Rolf Hagedorn
Encyclopedia
Rolf Hagedorn was a German theoretical physicists working at CERN
. He is known for the idea that hadronic matter
has a "melting point
". The Hagedorn temperature
is named in his honor.
in Europe. He graduated from high school in 1937 and was drafted into the German Army
. After the war begun, he was shipped off into North Africa
as an officer in the Rommel
Afrika Korps
. He was captured in 1943, and spent the rest of the war in an officer prison camp
in the United States
. Most prisoners were young people and there was not much to do, Hagedorn and others set up their own 'university' where they taught each other what they happened to know. There, Hagedorn ran into an assistant of David Hilbert
, who taught him mathematics.
prison camp, he was accepted as a fourth-semester student at the University of Göttingen – one of the few remaining universities.
After having completed his studies with the usual diploma (1950) and doctorate (1952), with a thesis under R. Becker on thermal solid-state theory, he was accepted as a postdoc at the Max Planck Institute for Physics
(MPI), still at Göttingen at the time. The MPI director was Werner Heisenberg
. He was there among a group of physicists including Bruno Zumino
, Harry Lehmann
, Wolfhart Zimmermann
, Kurt Symanzik
, Gerhard Lüders, Reinhard Oehme
, Vladimir Glaser, and Carl Friedrich von Weizsäcker
.
for a few of months. There, he helped with particle accelerator
designs, particularly to calculate non-linear oscillations in particle orbits. The pioneering work on linear orbit theory had just been completed by Gerhard Lüders, who wished to go back to Göttingen
. Lüders asked Werner Heisenberg
, the then-director of CERN, to send somebody to replace him. Heisenberg asked Hagedorn if he was interested for a couple of months.
When the CERN theory group came to Geneva
from Copenhagen
, where it had been located at first, Hagedorn joined it. Hagedorn brought to the Theory Division (TH) an unusual interdisciplinary background which included particle
and nuclear
as well as thermal
, solid state and accelerator
physics. Once at the TH, he exclusively focused on the statistical models of particle production.
studies and used it to make predictions about particle yields (and therefore the secondary beams to be expected from the main beam directed at a target).
Many key ingredients brought soon afterward by experiment helped refine the approach. Among them is the limited transverse momentum with which the overwhelming majority of the secondary particles happen to be produced. They show an exponential drop with respect to the transverse mass. There is also the exponential drop of elastic scattering
at wide angles as a function of incident energy. Such exponential behaviors strongly suggested a thermal distribution for whatever eventually comes out of the reaction. Based on this, Hagedorn put forth his thermal interpretation and used it to build production models which turned out to be remarkably accurate at predicting yields for the many different types of secondary particles. Many objections were raised at the time, particularly as to what could actually be 'thermalized' in the collisions, applying straightforward statistical mechanics to the produced pion
s gave the wrong results, and the temperature of the system was apparently constant when it should have risen with the incident energy or with the mass of the excited fireball (according to Boltzmann's Law).
, which is of the order of ~160 MeV
.
The impressive number of states which have now to be considered at the same time leads to a new writing of equations based on statistical physics. The factorial factor, which was plaguing statistical calculation focusing on pion
s only, and which was introduced to rightfully avoid multiple counting in phase space integrals, had now become unimportant since each one of the many states was unlikely to have a population exceeding 1. This reconciled experimental results and statistical calculations.
Rolf's great achievement was pioneering the development of the Statistical Bootstrap Model. To put it in a nutshell one may say that each of the many resonant state in which hadrons can be excited through a collision is itself a constituent of a still heavier one while being also composed of lighter ones. What Rolf showed is that when one puts logic and hard work into the idea one cannot escape an exponential spectrum of resonant states. The temperature of such a system is then limited from above. This limit is the Hagedorn temperature. If one takes a more global view talking about 'fireballs' (in the old language) or 'clusters' (in the more modern vernacular) rather than of resonances, the conclusion is that the temperature of such objects is independent of their mass. One can then also understand why the limiting temperature is of the same order as the mass of the smallest mass state, the pion.
