Revenge of the Nerds

Yesterday, I spent some hours in a cafe, scribbling on a notepad. Next to me a guy was browsing a shiny brochure. From the corner of my eye I read “So what, you may be asking, do they actually do in that ominous building beside Waterloo Park?” Yeah, I wondered. What do they do there? More interestingly, what do people think we do there?

The guy left behind the brochure on the table, and it turned out to be the fall/winter 2008 issue of “Waterloo Revealed”. They list a website that however is under construction, neither does it seem to be cached, so I indeed hat to retype it (!).

The brochure features an article with “Revenge of the Nerds” by Marc Cameron about Perimeter Institute. The author seems to confuse Quantum Foundations with Quantum Gravity and Quantum Information, but otherwise his writing is a nice laudatio on fundamental research, and PI's outreach and art program:

“Researchers at PI, a self-proclaimed “Independent, non-profit, scientific research and education outreach organization,” operate under the auspices of what many might consider “pure research”. It's the kind of thing that some fear may be going out of style in corporate laboratories and universities: the notion of research for research's sake.

[...]

So what, you may be asking, do they actually do in that ominous building beside Waterloo Park? The research done there in areas like Cosmology, Particle Physics, and Superstring Theory improve our scientific understanding of the universe (once it trickles down from the halls of academe), but they also contribute to the pioneering of new technologies. It's hard to predict how scientific breakthroughs and new theories will impact technological advances, but fundamental discoveries - like Einstein's reckoning of light as a particle - lead to new ways of understanding the basic parts of the physical universe which allows for improvements in quality of life through technology for people everywhere.”

The last sentence suspiciously sounds as if it came from our PR department, but anyway. Einstein of course has to be mentioned when it comes to nerds and theoretical physics. About PI's outreach program Cameron writes:

“While theoretical physics bears the stigma of nerd-dom, PI goes to great length to bring physics to the people through numerous public and education outreach programs. Their (free!) public lecture series is probably the most well-known of PI's offerings to the community [...] The lectures have been televised on Rogers Cable channels in many Ontario markets on the program Celebrating Science, as well as special episodes of TVOntario's Big Ideas. Starting this fall, select PI public lectures will also be airing on Discovery Channel.”

The latter was news to me. But the upshot of the article is this highlighted paragraph:

“Science they say, is the new religion. For certain it's a belief system and a philosophy about life and the rhythms of the universe. When it comes down to it, religion and science are each ways of asking questions about the intangible. If the architecture of the PI building is any indication, Waterloo has its own Cathedral of Theoretical Physics. And, like most Holy sites, they open up their doors to share freely what they have with the scientific layperson, like you or me, not because they'd like to convert us, but because they've found something exciting that maybe, just maybe, could make life a little better for all of us.”

Well. One would have hoped that after all the public outreach the message would have gotten across that science is the very antithesis of a belief system. You'd better call it a 'doubt system'.

The title of the article is btw completely unmotivated. Maybe however it's indeed time for the revenge of the nerds.

It's a man's world...

I recently stumbled across the GenderAnalyzer, a text classifier that according to their description “has been trained on blogs written by men and women” and “uses Artificial Intelligence to determine if a homepage is written by a man or woman”.

So, I piped in some links from my blogroll. Here are the results, sorted by male-ness:

• We think FemaleScienceProfessor is written by a man (72%).
• We think Backreaction is written by a man (74%).
• We think Asymptotia is written by a man (77%).
• We think Cosmic Variance is written by a man (80%).
• We think Eva Amsen's blog is written by a man (82%).
• We think Tommaso Dorigo's blog is written by a man (82%).
• We think Chad Orzel's blog is written by a man (83%).
• We think Shores of the Dirac Sea is written by a man (83%).
• We think Michael Nielsen's blog is written by man (84%).
• We think Grrlscientist's blog is written by a man (86%).
• We think Not Even Wrong is written by a man (87%).
• We have strong indicators that The Reference Frame is written by a man (93%).

And here is the absolute high-score of male-ness:

• We have strong indicators that Theorema Egregrium is written by a man (96%).

Yep.

Sorry Christine.

Having come so far I concluded that writing about science generally must count as an indicator for male-ness, and I discarded the 'GenderAnalyzer' as crap.

My homepage btw, is "quite gender neutral".

This and That

• Mark Newman from the University of Michigan provides an interesting visualization of the results of the US presidential election.



• The fundamentals of our economy:
  
  [via Nouriel Roubini]



• Lee Gomes blames computers for the economic crisis:
  

  “It's easy to camouflage a fatal bit of wishful thinking deep inside an elegant but opaque bit of computer modeling. Especially when, as was the case in the last few years, the practice had begun to take on an air of end-of-history infallibility, rather like the scientists who after discovering penicillin began to believe that infectious diseases would be a thing of the past.”



• NewScientists answers dumb eco-questions you were afraid to ask:
  

  “Q: What is the single most effective thing I can do for the environment?
  
  A: Over a 75-year lifespan, the average European will be responsible for about 900 tonnes of CO2 emissions. For Americans and Australians, the figure is more like 1500 tonnes. Add to that all of humanity's other environmentally damaging activities and, draconian as it may sound, the answer must surely be to avoid reproducing.”

• Santa Barbara has proclaimed a Local Emergency and requested the govenor to proclaim a State of Emergency due to a fire that broke out at approximately 5:50 p.m. on November 13, 2008. A fire chief in Santa Barbara, California says control of the wildfire that's destroyed more than 100 homes is “not even in sight.” If you are living in the area, my thoughts are with you.



