Archive for August, 2007

How String Theory Solved a Sticky Problem, or Hadrons, Hydra of the Strong Force

August 30, 2007

I’m in the midsts of playing paper ping-pong with collaborators in Europe. That is to say that we’re writing a paper together and it’s only efficient for one person to be working on the draft at any one time.

In the mornings here in Beijing I have been writing the paper and performing calculations. Then when my collaborators come online in Europe I send them the draft and my latest findings, we discuss changes and additions and then as I leave the office in the evening here they start working on their changes, e-mailing it to me when they leave the office. I then pick it up Beijing am. etc.

We’re getting near the end, I hope, but there’s still more to do.


Anyway, while the paper is in the other court I have a few minutes to explain roughly what I do, having introduced myself at length in the previous post.

My primary interest is in using string theory (see several previous posts to find video material on string theory at all levels) to try and understand one of the four forces of nature – the strong force. A force with a peculiarly tricky set of properties.

I’ll explain a little about the strong force (which holds the nucleus of an atom together and is felt by particles called hadrons) in a bit and tell you why it’s so hard to understand its properties.

It’s rather strange that we have any problems with understanding this force because we can write down exactly its fundamental constituents and interactions. In fact we’ve been able to do this for about 30 years. The theory is described by QCD (quantum chromodynamics). QCD describes how the quarks (the constituent particles of hadrons) interact with each other by exchanging gluons (the QCD equivalent of photons in electromagnetism)

The form of this QCD theory doesn’t look vastly different from that of the electromagnetic force, described by QED (quantum electrodynamics) though there are some very important differences between the two.

We can perform calculations in QED to immensely high accuracy and can test these calculations against experiment. The answers come out time and again to be correct to many many decimal places. This theory and its applications are amongst the greatest triumphs of 20th century physics.

The method that we use to perform calculations in QED is called perturbation theory. QED describes photons and charged particles (for instance electrons) and how they interact. The lucky thing about QED is that they don’t feel each other’s effects very strongly. We say that they are interacting weakly.

In fact in the limit that they don’t interact at all we can calculate exactly what happens – it’s usually a completely solvable computation. Perturbation theory says that we start with the solution in the case where they don’t interact at all and ask what happens when we turn on the interactions a tiny bit. Let’s say we turn on the strength of the interaction to be some tiny value epsilon.

Well, we can calculate what the interaction looks like when we’ve turned the strength above zero in a series expansion in this value epsilon. First there will be terms which come with a single power of epsilon, then terms with two powers of epsilon, then three, etc. etc. This will go on indefinitely.

I’ll give you an example. Say my calculation gave me a series like this:

Answer = result if we had no interaction + epsilon O(1) +epsilon^2 O(1) + epsilon^3 O(1)+…

(The sort of question we might be asking is about the scattering amplitude of one particle off another. Clearly when there are no interactions these particles should pass each other as if there is nothing else about)

O(1) means that these terms are of order 1. They might be 0.5, or 3 say, but not some huge or tiny number which is dependent on epsilon (this is a simplification but for this line of argument it is enough)

So, if epsilon is really tiny, say 0.0001, then the third term is 10000 times smaller than the second and so it really shouldn’t be important to keep this, or other, ‘higher order’ terms. We can simplify everything by not calculating anything except the first two terms. The other infinite terms can be thrown away.

What if epsilon was 0.1? Well, then the third term would be 10 times smaller than the second, but maybe we are interested in getting our answer accurate to this precision (10%). The third term is 100 times smaller and we are not interested in 1% accuracy, for the sake of argument. If we wanted 1% accuracy then we would need to include the fourth term as well, but not the fifth.

How far we go is dependent on: How accurate we want our answer and also the strength of the interaction. For really weak interactions everything is very easy and we have no problems.

It’s lucky that in QED the value of this coupling, epsilon, is very small. We can calculate just a few terms in the series and get answers to extremely high accuracy.

But what if the value of epsilon wasn’t a small number, but a number, for instance, larger than 1? Well, we could still calculate the terms in the series in just the same way as before, but now the third term is more important than the second, and the fourth term more important still. This is clearly a problem because it looks like we have to calculate ALL THE TERMS and we so liked this method because we could stop when we’d had enough. Calculating all the terms one by one would be impossible.

