After discussions with Paul Cook I decided to move my blog, Thoughts on science and life from Blogger.com to WordPress instead (one reason being the ease of use of LaTeX commands). So currently, I’m moving some old post to this “new” blog…

## Weinberg Wandering in the Landscape

December 19, 2005*(This article was originally posted on blogger.com on Nov 4, 2005)*

Today, Steven Weinberg posted an article at the arXiv entitled ”Living in the Multiverse” (which is based on a talk he gave at a symposium in September at Cambridge on the topic “Expectations of a Final Theory”).

Weinberg is by any standard an exceptional physicist. He has made numerous contributions to particle physics and also cosmology. One of his controversial – but in many ways also successful – predictions was the prediction in 1987 of the size of the cosmological constant assuming that galaxies should have formed. If the cosmological constant is too large, galaxies and stars cannot have formed since then space would expand and dilute too quickly, before any kind of galaxy can be created by the gravitational pull. On the other hand, if the cosmological constant is too negative, the Universe would simply collapse – that is, approach the Big Crunch too early. Later experiments showed that Weinberg’s rough estimate was correct. Weinberg’s calculation of the cosmological constant is a typical application of the “Anthropic Principle”: the constants of nature (and everything else, I guess) should be such that galaxies and eventually life could form.

*As a side remark, we could ask the following question: What did we actually learn from Weinberg’s successful calculation of the cosmological constant? Basically only that nature is the way it is, since it is the way it is. I would have found it much more interesting if Weinberg’s estimate was completely off from what later experiments confirmed. Then we would have known, that our understanding of galaxy formation – and maybe even particle physics – was fundamentally flawed.*

In the talk mentioned above, Weinberg presents some novel ideas to support the anthropic principle. Weinberg argues that revolutions in physics not only answer questions in new ways (as for example by principles of symmetry as in the general theory of relativity or in quantum mechanics), but they even change our view of which questions are important and well-defined and which are not (as for example the one in quantum mechanics as: “what path did the electron follow?”).

Weinberg argues that the anthropic principle and the “landscape” of string theory seem to be implying something along these lines. As an example, he says:

The larger the number of possible values of physical parameters provided by the string landscape, the more string theory legitimates anthropic reasoning as a new basis for physical theories: Any scientist who study nature must live in a part of the landscape where physical parameters take values suitable for the appearance of life and its evolution into scientists.

The last statement is kind of trivial. The first one does not seem to be substantiated in any way: that the number of solutions is large (~10^500) does not imply, that there is no scientific principles which determine the “correct” solutions (and here I don’t count the anthropic principle as scientific). I find his comment about the hierarchy problem even more problematic:

If the electroweak symmetry breaking scale is anthropically fixed, then we can give up the decades long search for a natural solution of the hierarchy problem. This is a very attractive prospect, because none of the “natural” solutions that have been proposed, such as technicolor or low energy supersymmetry, were ever free of difficulties.

How can we ever know, that this scale is “anthropically” fixed? By realizing, that we could not solve the hierarchy problem in 30 years? In 120 years? Sorry, but to me, this kind of reasoning sounds much like “Intelligent Design”. Just because there is something – like the immune system, blood clotting or the relative masses of ‘fundamental’ particles – which we have not fully understood yet, does not imply that we should resort to aliens, a God (which I don’t think Weinberg would) or our own existence as beings for an “explanation”.

In conclusion, Weinberg seems to be suggesting that asking for an explanation of the values of the free parameters of the Standard Model is equally meaningless as asking how to describe the path followed by an elementary particle.

While writing this comment I realized that Lubos Motl and also Peter Woit already posted some comments to Weinberg’s paper. I tend to agree with their conclusions, but for different reasons…

## String Theory = Intelligent Design? (Part II)

December 19, 2005*(This article was originally posted on blogger.com on Nov 4, 2005)*

Of course I have to respond to Peter’s criticism – which is more than welcome – of the merits of string theory, which I listed below.