• After the BlackBerry and the Apple iPhone, we now have another fruit-flavored device, the Pomegranate Phone. The website takes forever to load, but if you click on 'release date' you'll figure it's an advertisement for Nova Scotia. (That's not a suitcase brand but a Canadian province that apparently wants to see more tourism.)

Chaos, Solitons and Self-Promotion

Recently, our attention was drawn to the Elsevier Journal Chaos, Solitons & Fractals, and its Editor-in-Chief M. S. El Naschie. Over the course of the years, El Naschie himself published about 300 mostly single authored papers in this journal, with abstracts of the kind:

“Von Neumann’s continuous geometry has been considerably developed by Connes and is characterized by two fundamental concepts. First it is formulated without any direct reference to points and second it possesses a dimensional function. The present work explores the relevance of these two points to string theory as well as E-infinity theory. In particular we show that point-lessness and dimensional function implies fractality. In turn fractality leads to the concept of average or fuzzy symmetry and the elimination of gauge anomalies.”

Now neither of us in an expert in Solitons or Fractals. So we instead want to ask the completely unrelated questions whether being an editor at Elsevier allows one to circumvent peer review. In case you are suspicious about the scientific merit of El Naschie's work, you are not alone. John Baez gave it a closer look in his recent post The Case of M. S. El Naschie and finds the result wanting.

The reason we got interested in this topic is that El Naschie lists himself on his website as a “distinguised Fellow of the Physics Institute of the Johann Wolfgang Goethe University, Frankfurt” - the Institute where we both made our PhD. However, this “Fellowship” has not been awarded by the physics department, but by a private association, called the “Frankfurter Förderverein für physikalische Grundlagenforschung” (Frankfurt association for the support of basic research in phyiscs). Gossip that we would never spread says the guy has money. Zoran Škoda wrote in an earlier comment:

“I was told that there is an investigation about using this affiliation now. I contacted some of the associate editors, most of whom did not respond to my question how such a behaviour is allowed. Two of them told me that they will quit from the editorial board, and one that his name was put on the editorial page without his consent!”

It is thus good to read that Herman van Campenhout, Elsevier CEO Science & Technology, writes in the Publishing Ethics Resource Kit: “Monitoring Publishing Ethics is a major aspect of the peer-review process, and as such lies within the area of responsibility of the Editor-in-Chief [].” And, he adds, “Fortunately, the area of science publishing is reasonably good at self-correcting, albeit sometimes later rather than earlier.”

Technetium-99

⁹⁹TcWhen nuclear physics hits the headlines, it's usually in unpleasant contexts, such as leakage of radioactive substances from reactors, the unsolved problem of disposal of nuclear waste, or the proliferation of nuclear weapons.

So, I was surprised by I story I had heard on the radio a few weeks ago, and read about again a while later: It was about the temporary shortage in the supply of a radioactive isotope heavily used in medicine, Technetium-99.

Technetium-99, a nucleus made up of 43 protons and 56 neutrons, has an excited state which decays with a half-life of about 6 hours. Similar to an excited atom emitting a photon of visible light when converting back to the ground state, the decay of the exited nucleus comes along with the emission of a γ photon. This γ photon has an energy of 140 keV – about 100.000 times the energy of a photon of red light. Here is schematic representation of the energy levels and the transitions involved:



To create nuclei of Technetium-99 in the excited state – also called Technetium-99m, where "m" stands for "metastable" –, one resorts to another isotope, Molybdenum-99. This isotope undergoes a β decay with a half-life of 66 hours, thereby ending up as Technetium-99 in the excited state. Like all isotopes of Technetium, Technetium-99 isn't stable either and finally ends up, following another β decay, as Ruthenium-99.

Technetium-99 thyroid uptake scans. Scan (A) shows the normal, healthy result. (from Petros Perros: Thyrotoxicosis and Pregnancy, PLOS Medicine 2(12): e370)

Now, what is this good for? As it came out from investigations at the Brookhaven National Laboratory done in the 1960s, the decay reaction of Technetium can be adapted as a very elegant and practical tool for medical diagnosis. To this end, "freshly produced" Tc-99m is extracted chemically from a probe of Mo-99, bound to suitable large molecules, and administered intravenously to the blood circuit. Then, the 140 keV γ photons emitted at the decay of Tc-99m map from inside the body the distribution of blood. They trace regions of lacking blood supply, for example after a stroke, or highlight spots with enhanced metabolisms, which could be tumours. Energy of the γ photon and lifetime of Tc-99m are just so that such an exploration does not produce to high a radiation exposure, and can be done in a very reasonable time.

To use this technique, Molybdenum-99 is needed, and this is where the current shortage comes from: Molybdenum-99 is created in nuclear reactions, either by bombarding more common isotopes with neutrons, or by fissioning of U-235 in highly enriched uranium targets. This second source, which is the most important one, is of course highly linked to weapon-grade stuff, so there are only a handful of civilian reactors in the world that produce Molybdenum-99. In Europe, the main source is a reactor in Petten in the Netherlands, which is currently shut down for maintenance and inspections. It seems, however, that the consequential shortage of Molybdenum-99 and Technetium-99m for medical purposes is not critical.

While trying to get some background on this news story, I realised that the decay scheme of Molybdenum-99 and Technetium-99m involves a few interesting questions:

Why does the decay of Mo-99 not end up in the ground state of Tc-99? Why is the lifetime of the γ decay of Tc-99m so long? Usually, γ transitions happen within fractions of a second. And finally, what a strange element is technetium in the first place, as without stable isotopes, it marks a gap in the middle of the periodic table? And as it comes out, the answers to these questions touch upon a few concepts very central to nuclear physics.

