CMS search for exotics at 5/fb, is that a HSCP at 700 GeV?

January 31, 2012

Today CMS have delivered a new report of searches for exotic particles including SUSY using datasets up to 5/fb. I dont think I have ever seen so many new results released in one presentation (Eva Halkiadakis). Sadly there are no new discoveries and nothing can be considered to be inconsistent with the standard model, but it would be exceptional if we could not pick at least one exceptional datapoint from so many plots and here it is.

This is from a search for heavy stable charged particles and three isolated events were seen in the same bin at 700 GeV

Update: A video of the talk has now been uploaded. Motl has posted a useful analysis for this plot.

Should you boycott Elsevier?

January 30, 2012

Some people include a few notable bloggers are saying that we should all boycott Elsevier who publish science journals and sell them at a good profit margin. Does this make sense? I wont answer that question but Iwill make this point: Elsevier is a profit making business who can set its margins according to how well it can persuade people that its products have good value (e.g. by attracting good authors to give it a high impact factor), and how well it can keep its costs down (e.g. by attracting unpaid reviewers) Elsevier have been doing this a little bit better than some of its rivals. If a boycott now reduces these margins they will increase them for any other publisher that is used instead by those authors and reviewers. Result: back to square one.

Of course there are non-profit organisations that publish journals, but the cost of their journals is not really that much better and they are not necessarily better at being open access either. If they were, then there would be no publishers making profits. So is there a real solution to the problem? If scientists don’t want to pay a high price for someone to organize their peer-review they have to find an efficient way to do it themselves. They have already found efficient ways to do the publishing and distribution (e.g. arXiv). Now they have to do the same for the more difficult task of peer-review. Until they do that any boycotts will be a futile game of pushing lumps and scientists will have to continue paying the market price for a commercial service.

That is my opinion, what do you think?

Update: John Baez has posted another follow-up discussing what else can be done to replace journals for peer-review. Apparently the life sciences are now ahead of maths and physics on this!


Seminar Watch 2012

January 28, 2012

The New Year is well under way and already ATLAS has released its first conference note for 2012 updating the search for supersymmetry at 2/fb. They see a small excess of events, i.e. four where 1.7 ± 0.9 were expected. This is nothing that trial error cannot account for but it shows that the update to 5/fb still has a potential to produce ground-breaking results. CMS will be the first to provide that update with a seminar scheduled for Tuesday covering various searches including SUSY and exotica. We can rule out the possibility of anything really startling being announced, by the lack of rumours 🙂 but there can always be first tantalizing hints.

After that the next big events for HEP results are the Aspen conference from 11th February and Moriond from 3rd March. The latter is the most likely venue for further results at 5/fb to be presented. The official Higgs combination for the LHC should appear and final Higgs results from the Tevatron using their full dataset are also expected.

Meanwhile the LHC itself has already entered its hardware recommissioning phase at the end of the Winter shutdown with half of the eight cryogenics plants already cooling down. The running schedule for 2012 is available showing a start date of 11st March for beams. This is 17 days later than last year. By then they will have decided on the running parameters for next year. The main ones to consider are the energy, bunch spacing and beta*. This year hopes are running high that the centre of mass energy will go up from 7 TeV to 8TeV but this depends on the results of hardware tests. They will not want to take any risk. The bunch spacing could go down from 50ns to 25ns which would please the experiments because it reduces pile-up, but realistically I think this would require too much scrubbing and preparation. It may result in a much lower luminosity for the year. They would be better to stick to 50ns and be sure of a good clean run. A better squeeze with a lower beta* is a promising option for pushing the luminosity to higher levels without risking higher intensities. These matters will be discussed at Chamonix from 6th February. If that is too technical a summary session will be webcast on 15th February.

It is too soon to list all the conferences where new results may appear this year but the biannual ICHEP meeting deserves a special mention. This is the largest conference for HEP and this year it will take place in Melbourne from 4th July. By then they may have doubled the LHC dataset if everything has run very smoothly. Discovery potential rises another notch.

Favorite Explanations

January 18, 2012

The Edge question for 2012 is “What is your favorite deep, elegant or beautiful explanation?” There are lots of interesting answers given but my favorite is not included. That’s partly because they did not have the foresight to ask me, but never mind I can post it here.