At the moment we actually have two separate theories; the Standard Model of particle physics and the general theory of relativity. String theory aims at finding a theory, which combines the two, i.e. is a theory of quantum gravity, and which in a certain sense is more “fundamental” and maybe “simpler” than the former two theories taken together. The point is not just that you would “like to” have a theory, which combines the two (and surely, this was not the historical reason for studying string theory, but that is rather irrelevant). There are some obvious reason for why we should try to find a theory of quantum gravity; I’ll just list some of them: 1) because of singularity theorems (originally formulated by Hawking and Penrose). It follows from general relativity, that singularities in space-time are unavoidable, so general relativity actually predicts its own breakdown in the sense, that the theory does not apply to the singularities themselves; 2) because we should be able to understand the initial conditions in cosmology: cosmology is incomplete if its beginning cannot be described in physical terms; 3) because of the evolution of black holes: black holes radiate with a temperature proportional to Planck’s constant (the Hawking temperature). To understand the final evaporation, a full theory of quantum gravity is needed; (in this respect, black holes are important testing grounds for a quantum theory of gravity); 4) because we would like to have unification of all interactions: all non-gravitational interactions have so far been successfully accommodated into the quantum field theory framework (i.e. in the Standard Model); 5) because of the inconsistency of an exact semi-classical theory: all attempts to construct a fundamental theory where a classical gravitational field is coupled to quantum fields have failed up to now – –and there is an obvious reason for this; if matter is quantum-mechanical, then the energy-momentum tensor in Einstein’’s equation is not a c-number, but an operator and should presumably be replaced by its expectation value. Then we end in turmoil, since the metric depends *nonlinearly* on the state of the matter system 6) because of the avoidance of divergences: String theory (and to a certain extend also loop quantum gravity) provides indications for a discrete structure at smaller scales, and therefore the emergence of a natural cutoff at small distances.

Peter is of course correct in saying, that what I said below (the list of credits of string theory) has been said many times before. That, however, does not make it less true -or more correct for that matter. Science should not be like politics, philosophy (or intelligent design), where you can discuss the pros and cons without ever reaching a “final” conclusion. So, I’ll defend some (for now, only a few) of the comments I made below.

My statement about the “reproduction” of the Standard Model in string theory was clearly not precise enough.

The Standard Model in itself contains a lot of unexplained assumptions; a gauge group (SU(3) x SU(2) x U(1)), some 21 free parameters, the number (three) of fermion generations, the 3+1 dimensions of space-time, chiral fermions in certain representations; gauge bosons, such as the gluons, the W^(+-) and the photon. The masses of these particles have not been computed in string theory (which was also secretly implied in what I was saying since I did not claim, that we understand how supersymmetry should be broken). What we *can* get is the gauge group and chiral fermions. Let’’s see how this could work: the gluons, for example, are described by a four-dimensional SU(3) Yang-Mills theory -– and this theory is closely related to the U(3) Yang-Mills theory which arises at low energies on the world-volume of three coincident D3-branes. This is because the U(3) gauge theory of nine (3 times 3) interacting gauge fields on three coincident D-branes contains a decoupled U(1) theory – the remaining eight interacting gauge fields define the SU(3) gauge theory (since, locally, U(3) = SU(3) x U(1)). Likewise, the SU(2) x U(1) electroweak Yang-Mills theory can be realized by including two additional coincident D3-branes; these two D-branes should obviously not coincide with the three color D-branes, since otherwise we would get a U(5) Yang-Mills theory. Furthermore, at low energies the gauge group is SU(3) x U(1) and this symmetry breaking is triggered when certain charged scalar fields, the Higgs fields, acquire expectation values. But in order to use string theory to describe the full Standard Model, we must study the matter particles and the charges they carry. Roughly, the fermions are represented as strings ending on the D-brane configurations that carry the gauge bosons. A central property of the Standard Model is that the spectrum of fermions is chiral (i.e. the left- and right-handed particle states do not have the same charges). How can we get chiral fermions?

First of all, in the Standard Model, the electroweak interactions SU(2) x U(1) acts chirally, so the fermions remain massless until the Standard Model gauge group is broken down to SU(3) x U(1), after which the masses are determined by the Higgs sector mentioned above. In the string theory picture, quarks, for example, are simply open strings that have one endpoint on one of the three coincident D-branes mentioned above (so that the color charges are determined by which D-branes the open strings end on) -– and the anti-quarks are simply oppositely oriented open strings. Now, where should the other endpoints of the open strings lie?

