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Renormalization

From Wikipedia, the free encyclopedia
Renormalization and regularization
Quantum field theory
Feynmann Diagram Gluon Radiation.svg
History
Background[show]
Equations[show]
Incomplete theories[show]
Scientists[show]

Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of quantities to compensate for effects of their self-interactions. However, even if it were the case that no infinities arise in loop diagrams in quantum field theory, it can be shown that renormalization of mass and fields appearing in the original Lagrangian are necessary.

...

Attitudes and interpretation

The early formulators of QED and other quantum field theories were, as a rule, dissatisfied with this state of affairs. It seemed illegitimate to do something tantamount to subtracting infinities from infinities to get finite answers.

Freeman Dyson argued that these infinities are of a basic nature and cannot be eliminated by any formal mathematical procedures, such as the renormalization method.[13][14]

Dirac's criticism was the most persistent.[15] As late as 1975, he was saying:[16]

Most physicists are very satisfied with the situation. They say: 'Quantum electrodynamics is a good theory and we do not have to worry about it any more.' I must say that I am very dissatisfied with the situation, because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small – not neglecting it just because it is infinitely great and you do not want it!

Another important critic was Feynman. Despite his crucial role in the development of quantum electrodynamics, he wrote the following in 1985:[17]

The shell game that we play ... is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate.

While Dirac's criticism was based on the procedure of renormalization itself, Feynman's criticism was very different. Feynman was concerned that all field theories known in the 1960s had the property that the interactions become infinitely strong at short enough distance scales. This property, called a Landau pole, made it plausible that quantum field theories were all inconsistent. In 1974, Gross, Politzer and Wilczek showed that another quantum field theory, quantum chromodynamics, does not have a Landau pole. Feynman, along with most others, accepted that QCD was a fully consistent theory.[citation needed]

The general unease was almost universal in texts up to the 1970s and 1980s. Beginning in the 1970s, however, inspired by work on the renormalization group and effective field theory, and despite the fact that Dirac and various others—all of whom belonged to the older generation—never withdrew their criticisms, attitudes began to change, especially among younger theorists. Kenneth G. Wilson and others demonstrated that the renormalization group is useful in statistical field theory applied to condensed matter physics, where it provides important insights into the behavior of phase transitions. In condensed matter physics, a physical short-distance regulator exists: matter ceases to be continuous on the scale of atoms. Short-distance divergences in condensed matter physics do not present a philosophical problem, since the field theory is only an effective, smoothed-out representation of the behavior of matter anyway; there are no infinities since the cutoff is actually always finite, and it makes perfect sense that the bare quantities are cutoff-dependent.

If QFT holds all the way down past the Planck length (where it might yield to string theory, causal set theory or something different), then there may be no real problem with short-distance divergences in particle physics either; all field theories could simply be effective field theories. In a sense, this approach echoes the older attitude that the divergences in QFT speak of human ignorance about the workings of nature, but also acknowledges that this ignorance can be quantified and that the resulting effective theories remain useful.

Be that as it may, Salam's remark[18] in 1972 seems still relevant

Field-theoretic infinities — first encountered in Lorentz's computation of electron self-mass — have persisted in classical electrodynamics for seventy and in quantum electrodynamics for some thirty-five years. These long years of frustration have left in the subject a curious affection for the infinities and a passionate belief that they are an inevitable part of nature; so much so that even the suggestion of a hope that they may after all be circumvented — and finite values for the renormalization constants computed — is considered irrational. Compare Russell's postscript to the third volume of his autobiography The Final Years, 1944–1969 (George Allen and Unwin, Ltd., London 1969),[19] p. 221:
In the modern world, if communities are unhappy, it is often because they have ignorances, habits, beliefs, and passions, which are dearer to them than happiness or even life. I find many men in our dangerous age who seem to be in love with misery and death, and who grow angry when hopes are suggested to them. They think hope is irrational and that, in sitting down to lazy despair, they are merely facing facts.

In QFT, the value of a physical constant, in general, depends on the scale that one chooses as the renormalization point, and it becomes very interesting to examine the renormalization group running of physical constants under changes in the energy scale. The coupling constants in the Standard Model of particle physics vary in different ways with increasing energy scale: the coupling of quantum chromodynamics and the weak isospin coupling of the electroweak force tend to decrease, and the weak hypercharge coupling of the electroweak force tends to increase. At the colossal energy scale of 1015GeV (far beyond the reach of our current particle accelerators), they all become approximately the same size (Grotz and Klapdor 1990, p. 254), a major motivation for speculations about grand unified theory. Instead of being only a worrisome problem, renormalization has become an important theoretical tool for studying the behavior of field theories in different regimes.