My favorite explanation is Stephen Hawking’s argument for why the area of a black hole horizon increases. This is a very non-trivial result from gravitational dynamics and yet the explanation can be summarized almost rigorously in words without any equations. Not only is it elegant but it is also very deep since it leads to the idea that the area of a black hole is related to entropy, a hunch that Hawking later clarified with his theory of black hole radiation and thermodynamics. This in turn led to the information loss paradox which was explained by the holographic principle. It is a remarkably persuasive train of thought that takes us on a journey far beyond anything that experiment or observation can currently reach, an amazing demonstration of the power of the human mind. I am sure I do not need to describe the details of these ideas to most readers of this blog. Any of you that are not familiar can read about them in Wikipedia when it comes back from its anti-anti-piracy sulk.

Anyway, here is Hawking’s beautiful explanation quoted from “a Brief History of Time”

“I had already discussed with Roger Penrose the idea of defining a black hole as the set of events from which it was not possible to escape to a large distance, which is now the generally accepted definition. It means that the boundary of the black hole, the event horizon, is formed by the light rays that just fail to escape from the black hole, hovering forever just on the edge. It is a bit like running away from the police and just managing to keep one step ahead but not being able to get clear away!
Suddenly I realized that the paths of these light rays could never approach one another. If they did, they must eventually run into one another. It would be like meeting someone else running away from the police in the opposite direction – you would both be caught! ~ But if these light rays were swallowed up by the black hole, then they could not have been on the boundary of the black hole. So the paths of light rays in the event horizon had always to be moving parallel to, or away from, each other. ~ If the rays of light that form the event horizon, the boundary of the black hole, can never approach each other, the area of the event horizon might stay the same or increase with time but it could never decrease because that would mean that at least some of the rays of light in the boundary would have to be approaching each other. In fact, the area would increase whenever matter or radiation fell into the black hole. ~ This nondecreasing property of the event horizon’s area placed an important restriction on the possible behaviour of black holes.”


Relativity FAQ: Why is “c” used for the speed of light?

January 8, 2012

Back in the days before blogs and web forums when we used to discuss physics on usenet I was for a short while the editor of the Physics FAQ. Although the FAQ is still cared for by Don Koks it’s role has been mostly superseded by Wikipedia for better or for worse. In my time I wrote a number of articles for the FAQ with a special interest in the relativity questions. A lot of new discoveries have been made since then and some of them impact the cosmology sections. I’d like to update a few of my earlier articles and rewrite some others in my own words. I’ll post them here over time and I may even write some new ones. Feel free to add comments or ask further questions.

Why is “c” used for the speed of light?

The short answer

According to the science fiction writer Isaac Asimov, the reason why c is used as the symbol for the speed of light is that c stands for celeritas, the Latin word for speed [1], but is this really true?

Tracing the origin of the use of a given symbol in science is not always straight forward. Scientists rarely trouble to note the origin of the notations they use. When Einstein wrote his first papers on the theory of relativity he chose V as his symbol for the speed of light [2]. In 1907 he suddenly changed it to c [3] without explanation but it is likely that he was being influenced by earlier usage rather than choosing his own notation. From that point on the notation was used by everyone.

When you try to track where this came from and why, three possible explanations come up. There is indeed some evidence to show that c was sometimes used as a generic symbol for speed because it stands for celeritas, but there are two more specific influences that seem more concrete. One comes from the use of the letter c as the speed variable in the wave equation. This can be traced back to the work of Euler who developed it in two and three dimensions during the eighteenth century. When he choose the symbol c he had already used a and b as other variables so the most obvious reason for his choice was that c was simply the next letter in the alphabet.

Another equally plausible explanation has its origins in a paper from 1856 by Weber and Kohlrausch on electricity and magnetism [4]. They introduced a constant c with dimensions of speed that was important to the interrelationships between the two forces. It is clear from the text and subsequent usage that c simply stood for constant. Later this quantity was shown to be  related to electromagnetic wave propagation and was then popularised as a symbol for the speed of light.

It is surprising that the notation seems to have more than one origin and it is not easy to determine which of these was the most influential, but probably all three played a part over time in establishing the latter c as the universally accepted symbol for the speed of light.

Does c stand for celeritas?