The concept of an exponential spectrum is now part of our understanding of hadron phenomena. It has been reached through different approaches such as that offered by dual models. It fits beautifully the hadronic level counting which can now be followed up to over 4000 cataloged resonances Rolf was first at pinning it down through his Statistical Bootstrap Model, which has been at the origin of much further work. At first the Statistical Bootstrap was looked upon with considerable skepticism, also 'at home' within the TH, but as time has gone on, it has taken on bigger and bigger dimensions and has become more and more important. Such is the sign of truly original work, of something that really had influence on our thinking.
Among the most cited physic papers of the period is "Statistical Thermodynamics of Strong Interactions at High Energies" Nuovo Cim. Suppl. 3 pp147–186, 1965, which proposes the statistical bootstrap model of particle production, and introduces the maximum hadron temperature into the particle physics vocabulary.
Can one go beyond the limiting temperature set by Hagedorn? The answer is yes but one has to consider a phase transition whereby one leaves the hadronic phase to reach a new phase where the hadron constituents, the quarks and the gluons, are no longer confined. The limiting temperature becomes a phase transition temperature which can be calculated through lattice gauge theory calculations.
He was an eloquent lecturer, and he went to great detail in preparation of his numerous colloquia and seminars. His didactic style was unique and he employed presentation methods today imitated in power point presentations, with several transparencies overlapping to make the physics point. He enjoyed the post-seminar discussion, addressed every question very seriously, and followed through with clear answers and explanations.
Hagedorn taught several CERN fellows how to use statistical methods in the study of strong interaction physics, developed and passed on the technical expertise we wield today in this area. Hagedorn enjoyed doing both 'theory' and 'computing'. He was instrumental in the development of the early user oriented computer language Sigma
.
Rolf Hagedorn was the test case when the CERN Management Board created the special status for "retired scientists willing to continue research" and was the first person at CERN to be granted the new status. After his retirement in 1984 he remained an active emeritus researcher.
Hagedorn was a person of the highest scientific integrity and standards of reasoning. He was engaged in support important international causes and helped individual scientists suffering under politically oppressive regimes.
CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
. He is known for the idea that hadronic matter
QCD matter
Quark matter or QCD matter refers to any of a number of theorized phases of matter whose degrees of freedom include quarks and gluons. These theoretical phases would occur at extremely high temperatures and densities, billions of times higher than can be produced in equilibrium in laboratories...
has a "melting point
Melting point
The melting point of a solid is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at standard atmospheric pressure...
". The Hagedorn temperature
Hagedorn temperature
The Hagedorn temperature in theoretical physics is the temperature above which the partition sum diverges in a system with exponential growth in the density of states. It is named after German physicist Rolf Hagedorn.Phase transitions The Hagedorn temperature in theoretical physics is the...
is named in his honor.
Early life
Hagedorn's younger life was deeply marked by the upheavals of World War IIWorld War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
in Europe. He graduated from high school in 1937 and was drafted into the German Army
German Army
The German Army is the land component of the armed forces of the Federal Republic of Germany. Following the disbanding of the Wehrmacht after World War II, it was re-established in 1955 as the Bundesheer, part of the newly formed West German Bundeswehr along with the Navy and the Air Force...
. After the war begun, he was shipped off into North Africa
North African campaign
During the Second World War, the North African Campaign took place in North Africa from 10 June 1940 to 13 May 1943. It included campaigns fought in the Libyan and Egyptian deserts and in Morocco and Algeria and Tunisia .The campaign was fought between the Allies and Axis powers, many of whom had...
as an officer in the Rommel
Erwin Rommel
Erwin Johannes Eugen Rommel , popularly known as the Desert Fox , was a German Field Marshal of World War II. He won the respect of both his own troops and the enemies he fought....
