Crtd 15-11-06 Lastedit 17-10-11
Bert Goes In Relativity Theory
The Start: Finding Special Relativity on Utrecht University Campus
This blog describes why I always wanted to study Special Relativity theory and my personal practical vicissitudes in the first 2 months I visited an Utrecht Campus course. For how after these 2 months I explained the theory to myself see Bert Reads Einstein [math] and [exercise]. (Even after these campus course visits and writing these two texts I did not foresee I would need almost 2 years more to acquire a fully clear understanding of the subject [more about this]).
After recently finishing the part of Musil's Der Mann Ohne Eigenschaften that I had set out to relate [see my Musil relation], I had promised myself to finally acquire understanding of relativity theory, probably because Musil's protagonist Ulrich's last career disappointment that the book starts with had been ... mathematics! It arose when recently for the first time a horse had been called a "genius" in a newspaper. This had prompted Ulrich to abandon his university math post, where he already had booked some achievements and was considered highly promising, with immediate effect. He was 32. Though it is not mentioned, the profile Musil gave to Ulrich's character leaves no doubt he studied and understood relativity theory: it was new at the time, the entire educated public was aware of it, it gets mentioned in the book, and Ulrich was trained to read such stuff. But then came the horse-genius. At the start of Musil's book, Ulrich had lost his very last jealousy and ambition and, now firmly aware of the ridiculous state of man, from small to great, and his history, took time off to search back in Vienna for purpose, albeit with a worryingly blank agenda.
Not me at the time I first read the book (I was 31). I would need quite a bit more time than Ulrich to loose my social career ambitions. Once it did, in my mid fourties, its effect on me was quite different than the one it had - the core of the book - on Ulrich: I felt the joy of liberation and embarked on adventure [more].
In my early twenties while in my study in logic of scientific theories, I had done some quick searches in relativity theory, for in my field it was often referred to in awe as the best specimen of science, after which illustrations invariably got taken from simpler theories like Newton's mechanics. Those were hard enough for me to transfer to mathematical economics, where logical analysis of theory structure, at the time, had only scarcely and crudely been exercised. I went into that.
In 1913, while Einstein was engaged in publishing his general version of relativity theory while few yet had understood the previous, very simple, first version, Mann ohne Eigenschaften-character top Austrian Imperial government dignitary Graf Leinsdorf on a tense moment in the middle of the book shouts: "This psychoanalysis and relativity theory or how you call all that crap, it bubbles up irresponsibly, and does not care for the larger social consequences! ... we quickly knock something together and before we even started to look whether it is something viable we are already engaged with the next, or even missed the whole thing! A piggery!". Of course these zillions of petty Freudian therapists setting out to cheat us for good money indeed were all pigs, and I can't help thinking of those cats and dogs of new Microsoft Windows versions raining on us. And more. His Serene Highness Count Leinsdorf sure had a point. He led me again to aspire understanding relativity theory, though a case in which the count's eruption misses the point completely - and Musil no doubt was fully aware of that.
But I had no time: my head, in 1982, was fully occupied with my dissertation that a year later caused, to my total surprise, a row among the midget economics professors of Amsterdam University and then got read by nobody, at least nobody serious - probably no reason for the world to mourn, though it is excellent, original and could have helped the intelligent mathematical economist to efficiently order his procedures - but I can't claim that could have prevented a disaster, since there was none about to happen. I had gone into it out of personal curiosity. No wonder the need for my results was not widely felt, though in physics there was interest in this type of work, and even in the economic academics of the years after, quite some young talented successful career scholars joined the fashion of what got called "economic methodology". However, they lacked the formal training to deal with my stuff, and were not prepared to acquire it. A career "methodologist" aspires to talk with academic economists, that's where money and career are, not in founding a new obscure field for a new class of insiders rarely deemed of interest by their research objects: mathematical economists.
But I am still remembering pleasure of the making of that analysis, starting when 25 years old, with a university salary that I totally failed to consume, a 25% teaching load and no publication pressure to threaten the quality of my work.
... my summer 1982 first reading (it looks I've just started!) of Musil's Der Mann ohne Eigenschaften (got into it through Wittgenstein's Tractatus Logico-Philosophicus by Ulrich's contemporary Viennese Ludwig Wittgenstein, parts of whose personality strongly remind of Ulrich). Meanwhile I wrote my dissertation on dynamic logico-mathematical analysis of economic theories (published as Neoclassical Theory Structure and Theory Development, Studies in Contemporary Economics, Vol. 4, Berlin, Heidelberg, New York, Tokyo: Springer Verlag, 1983 ...