If a theory featuring renormalization (e.g. QED) can only be sensibly interpreted as an effective field theory, i.e. as an approximation reflecting human ignorance about the workings of nature, then the problem remains of discovering a more accurate theory that does not have these renormalization problems. As Lewis Ryder has put it, "In the Quantum Theory, these [classical] divergences do not disappear; on the contrary, they appear to get worse. And despite the comparative success of renormalisation theory the feeling remains that there ought to be a more satisfactory way of doing things."[20]

...

https://en.wikipedia.org/wiki/Renormalization

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Shelter Island Conference

From Wikipedia, the free encyclopedia
 
For the conference on quantum mechanics in valence theory, see Shelter Island Conference on Quantum Mechanics in Valence Theory, 1951.
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The first Shelter Island Conference on the Foundations of Quantum Mechanics was held from June 2–4, 1947 at the Ram's Head Inn in Shelter Island, New York. Shelter Island was the first major opportunity since Pearl Harbor and the Manhattan Project for the leaders of the American physics community to gather after the war. As Julian Schwinger would later recall, "It was the first time that people who had all this physics pent up in them for five years could talk to each other without somebody peering over their shoulders and saying, 'Is this cleared?'"

The conference, which cost $850, was followed by the Pocono Conference of 1948 and the Oldstone Conference of 1949. They were arranged with the assistance of J. Robert Oppenheimer and the National Academy of Sciences (NAS). Later Oppenheimer deemed Shelter Island the most successful scientific meeting he had ever attended; and as Richard Feynman recalled to Jagdish Mehra in April 1970: "There have been many conferences in the world since, but I've never felt any to be as important as this.... The Shelter Island Conference was my first conference with the big men.... I had never gone to one like this in peacetime."[1]

 

Contents

 

Organization

The conference was conceived by Duncan MacInnes, a scientist studying electrochemistry at the Rockefeller Institute for Medical Research. Once the president of the New York Academy of Sciences, MacInnes had already organized a number of small scientific conferences. However, he believed that the later conferences had suffered from a bloated attendance, and over this issue, he resigned from the Academy in January 1945. That fall, he approached the NAS with the idea of a series of 2–3 day conferences limited to 20–25 people. Frank Jewett, the head of the NAS, liked the idea; he envisioned a "meeting at some quiet place where the men could live together intimately", possibly "at an inn somewhere", and suggested that MacInnes focus on a couple of pilot programs. MacInnes' first choice was "The Nature of Biopotentials", a subject close to his own heart; the second would be "The Postulates of Quantum Mechanics", which later became "Foundations of Quantum Mechanics".

Karl K. Darrow, a theoretical physicist at Bell Labs and secretary of the American Physical Society, offered his help in organizing the quantum mechanics conference. The two decided to try to emulate the success of the early Solvay Conferences, and they consulted with Léon Brillouin, who had some experience in that area. In turn, Brillouin suggested consulting Wolfgang Pauli, the recent Nobel medalist at the Institute for Advanced Study in Princeton.

In January 1946, MacInnes, Darrow, Brillouin, and Pauli met in New York and exchanged letters. Pauli was enthusiastic about the topic, but he was primarily interested in bringing together the international physics community after the ordeal of the war. He suggested a large conference, including many older, foreign physicists, much to MacInnes' chagrin. With Jewett's encouragement, MacInnes asked Pauli for suggestions of "younger men" such as John Archibald Wheeler, explaining that the Rockefeller Foundation would support only a small conference. Pauli and Wheeler replied that MacInnes' conference might be merged with Niels Bohr's conference on Wave Mechanics in Denmark in 1947; they pointed out that the Niels Bohr Institute had close ties with the Rockefeller Foundation anyway. Darrow wrote to Wheeler that Bohr's conference was a poor replacement because it would draw few Americans. Finally, Shelter Island was explicitly an American conference. Darrow was chairman of the conference.

Proceedings

Lamb shift

Willis Lamb had found when probing hydrogen atoms with microwave beams that one of the two possible quantum states had slightly more energy than predicted by the Dirac theory; this became known as the Lamb shift. Lamb had discovered the shift a few weeks before (with Robert Retherford), so this was a major talking point at the conference. As it was known that the Dirac theory was incomplete, the small difference was an indication that quantum electrodynamics (QED) was progressing.[2]

Electron magnetic moment

Another dramatic discovery was reported at the conference by Isidor Rabi; a precise measurement of the magnetic moment of the electron, though this was overshadowed by Lamb’s work.

Mesons

Marshak presented his two-meson hypothesis about the pi-meson, which were discovered shortly thereafter.[1]

QED

Richard Feynman gave an informal presentation about his work on quantum electrodynamics. He gave a more formal, and less successful, presentation on QED at the Pocono Conference next year.