But this will be the stuff of another post.

Bullshit with Equations

“In [high energy] quantum physics, to observe something, you have to create it. Now this sounds scarily close to bullshit. But if it is bullshit, then at least it's bullshit with equations.”

~Frank Wilczek, at PI's recent public lecture

via Sundance Bilson-Thompson, thanks :-)

The Other Side

New painting




For a 360° view, try this (requires Quicktime). For more paintings, see my homepage.

Trickle Down

Spiegel: 'Financial Contagion' Spreading in Developing World -- G&M: Ford loses $129-million, will cut more jobs -- Reuters: Retail sales worst in decades; holiday view cut -- Spiegel: Sinking into a Recession. Economic Crisis Mounts in Germany -- G&M: JPMorgan warns consumer loan losses may rise --NYT: U.S. Jobless Rate Hits 14-Year High -- G&M: AGF Trust cuts staff by 10% -- NYT: A $50 Billion Bailout in Russia Favors the Rich and Connected -- G&M: Mattel to cut 1,000 jobs worldwide -- Spiegel: Global Recession? ECB Drops Rates amid Gloomy IMF Forecasts -- Reuters: USG cuts 900 jobs as economy deteriorates -- NYT: Tough Times Strain Colleges Rich and Poor -- World Bank head warns financial crisis could drive up number of poor -- Nortel cuts another 1,300 jobs -- GM adds 1,900 more layoffs

Gallery of Fluid Motion

The motion of fluids can be surprising, beautiful, and sometimes just funny to watch. At its annual meetings, the Division of Fluid Dynamics of the American Physical Society organizes exhibits with stunning photographs and videos of fluid. Each year, awards are assigned to "photographs and videos [that] illustrate both experimental and numerical investigations of a wide variety of flow phenomena. Judged by a distinguished international panel of referees, winning entries were selected based upon criteria of scientific merit, originality, and artistry/aesthetic appeal."

Here is a winning entry from the Gallery of Fluid Motion 2008, chosen from the exhibition at the Annual Meeting of the APS Division of Fluid Dynamics in Salt Lake City last November (click on the still to get to the movie, requires some patience and Quicktime):

"BLACK HOLE" NUCLEATION IN A SPLASH OF MILK, by Laurent Courbin, James C. Bird, Andrew Belmonte, and Howard A. Stone: This video shows the impact dynamics of a millimeter-size drop of milk onto a superhydrophobic substrate that is spinning at a constant rate. (explanation as PDF file).

And here, a winning entry from the Gallery of Fluid Motion 2007 (Bee's absolute favourite):

CREEPING, WALKING AND JUMPING DROP by A. Renaudin, E. Galopin, V. Thomy, C. Druon, and F. Zoueshtiagh: This video shows the movement of a deionized water drop provoked by surface acoustic waves. (explanation as PDF file)

Don't be put off by the lengthy, silent-picture style explanations of the experimental setup at the beginning of the clips.

To see the amazing behavior of these drops rewards a little patience - enjoy!

Congratulations, Obama!

German Chancellor Angela Merkel

“My heartfelt congratulations on your historic victory in the presidential elections.

At the beginning of your administration, the world faces momentous challenges. I am convinced that, with closer and more trusting cooperation between the US and Europe, we can resolutely confront the novel challenges and dangers facing us [...] You can be sure that my government is fully aware of how important the trans-Atlantic partnership is for our futures.

It is my pleasure to invite you to visit Germany in the near future.”

French President Nicolas Sarkozy

“With the world in turmoil and doubt, the American people, faithful to the values that have always defined America's identity, have expressed with force their faith in progress and the future. At a time when we must face huge challenges together, your election has raised enormous hope in France, in Europe and beyond.”

European Commission President Jose Manuel Barroso

“We need to change the current crisis into a new opportunity. We need a new deal for a new world. I sincerely hope that with the leadership of President Obama, the United States of America will join forces with Europe to drive this new deal - for the benefit of our societies, for the benefit of the world.”

British Prime Minister Gordon Brown

“It has been an important election. I think the most important thing that follows from it is that America and Europe will have to work together to deal with the international problems we face, not just the financial crisis, but also stopping protectionism, making sure we work for stability and particularly peace in the Middle East.”

Dutch Prime Minister Jan Peter Balkenende

“The necessity for cooperation between Europe and the United States is bigger than ever. Only by close trans-Atlantic cooperation can we face the world's challenges.”

Chinese President Hu Jintao

“The Chinese Government and I myself have always attached great importance to China-US relations. In the new historic era, I look forward to working together with you to continuously strengthen dialogue and exchanges between our two countries.”

Indian Prime Minister Manmohan Singh

“Your extraordinary journey to the White House will inspire people not only in your country but also around the world.”

Afghanistan President Hamid Karzai

“I applaud the American people for their great decision and I hope that this new administration in the United States of America, and the fact of the massive show of concern for hhuman beings and lack of interest in race and color while
electing the president, will go a long way in bringing the same values to the
rest of the world sooner or later.”

Australian Prime Minister Kevin Rudd

“Senator Obama's message of hope is not just for America's future, it is also a message of hope for the world as well. A world which is now in many respects
fearful for its future.”