The huge admiration in logic of science for relativity theory surely was caused by its overturning of a very admired and totally established general theory of physics, Newtonian mechanics, replacing it with something looking very weird to the ordinary eye which nevertheless yields, in a simpler way, more accurate predictions and descriptions of physical processes.
In the nineteenth century, the prediction and description problems of Newtonian mechanics had increased with the increase in the number of ways and of the accuracy by which one learned to measure not only body movements, but especially electricity and light. A proliferation of imperspicuous and unsatisfactory special laws and corrections to match theory with measurement began to cause more and more headaches and frustrations among theoretical physicists: physics was in danger to become an unordered toolbox of partly irreconcilable theories!
Roughly the choices were to 1) hope for piece by piece reduction of the chaos by harmonizing the worrying amount of anomalies one by one, 2) to concede that the values we measure for basic magnitudes like distances and times may differ under different circumstances of measuring. This absurd second option to straighten the growing mass of measurement "errors" out (implying they were no errors after all) turned out, in the end, to win the race.
First, as so often in such cases, the idea was proposed by a young eccentric outsider who had tried but failed to find a living in the academic world. After all, universities were originally founded to maintain tradition, and even today do so, up into the wearing of those ridiculous black guild suits of three centuries ago. Universities, the only guilds left! We should be happy that this outsider wrote a century ago, since nowadays it would have been hard to find people willing to consider such a very strange and difficult solution of a puzzle. There are so many of those fools with weird thoughts aren't there? And we have no more time nowadays to read other people's thoughts: we have to publish!
Many influential career physicists opposed relativity theory so vigorously that even 16 years after the start of relativity theory they managed to have Einstein's Nobel prize ascription redrafted to exclude relativity theory (an illustrative case of a guild-like network, as still regularly operative today, of professors with more power and influence than brains - but already in the 17th century Huygens (in Zedeprinten) and others complained of "gepromoveerde ezels" ("PhD donkeys"). Such academic types of equus africanus asinus still called the shots at most reputable universities in Einstein's time - they do today. But despite the extremely restrictive conditions of the first version of relativity, these Heroic Defenders of the Traditional Standards of the Guild lost the battle, due to overwhelming success of relativity in applying to many cases with far less need for cumbersome special corrections to make things fit. But, more spectacular, the general version that succeeded it yielded some astronomical predictions totally alien to the Newton-type of thinking that got dramatically corroborated and reached the world press. Soon, relativity theory did better in quite some applications than Newtonian mechanics in describing lots of processes involving speeds in the order of the speed of light. Those are areas way off the public domain, only known to specialist physics experimenters, and were even more so in Einstein's early life, when mankind still predominantly relied on the power of the horse (in the first World War 8 million horses died). In such everyday processes relativity should be better than Newton as well, but measurement in Einstein's days had by far not yet reached the precision required to measure the difference, and once it finally started to do so, these differences were, usually, only of interest to experts. Today, with cesium clocks, even during ordinary long distance air flights time dilation shows.
My good luck was to find an emeritus professor of physics in the 12footdinghy racing competitions, so I could get some help collecting the literature and solving problems. But I got no answer that enabled me to pass the graph below in a popular exposition of relativity theory (Einstein, A., Uber die spezielle und die allgemeine Relativitätstheorie, Braunschweig: Vieweg 1956, orig. 1916). It is used to explain the fundamental Lorentz transformation. The most simple case even. The math is easy, but I got no clue whatsoever what he was talking about: space and time shift relative to the objects moving around but the speed of light is assumed constant, that is, the same if measured from whatever object (planet, space vessel) moving with whatever speed in whichever direction.
... Lorentz-transformation. This was most of what Einstein needed for his first (1905) revolution ...
... but what does it mean? ...
I did not see the light, literally: I failed to see how light was meant to move through this graph. I might need a real teacher.
Help! Utrecht University is a twenty minutes drive from my Linge river shore site. Its web site turned out to be, excuse me, a bit of a disaster. Paddling around a home page that was aggressively trying to divert my attention to a "virtual sleeping coach" and an "anti-teasing program", in the end I found a course name "mechanics", but could not find the address of the offices of the physics staff, nor the material to be studied, the lecture rooms and times of service. I took my car to head for the "Uithof".
