Monday, January 13, 2014

Wilhelm Wien: 150th birthday



He would do his key work in his early 30s. He experimentally determined the distribution of the black-body radiation in the limit \(\hbar\omega\gg kT\). The amount of energy radiated per unit surface per unit time per unit solid angle per unit frequency is given by Wien's law\[

I(\nu, T) = \frac{2 h \nu^3}{c^2} e^{-\frac{h \nu}{kT}}

\] which was determined by Wien experimentally. Max Planck who was 5.7 years older would present some theoretical basis for this law valid in the Wien approximation which is why it would be called the Wien-Planck law.

Needless to say, a few years later, in 1900, Planck would guess and, within three more months, derive the right black-body curve that was valid for low frequencies, too. Planck was a much better theorist who wouldn't just "believe" experiments and his formula was a superior one, of course.

But even when it comes to lower (intermediate) frequencies, Wien determined something before Planck, namely Wien's displacement law\[

\lambda_{\rm max} = \frac{\rm const}{T}

\] which says that the black-body curves for different frequencies are similar to each other, just the width and height of the graph scales with \(T\) and the wavelength at which the curve is maximized is inversely proportional to the absolute temperature \(T\). It's really easy to see this law using the knowledge we have today. All the nontrivial Planck functions only depend on the ratio \(\hbar\omega/kT\) and the frequency is inversely proportional to the wavelength. Alternatively, we may connect the temperature with the energy and use special relativity (Doppler shift etc.) to derive the scaling above.

Note that Wien was really the first man who used the Planck constant in his formula – who determined that a function was exponentially decreasing and the rate of decrease depended on the new constant \(h\) – or \(\hbar\), using the currently preferred rationalized conventions. For this reason, the constant could have been named the Wien constant, too. I think that it was a good choice to name the constant after Planck whose insights to these questions were much more meaningful and more complete.

In 1898, Wien was playing with ionized gas and pretty much discovered the proton. Well, something similar was already done by Eugen Goldstein in 1886. Other experiments and discoveries by J.J. Thomson and Ernest Rutherford etc. were needed for the dust to settle. Rutherford's idea to name the new particle "proton" was only accepted in 1920.

As you could have noticed, Wien's career was all about the electromagnetic radiation. So you shouldn't be surprised that he tried to reduce everything else to electromagnetism. For example, he would propose in 1900 – five years before special relativity – that all mass had electromagnetic origin, according to his formula\[

E = \frac 34 mc^2.

\] You may think it is cute, of course. It's like Einstein's most famous T-shirt formula and is dimensionally correct for the same reason. The extra (wrong) factor of \(3/4\) followed from some particular models how the mass was constructed out of the electrostatic repulsion etc. The derivations are sort of cool and semi-convincing but ultimately they are wrong so unless you are really a big fan of the history of physics, you shouldn't spend much time with learning his detailed arguments. (You may see this paper analyzing more or less equivalent arguments by Fritz Hasenohrl.)

Einstein's \(E=mc^2\) is fully correct and may be defended from all viewpoints, of course, and one may also isolate Wien's technical errors and omissions. But special relativity has changed the status of the energy-mass equivalence conceptually, too. Einstein wouldn't claim that "electromagnetism was fundamental". After all, electromagnetism cannot really be "strictly separated" from other degrees of freedom that the electromagnetic field interacts with. Instead, Einstein's \(E=mc^2\) became a universal law that applies to all forms of mass and energy and that may be derived by very general arguments boiling down to the spacetime symmetries.

So Wilhelm Wien has made important contributions and he deserved his Nobel prize but you may still see that he wasn't in the same league as Planck or Einstein.


  1. I'm not seeing any original thoughts in those quotes, just a hodgepodge of famous thinkers like de Tocqueville and Nietzsche, among many others.
    However, I find the style highly original. It's intellectual yet anti-academic, melding American exceptionalism, Yankee can-do spirit, and pull-yourself-up-by-your-bootstraps self-help ideology with snippets of old-world wisdom. I think it has reached many people who otherwise might have succumbed to a counsel of despair.

    On balance, a force for the good.

  2. Some fun. Aynd Rand has been featured several times in The Simpsons, being the most clear reference in this episode:

    Is the first time that Maggie Simpson speaks, and she do with a mimic of this sequence of King Vidor's Fountainhead.

