? There should be a difference---particularly with this kind of subject matter---between someone who has the background to engage with the material and clarify for the rest of us what it's all about, and actually judging whether or not it is RIGHT. Some proofs the rest of us need mathematicians to explain to us---but the mathematician who explains the proof may not have the right background to see what is going on. I think you are being a bit unfair here.

 

[Slothrop]

Here is another basic question. What kind of mathematics forms the basics of this kind physics? Newtonian physics is based on calculus (well maybe this is more chicken-eggy than this way of putting things makes it seem). Presumably it's an applied area of some kind of abstract math right? (You see I have no idea ...)

It's basically abstract algebra with a bit of geometry and analysis.

The fundamental object he's looking at is a Lie (pronounced Lee) algebra. Basically, a vector space is a space of objects that can be added together and multiplied by numbers in a base field (normally the real numbers or the complex numbers) to give more objects in the space. The vectors they teach you about at school are the classic example, hence the name. You get something which (in finite dimensions, which I think is what we have in this case) is a basically an n-dimensional space given by a coordinate system based at a specified origin.

To get a Lie algebra, you basically add to this a rather specific sort of multiplication between the members, generally written as a bracket, [x,y]. This has to have various sorts of properties, eg anticommutativity: [x,y] = -[y,x]. The structure of the space with respect to this multiplication then becomes rather interesting - you can ask questions about whether smaller subspaces of the set have self-contained Lie-algebra structure, or which subsets of it are closed under other operations. You can ask about the structure of specific subsets of the space or about the existence of certain sorts of element, or about the properties of certain sorts of function acting on it.

I think that what Lisi is suggesting is that certain aspects of the structure of E_8 correspond to certain physical concepts. But I'm not sure how.

This is the sort of stuff you generally run into at about masters level in pure maths - doing it properly really requires you to understand quite a lot of other simpler structures - so yeah, it's fairly hard abstract pure maths.

 

[Mr. Tea]

Here is another basic question. What kind of mathematics forms the basics of this kind physics? Newtonian physics is based on calculus (well maybe this is more chicken-eggy than this way of putting things makes it seem). Presumably it's an applied area of some kind of abstract math right? (You see I have no idea ...)

It's all about group theory, and in particular the symmetries of mathematical groups. The field theories that form the Standard Model (which is all the particles and forces we know of and can adequately describe at present) can be mathematically constructed if we take the equations of motion that apply to the so-called wave function of the matter particles and demand that they remain invariant (i.e. unchanged) if we apply a certain kind of 'rotation' to the wave function. (This isn't a rotation in real space but in an abstract mathematical space.) If the wave function is invariant, it is said to have symmetry, just as a spoked wheel has rotational symmetry because you can turn it around its axis by a certain angle and it looks the same as it did before. With wave funtions, it turns out that to keep symmetry maintained you need to introduce a term describing a new field, which represents the interation between the matter particles. For instance, if you start with a bunch of electrically charged particles (electrons, say) and apply a very simple kind of rotation, you have to introduce a field which corresponds to photons, i.e. the 'messenger' particles of the electromagnetic force. It's very clever and rather beautiful!

Attempts at unifying the known forces usually (as in this case) involve trying to find bigger, more generalised symmetry groups (like E8) of which the groups describing known particles are component parts (sub-groups).

Edit: also, see Slothrop's post for a good clear description of Lie algebras (which inform the structure of the symmetry groups I've been wibbling on about here).

 

[Slothrop]

Ooh, nice explanation.

I have no idea who this Lubos guy is (the bloke you quoted from the blog). Maybe he knows what he's talking about in cutting-edge field theory, but with phrases like "more impossible" he's clearly not a professor of language, at any rate.

I posted the original article to the PhDComics forums.

Re Lubos Motl, someone there responded:

Two things - in the string theory community Lubos Motl is known to be someone who expresses views very strongly, and an extreme partisan of string theory.
Motl also has an ax to grind with Lee Smolin (who, if you look at the acknowledgements of the paper contributed 'enthusiastic discussions') and (from what little I've seen of the popular coverage) was likely a hand pushing this to prominence.
The reason for the grudge is that Smolin doesn't like string theory. (See his recent book) The short version of why is that he thinks it has been pushed without any experimental verification to the point that it has crowded out other streams of inquiry, that it has sucked up too many man-years without much to show in terms of predicive power, and that he thinks the starting point (perturbation theory about the Minkowskian background) is flawed. The average response from someone in the field to this is that the criticisms would sound better coming from someone who doesn't work on loop-quantum-gravity (which is even less predictive, although with dozens, as opposed to thousands of adherents)

I think that most of the vitriol comes from the personality and conflicts that are outside of the scope of the 'paper'.

Basically, this is the sort of thing that can happen when scientists can't currently check who's barking up the wrong tree by using concrete evidence, and Lubos Motl is a particularly entrenched specimen.

The general response to the paper there seems to be that it's quite nice looking but includes a couple of mistakes (note that it's only up on arXiv so far and hasn't been peer-reviewed yet, but don't expect that to get much mention in the reporting) and doesn't come close to making any predictions - or even check against existing data in any very meaningful way. If he could clear up the mistakes and then get some sort of concrete testable stuff out of it it could be nice, but whether he's going to be able to do that is anyone's guess.

 

[Mr. Tea]

Hmm, an opinionated, hyper-acerbic academic of Slavic extraction - Motl sounds like the kind of guy Dissensians should love to bits!

LQG is certainly a far younger field than string theory and, as Slothrop says, has far fewer adherents, so it remains to be seen how much (if any) real physics work has been done with it in ten or twenty years' time.

 

[Eric]

Thanks guys. Very interesting and sounds like very much fun. I think I need to do some more work to get at the details---a project I may have space to undertake now I've been offered tenure . Thanks also Slothrop for pointing out the existence of the PhD Comics forum. I never noticed that even though I look at that site almost daily---it is on my `internet procrastination loop' along with this place ...

 

[bruno]

Oh blimey, it's hard to say. I work in experimental particle physics and this is hardcore field theory, which is a related but in practice quite distinct discipline. Accusations that his algebra doesn't stand up to dimensional analysis (loosely, that he adds things that in principle can't be added, like masses and distances) are pretty serious, but when you get into this very rarefied kind of mathematical physics, intuitions you may have from more 'down to earth' physics can't necessarily be trusted.

So I guess I'm not really expert enough in this subject to make pronouncements on it myself, and there may be some legitimate criticism but then it may just be jealously from people who can't handle the idea that he's produced this all on his own outsided the mainstream scientific community.

it's the interplay of actual people with virtues and faults that makes a discipline, i don't know why i act surprised when it's like that in everything, people tend to be idiots* (i include myself). from what i gather string theory is giving a lot of people work at the moment, that would explain the virulence at least in part. i think i idealise science somewhat, the whole lab technician thing, divorced from actual human debate. sorry for the pathetic delayed answers, i'm a mess (and in a different time zone).

* i don't know how this translates but a saying goes if idiots could fly, we would never see the sun again