Japanese Prime Minister Taro Aso

“The Japan-US alliance is key to Japanese diplomacy and it is the foundation for peace and stability in the Asia-Pacific region. With President-elect Obama, I will strengthen the Japan-U.S. alliance further and work towards resolving
global issues such as the world economy, terror and the environment.”

Israeli Foreign Minister Tzipi Livni

“Israel expects the close strategic cooperation with the new administration, president and Congress will continue along with the continued strengthening of the special and unshakeable special relationship between the two countries.”

Former PI postdoc representative Sabine Hossenfelder

“Please don't switch off your brain the moment you move into the White House.”

[via Spiegel Online]

Infinity Really is Different

After a couple of crazy weeks, I finally had the time to read some of the papers on my desk, and that's where this article reappeared

More Really is Different
By Mile Gu, Christian Weedbrook, Alvaro Perales, Michael A. Nielsen
arXiv:0809.0151v1 [cond-mat.other]

Abstract: In 1972, P.W.Anderson suggested that `More is Different', meaning that complex physical systems may exhibit behavior that cannot be understood only in terms of the laws governing their microscopic constituents. We strengthen this claim by proving that many macroscopic observable properties of a simple class of physical systems (the infinite periodic Ising lattice) cannot in general be derived from a microscopic description. This provides evidence that emergent behavior occurs in such systems, and indicates that even if a `theory of everything' governing all microscopic interactions were discovered, the understanding of macroscopic order is likely to require additional insights.

Since Stephen Luttrell asked last week what I think about the paper, I thought I should come back to it.

The paper is really neat. Here is a quick summary. The authors consider a 2-dimensional spin lattice with nearest neighbor interaction. We thus have a lattice of ups and downs that can influence the other ups and downs around them according to some rule given by the Hamiltonian of the system. On this lattice, the authors put certain “designer Ising blocks” with an associated Hamiltonian, composed of several spin states. These blocks have the property that if they are in the ground state (the state of lowest energy), and one forces the spins on one side to be in a certain pattern of ups and downs by applying a field, then the other side will produce a certain output. They give specific examples in the appendix.

If one covers a 2-dimensional semi-infinite plane with these blocks and has an input on one side of the first row, the spin-spin interactions give a rule determining what is on the other side of that row, which is the input for the second row. And so on. Thus, the ground state of the system is fully determined. But what can we say about this ground state?

Now here is the clue of the paper. The authors show that with the appropriate initialization and designer blocks, one can map a cellular automaton to this spin-system. A cellular automaton operates on a one dimensional input line according to a specific rule. This rule crates a new state, on which the rule is applied again etc. This is commonly shown in a diagram with all the so created states below each other, each corresponding to a certain time step. In the spin-lattice, there are no time steps, but the ground state would be a picture of these states of the cellular automaton. Note however that for the spin-lattice this is not a time-dependent realization of this state. The ground-state just is specified according to some rules.

However, there exists cellular automata for which it can be proven that no non-trivial questions can be answered about their evolution, without actually running them and looking, thus one can never say anything about the total evolution. Because of the correspondence to the spin-lattice this then means there are questions about its ground state that can't be answered either. An example for such a question would be what the overall magnetization is of the system. There is thus no way to derive this quantity from the Hamiltonian, the question is undecidable.

It should be noted that it is important for this conclusion the spin-lattice is indeed infinite. The approximation that a system is infinite is very common in physics and often used to simplify computations. What this argument thus shows is that in this limit, there can remain questions open that fundamentally can not be answered about the whole system.

The title of the paper is a reference to Anderson's paper “More is Different,” an argument against reductionism, claiming that not every system can be understood by merely analysing its parts. Gu et al's paper provides an explicit example for which it can be proved that it indeed is not possible to understand the whole system from the behavior of its constituents. For this argument to hold however “more” isn't enough, it has to be infinitely more.

On the risk of merely expressing my utter ignorance, this doesn't surprise me much. What the authors have shown in the paper is a map from a cellular automata, commonly run on a computer, to a 2-d spin lattice. This lattice is a physical realization of a computer code and thus similar conclusions hold for both. As far as I am concerned, if I run the code and visualize it on my screen (for an infinitely long time of course) this is also a physical realization of the code, it is a state my computer's hardware is in. However, the map to the spin system is without doubt much cleaner and better to analyze.

It would be interesting to see whether one could find a possibly weaker statement for large, but finite systems.

For more on the topic, see also my post Emergence and Reductionism, NewScientist's article Why nature can't be reduced to mathematical laws, or check out Stuart Kauffman's last week talk The Open Universe: Toward a Post-Reductionist Science, PIRSA:08100058.

---

Mile Gu, Christian Weedbrook, Alvaro Perales, Michael A. Nielsen (2008). More Really is Different arXiv

Lorentz Transformations

If you know anything about theoretical physics, you have probably seen one of the derivations for the Lorentz transformations in Special Relativity. These are the transformations that relate two observers with different constant velocities to each other, and tell them how to compare their measurements. These derivations typically come with a lot of rockets and spaceships sending light signals etc. Here, I want to give you a different approach that strips off some of the interpretational baggage and adds some maths baggage. But don't panic, it's not that complicated.

Special Relativity assumes time is a dimension, i.e. space-time is Minkowski space. There are thus four coordinates in this space, xⁱ with the index i taking the values 0,1,2,3. Since time has different units than length, to be able to describe space and time as elements of one space-time we have to multiply time by a constant of dimension length/time, i.e. a velocity. This constant is usually denoted c. It is then x⁰ = c t. We will come back to the meaning of this constant later.