Afrika Korps
Afrika Korps
The German Africa Corps , or the Afrika Korps as it was popularly called, was the German expeditionary force in Libya and Tunisia during the North African Campaign of World War II...
. He was captured in 1943, and spent the rest of the war in an officer prison camp
Internment
Internment is the imprisonment or confinement of people, commonly in large groups, without trial. The Oxford English Dictionary gives the meaning as: "The action of 'interning'; confinement within the limits of a country or place." Most modern usage is about individuals, and there is a distinction...
in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
. Most prisoners were young people and there was not much to do, Hagedorn and others set up their own 'university' where they taught each other what they happened to know. There, Hagedorn ran into an assistant of David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
, who taught him mathematics.
Becoming a physicist
When Hagedorn came back home in January 1946, most German universities were destroyed. Because of his training in the Crossville, TennesseeCrossville, Tennessee
Crossville is a city in and the county seat of Cumberland County, Tennessee, United States. The population was 10,795 at the 2010 Census.-Geography:Crossville is located at...
prison camp, he was accepted as a fourth-semester student at the University of Göttingen – one of the few remaining universities.
After having completed his studies with the usual diploma (1950) and doctorate (1952), with a thesis under R. Becker on thermal solid-state theory, he was accepted as a postdoc at the Max Planck Institute for Physics
Max Planck Institute for Physics
Max Planck Institute for Physics is a physics institute in Munich, Germany that specializes in High Energy Physics and Astroparticle physics. It is part of the Max-Planck-Gesellschaft and is also known as the Werner Heisenberg Institute, after its first director.It was founded as the Kaiser Wilhelm...
(MPI), still at Göttingen at the time. The MPI director was Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
. He was there among a group of physicists including Bruno Zumino
Bruno Zumino
Bruno Zumino is an Italian theoretical physicist and emeritus faculty at the University of California, Berkeley. He got his bachelor degree from the University of Rome in 1945...
, Harry Lehmann
Harry Lehmann
Harry Lehmann was a German physicist.Lehmann studied physics at Rostock and the Humboldt-Universität zu Berlin....
, Wolfhart Zimmermann
Wolfhart Zimmermann
Wolfhart Zimmermann is a German theoretical physicist. Zimmermann attained a doctorate in 1950 at Freiburg im Breisgau in topology . In the 1950s he was at Göttingen one of the pioneers of the mathematical quantum field theory; along with Kurt Symanzik and Harry Lehmann he developed the LSZ theory...
, Kurt Symanzik
Kurt Symanzik
Kurt Symanzik was a German physicist working in quantum field theory.- Life :Symanzik was born in Lyck , East Prussia, and spent his childhood in Königsberg. He started studying physics in 1946 at Universität München but after a short time moved to Werner Heisenberg at Göttingen...
, Gerhard Lüders, Reinhard Oehme
Reinhard Oehme
Reinhard Oehme was a German-American physicist known for the discovery of C non-conservation in the presence of P violation, the formulation and proof of hadron dispersion relations, the "Edge of the Wedge Theorem" in the function theory of several complex variables, the...
, Vladimir Glaser, and Carl Friedrich von Weizsäcker
Carl Friedrich von Weizsäcker
Carl Friedrich Freiherr von Weizsäcker was a German physicist and philosopher. He was the longest-living member of the research team which performed nuclear research in Germany during the Second World War, under Werner Heisenberg's leadership...
.
Life at CERN
In 1954, Hagedorn went to CERNCERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
for a few of months. There, he helped with particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...
designs, particularly to calculate non-linear oscillations in particle orbits. The pioneering work on linear orbit theory had just been completed by Gerhard Lüders, who wished to go back to Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
. Lüders asked Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
, the then-director of CERN, to send somebody to replace him. Heisenberg asked Hagedorn if he was interested for a couple of months.