For illustrational purposes, I’ll just mention the left-handed quarks. The quark states fall into representations of SU(2) (weak symmetry) and are characterized by their isospin. The state with isospin I=1/2 is an up-quark and the one with I=-1/2 is a down-quark. The D-brane picture is very simple: a u-quark is an open string that begin on one of the two coincident D3-branes mentioned above (which we can call the weak-branes), and end on one of the three coincident D3-branes (or color-branes).

However, with a group of three coincident (color) D3-branes and a *parallel* group of two coincident (weak) D3-branes as above, our construction is doomed to fail: the spectrum is not chiral since the spectrum contains left-handed and right-handed quarks with the same charges (this can also be seen by noticing, that a string stretching from a color-brane to a weak-brane is massive). So the color D3-branes should actually intersect with the other two coincident weak D3-branes (I will not go into detail with this).

This was just included to give an illustration of how the Standard Model can be incorporated in string theory – but the embedding of the Standard Model in string theory is obviously not unique. There are other ways to obtain a string theory model of the Standard Model; one, for example, includes intersecting D6-branes wrapped on a six-torus T^6 in the Type IIA theory. But of course we should note, that these models are not fully realistic – the breaking of the electroweak symmetry needs to be worked out, the mass parameters and other couplings should also be calculated etc, and we cannot have six extra non-compact dimensions as above, since these other dimensions would be visible.

What about the free parameters of the Standard Models?

In string theory, on the other hand, there are no adjustable dimensionless parameters; the parameters of the Standard Model should come out as vacuum expectation values of certain scalar fields. These values are determined by the correct vacuum – which we don’t know how to find yet (and I don’t think the anthropic principle will help much).

The discussion about the number of dimensions “‘predicted”’ by string theory is rather old, and often also a bit off-mark, I think. Some argue, that string theory started by predicting 26 dimensions (the bosonic string), then ten dimensions (the superstring) and then eleven dimensions (via M-theory). I don’’t think anybody thought of the 26-dimensional theory as a “realistic”’ one, since it does not include space-time fermions. In superstring theory, ten dimensions are required by a vanishing total central charge, which is a mathematical constraint. There are no obvious reasons for why the result should be exactly ten dimensions – in principle, it could have been five or seven. In the Standard Model, the 3+1 dimensions is something, which is an input, and the theory could have been mathematically consistent in, for example, 7+1 dimensions. In M-theory, we have not ten, but eleven dimensions, which can seem strange; however, if we think of M-theory as the strong coupling limit of the Type IIA theory, then the original ten dimensions were just a result of a calculation done in a perturbative superstring theory, so roughly, the string coupling interpolates between a ten-dimensional and an eleven-dimensional theory (that the question about the number of space-time dimensions is subtle, is also something we learn from the AdS/CFT correspondence).

But, sure, string theory (or whatever it is going to be called) is not in any way a final theory and much work has to be done…

*Note:* More comments relating to Peter’s critique will be posted later 😉

## The $100 Laptop

December 19, 2005*(This article was originally posted on blogger.com on Nov 21, 2005)*

On January 2005, the MIT Media Lab officially launched a research initiative (headed by Nicholas Negroponte, chairman and founder of MIT’s Media Labs) to develop the $100 laptop – a technology that could revolutionize how the world’s children are educated. For this purpose, a non-profit association, called One Laptop per Child (OLPC), was created by Negroponte.

The laptop basically looks like a mutated version of ordinary machines, and uses an LCD display. Some of its current specifications are: 500 Mhz processor, 1GB flash-based memory, 1 Megapixel LCD screen. The laptop will be WiFi-enabled and have USB ports.

It has a removable keyboard and has an *actual crank* (!) to turn so it can be powered anywhere (see the RHS of the picture above; [Image courtesy of MIT Media Lab]). This lends credence to the “laptops around the world” ideal. It’s a brilliant idea for children in the developing countries, where there are not too many powerlines avaliable, but also for poor children in the Western world, such as in Massachusetts, USA .

However, one should take notice, that (according to the develolpers at the Media Lab):

… the $100 laptops—not yet in production—will not be available for sale. The laptops will only be distributed to schools directly through large government initiatives.

But surely, this will be good for competition not only in the educational market for computers. When the $100 laptop is released, most likely a powerful laptop (like an Apple iBook) could end up costing maybe $150. News about the $100 laptop can be found at Google News. A FAQ-list about the $100 laptop is here. More pictures of the $100 laptop can be found at the following page.