The other ingredient of Special Relativity is that the laws of physics are same for all observers with constant velocity. That means there are sensible and well-defined transformations between observers that preserve the form of the equations.

A Word or Two about Tensors

The way to achieve such sensible transformations is to make the equations "tensor equations", since a tensor does exactly what we want: it transforms in a well-defined way under a change from one to the other observer's coordinate system. The simplest sort of a tensor is a scalar φ, which doesn't transform at all - it's just the same in all coordinate systems. That doesn't mean it has the same value at each point though, so it is actually a scalar field.

The next simplest tensor is a vector V_i which has one index that runs from 0 to 3, corresponding to four entries - three for the spatial and one for the time-component. Again this can be a position dependent quantity, so it's actually a vector field. The next tensor has two indices T_ij that run from 0 to 3, so 16 entries, and so on: U_ijklmn.... The number of indices is also called the "rank" of a tensor. To transform a tensor from one coordinate system in the other, one acts on it with the transformation matrix, one for every index. We will come to this transformation later.

Note that it is meaningless to say an object defined in only one inertial frame is a tensor. If you have it in only one frame, you can always make it into a tensor by just defining it in every other frame to be the appropriately transformed version.

The Scalar Product

A specifically important scalar for Special Relativity is the scalar product between two vectors. The scalar product is a symmetric bilinear form, which basically means it's given by a rank two tensor g^ij that doesn't care in which order the indices come, and if you shovel in two vectors out comes a scalar. It goes like this:

g^ijV_iU_j = scalar,

where sums are taken over indices that appear twice, once up and once down. This is also known as Einstein's summation convention.

I used to have a photo of Einstein with him standing in front of a blackboard cluttered with sum symbols. Unfortunately I can't find it online, a reference would be highly welcome. That photo made really clear why the convention was introduced. Today the sum convention is so common that it often isn't even mentioned. In fact, you will have to tell readers instead not to sum over equal indices if that's what you mean.

The scalar product is a property of the space one operates in. It tells you what the lengths of a vector is, and angles between different vectors. That means it describes how to do measurements in that space. The bilinear form you need for this is also called the "metric", you can use it to raise and lower indices on vectors in the following way: g^ijV_j = Vⁱ. Note how indices on both sides match: if you leave out the indices that appear both up and down, the remaining indices have to be equal on both sides.

Technically, the metric it is a map from the tangential to the co-tangential space, it thus transforms row-vectors V into column vectors V^T and vice versa, where the T means taking the transverse. A lower index is also called "covariant", whereas upper indices are called "contravariant," just to give you some lingo. The index jiggling is also called "Ricci calculus" and one of the common ways to calculate in General Relativity. The other possibility is to go indexless via differential forms. If you use indices, here is a good advice: Make sure you don't accidentally use an index twice for different purposes in one equation. You can produce all kind of nonsense that way.

In Special Relativity, the metric is (in Euclidean coordinates) just a diagonal matrix with entries (1,-1,-1,-1), usually denoted with η_ij. In the case of a curved space-time it is denoted with g_ij as I used above, but that General case is a different story and shall be told another time. So for now let us stick with the case of Special Relativity where the scalar product is defined through η.

Lorentz Transformations

Now what is a Lorentz transformation? Let us denote it with Λ. As mentioned above, you need one for every index of your tensor that you want to transform. Say we want to get a vector V from one coordinate system to the other, we apply a Lorentz transformations on it so in the new coordinate system we have V' = VΛ, where V' is the same vector, but how seen in the other coordinate system. With indices that reads V'_iΛⁱ_j = V_j. Similarly, the transverse vector transforms by V'^T = Λ^T V^T.

Lorentz transformations are then just the group of transformations that preserve the length of all vectors, length as defined through the scalar product with η. You can derive it from this requirement. First note that a transformation that preserves the lengths of all vectors also preserves angles. Proof: Draw a triangle. If you fix the length of all sides you can't change the angles either. Lorentz transformations are thus orthogonal transformations in Minkowski space. In particular, since the scalar product between any two vectors has to remain invariant,

V^T η U = V'^T η U' = V^T Λ^T η Λ U,

they fulfil (with and without indices)

Λⁱ_jη_kiΛ_l^k = η_jl <=> Λ^T η Λ = η   (1)

If you forget for a moment that we have three spatial dimension, you can derive the transformations from (1) as we go along. Just insert that η is diagonal with (in two dimensions) entries (1,-1), name the four entries of Λ and solve for them. You might want to use that if you take the determinant on both sides of the above equation you also find that |det Λ| = 1, from which we will restrict ourselves to the case with det = 1 to preserve orientation. You will be left with a matrix that has one unknown parameter β in the following familiar form

with γ^-2 = 1- β².
Now what about the parameter β? We can determine it by applying the Lorentz transformation to the worldline (cΔt, Δx) of an observer in rest such that Δx = 0. We apply the Lorentz transformation and ask what his world line (Δt', Δx') looks like. One finds that Δx'/Δt = βc. Thus, β is the relative velocity of the observers in units of c.

One can generalize this derivation to three spatial dimensions by noticing that the two-dimensional case represents the situation in which the motion is aligned with one of the coordinate axis. One obtains the general case by doing the same for all three axis, and adding spatial rotations to the group. The full group then has six generators (three boosts, three rotations), and it is called the Lorentz group, named after the Dutch physicist Hendrik Lorentz. Strictly speaking, since we have only considered the case with det Λ = +1, it is the "proper Lorentz group" we have here. It is usually denoted SO(3,1).