We may hope that we can add up these terms in a very simple way to give us something which is a nice function, rather than an infinite, divergent series.

The reason QCD is difficult to deal with is exactly because the value of this coupling constant, epsilon, can be large and there is no simple way to resum the series. We seem to be stuck! Our tried and tested method has broken down on us!

It turns out that there are some techniques we can use to look at what is happened to QCD at low energies (it turns out that this coupling constant epsilon is dependent on energy and at high energy it is small again and we can happily use perturbation theory). We can use large computer simulations to try and calculate the partition function (a function which encapsulates many properties of the theory) for our system by brute force, by summing over a huge number of field configurations generated by clever algorithms. In order to do this we have to discretise spacetime, amongst other approximations. This is called lattice QCD and gives us a lot of very interesting results. However, there are limitations and the computer power and time that goes into this is enormous.

There are other methods to understand QCD at low energies. We can use the symmetries of the theory to construct an effective low energy theory which doesn’t have the quarks and gluons as fundamental constituents but rather bound states of these objects – called hadrons.

One of the important points about QCD is that we never seem to see quarks moving around on their own, like we see electrons moving about freely. When you have two quarks and you try and pull them apart you find that the force between them gets greater as you pull, until, when you’ve put in enough energy you find you have created another two quarks which are now attached to the ones you were first pulling apart.

The particles which we do see in our particle accelerators are hadrons, in which the quarks are confined to live within close proximity of one another, two or three at a time.

We’d really like to be able to prove from our relatively simple theory of QCD that confinement must be seen – that we never see quarks (at normal temperatures and pressures) living alone. It turns out that this is a really hard problem.

In fact, when string theory came along in the 60s it was first developed to try and understand what was happening when these hadrons interacted. It worked pretty well, but there were some places that the predictions didn’t agree with experiments. Then came along QCD and we realised that this was actually the correct theory to describe the strong force.

String theory then took off when people realised that it was a consistent, quantum mechanical theory which included gravity. It turns out that having a quantum theory of gravity is really very tricky and when we try and use point particles to construct this, we get into trouble very quickly. However, string theory automatically gave us gravity and removed the problems which had been there in the point particle case.

String theory has (with periods of quiet reflection) moved forwards to give us many insights into how amazing our universe might well be, but this isn’t what I’m going to talk about here.

In 1997 it was found that string theory when formulated in a particular geometry seemed to be telling us something about strongly coupled theories – theories where the parameter epsilon is too big to perform a perturbation expansion. In fact what it told us was that string theory in this 10 dimensional geometry was equivalent to a particular strongly coupled gauge theory in four dimensions.

First of all, what this equivalence meant wasn’t really understood but we have learnt more and more about this over the last decade and amazingly string theory has come back to where it originated as we try to use it to understand QCD.

There is a lot to say about the equivalence of these two theories, what it tells us about QCD and what it tells us about the nature of spacetime. I will leave this for the next installment…

Jon Shock Introduces Himself

August 28, 2007

While I’m busy getting married, Jon has graciously assented to being Guest Blogger. Thank you, Jon!

I promised to write a note about myself, as a scientist, as a string theorist. I’ve taken a slightly strange route into this field and I’m also perhaps not an ‘average string theorist’ whatever one of those is.

I did my undergraduate degree at Bristol University, in the South West of England, a wonderful, vibrant city. A perfect sized city full of student haunts, extremely multicultural areas and a constant buzz, whether at the many great arts cinemas, the constant flow of bands coming through the city, the excellent restaurants popping up all over the place and wonderful countryside not far away.

I loved being an undergraduate in Bristol, not only because the city was wonderful but also because I quickly realised that I was one of the lucky few who had taken a subject which felt right from day one. I enjoyed physics a great deal, I loved the challenges, the eureka moments, the nights not sleeping because I had a problem buzzing round in my head. I took four years in Bristol fascinated by just about every course I took and doing well at them too.

In the final year it was necessary to pick a project to work on for the year. What appealed most was a project in particle physics. I’d realised that this was about the most fundamental aspect of physics I could hope to be studying. I ended up doing a project related to the Babar detector at the Stanford Linear Accelerator centre (SLAC). My project partner and I had the task of working out the most efficient way to sift through data for certain events that would occur at this detector after a particle collision, out of the mass of background events which were not interesting for our particular study.