Such IT leapfrogging may not do much to help the very poorest of the poor, but for people in China, India, throughout Latin America and the more successful states in Africa, it can be incredibly valuable. Life-changing, for some and – perhaps – even world changing.

## String Theory = Intelligent Design?

December 19, 2005*(This article was originally posted on blogger.com on Oct 27, 2005)*

Don’t get me wrong. I don’t think – as Peter Woit seems to be doing – that the scientific status of string theory is *in any way* comparable to that of the crazy set of ideas called “Intelligent Design”. Basically, Intelligent Design (ID) purports to ‘explain’ the complicated structures seen in life – as the DNA, the structure of a human eye, blood clotting, the immune system etc. by introducing a ‘designer’ (God, aliens, or whatever) clever enough to yield the blueprint of life in all its forms. But in reality, ID does not explain anything at all.

Commenting on Lawrence Krauss’ new book on extra dimensions, Peter Woit says:

The behavior of string theorists that Krauss identifies as most like religion is the argument that “the theory is so beautiful it must be true.” I actually don’t hear many string theorists making this argument these days. If the theory actually were beautiful in the sense of providing some impressive new understanding of physics in terms of some simple, compelling mathematical or physical idea, that actually would be a good reason for believing in it, although not a completely conclusive one. All attempts so far to connect the theory to real physics lead to hideously complicated and ugly constructions.

and,

Some string theorists such as Susskind, argue that one should believe in string theory anyway, and it is this argument which seems to me to be more like religion than science. It’s my impression that Susskind and others are believing something for sociological and psychological reasons, something for which they have no rational, scientific argument. This behavior is not distinguishable from that of many of the intelligent designers, and if it becomes more widespread it ultimately threatens to do real damage to the public perception of science in general and theoretical physics in particular.

Peter’s main argument for comparing string theory with ID is, that

[…] if after a lot of work, there still is no indication that an idea can produce predictions, the continued pursuit of it at some point stops becoming science and starts becoming something more like religion. Susskind and other anthropic landscapeologists have already gone past this point: they have no plausible idea about how to ever get real predictions out of their framework. String theorists who argue that the theory is still too poorly understood, that more work is needed to understand whether there is some way around the radical non-predictivity implied by the landscape, are nominally still doing science.

There are some obvious reasons for which ID is not in any way a scientific theory:

In comparison, string theory is *completely* different; some of the reasons are, I think, that in string theory:

So, when I say, that string theory is intelligent design, I mean, that string theory is the result of years of clever research in trying to find the most fundamental theory of physics and actually – in contrast to ID – is trying to solve a problem, namely that of finding a quantum theory of gravity. In opposition to Lubos Motl, I would call string theory “the Apple of quantum gravity” and not the Microsoft of quantum gravity (but only in the sense, that string theory has proven to be extremely fruitful, both for physics and mathematics, and is built on a tower of innovative new ideas, much like Apple is – and not measured by how popular Microsoft vs. Apple is, where Lubos’ analogy of course is completely correct 😉

## More Dangerous Pseudo-Science?

December 19, 2005** Updated on 04/09/2008**:

*link to video added.*

**Note: Updated on 02/22/2006**. I just recently received an email from S. Ventegodt, claiming that some of my comments below are wrong. I have no intend of writing anything which is plain wrong or misleading and therefore I’m reviewing his complains. Things which at this point have been corrected/made more precise are typed in bold-face.

It seems that the Danish holistic physician *Søren Ventegodt* “finally” is getting some attention in Denmark these days. Some articles in the Danish newspaper Ekstra Bladet (as well as other newspapers, such as Berlingske Tidende and Politiken) describe his rather “alternative” treatments of various disorders – such as psychological trauma, mostly in women.

It would not be fair for me to judge whether the stories described in the links above are actually true or not, so I’ll let you judge for yourself. Most likely, future will tell. Instead I’ll talk about his Quality of Life Research Center in Copenhagen – and of which Dr. Ventegodt is the director (he is also responsible for a Research Clinic for Holistic Medicine in Copenhagen).