    The full movie can be seen here:

  3. Dear Lubos
    Indeed Planck didn't box in the same category as Wien.
    I have a few copies of original Planck's papers and they are really perfect - both in spirit and in the content.
    For instance this one where Planck refers to Wien and proceeds to show that E=h.f by such a clear and fundamental argument that I can only admire.
    There didn't miss much to find QM ....
    He even openly writes that he made a mistake and explains why and how he must correct his theory, something that one would never see in climate "science" papers whose quality is many orders of magnitude below this century old paper anyway.
    "Da nun aber letzteres durch die Erfahrung nicht bestätigt wird, so ist man zu dem Schlusse gezwungen dass auch jener Satz in seiner Algemeinheit nicht richtig sein kann und daher aus der Theorie zu entfernen ist."
    Reading papers like Planck's, I can't stop thinking that there was something that the great scientists from 1 century ago possessed and that has largely disappeared today.
    Today we have computers that Planck or Bohr would have dreamed of but instead Plancks and Bohrs we have Smolins, Hansens and Lisis in an ever increasing number.
    How could this have happened ?

  4. Nice article, and the 7 names fully written down made me chuckle, in particular Fritz and Frantz ... :-D

  5. kashyap vasavadaJan 13, 2014, 2:19:00 PM

    Nice article. This is the first time I read about some one with seven names! Was it common in Europe in those days to have so many names?

  6. Hi, LOL, it's surely common among aristocrats. For example, the former (as recently as early 2013) Czech foreign minister and the presidential frontrunner

    is named "Karl Johannes Nepomuk Josef Norbert Friedrich Antonius Wratislaw Menas Fürst zu Schwarzenberg" in German (and a direct translation in Czech) which is composed of 11 names and 1 preposition to boot. :-)

    Czech bumpkins sometimes shorten his name as Karel Schwarzenberg (or Schlafenberg).

  7. I believe some Czech law does not allow Schwarzenberg to use his title of prince although I can't imagine how this law could be enforced.
    In Germany after the abolition of the empire in 1919 aristocratic titles such as Graf (count), Freiherr (baron) etc., were incorporated into the holders surnames so that Graf Walter von Brockdorff-Ahlefeldt became Walter Graf von Brockdorff-Ahlefeldt, thus making the surname longer.

  8. Right, Lucretius.

    Czechoslovakia outlawed the degrees in 1921, three years after its creation. It continued through communism and I think the ban wasn't formally repelled although no one will enforce it today.

    After all, the most frequent short nickname for Schwarzenberg is "kníže", i.e. "Der Fürst" or "The Prince". Even the current president likes to say the story about the sleeping prince Schwarzenberg. Someone told him "pane hrabě, mohl byste" - "Mr Graf, could you...". Schwarzenberg woke up, lifted his head from the table, and said "kníže vole" (Fürst, you idiot) and placed the head on the table again.


  9. Perhaps he was the first child and his parents didn't expect any more. ;-)

    Seriously though, tracing back through my ancestry (which doesn't have any "nobility" of note to mention as far as I can tell so far) I can't find anybody with that many names. Four appears to be the maximum and it wasn't uncommon.

    FWIW: There are about 1000 people recorded in my database, with about 10% known to have incomplete name details. Some names were "officially" abbreviated in the registers.

  10. "I have never been exposed to her work and thoughts"... you were fortunate. Like Nietzsche, she had some good and interesting thoughts, but Nietsche was a genius who was a good writer....
    'nuff said :)

  11. Dear Gordon, this comment makes the differences in our starting points and value systems way too manifest.

    What I was really saying in that sentence about "exposition" was that communism (plus places that imitate it) was hugely immoral (also) because they censored important ideas.

    Whether I am a big Rand fan or not, it is totally obvious that she is a thinker whose ideas *should* have been available to people like me from the beginning because I am clearly at least a *potential* consumer of these ideas.

    The lightness with which you say that we were "fortunate" to be isolated from this world of thought sounds a bit scary to me. Are the North Koreans fortunate, too?

  12. No, I understand and respect the differences in our starting points. I suspect that cultural and political differences in childhood are the root differences in our beliefs, or, at least, in how they are expressed. I in no way mean that, for example, her thoughts or writing should have been censored, and I certainly don't know much about her, and haven't read her books. It is a matter of degree---self interest is obviously a good evolutionary strategy to a degree. If it is pushed to the limit of crass narcissism and taking advantage of perceived weakness, then not so good for society. She may not fall in that category, but she is generally slotted into that description. I am sure that it does make an enormous difference that she experienced the corrosive evils of communism, and, in that sense, I have been living in Laputa :)

    I agree totally with your second paragraph, and I really don't think our value systems are all that different---just refracted through a different cultural and experiential lens.

