Werner Heisenberg And The Heisenberg Uncertainty P

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Werner Heisenberg and the Heisenberg Uncertainty PrincipleWerner Heisenberg, born in the dawn of the twentieth century became oneof its greatest physicists; he is also among its most controversial. While still in his early twenties, he was among the handful of bright,young men who created quantum mechanics, the basic physics of the atom,and he became a leader of nuclear physics and elementary particleresearch. He is best known for his uncertainty principle, a componentof the so-called Copenhagen interpretation of the meaning, and uses ofquantum mechanics. Through his successful life, he lived through two lost World Wars,Soviet Revolution, military occupation, two republics, political unrest,and Hitler s Third Reich. He was not a Nazi, and like most scientistsof his day he tried not to become involved in politics. He played aprominent role in German nuclear testing during the World War II era. At age twenty-five he received a full professorship and won the NobelPrize in Physics in 1932 at the age of thirty-two. He climbed quicklyto the top of his field beginning at the University of Munich when hisinterest in theoretical physics was sparked Heisenberg was born the son of August Heisenberg in W rzburg, Germanyon December 5, 1901. August Heisenberg was a professor of Greek at theUniversity of Munich. His grandfather was a middle-class craftsman who shard work paid enough to afford a good education for August Heisenberg. The successfulness of August Heisenberg allowed him to support hisfamily well. The professorship at the University of Munich put them inthe upper middle-class elite, and was paid three times the salary ofskilled workers. Through his life Werner Heisenberg was pestered with health problems. At the age of five, he nearly died with a lung infection which helpedhim get a little preferential treatment from his parents. During hisearly years, Werner was in constant competition with his brother Erwinwhich caused friction. The Heisenberg family were accomplishedmusicians. Every evening they would sit and practice together. Augustwas on the piano, Erwin played the violin, and Werner played the cello. Their mother insisted that she had no musical talent as an excuse to notbe involved in the male competition. Later Werner also learned thepiano and used his musical talents as a social vehicle during the courseof his life. This manly competition carried out in many otheractivities in the house. Sometimes August Heisenberg would make gamesout of difficult homework problems that the boys had. Werner once saidwhen reflecting back on his childhood, “Our father used to play allkinds of games with [us] . And since he was a good teacher, he foundthat the games could be used for the educating the children. So when mybrother had some mathematical problems in his schoolwork . he tried touse these problems as a kind of game and find out who could do themquickly, and so on. Somehow, I discovered that I could do that kind ofmathematics rather quickly, so from that time on I had a specialinterest in mathematics.” This constant competition caused many fightsbetween the brothers. As they grew older the fights became morevicious. One time the fight became particularly bloody where they beateach other with wooden chairs. After this confrontation the brotherscalled a truce and hardly interacted with each other except foroccasional family get togethers when they were adults. In school, Werner began to show his amazing ability early on. Heexcelled through school and always received complementary remarks fromhis teachers. As a result from the competition with his brother hedeveloped a hard work ethic and a strong drive to succeed. Even thoughWerner was not a good runner he would run around the track timinghimself with a stopwatch trying to improve his running times. A teacherof his once said, “The pupil is also extraordinary, self-confident andalways wants to excel.” Werner Heisenberg excelled in math, physics, andreligion in which he consistently received 1 s (the equivalent of A s). The subjects that he did not fair as well in were German and Athleticswhich he usually received 2 s (or B s). At the age of thirteen one ofhis teachers noted that his interests were moving to more”physical-technical things”. This change in interests moved Heisenbergalong the path from the geometry of objects into the realm oftheoretical physics, especially the mathematical analysis of physicalobjects and data. As a pupil at the Gymnasium, he was intrigued byEinstein s theory of relativity and it s explanation. He later recalledthat mastering the mathematics in Einstein s book gave him nodifficulty. At the age of sixteen he tutored a 24 year old universitycalculus student to pass her final examination. Having no previousknowledge in calculus, he set out to teach himself so in turn he couldteach the woman(by 1903 women were accepted to study at the Universityof Munich with the equal opportunities of men). During the three monthtime period he was able to teach the woman enough to pass herexamination. Heisenberg said, “And in that time I didn t know whethershe had learned it, but I certainly had.” In the Summer of 1920 Werner Heisenberg graduated Munich sMaximiliams-Gymnasium and entered the