At the entrance of the large university campus a signpost encouraged me to navigate on the name of the street I wish to reach. A bit discouraging for I had come in search of it. Now wanted me to tell them. "Physics"? To the university security officer engaged in writing number plates of illegally parked cars that word did not ring a bell, but he gave me a quarter of compass that held, in his opinion, an above-average chance.
I managed to park. Legally. Took a road on my foldable bike, entered a building. Its signpost featured the building's name, that of a person, not related, as far as I know, to any academic field. It did not list or say what was inside. An exiting student apologized for not knowing the whereabouts of physics: he was in informatics. The muscular Arabic receptionist's face made clear that both the term "physics" and the word "department" needed more explanation (where in the latter case I made no progress trying the word "faculty").
"Well you know", the muscular Arabic receptionist told me, "This is the beta building".
"That's not so bad at all", I was delighted to reply "physics is pretty beta. Is there any staff up here?"
"Staff ...", the man repeated with some hesitation.
"I mean the office rooms of the people who teach here".
"Oh yes, cross the hall and go up".
... I thought those would be two different institutes ...
Behind a door reading
I expected to find two entirely different institutes, for 17th century Spinoza, though a renowned grinder of very good lenses, restricted his physics to copying Descartes (while at the time the ground breaking ideas of Newton recently had become available in Holland). I simply could not believe somebody would name a physics institute after Spinoza, whose physics was just about his only weak point. In Spinoza's Cartesian view the universe is totally filled with a dust of very fine particles. There is no gravity. Dust particles push each other round to form kind of twisters, small and big. Those dust particles, Descartes held, pushed the planets round en kept pushing us against the earth's surface. I studied Spinoza's take of this in his Ethica while making my Spinoza Ethica Help Web. [my vicissitudes while making: Spinoza].
But not two institutes for the time being. Instead a huge staircase in police arrest wing colours and hardware.
... trotting up: police arrest wing colours and hardware ...
... blue darkness, blind doors ...
... Top floor: only the Spinoza Instituut, where's Theoretical Physics Institute? ...
But the top door was ... yellow! Behind it I suddenly was in a bright comfortable top floor unit with lots of roof light. A top research institute in ... physics. Spacy light rooms. In some, people were typing, in others two or three were talking matrices, tensors, equilibria and filling wallboards with wide gestures. One thing was clear: if I would be given a desk here and allowed to ask any question arising while studying relativity, I would be done in a few days. The other: I did not belong here. These guys and girls were too good. All around thirty, no Dutch people either, except for the manager who kindly indicated the building where they could tell me all about bachelor teaching.
Would not want to have missed this short digression.
... Homing in on target, my foldable bike did not mind me to stay away long ...
The "Buys Ballot" building was surrounded by bicycles! I told reception staff there was a physics course I could not find. They tried, did not find, but knew the room number of Els, the planner of physics courses. Els gave me all data of my mechanics course, and an efficient staff web address (not linked to from the university's home page) to find those data next time.
... reception knew Els' room, she helped me out ...
Not long after I had returned home, my schedule sported signs it had not seen for 16 years (though blue is 12footdinghy competition sailing):
... Last time my schedule sported this type of shit was 16 years before (but then even worse: as a lecturer) ...
They had already started some weeks ago, but classical mechanics (Newton, Kepler) had been done as well, most of which should be familiar to me.
So, the next Monday morning my alarm clock unchained me, I arrived early, students told me what books and what lecture notes were used, and what is the floor and room number of the physics student's association that sells them.
... this is serious! ...
There I sat, taking chalkboard shots every one of which seemed to require hours of work at home. Students are updated by a digital "blackboard" (forcing me to rename the analogue one to "chalkboard", but that's a better label anyway). For the digital "blackboard" you need a login, the end of the university as a public institution, we are now just another commercial shop. Well, no need. By now I should have enough. The login protected digital blackboard made me realize why my search for my target had been a bit erratic: I had accidentally taken an unused inroad over a campus security officer, muscular Arab receptionist, Spinoza and Els. Thus circumventing the university's web welcoming page's "virtual sleeping coach" and "anti-teasing program", I inadvertently managed to squeeze my rather oversized body through an unmonetized mouse hole entrance of the theatre! I saved a value of at least some sizeable boxes of excellent Cuban cigars, very agreeable smoking while, as I would soon start to do, covering paper with math.