When the CERN theory group came to Geneva
Geneva
Geneva In the national languages of Switzerland the city is known as Genf , Ginevra and Genevra is the second-most-populous city in Switzerland and is the most populous city of Romandie, the French-speaking part of Switzerland...
from Copenhagen
Copenhagen
Copenhagen is the capital and largest city of Denmark, with an urban population of 1,199,224 and a metropolitan population of 1,930,260 . With the completion of the transnational Øresund Bridge in 2000, Copenhagen has become the centre of the increasingly integrating Øresund Region...
, where it had been located at first, Hagedorn joined it. Hagedorn brought to the Theory Division (TH) an unusual interdisciplinary background which included particle
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
and nuclear
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...
as well as thermal
Thermal physics
Thermal physics is the combined study of thermodynamics, statistical mechanics, and kinetic theory. This umbrella-subject is typically designed for physics students and functions to provide a general introduction to each of three core heat-related subjects...
, solid state and accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...
physics. Once at the TH, he exclusively focused on the statistical models of particle production.
Particle Production Work
Hagedorn's work started when Bruno Ferretti (then-head of the Theory Division), asked him to try to predict particle yields in the high energy collisions of the time. This he started with Frans Cerulus. There were few clues to begin with but they made the best of the "fireball concept" which was then supported by cosmic rayCosmic ray
Cosmic rays are energetic charged subatomic particles, originating from outer space. They may produce secondary particles that penetrate the Earth's atmosphere and surface. The term ray is historical as cosmic rays were thought to be electromagnetic radiation...
studies and used it to make predictions about particle yields (and therefore the secondary beams to be expected from the main beam directed at a target).
Many key ingredients brought soon afterward by experiment helped refine the approach. Among them is the limited transverse momentum with which the overwhelming majority of the secondary particles happen to be produced. They show an exponential drop with respect to the transverse mass. There is also the exponential drop of elastic scattering
Elastic scattering
In scattering theory and in particular in particle physics, elastic scattering is one of the specific forms of scattering. In this process, the kinetic energy of the incident particles is conserved, only their direction of propagation is modified .-Electron elastic scattering:When an alpha particle...
at wide angles as a function of incident energy. Such exponential behaviors strongly suggested a thermal distribution for whatever eventually comes out of the reaction. Based on this, Hagedorn put forth his thermal interpretation and used it to build production models which turned out to be remarkably accurate at predicting yields for the many different types of secondary particles. Many objections were raised at the time, particularly as to what could actually be 'thermalized' in the collisions, applying straightforward statistical mechanics to the produced pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
s gave the wrong results, and the temperature of the system was apparently constant when it should have risen with the incident energy or with the mass of the excited fireball (according to Boltzmann's Law).
Limiting Temperature
Hagedorn interpreted the apparently limiting temperature which could be associated with the transverse mass distribution of the secondary particles as resulting from an exponential spectrum for the many resonant states into which hadrons can be excited. The rise of the temperature is associated with the population of higher and higher energy levels by the elements of a system. If there is an exponentially increasing number of levels offering themselves to be filled, the temperature saturates. It is the entropy which eventually increases linearly with the collision energy but the temperature gets stuck to a limiting value. This is the Hagedorn temperatureHagedorn temperature
The Hagedorn temperature in theoretical physics is the temperature above which the partition sum diverges in a system with exponential growth in the density of states. It is named after German physicist Rolf Hagedorn.Phase transitions The Hagedorn temperature in theoretical physics is the...
, which is of the order of ~160 MeV
MEV
MeV and meV are multiples and submultiples of the electron volt unit referring to 1,000,000 eV and 0.001 eV, respectively.Mev or MEV may refer to:In entertainment:* Musica Elettronica Viva, an Italian musical group...
.
The impressive number of states which have now to be considered at the same time leads to a new writing of equations based on statistical physics. The factorial factor, which was plaguing statistical calculation focusing on pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
s only, and which was introduced to rightfully avoid multiple counting in phase space integrals, had now become unimportant since each one of the many states was unlikely to have a population exceeding 1. This reconciled experimental results and statistical calculations.