Participants

The participants arrived Sunday evening, 1 June 1947, and left Wednesday evening. They were:

https://en.wikipedia.org/wiki/Shelter_Island_Conference

 

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Hans Bethe

From Wikipedia, the free encyclopedia
 
Hans Bethe
Hans Bethe.jpg
Born Hans Albrecht Bethe
July 2, 1906
Strasbourg, Germany
Died March 6, 2005 (aged 98)
Ithaca, New York, United States
Residence Germany
United States
Nationality German
American
Alma mater University of Frankfurt
University of Munich
Known for
Spouse(s)
Rose Ewald (married in 1939; two children)
Awards
Scientific career
Fields Nuclear physics
Institutions
Doctoral advisor Arnold Sommerfeld
Doctoral students
Other notable students Freeman Dyson
Signature
Hans Bethe (signature).jpg

Hans Albrecht Bethe (German: [ˈhans ˈalbʁɛçt ˈbeːtə]; July 2, 1906 – March 6, 2005) was a German and American nuclear physicist who made important contributions to astrophysics, quantum electrodynamics and solid-state physics, and won the 1967 Nobel Prize in Physics for his work on the theory of stellar nucleosynthesis.[1][2]

For most of his career, Bethe was a professor at Cornell University.[3] During World War II, he was head of the Theoretical Division at the secret Los Alamos laboratory which developed the first atomic bombs. There he played a key role in calculating the critical mass of the weapons and developing the theory behind the implosion method used in both the Trinity test and the "Fat Man" weapon dropped on Nagasaki in August 1945.

After the war, Bethe also played an important role in the development of the hydrogen bomb, though he had originally joined the project with the hope of proving it could not be made. Bethe later campaigned with Albert Einstein and the Emergency Committee of Atomic Scientists against nuclear testing and the nuclear arms race. He helped persuade the Kennedy and Nixon administrations to sign, respectively, the 1963 Partial Nuclear Test Ban Treaty and 1972 Anti-Ballistic Missile Treaty (SALT I).

His scientific research never ceased and he was publishing papers well into his nineties, making him one of the few scientists to have published at least one major paper in his field during every decade of his career – which, in Bethe's case, spanned nearly seventy years. Freeman Dyson, once one of his students, called him the "supreme problem-solver of the 20th century".[4]

Contents

...

https://en.wikipedia.org/wiki/Hans_Bethe

 

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^_^

...Bethe entered the University of Munich in April 1926, where Sommerfeld took him on as a student on Meissner's recommendation.[17] Sommerfeld taught an advanced course on differential equations in physics, which Bethe enjoyed. Because he was such a renowned scholar, Sommerfeld frequently received advance copies of scientific papers, which he put up for discussion at weekly evening seminars. When Bethe arrived, Sommerfeld had just received Erwin Schrödinger's papers on wave mechanics.[18]

For his PhD thesis, Sommerfeld suggested that Bethe examine electron diffraction in crystals. As a starting point, Sommerfeld suggested Paul Ewald's 1914 paper on X-ray diffraction in crystals. Bethe later recalled that he became too ambitious, and, in pursuit of greater accuracy, his calculations became unnecessarily complicated.[19] When he met Wolfgang Pauli for the first time, Pauli told him: "After Sommerfeld's tales about you, I had expected much better from you than your thesis."[20]"I guess from Pauli," Bethe later recalled, "that was a compliment."[20]

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...Sommerfeld recommended Bethe for a Rockefeller Foundation Travelling Scholarship in 1929. This provided $150 a month (about $2,000 in 2016 dollars[A]) to study abroad. In 1930, Bethe chose to do postdoctoral work at the Cavendish Laboratory at the University of Cambridge in England, where he worked under the supervision of Ralph Fowler.[26] At the request of Patrick Blackett, who was working with cloud chambers, Bethe created a relativistic version of the Bethe formula.[27]Bethe was also known for his sense of humor, and with Guido Beck and Wolfgang Riezler, two other postdoctoral research fellows, created a hoax paper On the Quantum Theory of the Temperature of Absolute Zero where he calculated the fine structure constant from the absolute zero temperature in Celsius units.[28]The paper poked fun at a certain class of papers in theoretical physics of the day, which were purely speculative and based on spurious numerical arguments such as Arthur Eddington's attempts to explain the value of the fine structure constant from fundamental quantities in an earlier paper. They were forced to issue an apology.[29]

:lol:

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This is the city I know and love and have been a citizen of ever since I first encountered it in person age 18 in 1977.