University of Munich thefollowing Fall. Not yet knowing which field of study he wished tocommit to, his father arranged an appointment for Werner with Ferdinandvon Lindemann, the professor of mathematics at the University ofMunich. When he arrived for the appointment he saw the older professorsitting in his dimly lit office with his poodle hiding under his desk. When Heisenberg began to speak, the dog started to bark. For theduration of the entire conversation, the dog kept yapping. In the briefconversation Lindemann only asked a few questions of Heisenberg, one ofwhich was what books he had been reading. Heisenberg responded withWeyl s Space, Time and Matter, through the noise of the dog Lindemannclosed the conversation with, “In that case you are completely lost inmathematics.” Rejected by Lindemann, Werner s father decided that heshould try his hand in theoretical physics. In his first meeting withSommerfeld, he also asked Heisenberg which books he had recently beenreading. Werner replied with the same answer but Sommerfeld s responsewas completely different, saying, “You are too demanding You can tpossibly start with the most difficult part and hope that the rest willautomatically fall into your lap.”The first semester that he attended at the University of Munich, Wernerwas conscientious not to sign up for too many theoretical physicsclasses just in case he found out that he was not cut out for it. Hetook a couple theoretical physics courses and the rest were mathclasses. By the next semester, it was not an issue anymore and hesigned up for all of Sommerfeld s course offerings. When Heisenbergfirst devoted himself in Sommerfeld s department, Sommerfeld wasstruggling, trying to find an explanation for the behavior of opticalspectrums emitted by atoms. When white light is sent through aspectrum, each color corresponds to a different band of frequencies. Ifthe atom if one element are stimulated by heat or high voltage they willemit not an entire spectrum of radiation but only certain colored linescorresponding to certain definite frequencies of light characteristic ofthat element. One year later, Heisenberg presented his atomic “coremodel” of complicated atoms that resolved every spectroscopic riddle inone stroke and still saved the phenomena. This model worked onlybecause he disregarded all other previous explanations. This model wasway too controversial for widespread acceptance of his theory. In the duration of the first two years that he attended the Universityof Munich he published four physics research papers, submitting thefirst one eighteen months after graduating at the Gymnasium. Three ofthe papers dealt with atomic spectroscopy and one with hydrodynamics. These papers thrust Heisenberg at the ripe age of twenty to theforefront of quantum atomic physics research. This extraordinaryachievement was largely due to the marvelous training that he receivedfrom his university mentor, physics professor Arnold Sommerfeld who waswell respected in his field. Sommerfeld was the first of many men toinfluence Heisenberg and his research of quantum mechanics. During thattime period Bohr-Sommerfeld made a quantum theory of the atom thatutilized a puzzling combination of classical and quantum notions thatonly somewhat seemed to work. By the conclusion of World War Iexperimental techniques improved and many physicists tried to improvethe inadequate theory and overcome its limitations. Heisenberg fullyparticipated in all of these experiments. These new mechanics and itsCopenhagen interpretations achieved by the end of 1927 were combinedwith other innovations such as the electron spin and the exclusionprinciple. These new innovations opened up the realm of the atom andenabled entirely new and profound advances in understanding all aspectsof the physical world, from nuclei and quarks to the big-bang theorywhich had profound implications for the world in which we live, fromphilosophy to the technology of nuclear reactors, atomic bombs,semiconductors and superconductivity. Heisenberg played a leading rolein many of these developments from the moment he entered the Universityof Munich as an eighteen year old student. In October of 1921,Heisenberg traveled to Jena for his first physics conference. He wasable to briefly meet many top physicists in the world at that time suchas Max Planck, and Max von Laue. Unfortunately, to his dismay, AlbertEinstein was unable to attend this conference. During the nineteenthcentury German physicists concerned themselves more with theexperimental side of physics such as Newtonian Physics. By thetwentieth century the transformation from experimental physics totheoretical physics such as Einstein s theory of relativity were slowlytaking place. Sommerfeld accepted a guest professorship at the University of Wisconsinthe second year that Heisenberg attended the University of Munich. Withhis mentor in the United States, Werner decided to travel to G tingen tostudy with Professor Born. While in G tingen, his parents supported himmonetarily while he experienced much more knowledge in the field oftheoretical physics. After a while he was offered a job as an assistantwith a generous salary of twenty-thousand marks a month. As an exampleof inflation and political unrest inflation had brought the average wageof a skilled worker twenty years prior