Their main claim to fame is described as follows:

The Quality of Life Center at the State University Hospital generated grants, publicity with research and discussions among the professionals leading to the claim that quality of life was significant for health and disease.

and further,

However, if a substantial part of diseases is caused by a low quality of life, we can all prevent a lot of disease and operate as our own physicians, if we make a personal effort and work to improve our quality of life. A series of investigations showed that this was indeed possible. This view of the role of personal responsibility for illness and health would naturally lead to a radical re-consideration of the role of the physician and also influence our society.

Such statements are typical for people practicing “holistic” medicine in its most extreme form; quite generally they feel that “invasive” treatments, such as drugs or surgery should only be used as a last resort. The holistic view on diseases naturally leads to the emphasis on the role of *personal responsibility for illness*. Tell this again to somebody suffering from Alzheimer’s, melanoma, diabetes mellitus, polio, rabies or even AIDS.

More generally, “holistic medicine” is based on the observation that *many* factors affect a persons health, such as genetics, nutrition, stress, family relationships, living and working conditions. As it stands, this statement is of course rather trivial; I guess most traditionally trained doctors agree with this – the important point is to found out which factors are important, how important they eventually are, and which factors are – in the long run – basically of little relevance. Practitioners of holistic medicine have not been able in any way to quantify which of the above factors are relevant and which are not. Even though the idea of a holistic approach to health is as old as medicine itself, the same can be said to be true for the idea of an astrology-based explanation for your specific personality, your future possibilities and so on. Its marginally admirable that practitioners of holistic medicine attempt to obtain a more “complete” view of a patients health and general condition, but for somebody suffering from AIDS or cancer it might not help much asking them about their childhood, family relations and so on.

Another view articulated by *The Quality of Life Center* is:

There is a general consensus that many of the diseases that plague the Western world (which are not the result of external factors such as starvation, micro-organisms, infection or genetic defects) are lifestyle related and as such, preventable through lifestyle changes.

[I must admit, that there is something I really do not understand here; why do they classify genetic defects as an “external factor”? It is well-known, that one human cell contains around 30-40.000 genes and since genetic instructions are so complicated many mistakes can occur – and many of these errors can lead to diseases. Of course, some diseases can be caused by pathogens, which is what they must be talking about here. But it might also surprise them, that such diseases as bulimia and anorexia nervosa, which traditionally are viewed as simple emotional disorders caused by childhood conditions, low self-esteem and so on, actually could prove to be auto-immune diseases.]

More generally, I would like to know which diseases are really *caused* by the way we think about and perceive life? Only those as: depression? Psychosis? High blood pressure? Or even coronary hearth disease? How did the researchers at the *Quality of Life Center* show that a disease like cancer *even in a single case* was actually “caused” by the way people think? (Even though the progression of a specific disease can be much affected by external factors such as the loss or death of a spouse). Or were their results just a consequence of the trivial observation that the way people think is largely determined by certain distributions of a large number of chemicals of the brain, such as serotonin, which therefore in some cases is determined by genetic factors which again can appear together with certain diseases? Or did they actually observe something completely opposite of what they thought they observed – that the way people think is in many ways affected by which physical diseases they might suffer from? Did they follow like 1-10.000 patients for a period of years in something remotely close to a double-blind study with specific differences in their view of life – possibly both their own and in general – and later determined which “factors” caused which diseases?

It seems, this is what they claim to have been doing:

However there is more to Western culture and lifestyle than these factors [excessive use of alcohol, tobacco, a high-fat diet etc.] and if we only focus on them we can risk overlooking others. We refer to other large parts of our life, for instance the way we think about and perceive life (our life attitudes, our perception of reality and our quality of life) and the degree of happiness we experience through the different dimensions of our existence. These factors or dimensions can now, to some degree, be isolated and examined. The medical sociologist Aaron Antonovsky (1923-1994) from the Faculty of Health Sciences at Ben Gurion University in Beer-Sheva, who developed the salutogenic model of health and illness, discussed the dimension, “sense of coherence”, that is closely related to the dimension of “life meaning”, as perhaps the deepest and most important dimension of quality of life. Typically, the clinician or researcher, when attempting to reveal a connection between health and a certain factor, sides with only one of the possible dimensions stated above. A simple, one-dimensional hypothesis is then postulated, like for instance that cholesterol is harmful to circulation. Cholesterol levels are then measured, manipulated and ensuing changes to circulatory function monitored. The subsequent result may show a significant, though small connection, which supports the initial hypothesis and in turn becomes the basis for implementing preventive measures, like a change of diet. The multi-factorial dimension is therefore often overlooked.