We were studying the lepton flavour violating events tau to mu gamma and had a particular motivation for studying this event. This meant trying to understand the theory behind it, in order to give a good writeup (not in order to better accomplish the task of data analysis). Anyway, I learnt about a variety of subjects and spent many many weeks creating code to sift for the particular events that we would be searching for in the real data. I’ve talked a little in the past about the genetic algorithm I wrote for this task which was a lot of fun to create.

Anyway, after a successful project I was offered a dream PhD. I was to spend a year in Southampton University learning quantum field theory, group theory, supersymmetry and teaching myself B physics (the physics of mesons containing b-quarks). I was then to go to California, to SLAC where my original masters project had originated, to study CP violating in B meson systems – definitely not string theory. I would have an advantage over many of the students there who would have jumped straight into the detector physics and analysis, whereas I would have a year of theory behind me.

So, I started at Southampton and again loved it, I spent hours pestering the lecturers over points that didn’t seem to make sense, gaps in arguments, trying desperately to get a thorough understanding of the topics we were studying. I had a lot of fun discussing and arguing with my fellow students about what we were learning. I hugely enjoyed the first six months of theory and it seemed that I could do it. That is to say that I could keep up quite happily with the courses, knowing whether or not I could do my own original research was quite another matter.

After six months I went to California to get oriented with the setup at Babar, to meet the people and to learn some more about the project I was going to be involved with.

I arrived in sunny San Francisco, and made my way to Stanford through the lush green hills under perfect blue skies. The area around Stanford is extremely affluent, and I was greeted by multi-million dollar houses and a never ending stream of 4x4s (this did not impress me!). SLAC itself is a huge expanse of land dotted with buildings maintaining the accelerator and the detectors along with a theory division and many administrative buildings. The site is very peaceful, close enough to San Francisco to allow for entertainment when you need to get out and close enough to Palo Alto and the surrounding towns that there is a wealth of fine restaurants to sate the appetite.

I met many of the PhD students working on Babar and some of the more senior staff. I had a tour of the grounds and wandered around the surrounding area. All was perfect as far as I could tell. I spent some time continuing to learn more about the physics and speaking with the young researchers. A friendly, close knit community who seemed to have a good balance of work and play.

I was told a little more about the work that I would be doing and something became quickly clear to me. I asked about the physics that the students did. Physics? They asked, we don’t do physics! We do data analysis. I still don’t know how true these statements were but they claimed that they hadn’t done any physics since they were undergraduates. They spent their time doing either engineering on the accelerator, writing C++ codes to analyse data or software for the detector. All of this is vital for the progress of theoretical physics, and I truly wouldn’t want to put anyone off this genuinely fascinating area, but it was a shock to me at the time. It seemed that although I had a training in theoretical physics, I was still going to be spending a good deal of my time simply doing data analysis.

I should note that all these students loved what they did. They had an incredible life in California working on very exciting projects and having spent some time performing these tasks of data analysis they would get more and more involved with the physics. However, the gap between experimental and theoretical particle physics is not small and somehow I was going to have to straddle the gap – essentially fulfilling both roles at the same time.

In retrospect I may have been able to do this. At the time it felt like I was going to be pulled into the world of data analysis. Something which I had spent a year doing as an undergraduate, had found interesting at the time, but having now spent 6 months learning quantum field theory the prospect had rather lost its appeal. I was just so hugely enjoying exploring the arena of theoretical physics that I was horribly torn.

I got back to the UK with a huge decision to make. My week at SLAC had been great, but the thought of giving up the more theoretical end of the subject was a terrible one for me. The options were either to do something that I had done before and knew that I could do, live in California with a great group of people working on an important research topic with a relatively safe future and a very good pay (compared the studentship in the UK). Or, I could Take a plunge into an area which I knew I enjoyed hugely but had never been let loose on, stay in Southampton with an admittedly great group of people but without the Californian weather or the pay to match.

This was perhaps the hardest decision of my life – I knew that these were two very different routes on offer. I had many sleepless nights over this, but eventually made up my mind. I had to be true to what I really loved, and that was the raft of subjects which I had been studying in Southampton.