The Statistical Bootstrap
One day (as Torleif Erik Oskar Ericson remembers very vividly) some time in 1964, Torleif ran into Rolf, just bubbling over to a degree not seen ever before. Hagedorn's eyes were quite bright, and Rolf described to Torleif all these fireballs: fireballs going into fireballs living on fireballs forever and all in a logically very consistent way. This must have been just after he had invented the statistical bootstrap. I really had the impression of a man who had just found the famous stone of the philosophers, and that must have been exactly how he felt about it. Clearly, Rolf recognized at once the importance of the novel idea introduced there. It was very interesting to observe how deeply Rolf felt about it from the very beginning.Rolf's great achievement was pioneering the development of the Statistical Bootstrap Model. To put it in a nutshell one may say that each of the many resonant state in which hadrons can be excited through a collision is itself a constituent of a still heavier one while being also composed of lighter ones. What Rolf showed is that when one puts logic and hard work into the idea one cannot escape an exponential spectrum of resonant states. The temperature of such a system is then limited from above. This limit is the Hagedorn temperature. If one takes a more global view talking about 'fireballs' (in the old language) or 'clusters' (in the more modern vernacular) rather than of resonances, the conclusion is that the temperature of such objects is independent of their mass. One can then also understand why the limiting temperature is of the same order as the mass of the smallest mass state, the pion.
The concept of an exponential spectrum is now part of our understanding of hadron phenomena. It has been reached through different approaches such as that offered by dual models. It fits beautifully the hadronic level counting which can now be followed up to over 4000 cataloged resonances Rolf was first at pinning it down through his Statistical Bootstrap Model, which has been at the origin of much further work. At first the Statistical Bootstrap was looked upon with considerable skepticism, also 'at home' within the TH, but as time has gone on, it has taken on bigger and bigger dimensions and has become more and more important. Such is the sign of truly original work, of something that really had influence on our thinking.
Among the most cited physic papers of the period is "Statistical Thermodynamics of Strong Interactions at High Energies" Nuovo Cim. Suppl. 3 pp147–186, 1965, which proposes the statistical bootstrap model of particle production, and introduces the maximum hadron temperature into the particle physics vocabulary.
Can one go beyond the limiting temperature set by Hagedorn? The answer is yes but one has to consider a phase transition whereby one leaves the hadronic phase to reach a new phase where the hadron constituents, the quarks and the gluons, are no longer confined. The limiting temperature becomes a phase transition temperature which can be calculated through lattice gauge theory calculations.
Hagedorn remembered by his CERN Colleagues
Rolf was not a carfully planning physicist who took his time for careful reflection and penetration. In this way Rolf differed from a large number of other prominent physicists, who were recognized rapidly after their contribution. Later their impact disseminates and they are integrated, so people notice it less and less. With Rolf Hagedorn, the opposite happened. His influence increased over time.He was an eloquent lecturer, and he went to great detail in preparation of his numerous colloquia and seminars. His didactic style was unique and he employed presentation methods today imitated in power point presentations, with several transparencies overlapping to make the physics point. He enjoyed the post-seminar discussion, addressed every question very seriously, and followed through with clear answers and explanations.
Hagedorn taught several CERN fellows how to use statistical methods in the study of strong interaction physics, developed and passed on the technical expertise we wield today in this area. Hagedorn enjoyed doing both 'theory' and 'computing'. He was instrumental in the development of the early user oriented computer language Sigma
Sigma
Sigma is the eighteenth letter of the Greek alphabet, and carries the 'S' sound. In the system of Greek numerals it has a value of 200. When used at the end of a word, and the word is not all upper case, the final form is used, e.g...
.
Rolf Hagedorn was the test case when the CERN Management Board created the special status for "retired scientists willing to continue research" and was the first person at CERN to be granted the new status. After his retirement in 1984 he remained an active emeritus researcher.
Hagedorn was a person of the highest scientific integrity and standards of reasoning. He was engaged in support important international causes and helped individual scientists suffering under politically oppressive regimes.