A simple questionnaire based survey performed by the *Quality of Life Center* in the early 1990’s concluded, that:

…preventable diseases could be more effectively handled through a concentrated effort to improve quality of life rather than through an approach that focus solely on the factors that are traditionally seen to reflect an unhealthy life style.

Virtually all of Dr.Ventegodt’s findings have been published in a journal called the *Scientific World Journal* (**48 out of 53 original articles according to his own CV**). This journal is *in no way comparable* to peer-reviewed journals like *Nature* or *The New England Journal of Medicine* (**the five remaining original articles were published in:** *Danish Medical Journal, Eur J Surg, Arch Sex Behaviour, Child Care Health Dev and Int. J. Adolesc. Med. Health*), just to mention a few. Papers are accepted upon payment of some unknown amount of money, which immediately makes you think that the scientific value of such articles is comparable to that of commercials during the Super Bowl. (If any well-known and respected journals accepted Dr. Ventegodt’s findings please inform me about this by sending an email to: kasperolsen [AT] yahoo [dOT] com).

About the stories reported in the newspapers as mentioned above it’s now even more interesting to read some of the last comments at the homepage of the *Quality of Life Center*:

We believe that the trained physician today has three medical toolboxes: the manual medicine (traditional), the bio-medicine (with drugs and pharmacology) and the consciousness-based medicine (scientific, holistic medicine). What is extremely interesting is that most diseases can be alleviated with all three sets of medical tools, but only the bio-medical toolset is highly expensive. The physician, using his hands and his consciousness to improve the health of the patient by mobilizing hidden resources in the patient can use his skills in any cultural setting, rich or poor.

Patients “treated” by the controversial methods described in the media should know if this is in any way true, or if it is just another example of dangerous pseudo-science?

(**S. Ventegodt has asked me to tell my readers that he has been cleared for the accusations of being guilty of wrongdoing. However, concerning the case discussed in the media, 1) I’ve not said that Ventegodt is guilty of wrongdoing but rather this is for others to decide and 2) since I’ve not said this, it is not my job to clear him for suspicion and 3) I’ve not really discussed the case in question above, but rather made some critical remarks about the research performed at the Quality of Life Center and 4) finally – and most importantly – since Ventegodt still cannot practice as a physician, since his authorisation has been taken from him (the question about whether it should be returned, will be determined in court) it would be plain wrong of me to say that he has been completely cleared for suspicion**.)

Added link to a “consultation” with Ventegodt, see here.

## Warped Passages

December 19, 2005*(This article was originally posted on blogger.com on Oct 26, 2005)*

Prof. Lisa Randall’s new book, Warped Passages: Unravelling the Mysteries of the Universe’s Hidden Dimensions, was released last month in the U.S. (I got it three months ago from amazon.co.uk , where it was already out on June 6th.). This book is intended for a popular audience, but is also a *very* interesting read for anybody with a background in theoretical physics. The first part contains an overview of modern physics – Einstein’s theories of relativity, quantum mechanics and the Standard Model of particle physics. The last part concentrates on the idea of extra dimensions beyond the standard four we know about, which is motivated by string theory and its discovery of D-branes. Specifically, she explains the work, pioneered by herself, Raman Sundrum and others, on the so-called “braneworld scenarios”. Basically, this is the idea that our four dimensional space-time is embedded in some higher dimensional space, usually called the “bulk”.

What is it with those extra dimensions? Are they not just part of a set of crazy ideas? (Like string theory, which a rather well-known person in the “blogosphere” would claim). On the contrary. You should know, that the idea of extra dimensions is actually not at all new. Already in 1884, the original book, “Flatland: A Romance of Many Dimensions”* *(written by the English mathematician Edwin Abbott) described a world of two-dimensional beings, who only have indirect knowledge of the extra third space-dimension (you can think of these beings as a group of flat ants living on an infinite plane). But, from a mathematical point of view, one can imagine as many dimensions as one wants to.