from a little over one-thousandmarks a year to twenty-thousand a month for a professor s assistant. InMay 1923, Professor Sommerfeld returned to the University of Munich andso did Heisenberg. During Heisenberg s time in G tingen Born andHeisenberg did extensive studies on the helium atom. This researchyielded a strictly orthodox helium calculation that gained widespreadrecognition which was the beginning of the end for the earliersuccessful Bohr-Sommerfeld quantum theory of the atom. They modeledthis research off of the Balmer formula for the case of the outer heliumelectron and treated the excited helium electron the same as a hydrogenelectron. After a very successful three years of study at theUniversity of Munich, Heisenberg prepared for his oral examination forhis doctorate. The format had four professors to ask four questions onthree subjects. These subjects were Math, Astronomy, and Physics. Thephysics department at the University of Munich was split betweenexperimental physics and theoretical physics and therefore he would beasked two physics questions and would only receive one grade in whichboth professors would have to agree on. In math Perron gave him a I forhis explanation of the mathematical question. Seeliger asked theastronomical question that he received a II. For physics, Sommerfeld,head of theoretical physics, gave Heisenberg a I and Wein, head ofexperimental physics, gave him a V which is not passing. Heisenberg hadhad a confrontation with Wein the previous semester when he made hisfinal project for the class out of cigar boxes and cardboard. Duringthe final examination he was biased in his question as well as hisgrade. The average of his physics score became a III which was fairlydisappointing. The final score for Heisenberg s oral examination was aIII which is equaled to a C in the American grading system. AugustHeisenberg was troubled by Werner s low score and wondered if physicswas the correct field for him to be in. Werner shocked by hissurprising score and caught a late train to G tingen. The next morninghe appeared in Born s office. When he left G tingen he was promised ajob the next winter, in Born s office Heisenberg asked if the job wasstill out on the table because of his low score on his examination. Born asked what Wein s question was and they went over it together. Born said that it was a very tricky question and that he could

understand his answer. On September 1925 Heisenberg published a fifteen page article with thetitle “On a Quantum Theoretical Reinterpretation of Kinematic andMechanical Relations”. The intent of this paper was to establish abasis for theoretical quantum mechanics, founded exclusively onrelationships

between quantities which in principle, are observable. Itdealt with observed frequencies and intensities of emitted and absorbedlight, and in doing it enabled a momentous breakthrough in physics,ensuring Heisenberg s place in modern physics. Heisenberg then laid the groundwork for the new theoretical “matrixmechanics”. The next semester, Heisenberg wrote a paper on the topicbut was not sure if he should publish it. He gave it to Born to read,and while he was away at Cambridge, England Born sent the paper to the”Zeitschrift f r Physik”, a leading German physics journal. Theprinciple of matrix mechanics utilized the same principle of themultiplication of matrices. On March 22, 1927, Heisenberg submitted a paper to the “Zeitschrift f rPhysik” entitled “On the perceptual content of quantum theoreticalkinematics and mechanics” This twenty-seven page paper forwarded fromCopenhagen contained Heisenberg s most famous and far-rangingachievement in physics, his formulation of the uncertainty orindeterminacy principle in quantum mechanics. This uncertaintyprinciple formed a fundamental component of the Copenhageninterpretation of quantum mechanics. The other two portions were Bohr scomplementary principle and Born s statistical interpretation ofSchr dinger s wave function. The Copenhagen Interpretation was anexplanation of the uses and limitations of the mathematical apparatus ofquantum mechanics the fundamentally altered our understanding of natureand our relationship to it. This was the most controversial andprofound transformation in physics that has not been equaled since. Heisenberg compared this to how Newtonian mechanics had to be replacedby a new relativistic mechanics such as how the effects of Einstein stheory of relativity transformed our notions of space and time undercertain conditions, which are high speeds, and enormous expanses ofspace and time. Heisenberg continued how a similar transformation isrequired in the realm of small masses and short distances such as theorder of atoms and electrons. It was impossible to observe theindividual workings of atoms, only the external workings of largenumbers of atoms. Prior to the Heisenberg Uncertainty Principle it wascommon belief that it was able to describe the electron s motion bynoting its position and velocity at any given moment. In his essay,Heisenberg argued this belief and stated that this concept would notwork; the previous belief would only be accurate if the object weremacroscopic and in the viewable world. When objects are sill viewableand measurable, Newtonian physics still applies, but when objects becomeso minute they are not able to be