150 audience or so. Astronomy and physics bachelors. Among these 17 and 18 year olds there were quite some Asians. But a surprising lot of Arabic and Turkish students, native speakers of what unlike Dutch are world languages (Arabic 300x106 speakers, Turkish 200x106, until deep in Siberia and China). These brightest children of what the Dutch call "backward quarters" abound all over the university's beta quarter - good idea: if you learn something too difficult for others you can't be discriminated against. Let the Dutch youth study "management" whatever that may be. But everybody there perfectly understands the Dutch of Flemish teacher Professor Stefan Vandoren, engaged in translating the English lecture notes of his predecessor De Wit back into real Dutch. I saw De Wit's English version of the lecture notes in some student's hands.
Ok. Dutch. Our midget German dialect on exit, as some say? Dutch physics terms are sometimes badly chosen and confusing: impulse is called "stoot", momentum is called "impuls", they also use the word "moment". It means torque. They use "dilation" and "dilatation" in a random mix. A murky mess, like Dutch language generally, historically indeed pidginized German. Dutch physics at first had nothing to do with it for it proceeded in Latin. The problem arose when deep in the 18th century The Netherlands got in unbelievable decay, chickens and their shit in the lecture halls, Latin started to wane at Dutch universities and nitwit physics professors on hunger wages started to copy physics from Latin into Dutch language. That was the period in which foreigners started to say "in The Netherlands everything happens 50 years later". But today the Rhine wetlands are catching up again: surely fifty years from now under the management of our immigrated talent, we shall be top of the heap and Dutch language will be in the league of Frisian, Lower Saxon and other obsolete European dialects.
But where was I? O yes: so, I longed for De Wit's English, but, ... not sold anymore by the students association, only on the "blackboard". OK shit happens.
By far most students were white and Dutch, clearly from all strata of society: here selection had been on brains only! What a relief hearing all these youngsters talking functions and equations in the intermission instead of the ordinary adolescent Facebook bullshit.
The week after, also an African young man joined and sat next to me. By way of test, I pretended not to understand a fairly simply thing and asked him.
After a silence of a length that made my sweat break out he said: "... yes I also found that a bit odd ..."
I: "Well, I believe it is correct, I just do not understand why"
He: "Yes, I'll have to look at that too".
Not the surprise I hoped for (thought Dutch, I am a Ugandan resident now for 12 years [more] and have closely worked, often as the only white, in groups of Africans on many different issues from language analysis to shipbuilding).
I asked the fat rosy white acne ridden highly +-dioptric adolescent at my other side who swiftly produced the explanation.
I turned to my black neighbour again: "Have you heard?"
He hadn't. Managed to wheedle a scholarship off a European philanthropist? That's what they're damned good at ... anyway, postman soon.
To be sure: I rarely meet highly intelligent Africans but I do.
Professor Vandoren is an entertaining teacher. He is not copying a sheet of formulas on the chalkboard but starts calculating right in front of us. Live calculation! As a jazz player [more] I know how you enhance your connection to band and public by NOT putting a score sheet in front of you, here it was the same! And more: when you make a truly live mistake there is no disappointment. It shows how difficult the subject is you are about to master! A mistake, especially one that blocks the proper outcome and leads to Vandoren taking distance from the blackboard, silence, hand at chin in frantic scanning of the rows of symbols, sends a shivering through the smart part of the audience. Then someone sets out to help him. But he's wrong. "No that cannot be the error", Vandoren explains calmly "because if you look here, these two ..." Now the crowd is at peak concentration! Another student discovers somewhere a c2 copied to c1.
As for intensive and successful teaching, nothing works better than the tension of an error on the chalkboard.
Vandoren looks, corrects, looks back, laughs and says. "Sharp!". Looks back to the board and back to the student, says again: "Very sharp".
Lesson #1 to the freshman and -woman: there is never need for shame.
At another calculation derailment Vandoren judged he was loosing too much time "... I think I did not go the easiest way ... anyway you should be able to do this at home ...", looks again to the blackboard, clearly nervous, finds the error, quickly writes the result and says, with a shy smile: "... yes when everybody is looking at you, it sometimes is less easy to get out ...".
Important lesson #2: you may feel shy, but you don't give up!
How's that for a teacher! Never seen that! I myself know that situation when lecturing, but never could smile getting in and out of trouble on the blackboard - excuse me chalkboard. Now I have Vandoren's example, I could do it but fortunately my savings made my sentence to academic teaching expire long ago.
Home with the 4 euro 23 cents or so Flemish teaching doc "Special Relativity Theory" and a fairly cheap thick English physics text book bought in the physics student's association room.