In physics, there are basically two distinct ways in which one can add extra dimensions to our four-dimensional (including three spatial dimensions and one time) universe. Already in the 1920’s, Klein suggested that our universe is five-dimensional, where the extra dimension is topologically a circle, which is so tiny, that the universe looks four-dimensional at long enough distance-scales. The motivation was to give a unified geometrical description of electromagnetism and gravitation using Einstein’s general theory of relativity. So, locally, space-time is a product R^4 x S^1 (to be more correct, it is actually R^{1,3} x S^1, but that’s not important here). However appealing, this theory was destined to fail. Today we know, that there are other forces which should be included in a unified theory: namely the weak and strong nuclear forces. Presently there is only one theory which can possibly do the work, and this is string theory. Perturbative string theory tells us, that our space-time is ten-dimensional, and that the extra six dimensions should be rolled up in a small but complicated shape. The topology is then R^4 x M^(6), where M^(6) is a six-dimensional Calabi-Yau manifold (i.e. that determines the possible shapes of the compactification manifold).

Another way to achieve hidden extra dimensions of space is to suppose, that all normal matter, as well as the light by which we see the world, is confined to a four-dimensional “brane” embedded in a five-dimensional bulk. These so-called braneworld theories are the ones of Lisa Randall, Raman Sundrum (and others – most notably Nima Arkani-Hamed of Harvard University). Warped Passages explains the logic behind these seemingly fancy ideas.

What I particularly liked about the first part of this book is how Lisa makes people envision extra dimensions. As Lisa writes, “we are not physiologically equipped to envision more than three dimensions of space”. But, as Lisa also explains, readers need not imagine a dimension only in spatial terms. Here is an example from the book: If you are buying a house, the factors you might consider include its location (specified by three numbers), price (one number), size (one number), and possibly many other things. So, the number of dimensions in your house search simply equals “the number of quantities you find worth investigating”.

What Lisa describes in the last part is the work concentrating on the following papers:

1. The idea of Arkani-Hamed, Dimopoulos and Dvali on large extra dimensions, which explains the weakness of gravity (the hierarchy problem) as due to the large size (originally ~1 mm, depending on the number of extra dimensions) of some of the extra dimensions, with only gravity propagating in them (hep-ph/9803315).

2. Work with Raman Sundrum on solving the flavor-changing problem, the gaugino mass problem (and other things) that occur in supersymmetric models with the supersymmetry breaking sector on another brane, separated from ours, or in the bulk (hep-th/9810155).

3. The Randall-Sundrum warped geometry with two branes (a so-called weak-brane, where we are supposed to live, and a gravity-brane) (hep-ph/9905221).

4. The Randall-Sundrum warped geometry with an infinite extra dimension, using AdS geometry (hep-th/9906064).

5. Work with Andreas Karch on “localized gravity” (hep-th/0011156).

The main point guiding Lisa’s research is the fact that gravity is such a profoundly weak force. Indeed, gravity is the puniest of the fundamental forces governing the matter in the universe, by a huge margin (typically a 10^36 times weaker than the electromagnetic force between two charged particles). Why is this so?

Lisa Randall suggests, that we live in a universe containing at least one extra dimension beyond those we can perceive. And gravity is weak because it has been diluted into this extra space. This is indeed a very simple and persuasive idea. (And also from the point of view of string theory a very compelling idea: we live on a three-brane embedded in a higher dimensional space with gauge interactions described by open strings attached to this brane, while gravity is interpreted as excitations of closed strings, which are free to leave the three-brane. But note that Lisa’s original models are not inherently string-theoretical; it is just that her models have an elegant and simple interpretation in string theory).

The breakthrough paper #3 above by Randall and Sundrum proposed that gravity’s dilution can be explained in terms of a cosmic configuration featuring two branes, separated by a higher dimensional bulk space. Roughly speaking, the “center of gravity” is on the “gravity-brane” – and some gravity leaks out of this brane, through the bulk, and onto the other brane, usually called the “weak-brane”, which is where we live, and which contain the Standard Model fields. In paper #4 above, Randall and Sundrum found that their concept is also theoretically consistent with a configuration which includes only one brane (and incidentally, this also sounds like a much simpler idea). Usually, one would think that Newton’s 1/r^2 law of gravitation implies that there are four and only four non-compact dimensions. Randall and Sundrum showed that this is not correct.