measured with an accurateness. It isimpossible for the physicists to know any more than it is possible forthem to measure. This is his explanation for this concept, “If oneseeks to measure the exact position of an electron, one could use amicroscope of very high resolving power, which would require theillumination of the electron with the light of very short wavelengths. But the shorter the wavelength, the grater the energy of the lightquantum (or the greater the pressure of the light wave) hitting theelectron – thus the greater the recoil velocity of the electron.” Henoted that there seemed to be a reciprocal relationship between theuncertainties with which it is possible to simultaneously measurevelocity and the position of the electron in any given instant. “Themore precisely we determine the position, the more imprecise thedetermination is the determination of velocity in this instant, and viceversa” This statement had profound implications on the way physicistswould look at the quantum world. In the essay, Heisenberg also statedthat with the new boundary of precision, the causalty theory becameinvalid. The causalty theory stated that with every action or effect,there is a cause for that action or effect. In Heisenberg expressed,”In the strict formulation of the causal law – if we know the present,we can calculate the future – it is not the conclusion that is wrong butthe premise.” This basically states that without knowing the preciselocation and velocity of the electron, it is only possible to calculatea range of possibilities for the location and velocity of the electronat any point in the future. The uncertainty relations that Heisenbergused to mathematically explain are: DpDq | h/2p DEDt | h/2p This first equation expresses the relationship when the position q, andthe velocity p are measured simultaneously. The error in the precisionof p and q are expressed as Dp and Dq at a given instant. The productof these uncertainties have to be at least equal to h/2p. This numberis very small, (h represents the number 6.6 X 10-27 erg-sec). In theremote possibility that Dp would equal zero, then Dq would becomeinfinite and vice versa. Heisenberg was also able to not only showthese mathematical relations but it was also consistent with otherexperimental data which pointed all evidence to show that this theoremwas true. Heisenberg also said that even if you could accuratelymeasure the position of the electron, it would disrupt the velocity ofthe electron because the light necessary for seeing the electron wouldinterrupt the electron s previous course, thus changing all futuremotion of the electron and making it impossible to predict its positionand velocity. This principle would change the course of the wayphysicists looked at quantum mechanics and further experiments with theelectron. After the publication of his paper, Heisenberg realized that itcontained some errors. Born advised Heisenberg to write a post-scriptdescribing these errors; Heisenberg did write “Essential points that Ihad overlooked” to describe his error. In this post-script itmentioned, “uncertainty in the observation – arises not exclusivelyfrom discontinuous particles or continuous waves but also from theattempt to encompass simultaneously the phenomenon that arises from bothwave and corpuscular origins.” This error was noticed when experimentaldata was not congruent with his original writing and other physicistsbegan to realize this. In response to the new advances in quantum mechanics, Einstein wrote, “Above all . The reader should be convinced that I fully recognize thevery important progress that the statistical quantum theory has broughtto theoretical physics . This theory and the (testable) relations,which are contained in it, are within the natural limits of theindeterminacy relation, complete . What does not satisfy me in thattheory, from the standpoint of principle, is its attitude towards thatwhich appears to me to be the programmatic aim of all physics: thecomplete description of any (individual) real situation (as itsupposedly exists irrespective of any act of observation orsubstantiation).” It was Einstein s opinion that the quantum theory washeading in the right direction, but they were not quite there yet. Physicists could not yet explain or fully prove the inner workings of anatom. During the year of 1927, Heisenberg was offered a full professorship atboth Leipzig and Zurich. He chose to teach at Leipzig for theopportunity to work with a great experimental physicist, Peter Debye. The first seminar that Heisenberg taught was only attended by onestudent. He still remained optimistic that he would become moreaccepted with perseverance. Before taking over this new position, he wasgranted a year s leave of absence to go on a lecture tour to the UnitedStates. In February of 1929, Heisenberg boarded a ship leavingBremerhaven for New York. In the United States, Heisenberg had beenoffered to teach at a number of schools, giving him the opportunity tosee all aspects of the country. He found it refreshing to see theopen-mindedness of the young American students. At the end of hisone-year term, he returned to his original post at Leipzig. At Leipzig,Heisenberg enjoyed the academic variety of teaching. Heisenberg published “The Physical Principles of Quantum Theory” in1928 which described