Once you have the group structure, you can then go ahead and derive the addition-theorem for velocities (by multiplying two Lorentz-transformations with different velocities), length contraction, and time dilatation (by applying Lorentz transformations to rulers).

Kinematics

Now let us consider some particles in this space-time with such nice symmetry properties. First, we introduce another important scalar invariant of Special Relativity, which is an observer's proper time τ. τ is the proper length of the particle's world line, and an infinitesimally small step of proper time dτ is consequently

dτ² = c² dt² - dx²

One obtains the proper time of a curve by integrating dτ over this curve. Pull out a factor dt² and use dx/dt = v to obtain

dτ² γ² = dt²

A massive particle's relativistic four-momentum is pⁱ = muⁱ, where uⁱ=dxⁱ/dτ = γ dxⁱ/dt is the four-velocity of the particle, and m is its invariant rest mass (sometimes denoted m₀). The rest mass is also a scalar. We then have for the spatial components (a = 1,2,3)

p^a = m γ v^a .

What is c?


Let us eventually come back to the parameter c that we introduced in the beginning. Taking the square of the previous expression (possibly summing over spatial components), inserting γ and solving for v one obtains the particle's spatial velocity as a function of the momentum to
In the limit of m to zero, one obtains for arbitrary p that v=c. Or the other way round, the only way to get v=c is if the particle is massless m=0.

So far there is no experimental evidence that photons - the particles that constitute light - have mass. Thus, light moves with speed c. However, note that in the derivation that got us here, there was no mentioning of light whatsoever. There is no doubt that historically Einstein's path to the Special Relativity came from Maxwell's equations, and many of his thought experiments are about light signals. But a priori, arguing from symmetry principles in Minkowski-space as I did here, the constant c has nothing to do with light. Nowadays, this insight can get you an article in NewScientist.

Btw, note that c is indeed a constant. If you want to fiddle around with that, you'll have to mess up at least one step in this derivation.

See also: The Equivalence Principle

Excusable

I just received a Service Agreement Contract from an US research institution. Under point 19, it explains

19. Excusable Delays

[The Institution] will be excused from performance hereunder if a delay is caused by inclement weather, fire, flood, strike, or other labor dispute, acts of God, acts of governmental officials or agencies, terrorism, or any other cause beyond the control of [the Institution].

Gibberish

IIB supergravity axion-dilaton coset, SL(2,R)/SO(2), 7-branes in the conjugacy classes of the Q7-branes. In order to realize a gauge fields of the Q7-branes in the brane to the Q7-branes that belong to different conjugacy classes are determined by an SL(2,R) naturally couple to IIB supergravity with appropriate source terms characterize the conjugacy classes are determinant of Q. The 7-branes with conjugacy class det Q = 0. We construct the Q7-branes. We construct the matrix Q and it will be called by three numbers (p, q, r) which parameterize the matrix Q and will be called Q7-brane world-volume labelled by three numbers (p, q, r) which parameterize the full bosonic Wess-Zumino term for the gauge invariant coupling of the full bosonic Wess-Zumino term for the gauge invariant couplingof the matrix Q and will be called Q7-branes. In order to realize a gauge fields of IIB supergravity it is necessary.

Tragically, the original text was on the same level of comprehensibility. For more fun of that sort, try the Gibberish Generator.

Socialism and Social Democracy

For no particular reason I just want to clarify a confusion that I have encountered fairly often, that's what the difference is between Socialism and Social Democracy. Socialism aims to achieve a more just society by putting the means of production in the hands of the government, it is against privatization (though not necessarily for common ownership, that's communism). That has a priori nothing to do with planned economy in case you wonder.

Social Democracy means you acknowledge that the free market fails to automatically take into account certain goals your society might value, that are most often those based on solidarity and long-term plans. For example environmental protection, help for medical emergencies, social help etc. An unregulated free market is merciless on the sick, the old, the poor, or the unlucky, simply everybody who fails to contribute directly to economic growth for whatever reason, e.g. by having too many kids. Social democracy includes the human wish not to see your neighbors starve the moment they can no longer be productive, and recognizes that one day you might be in that same situation.

The way it is typically done is to take away money from those who have plenty, e.g. by taxes, and give it to those who need it to survive. Yes, that means redistribution of wealth. You do that backed up by a democratic system to ensure this redistribution is considered just by the majority of people and not in conflict with more fundamental laws. Needless to say, the people who have the big money will complain about it. Keep in mind they made their money in a system that is considered unjust by the majority of people living around them. The outcome is a social market economy, that is, one that combines a capitalist mode of production with the belief that society should protect all its members from economic and social need.

Justice is however something that is perceived very different depending on what culture one has grown up in. I for example find it quite amusing that Americans like to talk about Germany as a 'social welfare' state as if that was something undesirable. As far as I am concerned, I am very relieved that if I am in Germany I know all my neighbors do have a health insurance, I know all my friends have an unemployment insurance, and I know they can live from social help should it be necessary. Of course there's parties in Germany who are more left or right leaning, more or less liberal, more or less conservative, but overall the idea of a social market economy is more generally accepted.

Choose what you want. That's what democracy is good for.

Project Help

I need some help with a project I'm currently working on. No PhD required, not physics related, you can do it after hours. It will take about a month, you'll get a paycheck and I'm told it's tax deductible. Must be US/Canadian resident. If you are interested, please send email to sabine[@]perimeterinstitute.ca for more info.

Update Oct 29: Thanks everybody for your interest, I do no longer consider applicants.