  13. But you didn't seem to be aware the "Atlas Shrugged" was her version of Nietzsche for Dummies.

  14. And I will generously remain unaware of that. On the contrary, I will continue to be aware that left-wing demagogic jerks like you love to spam websites with insulting "alternative names".

  15. Rand, Hayek, von Mises, all from communist backgrounds and spent so much of their lives addressing its evils. Communism was always doomed to failure but to then think that we must swing the pendulum all the way is not warranted. There never has been a country that has fully conformed to some capitalist economic philosophy and that is probably a good thing because it may well have lead to the same tragedies as communism. It is easy for people like Rand to dictate to decision makers how the world should be because she never had to make those big decisions. We cannot roll the world into a philosophy. That is why we have "mixed economies", I prefer pragmatism over philosophy and economics is not a shining beacon to guide our way forward.
    I do find it interesting that people like Rand devote so much time to complaining about the evils of communism, it is as if their experience left them permanently scarred. It may well have done that and that is not a weakness on their part, it can happen to the best of us. But for such people to then claim the objective status of their ideas about how the world should be is arrogant. Hayek was not that naive, he matured in this thinking, but if Lubos is correct that Rand's philosophy was basically the same as when she was a child, that alone should make us very suspicious.

  16. OK, I consider people like you communists lite.

    Oh, look, "see more" in the long comments has a readable color now. ;-)

    There is no reason why the right society should be "a little bit communist". Communism is fundamentally wrong.

    I have some scars from communism - every person who lived in that system and who at least slightly cherishes freedom has them. And many more. Even millions of people who didn't care about freedom were still hurt or executed.

    But I personally don't spend almost any time by complaining about the evils of communism as we knew it. There are different brands and threats - and already ongoing detrimental developments in the society - today. Their essence is similar or the same but they don't call themselves communism.

    Rand's comment about her stability of the basic skeleton of political opinions since the age 2.5 is sort of amusing or bold but I would say the same thing with the figure 8 years. There are certain things one is simply unlikely to "learn" as an adult. They're so easy in principle (yet arguably demanding a conceptual leap) that one can see them early or never.

  17. The idea that Hayek and von Mieses, both of whom were born in the Austro-Hungarian Empire and were students of Carl Menger (of Polish-Czech noble background) had "communist backgrounds" says all that one needs to know about him.

    Actually, I would not even call him a "communist light" he seems to be perfectly suitable to work for the Fars news agency, as exemplified by this latest piece of exciting "information":

  18. Do you now about the Hungarian Soviet Republic and that von Mises was fleeing the Nazis? Fair enough, "communist background" was too broad, I meant "communist threat" and in their lifetimes it was very real, they probably lost friends to it. The HSR was short lived(1919) but when something that horrendous is that close to home and has probably impacted on friends and family if it doesn't "scar" you and in some way shape your view of the world, especially given the militarist aggression of the Soviets and Nazis, then you are probably one of those who will just walk in line. Hayek and von Mises recognised the danger but unlike Rand they devoted their lives to thinking through economic theories and providing solid working ideas that could be embraced by both governments and individuals. One reason Hayek was appointed to the LSE was to counter the insurgent socialist thinking there. Rand wrote bad novels, no comparison at all.

    You can call what whatever you wish but remember that pejorative appellations explain little and are cheap. Forget the names, deal with the problem: how much legislation and of what kind is necessary to maximise economic activity? What is the role of family, personal, and corporate welfare? Should governments be entirely removed from providing assistance to the disabled and old? Those are the important issues, not your cheap shots. You wanna get rid of govt debt. Dead easy: stop paying pensions, sickness, and unemployment. Literally, dead easy. We know that can't happen, we need a better strategy than that.

    The idea that I entertain communist or even socialist ideals is ridiculous. I'm celebrating the recent announcement of my government to eliminate my govts recent announcement to eliminate 8000 laws.

  19. Note that it was not me who called you a “communist light” - in my opinion that would constitute overestimation. I wrote that you are perfectly suited to working for the Fars News Agency, where the main job is writing stuff that has essentially no relation to reality at all, like the space aliens who are supposedly in charge of the US foreign policy.