his work in matrix mechanics beginning from 1925. In 1932, Werner Heisenberg won the Nobel Prize in Physics for hisdevelopment of matrix mechanics and his early development in the. During that same year, Heisenberg wrote a three part paper whichdescribes the modern picture of the nucleus of an atom. He explainedthe structure of various nuclear components discussing their bindingenergies and their stability. This helped opened the door for furtherstudy of the atomic nucleus using the quantum theory. Hitler came to power during 1933 and began to expel all Jews from theuniversities. From this time on, war was immanent and it was impossibleto separate the scientific world from the political world. In Septemberof 1939, Hitler began his war with Poland. Heisenberg had moved hiswife and child to Urfeld, in the mountains of Southern Germany, hopingto keep them safe for the duration of the war. Heisenberg was a memberof mountain troop reserves, the Alpenj ger, and felt that he soon wouldbe called to report for duty. A few days after the war had begun withPoland, he got orders to report to Berlin. To his surprise he did notmeet his fellow Alpenj ger troops but the Heereswaffenamt, the ArmyOrdinance Research Department. Along with himself, he was met by otherwell known theoretical physicists. The Germans wanted these topphysicists to develop the technology for a nuclear weapon. The Germanswanted all of the research to take place under one roof in Berlin, butHeisenberg protested and persuaded them to allow each scientist toconduct their research in their own laboratories. Already with thetechnology of fission, the first plan was to allow the bomb to simply bea runaway reactor, but it did not prove to be as easy as they had firstimagined. Through 1940 and 1941, the Heereswaffenamt was concentrating on twoline of research, how to make a chain-reacting pile, and how to separateU-235. Heisenberg wrote two papers for each subject. Both papersregarding separating U-235 suggested using heavy water as a moderator. He conceded that other pure substances such as various forms of carbonand other likewise pure elements. He recommended using heavy waterbecause of its low neutron absorption rate and would therefore requireless uranium. On June 23, 1942, Heisenberg s laboratory in Leipzig underwent a slightcatastrophe. Near six o clock, Heisenberg s assistant interrupted hisweekly seminar to tell him that he should come to see his laboratory. Once they arrived, Heisenberg noticed that bubbles were emerging fromthe pile called L-IV. All had gone as expected for the twenty days thatthe sphere had already been emerged. They tested the gas that wasleaking, and discovered that it was hydrogen. Both men concluded thatthe seal in the sphere containing the uranium oxide had been broken. The lab mechanic helped lift the sphere out of the moderator. He thenunscrewed the metal cover to remove the uranium oxide and there was ahissing sound like air rushing into a vacuum. For a couple secondsnothing happened, then flames and gas bust out around the cover, spewingburning particles of uranium around the laboratory. They dowsed theflames, and they slowly subsided. Then the lab assistant, RobertD pel, tried to salvage the precious heavy water from inside thesphere. Heisenberg concluded that oxygen must have seeped into thesphere, so not knowing what else to do Heisenberg had his assistantlower the sphere back into the tank to keep it away from oxygen and tokeep it cool. Later when observing the sphere, Heisenberg and D pelnoticed the steam threateningly rise from the water in the tank. Nextthey saw the pile within shudder, then swell. Without having to sayanything, both men leapt for the door in one motion. Seconds later, thesound of an explosion rushed from the laboratory. Burning uranium flewaround the laboratory and set the whole building on fire. The force ofthe explosion split the sphere apart which severed a hundred bolts. Thefire within the sphere continued for two days until it finally diedaway. With extensive damage done to his laboratory, many of hisexperiments in effect were delayed. Despite all of his hard work forthe development of nuclear weapons, he was not able to produce asuccessful model by the end of World War II. After the war, Heisenberg was interned in Britain with other leadingGerman scientists. In 1946, he returned to Germany where he wasappointed director of the Max Planck Institute for Physics andAstrophysics at G ttingen. In 1958, the institute moved to Munich andHeisenberg continued to be its director. Werner Heisenberg was an exceptional physicist that made many leapsforward in the knowledge of quantum mechanics. From a young prodigygrowing up in Munich through his very successful career in the field oftheoretical physics. His unsuccessfulness of creating powerful nuclearweapons ended up benefiting man kind. Through his career, Heisenbergremained controversial on many of his theories because he did not alwaysfollow the orthodox laws of physics. This allowed him to be able todevelop his uncertainty principle and other models of the atom that hecreated throughout his life. On the first day of February 1976, WernerHeisenberg the renowned physicist died in Munich Germany. His work isstill highly regarded by physicists today and his notoriety willcontinue years to come.