The Lightcone Institute

After you have stared at the link to the Lightcone Institute in my sidebar for a year or so, I think the time has come to tell you what it is about. It's what I spend my time on that is not occupied by physics - which is typically not much, and presently not any, but has added up over the last decade to make this a more concrete project which managed to attract a moderate but existent amount of interest. It's my way to make constructive use of my desperation about the state of the world, and an antidote to the nagging feeling that what I work on isn't particularly useful for the vast majority of people on this planet.

Sure, I can give you a long speech about the purpose and importance of fundamental research and how it is interesting for the broader public, not to mention that it is where my personal interests are. But it remains a fact that investing into fundamental research is a luxury of societies at a very advanced level. And if I open a newspaper after a day sitting through seminars it tells me the world really has other problems than axion-dilaton coset SL(2,R)/SO(2) 7-branes or similar fun. Sometimes more, sometimes less so. Presently more so.

But hey, as I told you previously, to me science is more than a profession, to me science is a worldview. And thus my interpretation of the problems we are currently facing on a global scale is a lack of scientific method, which has resulted in an erosion of trust in the systems that govern our lives. We are failing to update these systems and their institutions so they be able to deal with our increasingly complex global problems.

Finishing the Scientific Revolution

Science is as old as mankind. We analyze the world we observe to better understand it, and to make our lives more pleasant. The scientific method has proven to be extremely useful to achieve this; this method being nothing but inventing a model for the world based on previous knowledge, and testing how well it works. If it works well or at least better than available models, we call that progress and use it for further examinations. If not, we discard it and look for something better. At least that's the idea. A lot can be said about how this so straight-forwardly sounding manner has worked out during our history in less straight-forward ways, but to say the very least, it has worked tremendously well for the natural sciences.

Science in its organized form has taken off in the 16th and 17th century, and has changed our world dramatically. This period in our history during which we saw a tremendous amount of progress in the fields astronomy, physics, biology, medicine and chemistry is often called the “Scientific Revolution” - a revolution of thought rather than a revolution of governance that kick-started the development of technologies and established scientific research as one of the most important drivers of progress in our societies. We find during this period the names of great thinkers like Copernicus, Brahe, Kepler, Galileo, Bacon, Newton, Franklin and Descartes, to only mention a few.

Today we study as sophisticated areas as neuroscience, nanotechnics, immunology, microbiology or endocrinology. Don't worry if you don't know the latter, I didn't know it either, I Googled it and found it's the study of the glands and hormones of the body. And then there are of course the computer sciences, which are possibly the most impressive outcome of the technological developments altogether and the advancements of computing power itself has had a large impact on the possibilities in scientific research.

I'm not a historian and this isn't an essay about the history of science. I'm just telling you that because this revolution doesn't include the social sciences. Most notably, academic research in the fields that we would today call sociology, politics and economy are still waiting to obtain the attention they deserve. In these areas, the dark middle ages of trial and error in applications have lasted some more centuries, with the situation only slowly changing today. The reason for this is not hard to find. Understanding political or social systems is much more complicated than understanding the motion of planets, since the latter is a system that can very easily be simplified to a model that is computable even by hand. In the political and social sciences, arguments are lead mostly in the narrative, and have for long been detached from what actually was happening in politics. Neither did much of these studies reach the broad public for most of it is not part of the standard school education, as is physics, biology and chemistry.

It is only now, in the 21st century, that the advances have gotten far enough so we begin to understand some aspects of systems as complex as for example our global economy. In fact, the economical system is probably the best investigated case that falls into this category, for there is money to make there. The political system lags behind. This lag is is crucial because it is needed to deal with the progress driven by the natural sciences. What we are running into is a dangerous imbalance in which new technologies change our societies faster than the governing institutions can deal with these changes.

Results from the natural sciences are today very well integrated into our daily lives. Think about architecture, engineering, drug tests, health checks, and numerous investigations behind every single consume item, from your car to canned food.

In the last decades one also finds increasingly more examples for a similar integration of the social sciences. Think about architecture again, but take into account the question what group of people the building will host and what amount of interactivity you want to create. A lot of thought has been put into this for example with PI's building. Or think about city planning in general. Economic modeling too has become quite common, though it is tainted by ideological believes and lacks scientific rigor. And then there are the cases where governments commission models to better understand the outcome of planned regulations, like various forms of carbon taxes. These are all cases where one sees some first glimpse of a development I am sure will speed up rapidly in the coming years: an increasing application of insights from the social sciences to our daily lives, in a more organized manner.

And after four centuries, it is really about time to finish the scientific revolution.

Reestablish Trust

And why is this necessary? It is necessary because we simply are no longer able to deal with the problems we are facing. Just look at the present economic crisis. If you stop for a moment trying to find somebody to blame, then the problem comes down to:

1. Lack of understanding how the system works, i.e. studies that would have been necessary are missing.


2. Paying more attention to ideology than to scientific argumentation, i.e. failure acknowledge the importance of objectivity.


3. Failure of our political system to incorporate knowledge in a timely manner.

You can say the same with regard to the question why climate change is so slow to be addressed. You can say the same about lots of other outstanding problems, may that be the increasing gap between the rich and the poor, water shortages, or even your country's inability to come to any conclusion of how to address coming energy scarcity. These are processes that happen, but they happen excruciatingly slow and are hindered by unnecessary rhetoric and psychological games.

Is it really surprising then that many people have lost trust in what politicians say? Is it really surprising that we are now facing several years of aftermath of a economic crisis because of lacking faith in this system?