    In the same spirit you asserted that Hayek and Von Mises had “communist background” and when challenged “clarified” that the former was under the effect of the shock of the short-lived Bela-Kun regime in neighbouring Hungary (at least if you had been writing about von Neumann that would have had some semblance of sense). This communist regime was, by the way, smashed with the greatest easy by the Rumanian army, which after vicrtory handed over power to the Hungarian Social Democrats (yes, Social Democrats, not some free market liberals or conservatives). Von Mises’s “communist backgrount” it turns out, consisted of “fleeing from the Nazis”.

    On the other hand, facts such as the one that I already pointed out, which was the the main ideas of the so called “Austrian School of Economics” to which both Hayek and Mises belonged, were due to Carl Menger well before the First World War, are for you insignificant. Karl Polanyi, the famous Hungarian economist who presumably you have not heard about, was actually in Hungary during the Bela Kun regime and was a leading opponent of it. He escaped from Hungary when Bela Kun’s communists took power. But Polanyi remained a strong critic of free market economic ideas of the Austrian School and a believer in need for a role of the state in the economy. So by your argument, von Hayek in Viena was scarred by the communists in Budapest and than turned him into a dogmatic free marketeer, while Polanyi, fleeing for his life from the communists, was not “not scarred” and remained a social democrat.

    What an interestingly objective way of looking at these matters!

    Let’s make things more personal. I freely admit to having had a “communist background” since I left communist Poland at 15. When I left, my views were rather close to Polanyi’s - basically social democratic. My father, a fierce anti-communist (and a professor of economics) till the end of his life remained a devoted Keynesian. (Actually Keyne’s was every bit as anti-Communist as Von Hayek. He wrote about Hayek’s “Road to Serfdom”: “"In my opinion it is a grand book...Morally and philosophically I find myself in agreement with virtually the whole of it: and not only in agreement with it, but in deeply moved agreement." And he repeatedly referred to communism as ”an insult to our intelligence.”).

    As for me, what above all turned me into an opponent of social democratic “managed economy” was, first of all, not my experience of communism but pre-Thacher Britain, where my parents settled after leaving Poland. In addition to that, I had more than 20 years of experience of living under the Japanese “industrial policy” or “state directed capitalism” as well as several years in the US in the Reagan period. But for your way of thinking any such experience obviously constitutes a disadvantage, for to be really unbiased a person should have no “scars”, i..e no experience, at all - which obviously is true of yourself, judging by you posts here. But for others that is an excellent reason to ignore them, which is what I am going to do from now on.

  20. Yes and thankfully it was quickly squashed but my point was when it gets that close to home it must be bloody terrifying. We all carry scars. How we let those influence us is important. Hence the distinction between Hayek and Rand. One used the experience to good effect, the other wrote poor novels. An experience is not an intrinsic disadvantage, it is the response that can be mal-adaptive. The idea though that people can be objective agents in social world is contradicted by a great many studies. We all bring our biases to the table which is why finding agreement on social and economic policies is nigh impossible to achieve. When one group claims that in social matters they have all the answers from some philosophical perspective they are using the same cognitive structures as fundamentalists of any ilk. I wish it were that easy but history doesn't support simple philosophising as an answer to our woes.

    "Road to Serfdom" is great, loved it. "The Sensory Order" is a remarkable book of insights for its time, shows the brilliance of Hayek independently of his economic ideas. Pre-Thatcher Britain was a mess, so much is obvious, and irrelevant. We know all this. Whoopee do. The problem is the world today.

    All economies are to some extent managed. It is always a matter of degree. There are no rosetta stones here, that's why I referred to China because it demonstrates that differing circumstances require differing approaches. That's the problem with grand philosophical imperatives. Whether they be from the left or right they too often ignore the context in which an economy must function. China could be one huge mirage, I have concerns about how much of that "economic miracle" is just fudging figures, but on present indications China has done a striking job in modernising its economy and lifting people out of poverty. Yet this current economic trouble emerged from the one country that promoted free trade more than all the others. That country has by far the widest distribution of wealth in the OECD, a poor education system, a very expensive health system, and a massive deficit. That crisis happened under Bush. It is how an economy is managed, not whether or not it is managed. Governments shouldn't set prices but they do need to establish some parameters within which an economy must function.

    Of course you'll ignore me, that is what left and right ideologues do, ignore people who disagree with them. Me, I argue with people of differing views all the time. It's fun, even with ideologues.