In 1959 Isaac Asimov penned an article for a sci-fi magazine entitled “C for Celeritas” in which he claimed he knew why c is used for the speed of light. “As for c, that is the speed of light in vacuum, and if you ask why c, the answer is that it is the initial letter of celeritas, the Latin word meaning speed.” he wrote. The article was reprinted in some of his books [1] which sold many copies to budding scientists, so it is not surprising that since then, Asimov’s answer has become a factoid repeated in many other articles and books.

However, if you go back and read his essay you discover that Asimov merely stated his case in that one sentence. He made no further attempt to justify his theory for the origin of the c notation. So is his claim really born out by history, or was c originally introduced as a variable standing for something else?  The special theory of relativity is based on the principle that the speed of light is constant; so did c stand for “constant”, or did it simply appear by accident in some text where all the other likely variables for speed had already been used up?

It is certainly true that the letter c has been used as a generic symbol for speed since at least the 18th century. For example it is also usually used as the standard symbol for the speed of sound. Starting with the Latin manuscripts of the 17th century, such as Galileo’s “De Motu Antiquiora” or Newton’s “Principia”, we find that they often use the word “celeritas” for speed.  However, their writing style was very geometric and descriptive.  They did not tend to write down formulae where speed is denoted by a symbol.  Possibly the earliest example of the letter c being used for speed can be found in a work written in the eighteenth century.  In 1716 Jacob Hermann published a Latin text called “Phoronomia”, meaning the science of motion [5].  In it he developed Newton’s mechanics in a form more familiar to us now, except for the Latin symbols.  His version of the basic Newtonian equation F = ma was dc = p dt, where c stands for “celeritas” meaning speed, and p stands for “potentia”, meaning force.

Physicists of the nineteenth century would have read the classic Latin texts on physics, and would have been aware that c could stand for “celeritas”.  As an example, Lorentz used c in 1899 for the speed of the Earth through the ether [6].  Typically Einstein had little interest in Latin at school considering it to be a useless subject. Yet we know that even Einstein used c for speed outside relativity. In a letter to a friend about a patent for a flying machine, he used c  for the speed of air flowing at a mere 4.9 m/s [7].

All this lends plausibility to the argument that c stands for celeritas but there is also persuasive evidence for other origins of the notation, so the best we can really say is that the generic use of  c as a symbol for speed helped the notation to prevail over other alternatives in use around the turn of the twentieth century.

Does c stand for constant?

The idea that c might stand for constant rather than celeritas may seem a little too obvious to be true, but there is good reason to propose that this is really the correct origin of the notation.

Although c is now the universal symbol for the speed of light, the most common symbol in the nineteenth century was an upper-case V which Maxwell had started using in 1865 [8]. Maxwell may have borrowed this from Foucault who had used the same symbol earlier in his thesis of 1853 [9].  That was then the notation adopted by Einstein for his seminal papers on relativity from 1905.

The most convincing origin of the letter c being used for the speed of light can be traced back to a paper of 1856 by Weber and Kohlrausch [4].  They defined and measured a quantity denoted by c that they used in an electrodynamics force law equation.  It became known as Weber’s constant and was later shown to have a theoretical value equal to the speed of light times the square root of two.  In 1894 Paul Drude modified the usage of Weber’s constant so that the letter c became the symbol for the speed of electrodynamic waves [10].  In optics Drude continued to follow Maxwell in using an upper-case V for the speed of light.  Progressively the c notation was used for the speed of light in all contexts as it was picked up by Max Planck, Hendrik Lorentz and other influential physicists.  By 1907 when Einstein switched from V to c in his papers, it had become the standard symbol for the speed of light in vacuum for electrodynamics, optics, thermodynamics and relativity.

In France and England the electromagnetic constant was often symbolised by a lower case v rather than Drude’s c.  This was directly due to Maxwell, who wrote up a table of experimental results for direct measurements of the speed of light on the one hand and electromagnetic experiments on the other.  He used V for the former and v for the latter.  Maxwell described a whole suite of possible experiments in electromagnetism to determine v.  Those that had not already been done were performed one after the other in England and France over the three decades that followed [11].  In this context, lower case v was always used for the quantity measured.  But using v was doomed to pass away once authors had to write relativistic equations involving moving bodies, because v was just too common a symbol for velocity.  The equations were much clearer when something more distinct was used for the velocity of light to differentiate it from the velocity of moving bodies.