Having made this decision and mucked people around in the process I had to make up my mind which of the fascinating areas of theoretical physics I was going to work on. I had done a very basic project as an undergraduate on string theory and five or so lectures in Southampton on this subject from Nick Evans helped to make up my mind.

I went to speak with him about his research and about the possibility of working with him and before I knew it I was calculating D7 brane actions in non-supersymmetric supergravity backgrounds in order to understand chiral symmetry breaking in strongly coupled gauge theories. I loved it!

A PhD in the uk is a bit of a strange beast, though it has changed slightly since I did it. My PhD was three years long. The first year was spent learning quantum field theory, group theory, supersymmetry and a bit of strong coupling dynamics. Then with two years left, including the daunting task of writing up you dive into research.

Normally one applies for a postdoctoral position a year before completing your PhD. This essentially gives a year of research, from the end of learning the groundwork to applying for positions. This puts a lot of pressure on the student to start on research work as soon as possible.

As I say, things have changed now and the PhD is four years rather than three. This doubles the time between starting research and applying for postdocs, which is a big difference, I feel.

Anyway, after a year with a paper and a reasonable number of citations under my belt I applied for positions and was offered a postdoc in China. I figured that now was the perfect time in my life to have a bit of an adventure, giving me the opportunity to pursue what I so enjoyed.

I shouldn’t give the British system a bad name. Many people in England come out of a three year theoretical physics PhD with a great wealth of knowledge under their belts. I left with three papers and feeling a bit overwhelmed by the task of being let loose on the world. My supervisor was however superb, a paragon of patience in the face of a constant barrage of questions and puzzles, and disbelief. He came up with great projects to work on and gave me enough responsibility to explore some interesting questions. During my two years of research I made some interesting finds and spent some time bashing my head against brick walls (I spent about 6 months trying to solve a system of equations which just never worked out in the end – it’s still on my mind).

Two years of study whizzed by, I did my research and I was lucky enough to travel to some great places for exciting conferences, meeting hugely inspiring and occasionally dauntingly intelligent people.

Two years on and here I am, currently sitting in a cafe in Beijing where I seem to spend a lot of time doing my work these days. I’ve loved China, as can be seen from my blog, I hope. There have been definite ups and downs but overall it has been a truly life changing experience. Working at the ITP in Beijing has also been a life of contrasts. There are many excellent researchers here, but I was essentially employed by my boss because there was nobody working directly in the area in which I had expertise. Suddenly I was the expert in this area, essentially in China, and while this responsibility has been excellent, it has meant that I haven’t had many other people to learn from and discuss questions with directly. I’ve given lots of talks around Asia over the last two years at a variety of levels to audiences ranging from entire groups of string theorists to a department full of scientists researching optics. That was actually quite a lot of fun!

So, that takes us roughly up to now, though I haven’t actually spoken about my research at all. I’d like to leave that to another post but I think I do need to make a disclaimer. It may sound strange but I don’t count myself as an expert in string theory. I’ve studied aspects of string theory but my expertise lies in using a particular area of the subject to try and understand one of the four forces of nature – the strong force – and some of its particularly unique properties. There are many questions in string theory which I still want to know about and I am learning more all the time. In fact one of the reasons that I’m very interested in Scitalks is precisely because I want to learn more string theory! I’ve read many papers and books on different areas of the subject, but having an added media format to learn from is really a very useful extra. It adds connectivity wherever you are in the world and whatever situation you may be in. I’m really keen on making this resource work!

Anyway, I hope to discuss a little more about my research next time.

Jon Shock’s Advanced String Theory Recommendations

August 21, 2007

Jon is my hero this week. While I’m busy cooking for sixty people and organizing my wedding, he’s really coming through. Thank you so much, Jon.

For the last installment before Jon comes online, here are his recommendations. Unfortunately, most of the lectures don’t have their own home pages and are links on pages with many other juicy looking lectures, so while I’m trying to figure out how to enter them into our database, I’m not going to hold things up. I’m posting them right here so people can find them. This is pretty exciting stuff! Meanwhile, don’t forget to check out Sean Carroll on our featured video. He’s great!

Here’s what Jon says:

…a few thoughts on more advanced lectures:

First I will give some ideas for lectures which are mostly in my area, the AdS/CFT correspondence.