... Back to my heavenly solitary riverside home with the teaching docs ...
... On September 28, 2015, I starting filling my dustbin with math-covered paper ...
... my old habits revived: non-digital hardware use ...
Since I last used non digital studying hardware twenty years ago (I lost my last books and paper notes in a tornado on Lake Victoria, without much regret: after all it's all on internet now) the quality of colour pencils has risen, clickable ring binder handling has become even more comfortable, pencil sharpeners have further improved, geo-triangles are thinner and more flexible and there still is replacement filling for my beloved graphite pencil (left at arrow) I kept on me for over 15 years living in the Alps, Africa, and wandering with my Kangoo microcamper from Inverness to Marrakech.
After some weeks of Utrecht lectures my despair, frustration and agitation all peaked. Little did I know, immersed as I was in trying to follow the Utrecht version of the relativity story, that what Vandoren told on the very first lecture already implied that Einstein's pen made a small slip where he wrote in Anhang 1, to explain that graph reproduced above : "längs der negative X-Achse sich fortplantzenden Lichtstralen", while he clearly means "sich in negative Richting fortplantzenden Lichtstralen" (which can be along the positive x-axis too!). If he had written the latter, which clearly is what he had in mind - it's just a slip, no wonder when you have explained it a thousand times - I would never have considered to go to those Utrecht physics lectures.
Another proof of my observation above that nothing boosts progress more than errors. Thank you Einstein! No way to sniff out that slip when you do a first relativity theory reading, like I did. And when the stuff to sniff it out came along in Utrecht, I failed to notice, since I had laid Einstein's booklet aside in utter disappointment after even checking the Dutch translation, which had literally copied the slip ("lichtstralen die zich langs de negatieve x-as voortplanten"). So I thought: this looks crap but he's serious, so I need a live teacher.
In the meantime the Utrecht exposition had begun to firmly blur my brains on other unrelated issues ... How long would it take before I would get the idea to turn back to Einstein's little book and see that Vandoren in the first 10 minutes I heard him had given the stuff needed to understand what had blocked me in Einstein's derivation of the Lorentz transformation en read on from there?
Clearly, since its first appearance 1916, nobody can have understood the Lorentz transformation from Einstein's little book or its Dutch translation except those who somehow understood this "negative X-Achse"-thing was a slip of our hero's pen (details).
... Brain-blurring physical reasoning ... Help! This guy is CRAZY!!! ...
In those weeks of desperate and frustrated search I noticed myself starting cooling my rage on ordering everything else around me! Ridiculous, but I could not stop myself.
... cooling rage on hardware order ...
First the pencil box, then the rest of the shelf where it stands (up-left in picture), then the opposite shelf with its hardware boxes (up-right), then an ergonomic lighter suspension (down left,) then my coffee making system (down middle), finally introducing a pill box to put 7 of my one-a-day pills on Monday and sync day-awareness with that of whether I took my pill ... all to no avail of course: the shit was in my brains.
And I had headaches. Literally. I NEVER have headaches.
... Finally it was Einstein's 1916 explanation to the educated general public (middle) who made me understand the Lorentz transformation ...
It took three weeks of filling my dustbin with papers full of graph and formula trials. But then, on October 22, 2015, after almost a full month of wandering through a dense forest in circles, I was desperate enough to draw Einstein's little book from the shelf again. Only then I realized that Vandoren's take implied this "negative Achse"-thing should be a slip, could I read on. In Einstein. That same afternoon I understood the Lorentz transformation.
I wrote it down too in Bert Reads Einstein [math] and [exercise]. There, unlike Vandoren-De Wit, I first completely prepare the Lorentz gymnastics-floor following Einstein's exposition [math] , After that is clear, Vandoren's illustrative examples and exercises are of great help to turn your first successful relativity moves into a smooth vegetative routine of relative time and distance measurement. Acquiring that is more like coming home with a new scale for your musical instrument en start playing it. Sounds rusty at first and will take weeks of daily exercise to get smoother. It did: [exercise].
[Postscript note October 2017: later I would feel that these accounts are relatively clumsy. I wrote a new one starting from hyperbolic presentation which I abandoned in turn in favour of my totally easy final account: see relativity index "Bert reads Einstein"]
Meanwhile I had spent roughly the equivalent of a reasonable tuition fee on Cuban cigars, and shall have to gear down the addiction by means of a week of, can you believe it, no smoking.