While Maxwell always used v in this way, he also had a minor use for the symbol c in his widely read treatise of 1873.  Near the end he included a section about the German electromagnetic theory that had been an incomplete precursor to his own formulation [12].  This theory, expounded by Gauss, Neumann, Weber, and Kirchhoff, attempted to combine the laws of Coulomb and Ampère into a single action-at-a-distance force law.  The first versions appeared in Gauss’s notes in 1835 [13], and the complete form was published by Weber in 1846 [14].  Many physicists of the time were heavily involved in the process of defining the units of electricity.  Coulomb’s law of electrostatic force could be used to give one definition of the unit of charge while Ampère’s force law for currents in wires gave another.  The ratio between these units had the dimension of a velocity, so it became of great practical importance to measure its value.  In 1856 Weber and Kohlrausch published the first accurate measurement [4].  To give a theoretical backing they rewrote Weber’s force law in terms of the measured constant and used the symbol c.  This c appeared in numerous subsequent papers by German physicists such as Kirchhoff, Clausius, Himstedt, and Helmholtz, who referred to it as “Weber’s constant”.  That continued until the 1870s, when Helmholtz discredited Weber’s force law on the grounds of energy conservation, and Maxwell’s more complete theory of propagating waves prevailed.

Two papers using Weber’s force law are of particular note.  One by Kirchhoff [15] and another by Riemann [16] related Weber’s constant to the velocity at which electricity propagated.  They found this speed to be Weber’s constant divided by the square root of two and it was very close to the measured speed of light.  It was already known from experiments by Faraday that light was affected by magnetic fields, so there was already much speculation that light could be an electrodynamic phenomenon.  This was the inspiration for Maxwell’s work on electrodynamics, so it is natural that he finally included a discussion of the force law in his treatise [12].  The odd thing is that when Maxwell wrote down the force law, he changed the variable c so that it was smaller than Weber’s constant by a factor of the square root of two.  So Maxwell was probably the first to use c for a value equal to the speed of light, although he defined it as the speed of electricity through wires instead.

So c was used as Weber’s constant having a value of the speed of light times the square root of two, and this can be related to the later use of c for the speed of light itself.  Firstly, when Maxwell wrote Weber’s force law in his treatise in 1873, he modified the scale of c in the equation so that it reduced by a factor of the square root of two.  Secondly, when Drude first used c in 1894 for the speed of light [10], the paper by Kirchhoff that he cited [17] was using c for Weber’s constant, so Drude had made the same adjustment as Maxwell.  It is impossible to say if Drude copied the notation from Maxwell or invented it indepednently, but he did go one step further in explicitly naming his c as the velocity of electrodynamic waves which by Maxwell’s theory was also the speed of light.  He seems to have been the first to do so, with Lorentz, Planck, and others following suit a few years later.

So to understand why c became the symbol for the speed of light we now have to find out why Weber used it in his force law.  In the paper of 1856 [4] Weber’s constant was introduced with these words “.. and the constant c represents that relative speed, that the electrical masses e and e must have and keep, if they are not to affect each other.” This was written in German and the modern German word for constant is “konstant” but at that time before spelling was completely fixed it was often written in German with an initial “c”. This was the case here. So it appears that c originated as a letter standing for “constant” rather than “celeritas”.  However, it had nothing to do with the constancy of the speed of light until much later.

Why is c used in the wave equation?

The speed of light is not the only place in physics where c is commonly used to represent speed. It is also the standard notation for the speed of sound and is used in the linear wave equation. In its simplest scalar form it can be written like this

\frac{\partial^2 u} {\partial t^2} = c^2 \nabla^2 u

You might think that this form of the wave equation is used because physicists most commonly think of the wave equation in the context of relativistic physics where c represents the speed of light. It would be a natural progression to then use the same symbol for other wave equations even if c then stands for a different speed such as the speed of sound or water waves. The literature shows that this is not the correct explanation because this usage in the wave equation goes back before light was even known as a wave phenomena.

In 1747 Jean d’Alembert made a mathematical study of the vibrating string and discovered the one dimensional wave equation [18], but he wrote it without the velocity constant.  Euler generalised d’Alembert’s equation to include the velocity, denoting it by the letter a [19].  The general solution is y = f(x – at) + f(x + at), representing a supposition of two waves of fixed shape travelling in opposite directions with velocity a.