Eric D’Hoker’s lectures from here are great:

Though I would suggest that just about every lecture from TASI is worth watching. I haven’t seen them all but most of the lecturers are really very good.

On the same subject, those by Mark Van Raamsdonk here are good:

But again, the level of this school is just right for those who have are just about familiar with the previous material.

I can’t view these lectures by Juan Maldacena who discovered the AdS/CFT correspondence but they may well be good, no promises:

This isn’t specifically related,but I just found a HUGE resource of videos, for when you have a spare moment:

I’ve seen Eva Silverstein talk a couple of times on string cosmology. She’s one of the leading researchers on the subject. Again, I haven’t seen this particular video of her but she’s usually a good, clear speaker:

A little old now (2004) but still excellent is this workshop on QCD and string theory:
and the conference here:

My work is most closely linked to Rob Myers’ talks on holographic mesons.

Trying to give a broad range of stringy subjects, the lectures on string phenomenology are here:

More on stringy cosmology here:

and some of the more mathematical aspects here:

As before I haven’t seen all these videos but I’ve seen a few from each conference and can say that there are certainly some which are worth watching. We really need more, interested people to watch them and then advise which are the best. I’m just giving a general selection of some of the more cutting edge areas of the subject.

In fact in general there are thousands of videos to be found here:

If you get a chance, click on over to Jon’s blog, where you can read about Beijing, great jazz and of course, string theory.

We are the Olive in the Martini…

August 16, 2007

Jon Shock put me onto this video where Sean Carroll of CalTech gave a rollicking talk at the Yearly Kos Conference and it’s great fun. (You can find his weblog at Cosmic Variance.) He’s a terrifically engaging speaker, and especially excellent for this particular audience. There isn’t a moment that lags. Here’s just a taste of it:

The interesting fact about this story is that it puts us in our place. We live in a universe where only five percent of the stuff in the universe is the same kind of stuff that we are made of. We are not what the universe is about. We are the olive in the martini, which is not what the martini is about. We are the blinking lights on the Christmas Tree. We are not the substance of what is going on.

So this is an interesting fact about the universe that we never would have been led to had we just sat around and thought. This is a story that is forced on us by going out there, collecting data and dealing with it.

And I want to contrast that way of thinking … A movie, you may be familiar with, called _What the Bleep do we Know?_ … Someone had the bright idea of making a movie about quantum mechanics, so I applaud them for their chutzba when it comes to that. But the problem is that the movie is full of nonsense. The movie tries to get across the message, that what quantum mechanics teaches us, is that we can change the nature of physical reality just by thinking about it – that by putting ourselves in the right mental state, we can make the real world what we want it to be. And after the movie came out, the filmmakers were all given high ranking jobs in the Bush administration.

David Albert is a Philosopher of Science at Columbia University, and he appeared in the movie and he’s an extremely sensible person who knows what’s going on. Basically, he was snookered into appearing in the movie where they interviewed him for four hours and took ten second snippets out of that where he says “oh yes, that’s very interesting”. When the movie came out, he was outraged at how he was portrayed in the movie and he went around giving talks to people who liked this movie. He tried to explain to them what was going on.

David would basically say this: Look, when you’re trying to understand the world, there are two approaches you can have. One kind of approach is that when you try to look at the world, you come with a precondition – you come with a set of demands that the world tell a story that is flattering to you. The other thing you could do is come with an authentically open mind and open heart and expend many different hypotheses, and compare them to the evidence and accept what the evidence tells you, discard the hypotheses that don’t fit the evidence and believe in the hypotheses that do. That second method is called Science. I would like to say that it’s more than that. That second method is called honesty and it probably is a good method to use in all sorts of fields of human endeavor. Science is one of them, but there are probably others that you can also think of.

Check out: Cosmology at YearlyKos Science Panel, Part 1 and Cosmology at YearlyKos Science Panel, Part 2.

Read more about this speech on his post on the Cosmic Variance weblog.

Visualizing 4+ dimensions…

August 14, 2007

Jon Shock of Jon’s Travel Adventures and our guest blogger for the month has kindly written a clear and elegant post on how to visualize more than 3 dimensions. He’s even created a movie for it!

Enjoy -L


You mentioned emergence as an alternative for string theory. In fact it turns out that emergence is one of the most exciting and active areas of string theory itself. This comes from the study of black holes and, more recently a discovery of a holographic correspondence in string theory where it was found that there were dual descriptions of a set of physical theories.