The conclusion that I draw from this is that the most important thing we need is a solid basis for arguments, and a way to integrate won insights. We need to improve the systems we are operating in, the systems that are meant to allow us to live together with a minimum amount of friction and a maximum amount of progress.

I neither believe that human behaviour is predictable, nor do I think the goal can be to replace human decisions with 'scientifically correct' decisions - this is plain nonsense. What I think however is possible, and necessary, is to make sure decisions can be reached and incorporated fast and easily. One should make a clear distinction here between opinion and the process to reach and implement a decision from opinions. What I am talking about is to set up the system, based on scientific insights, to provide a better environment for those living within it to pursue individual goals without being hindered by outdated institutions.

Or, in short, make sure the system can correct its own mistakes.

The Lightcone Institute

So that's what the institute is about. It is about bridging the gap between the natural, the social, and the computer sciences to initiate this change. And since it is a change in which the scientific community plays a pivotal role, one can't do it without addressing the problems of the academic system itself. The problems of the academic system are in many ways reflections of the larger problems we see in our societies: We have a system that is hindering progress, and knowledge about this dysfunctionality is not incorporated. The system is outdated and unable to correct itself.

You see the above discussed points reflected in the four pillars of the Institute's research. There is the interdisciplinary research to make these connections between the different areas of science, there is the basic research to provide the fundamental pieces that might be missing, there is researching research to address the role of the scientific community. And then there is the essential public outreach to get the hopefully won insights to where they needs to be. The latter point is meant to include communication to the public, as well as to private, academic, and governmental institutions.

You will find that on the website the areas of research are populated with some possible research topics that fall into these categories, like Social-Ecological Systems, Network Science, or the Future of Scientific Publishing.

As to the operation of the Institute, it is a directed research in that the Institute has a clearly defined mission that studies should be dedicated to. Here are the mission statements:

• The Institute's research is to be beneficial and relevant for society.


• The research is focused on interdisciplinary work between the natural and social sciences, fundamental research, and the sociology of science.


• The Institute aims to strengthen the public outreach of the scientific enterprise and actively communicate its research endeavors.


• The Institute will collaborate closely with political institutions, businesses and academia.

All that's missing is money and people.

“I am not an advocate for frequent changes in laws and constitutions. But laws and institutions must go hand in hand with the progress of the human mind. As that becomes more developed, more enlightened, as new discoveries are made, new truths discovered and manners and opinions change, with the change of circumstances, institutions must advance to keep pace with the times.”

~Thomas Jefferson

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Think ahead

Here is a self-quote, dated January 3rd 2008, from my post On the Edge:

“What is currently much more scary is the global economical instability. I am not much of an an economist, but even I sense there will be some major economical crisis rather soon, possibly even this year. If you need any indicators, take Bush talking about the 'fundamentals of the economy being strong'. The whole situation in the US is incredibly unstable. There is a large percentage of people living damned close by poverty level. If their situation gets only slightly worse, they will be pushed to fight for survival, not because they want to, but because they have no other way out.”

This just came back into my mind after reading “Crises on Many Fronts” by Bob Herbert in today's NYT.

“But if we are indeed caught up in the most severe economic crisis since the Great Depression, the ones who will fare the worst are those who already are poor or near-poor. There are millions of them, and yet they remain essentially invisible. A step down for them is a step into destitution.”

Right. And if we wait another year, then maybe somebody will come to realize what I meant with unstable did include the political situation.

Shut up and Calculate

As a PS to Step 11 of '10 Steps to Improve the World', here is a recent quote from Jeffrey Sachs:

“Now what I know about our training since the early 1980s [...] the way we train people to think [...] in mainstream economics and in mainstream politics, has left them almost unable anymore to distinguish the surface from the underlying reality. Not only was it the age of Reagan and the beginning of market fundamentalism that came in the early 80s, and the rational expectations revolution and all the rest, but a fundamental break in how we actually train our students to think [...] the way we see it in our universities.

Because the new kind of economic modeling for 25 years, the one that won all the Nobel Prizes said: you don't have to understand the deep picture, you have to look at the prices you see on the surface and infer the deep picture from that. In other words, the surface tells you the depths in fact because the surface and the depths couldn't be two different things. You don't really have to know underlying mechanisms in the economy because the prices reflect the underlying mechanism. In fact you fit the deep model, if there is one, by looking at the surface and then inferring what the deep model must be, that's literally how students are trained. They're not trained to be skeptical, they're trained to fill in parameters of a system which assumes from the start that what you see on the surface is what you really have. Whereas what fundamental proper skepticism of the Popperian sort [...] and also what the logic of economic bubbles shows, and what the logic of biophysical bubbles show, is what you see on the surface can completely hide and obscure what's happening below.

And it's our job as scientists, and I would say as responsible citizens, to understand the deep points and therefore help to rectify the discrepancy and keep ourselves away from trouble.”

~ Jeffrey Sachs, October 20, 2008 “Can We Save the World Economy? A Conversation with Geroge Soros, Nouriel Roubini, and Jeffrey Sachs”, Recording here

Waterloonitis

Wa·ter·loo·ni·tis
Pronunciation: \ˈwä-tərˈ-lü-nī-təs\

An obsessive-compulsive disorder (ICD-10 F42), characterized by recurrent and persistent thoughts of sunny beaches, hourlasting complaints about potholes, cynical remarks about location advantage, and the distressing urge to spend thousands of dollars on a flight to anywhere. This rare condition has been observed in some regions of Western Ontario during the winter months.