Euler was one of the most prolific mathematicians of all time.  He wrote hundreds of manuscripts and most of them were in Latin.  Was it Euler then who established a convention for using c for “celeritas”?  In 1759 he studied the vibrations of a drum, and moved on to the 2-dimensional wave equation.  This he wrote in the form we are looking for with c now the velocity constant [20].

The wave equation became a subject of much discussion, being investigated by all the great mathematicians of the époque including Lagrange, Fourier, Laplace, and Bernoulli.  Through their works, Euler’s form of the wave equation with c for the speed of wave propagation was carved in stone for good.  To a first approximation, sound waves are also governed by the same wave equation in three dimensions, so it is not surprising that the speed of sound also came to be denoted by the symbol c.  This predates relativity and can be found, for example, in Lord Rayleigh’s classic text “Theory of Sound” published in 1877 [21].

So can we tell why Euler used the letter c? Most of his work on the wave equation was written in French rather than Latin and there is no reason to suppose he was thinking of the Latin word celeritas. It is true that the French sometimes use the word célérité to mean the phase velocity in the context of the wave equation. They even sometimes talk of “célérité du son” and “ccélérité de la lumière” for the speed of sound and light, but there is no evidence that this goes back to the time of Euler. Euler just used “vitesse” the more common French word for speed. It is more likely that the French usage was adopted later as a consequence of Euler’s use of c in the wave equation.

Euler’s style of notation for algebra and calculus was very similar to basic usage in mathematics and physics today. He commonly picked sequences of letters such as a, b, c or x, y, z for variables, sometimes changing to upper case or Greek letters with little indication that the letters actually stood for anything in particular. In fact Euler set many of the notations we use today including the use of the Greek letter \pi for 3.14159… One possibility for his choice of c is that when he moved from the one dimensional wave equation to the 2-dimensional case, he may have used a and b for the components of the wave velocity, then writing c^2 = a^2 + b^2 for the magnitude. Unfortunately there is no written evidence to support this theory either.

There is however a case for an even more mundane answer. When he introduced the variable c for possibly the first time he defined it with an equation that he wrote

\frac{a g}{b} = cc

a and b were simply two physical variables he had already introduced, so c seems to be chosen as merely the next letter in the alphabet.

Why did Einstein switch notation for the speed of light?

A lower-case c has been consistently used to denote the speed of light in textbooks on relativity almost without exception since such books started to be written. For example, the notation was used in the earliest books on relativity by Lorentz (1909) [22], Carmichael (1913) [23], Silberstein (1914) [24], Cunningham (1915) [25], and Tolman (1917) [26]. That was not the case just a few years before. In his earliest papers on relativity from 1905—1907 Einstein began by using an upper-case V for the speed of light [2]. At that time he was also writing papers about the thermodynamics of radiation, and in those he used up upper-case L [27]. All of these papers appeared in volumes of the German periodical Annalen Der Physik. Einstein’s notation changed suddenly in 1907 in a paper for the Journal Jahrbuch der Radioaktivität und Elektronik [3]. There he used the lower case c, and his most famous equation E = m c^2 finally took it’s familiar form.

It is not difficult to find where the upper case V had come from. Maxwell used it extensively in his publications on electrodynamics from as early as 1865 [8]. It was the principal symbol for the speed of light in his 1873 treatise on electrodynamics [28]. By the 1890s Maxwell’s book was in wide circulation around the world and there were translations available in French and German. It is no surprise then that the upper-case V is found in use in such papers as the 1887 report of Michelson and Morley on their attempt to find seasonal variations in the speed of light [29]. That was written in the United States, but the same notation was also found across Europe, from papers by Oliver Lodge [30] and Joseph Lamor [31] in England, to the lecture notes of Poincaré in France [32], and the textbooks of Paul Drude in Germany [33] and Lorentz in the Netherlands [34]. Einstein’s education at the Polytechnik in Zurich had not covered Maxwell’s theory of Electrodynamics in the detail he would have liked, but he had read a number of extra textbooks on the new Electrodynamics as self study, so he would have been familiar with the standard notations. From 1905 he wrote his first papers on relativity, and there is nothing extraordinary in his choice of the symbol V for the speed of light [2].