The fact that branes are an important part of modern string theory (thanks to Joe Polchinski and others) meant that string theorists took an early interest in the Randall-Sundrum models. Furthermore, since Lisa’s research didn’t directly challenge string theory models, the string theory community actually accepted and recognized the significance of her work very quickly. In particular, the fact that the Randall-Sundrum model uses the AdS geometry (as Juan Maldacena did), and has interesting relations to the AdS/CFT correspondence, has drawn a lot of interest from string theorists.

One of the long outstanding problems of the Standard Model that braneworlds do provide an interesting answer for is the “hierarchy problem”, or why the weak and Planck scales are so disparate (10^2 GeV compared with 10^19 GeV). In these scenarios, the fundamental gravitational scale is not the Planck scale, but something closer to the weak scale. The conjecture is that gravity is not weak because the Planck scale is so large, but because braneworlds provide various geometrical mechanisms for making the gravitational force much weaker than the others. (In technical terms it is because their bulk space-time metric is not factorizable, so the metric in the four familiar dimensions depends on the coordinate in the extra dimension).

The idea that the gravitational scale may be closer to and maybe even directly related to the weak scale is an appealing one, which is one of the reasons why Randall and Sundrum’s paper #3 has been cited 2640 times as of today.

All this would of course be pointless speculation unless there was some way for the extra dimensions to manifest themselves. So, can these ideas be experimentally tested? Yes indeed. It is possible that evidence supporting the braneworld models could appear within a decade or so, after the Large Hadron Collider (LHC), currently being built at the particle-physics laboratory CERN, starts operating in 2007. Since gravitons are not confined to branes, but can escape into the bulk, the traces of extra dimensions could come from such gravitons moving into the extra dimension(s) (i.e. missing transverse energy).

Some versions of the theory even predict that, as a result, small black holes could conceivably be created from the high-speed collisions between the LHC’s protons and antiprotons (but don’t worry, the black holes will only exist for ~10^{-26} sec due to Hawking radiation and will not soak up the Earth or the entire Solar System). If the LHC sees the kinds of effects predicted by these models, be sure that there will be some well-earned Nobel prizes for the people involved in this story.

Let me say a few words about the style of the book. The book’s central point – the possible existence of extra dimensions in space – is easy enough to explain; at least if the reader can comprehend that our universe has more than four space-time dimensions, which might not be easy. However, to motivate the conjecture of higher dimensions, Lisa must first explain the General Theory of Relativity, quantum mechanics and the Standard Model of particle physics, with its zoo of subatomic objects – quarks, leptons, bosons of various sorts – and the details of the forces that act between them. To ensure the convergence of her ideas in the readers mind, she then has to go into more advanced topics such as spontaneous symmetry breaking, the Higgs potentials and supersymmetry. Because unification physics is formulated in terms of quantum field theory – that has to be covered too.

All this is a prerequisite for being able to properly describe string theory, and must then proceed to the less understood generalization called M-theory (which is an eleven-dimensional theory containing two-branes and five-branes). Only then can Lisa explain how branes emerge from a jumble of concepts and ideas, that most likely might be is unfamiliar to the general reader. But as far as I can judge, she accomplish this tour de force with much success; still, I wonder how many non-physicists will be able to stay with the story to the very end. The immanent “problem” with such theories of unification is that one cannot leave anything out and therefore – to be explained and understood – they require background knowledge in virtually all of physics.

Finally I would like to stress that this book is very different from many of the random popular books about physics because Lisa Randall actually knows what she is talking about (and therefore I’ll suggest that you steer away from popular books on physics with suggestive titles as: “The Final Theory”, “The Road to Reality : A Complete Guide to the Laws of the Universe”, “Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos” and “Our Superstring Universe: Strings, Branes, Extra Dimensions and Superstring M-Theory”). And you should know, that Lisa is not a random person: she has become the most cited high-energy physicist since 1999.

A nice introduction to extra dimensions is the review, “To the fifth dimension and back”, by Raman Sundrum.

There are other reviews/comments about Lisa’s book – one by Lubos Motl, one by the anti-stringy Peter Woit, one by Paul Davies and one by John Gribbin (though, I’m not sure I would call the last one an honest review; I’ll let you judge for yourself), and reviews at amazon.com and

at amazon.co.uk.

**Update**: *Warped Passages* now has its own website (March 26’th, 2006).