The two descriptions of each theory are extremely different. One of them is of a four dimensional gauge theory.A gauge theory describes the interactions of the force carrying particles – the photon (mediating the electromagnetic force), the gluons (mediating the strong force), the weak bosons (mediating the weak force) and the graviton (mediating gravity). This particular gauge theory is somewhat like the strong force, which we know to be described by QCD (quantum chromodynamics). The dual description of this gauge theory is a ten dimensional theory of gravity, which is a string theory in a specific space-time.

The idea is that in a limit of the gauge theory, higher dimensions may be emergent from the dynamics of the lower dimensional theory. That is, in a limit of the gauge theory the appropriate description is one of a higher dimensional theory of gravity.

This emergence is termed holography because we find that a high dimensional theory can be described by a lower dimensional theory – just as a 2d hologram encodes a 3d image.

OK, so that’s the about the quickest description of emergence in string theory that I can come up with. I’d be happy to explain it in more detail some time. We first learnt about holography along these lines from studying black holes. There is a superb video by Bousso on this subject which can be found here:

OK, onto trying to visualise extra dimensions.

In fact it’s pretty easy to understand higher dimensions from some simple visualisations. The video you posted was fine, up to the fourth dimension, and then things started to get a bit cryptic.

One thing I should mention first is that trying to visualise objects in higher dimensions is good to feel comfortable with what you’re studying. However, sometimes if we try and visualise the things that we are calculating, we may stifle, or bias our calculations. In my opinion it is usually best to become familiar with the mathematics, the purest desciptions of our theory and try to ‘visualise’ in this language rather than trying to use common sense from what we see around us. A good example is quantum mechanics. If we try and visualise what is going on on very small length scales we will quickly tie ourselves in knots and not be able to progress as far as we can by exploring the mathematics of our system. Of course it’s important to be able to translate the mathematics back into what you will actually see in your experiment.

So, given that caveat I will explain how we can build ourselves a hypercube (or at least the frame of a hypercube), the higher dimensional generalisation of a cube.

The way we will do this is to start with less than three dimensions and see what rules we have to follow to go up in dimensions. We will see that we can extrapolate these rules to however many dimensions we want.

Start with a point, a zero dimensional object.

Take this point and turn it into two points. Now pull one of the points apart from the other one, say a distance L away, and join the two points with a piece of elastic. Now you have a line, a one dimensional object.

Now do a similar thing, but this time turn the elastic into two pieces of elastic (on top of each other – now you have four points given by the two ends of the pieces of elastic). Pull the pieces apart in the direction perpendicular to their length. While you’re pulling them apart keep the two ends joined by more elastic which will grow to length L. Now you have a square, something with four edges (pieces of elastic) and four points, or vertices. This object is two dimensional.

Now repeat the process. Take your square and replicate it with another square, on top of the first one. Join the vertices of the two squares with four pieces of elastic which will be stretched in the direction perpendicular to the face of the square. Pull the squares apart to a distance L. Now you have a cube. This object lives in three dimensions. It has six faces, 12 edges and eight vertices.

So, what rule have we developed? We have taken our previous object, replicated it, joined the vertices of the two objects together and pulled them apart in a direction perpendicular to the directions they lie, until the two copies are a distance L apart.

Let’s do that again.

Take your cube and replicate it. Join the vertices of the twin cubes to each other, again by elastic, and pull them apart to a distance L in the direction perpendicular to the direction they are living. There seems to be a problem though, in the last example, the square could live on a piece of paper and you could pull the two squares apart vertically to create the cube, we seem to have run out of directions. We need to pull the two cubes apart in the fourth dimension to a distance L.

Though we can’t really picture this realistically (at least I can’t) we can draw the projection of this onto 2-dimensions, just as easily as we can draw the projection of a cube onto a piece of paper.

When we pulled the one square from the other, we did this in the third dimension, say height, from your paper. So we don’t have another direction to go to pull the cube apart any more. This is where we have to imagine, as best we can, that we take the cube, split it into two and, joining the vertices of one cube with the other pull the two cubes apart to a distance L in the fourth direction, to create an object with 16 vertices and 40 edges. It’s almost as easy to draw the projection of this object onto a two dimensional piece of paper as it is to draw the projection of a three dimensional cube onto a piece of paper.