Why then, did he change it to c in 1907? At that time he still worked as a clerk in the Bern patent office, but for the previous two years he had been in regular correspondence with eminent physicists such as Max Laue, Max Planck, Wilhelm Wien and Johannes Stark. Stark was the editor of the Jahrbuch, and had asked Einstein to write the article in which he was to first use the letter c. Einstein mentioned to Stark that it was hard for him to find the time to read published scientific articles in order to acquaint himself with all the work others have done in the field, but he had seen papers by Lorentz, Kohn, Monsegeil and Planck [35]. Lorentz and Planck in particular had been using c for the speed of light in their work. Lorentz had won the 1902 Nobel prize for physics, and it is not surprising that physicists in Germany had now taken up the same notation. It is also not surprising that Einstein, who was looking for an academic position, aligned himself to the same conventions at that time. Another reason for him to make the switch was that the letter c is simply more practical. The upper-case V would have been easily confused with the lower case v appearing in the equations of relativity for the velocity of moving bodies or frames of reference. Einstein must have found this confusion inconvenient, especially in his hand written notes.

Looking back at papers of the late 1890s, we find that Max Planck and Paul Drude in particular were using the symbol c at that time. The name of Drude is less well known to us today. He worked on relations between the physical constants and high precision measurements of their value. These were considered to be highly worthy pursuits of the time. Drude had been a student of Voigt, who himself had used a Greek \omega for the speed of light when he wrote down an almost complete form of the Lorentz transformations in 1887 [36]. Voigt’s \omega was later used by a few other physicists [37, 38,50], but Drude did not use his teacher’s notation. Drude first used the symbol c in 1894, and in doing so he referenced a paper by Kirchhoff [10]. As already mentioned, Paul Drude also used V. In fact he made a distinction of using V in the theory of optics for the directly-measured speed of light in vacuum, whereas he used c for the electromagnetic constant that was the theoretical speed of electromagnetic waves. This is seen especially clearly in his book “Theory of Optics” of 1900 [39], which is divided into two parts with V used in the first and c in the second part. Although Maxwell’s theory of light predicted that they had the same value, it was only with the theory of relativity that these two things were established as fundamentally the same constant. Other notations vied against Drude’s and Maxwell’s for acceptance. Herglotz [38] opted for an elaborate script B, while Himstedt [40], Helmholtz [41] and Hertz [42] wrote the equations of electrodynamics with the letter A for the reciprocal of the speed of light. In 1899 Planck backed Drude by using c, when he wrote a paper introducing what we now call the Planck scale of units based on the constants of electrodynamics, quantum theory and gravity [43]. Drude and Planck were both editors of the prestigious journal Annalen Der Physik, so they would have had regular contact with most of the physicists of central Europe.

Lorentz was next to change notation. When he started writing about light speed in 1887 he used an upper case A [44], but then switched to Maxwell’s upper case V [45]. He wrote a book in 1895 [46] that contained the equations for length contraction, and was cited by Einstein in his 1907 paper. While Drude had started to use c, Lorentz was still using V in this book. He continued to use V until 1899 [47], but by 1903 when he wrote an encyclopedia article on electrodynamics [48] he too used c. Max Abraham was another early user of the symbol c in 1902, in a paper that was seen by Einstein [49]. From Drude’s original influence, followed by Planck and Lorentz, by 1907 the c symbol had become the prevailing notation in Germanic science and it made perfect sense for Einstein to adopt it too.

What was the earliest symbol used for the speed of light?

It is hard to be certain when a symbol was first used for the speed of light, but Doppler used the Greek letter \alpha in his paper on the frequency shift of light with velocity in 1842 [51]. There were other papers written about the speed of light before then but none of them seems to have used any symbol to represent it.


[1] Isaac Asimov “C for Celeritas” in “The Magazine of Fantasy and Science Fiction”, Nov-59 (1959), reprinted in “Of Time, Space, and Other Things”, Discus (1975), and “Asimov On Physics”, Doubleday (1976)
[2] A. Einstein, From “The Collected Papers, Vol 2, The Swiss Years: Writings, 1900—1909”, English Translation, he wrote five papers using V, e.g. “On the Electrodynamics of Moving Bodies”, Annalen Der Physik 17, pgs 891—921 (1905), “On the Inertia of Energy Required by the Relativity Principle”, Annalen Der Physik 23, pgs 371—384 (1907)
[3] A. Einstein, “On the Relativity Principle and the Conclusions Drawn From It”, Jahrbuch der Radioaktivität und Elektronik 4, pgs 411—462 (1907)
[4] R. Kohlrausch and W.E. Weber, “Ueber die Elektricitätsmenge, welche bei galvanischen Strömen durch den Querschnitt der Kette fliesst”, Annalen der Physik, 99, pg 10 (1856)
[5] J. Hermann, “Phoronomia”, Amsterdam, Wetsten, (1716)
[6] H.A. Lorentz, “Stokes’ Theory of Aberration in the Supposition of a Variable Density of the Aether”, Proc. Roy. Acad. Amsterdam I, pg 443 (1899)
[7] A. Einstein, “The Collected Papers, Vol 5, The Swiss Years: Correspondence, 1902—1914”, English Translation, Doc 86 (1907)
[8] J. Clerk Maxwell, “A dynamical theory of the electromagnetic field”, Philos. Trans. Roy. Soc. 155, pgs 459—512 (1865).  Abstract: Proceedings of the Royal Society of London 13, pgs 531—536 (1864)
[9] J. Foucault, “Sur les vitesses relatives de la lumiére dans l’air et dans l’eau” (Paris, 1853)
[10] P. Drude, “Zum Studium des elektrischen Resonators”, Göttingen Nachrichten (1894), pgs 189—223
[11] e.g. J.J. Thomson and G.F.C. Searle, “A Determination of `v’, the Ratio of the Electromagnetic Unit of Electricity to the Electrostatic Unit”, Proc. Roy. Soc. Lond. 181, pg 583 (1890), M. Hurmuzescu, “Nouvelle determination du rapport v entre les unites electrostatiques et electromagnetiques”, Ann. de Chim. et de Phys., 7a serie T. X April 1897, pg 433. (1897)
[12] J. Clerk Maxwell, “A Treatise on Electricity and Magnetism”, Oxford Clarendon Press, Vol II; Chapter 23, section 849 (1873)
[13] K.F. Gauss, “Zur mathematischen Theorie der elektrodynamischen Wirkung” (1835), in “Werke”, Göttingen 1867; Vol. V, pg 602
[14] W. Weber, “Elektrodynamische Maassbestimmingen uber ein allgemeines Grundgesetz der elektrischen Wirkung”, Abh. Leibnizens Ges., Leipzig (1846)
[15] G. Kirchhoff, “Ueber die Bewegung der Elektricität in Leitern” Ann. Phys. Chem. 102, 529—544 (1857)
[16] G.F.B. Riemann, “Ein Beitrag zur Elektrodynamik”, Annalen der Physik und Chemie, pg 131 (1867)
[17] G. Kirchhoff, “Zur Theorie der Entladung einer Leydener Flasche”, Pogg. Ann. 121 (1864)
[18] J. d’Alembert, “Recherches sur les cordes vibrantes”, L’Académie Royal des Sciences (1747)
[19] L. Euler, “De La Propagation Du Son” Memoires de l’acadamie des sciences de Berlin [15] (1759), 1766, pgs 185—209, in “Opera physica miscellanea epistolae.  Volumen primum”, pg 432
[20] L. Euler, “Eclaircissemens Plus Detailles Sur La Generation et La Propagation Du Son Et Sur La Formation De L’Echo”, “Memoires de l’acadamie des sciences de Berlin” [21] (1765), 1767, pgs 335—363 in “Opera physica miscellanea epistolae.  Volumen primum”, pg 540
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Stephen Hawking 70th Birthday Symposium

January 3, 2012

He may be the weakest man in the world barely able to flutter a cheek muscle to work his computer and speech synthesizer, but Stephen Hawking’s life has had a powerful impact on physics and its popular image. This month he turns 70 and to celebrate there will be a symposium at Cambridge this Sunday and it will be webcast. The technology for the broadcast is being organised by Intel who provided a powerful computer at Cambridge for cosmological simulations as well as the CPU for Hawking’s speech synthesizer of course. So here he is in lego (by Iain Heath)

and here is a youtube video from Intel