I’ve just animated this in Mathematica but can’t seem to make an avi from it. If you have Mathematica I can send you the file.

[Jon has put this up on YouTube here: -ed]

In terms of mathematics, it’s even easier to go to higher dimensions. As an example, we might want to know the length of a line in two dimensions, going from some point (0,0) to (x,y). The length, as we know is the square root of x^2+y^2.

In three dimensions for a line going from (0,0,0) to (x,y,z) the length is the square root of x^2+y^2+z^2.

Well, let’s stop labelling directions as x,y,z etc and label them x_1, x_2, x_3,x_4, etc. (1,2,3,4 are simply labels). Now it’s easier to keep track of them.

Now a line in four dimensions stretching from (0,0,0,0) to (x_1,x_2,x_3,x_4) has a length of the square root of (x_1)^2+(x_2)^2+(x_3)^2+(x_4)^2.

Well, if you can work out the 2-dimensional example, I would suggest that it’s pretty easy to calculate the 4, 10, or any dimensional example. Imagining it isn’t easy, but as long as you have a mathematical handle on the objects that are living in your higher dimensional theory, you should be doing fine.

I would suggest having a read of Flatland, a romance in many directions – not for it’s political correctness, but for an idea of how things would be if we didn’t live in 3 dimensions. Chapter 16 is particularly relevant.

Anyway, in terms of lectures for the next level, I would suggest the lectures by Clifford Johnson which you have already put up on the site. He’s an excellent speaker and his introductory lectures are very good. Also the lectures of Barton Zwiebach are very good.

There’s another series of lectures by Lerche here:

I have only been able to read the transparencies, which look broad ranging and reasonably detailed. In the cafe I’m in at the moment I can’t download the video. I would imagine it’s good, but couldn’t guarantee anything.

I’m afraid that I haven’t found many videos that you could embed, without ripping and putting onto youtube or the like. I don’t know what the copywrite situation is with this.

There is a nice colloquium by Shamit Kachru, who is an excellent speaker, talking about string theory and cosmology here:

If you go to this page:

and look on the left for ” Summer School: Strings, Gravity & Cosmology” you will find a host of great videos. Unfortunately it’s really difficult to try and view these independent from their special player (you need IE, too!). It would be great if you could persuade such institutes to let you have such material. The lectures on perturbative string theory, again by Clifford Johnson, are probably excellent and just the right level for first year grad students. I just wish I could rip them and watch them at my own comfort and time. I’ve watched a few, but I just don’t like this format of streaming.

All the best,


Those Pesky Dimensions!

August 9, 2007

This is what happens when a science generalist puts stuff up on the web. According to Dr Shock, my choice could have been better informed. Here’s what he says:

Unfortunately there’s a problem with the first video on the tenth dimension: It’s a) nothing to do with the ten dimensions of string theory and b) completely meaningless as far as I can tell. Sorry 😦

The ten dimensions of string theory are not mysterious at all. There are 9 spatial dimension which can be described perfectly well mathematically, just like the three dimensions we see around us and one time dimension. In special relativity time is described as a dimension just as much as the other three. String theory is completely self consistent with both quantum mechanics and relativity.

Sadly the tenth dimension video is not a good video to advertise either string theory or any good physics.

Woops! Sorry folks.

Jon recommends the Elegant Universe videos by Brian Greene as a nice introduction to String Theory.

A Website just for Newly Discovered Species…

August 8, 2007

Kurt Anderson at Very Short List has found a terrific website called Free Your Imagination, Species Discovered This Millennium, and Other Natural Wonders. It’s glorious and will restore your sense of childlike wonder in the world. There’s a new species of orchid that flirts with wasps! This site is highly addictive, so please view wisely…

August is String Theory Month!

August 6, 2007

Great news! String theorist Dr Jonathan Shock has graciously and generously consented to put together a month-long curriculum on string theory. (Hollywood scifi screenwriters take notice!) On the last week, he’ll be guest blogger and available to answer questions that you can post as comments right here on this blog during the month leading up to his appearance.

You can read Jonathan’s blog Jon’s Travel Adventures where you can read about his exploits in China, where he does his research. He also has wonderful taste in music.