New Yorkers Don't Scare Easily

https://www.nytimes.com/2017/12/11/opinion/port-authority-times-square-explosion.html?action=click&pgtype=Homepage&clickSource=story-heading&module=opinion-c-col-left-region&region=opinion-c-col-left-region&WT.nav=opinion-c-col-left-region

 

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wrong video can't delete! Arrrg!  The lack of post editing abilities here is frustrating. thank God this wasn't my latest sex tape posted in error! :lol:

 

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Artist Jasper Johns' studio assistant 'stole 22 unfinished works and resold them to unsuspecting gallery for $6.5MILLION'

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Robert Serber

From Wikipedia, the free encyclopedia
 
Robert Serber
Robert Serber ID badge.png
Robert Serber ID badge photo from Los Alamos.
Born March 14, 1909
Philadelphia, USA
Died June 1, 1997 (aged 88)
New York City, USA
Alma mater Lehigh University
University of Wisconsin–Madison
Scientific career
Doctoral advisor John Hasbrouck Van Vleck
Doctoral students Leon Cooper
Influences Eugene Wigner
J. Robert Oppenheimer

Robert Serber (March 14, 1909 – June 1, 1997) was an American physicist who participated in the Manhattan Project. Serber's lectures explaining the basic principles and goals of the project were printed and supplied to all incoming scientific staff, and became known as The Los Alamos Primer. The New York Times called him “the intellectual midwife at the birth of the atomic bomb.”[1]

 

Contents

 

Early life and education

He was born in Philadelphia as the eldest son of David Serber and Rose Frankel in a Jewish family.[2] He married Charlotte Leof (26 Jul 1911 – 1967) in 1933, the daughter of his stepmother's uncle.[3] Rose Serber died in 1922 and David married Charlotte's cousin Frances Leof in 1928. He earned his B.S. in Engineering Physics from Lehigh University in 1930 and earned his PhD from the University of Wisconsin–Madison with John Van Vleck in 1934, after which he was initially going to begin postdoctorate work at Princeton University with Eugene Wigner. He changed his plans and went to work with J. Robert Oppenheimer at the University of California, Berkeley (and shuttled with Oppenheimer between Berkeley and the California Institute of Technology). In 1938 he took a job at the University of Illinois at Urbana–Champaign where he stayed until he was recruited for the Manhattan Project. He later became a professor and chair of the physics department at Columbia University.

Manhattan Project

He was recruited for the Manhattan Project in 1941, and was in Project Alberta on the dropping of the bomb. When the Los Alamos National Laboratory was first organized, Oppenheimer decided not to compartmentalize the technical information among different departments. This increased the effectiveness of the technical workers in problem solving, and emphasized the urgency of the project in their minds, now they knew what they were working on. So it fell to Serber to give a series of lectures explaining the basic principles and goals of the project. These lectures were printed and supplied to all incoming scientific staff, and became known as The Los Alamos Primer, LA-1. It was declassified in 1965, and is available at this Wikipedia page. Serber developed the first good theory of bomb disassembly hydrodynamics.

325px-Agnew_RobertSerber.jpg
 
Serber on Tinian in 1945, just before the bombings of Hiroshima and Nagasaki

Serber's wife Charlotte was appointed by Oppenheimer to head the technical library at Los Alamos, where she was the only wartime female section leader.[4]

Serber created the code-names for all three design projects, the "Little Boy" (uranium gun), "Thin Man" (plutonium gun), and "Fat Man" (plutonium implosion), according to his reminiscences (1998). The names were based on their design shapes; the "Thin Man" would be a very long device, and the name came from the Dashiell Hammett detective novel and series of movies of the same name; the "Fat Man" bomb would be round and fat and was named after Sydney Greenstreet's character in The Maltese Falcon (from Hammett's novel). "Little Boy" would come last and be named only to contrast to the "Thin Man" bomb. This differs from the unsupported theory, now abandoned, that "Fat Man" was named after Churchill and "Thin Man" after Roosevelt (see Links).

Serber was to go on the camera plane for the Nagasaki mission, "Big Stink", but it left without him when Major Hopkins ordered him off the plane as he had forgotten his parachute, reportedly after the B-29 had already taxied onto the runway. Since Serber was the only crew member who knew how to operate the high-speed camera, Hopkins had to be instructed by radio from Tinian on its use. Serber was with the first American team to enter Hiroshima and Nagasaki to assess the results of the atomic bombing of the two cities.

Post-war work

In 1948 Serber had to defend himself against anonymous accusations of disloyalty, mostly because his wife Charlotte's family were Jewish intellectuals with Socialist leanings, and also because he tried to remove politics from discussions of the feasibility of the fusion bomb, leading to arguments with Edward Teller.[5] Serber went on to be consultant to numerous labs, businesses, and commissions.

In 1972 Serber was awarded the J. Robert Oppenheimer Memorial Prize.[6][7]

Robert Serber is interviewed in the Oscar-nominated documentary, The Day After Trinity (1980). In the 1989 movie dramatization of the Manhattan Project, Fat Man and Little Boy, the role of Robert Serber is played by Dr. H. David Politzer, a professor of theoretical physics at Caltech. Politzer was awarded the Nobel Prize in Physics in 2004.

Serber died June 1, 1997 at his home in Manhattan from complications following surgery for brain cancer.[1]

Bibliography

References

  1.  
  1. "Serber is recipient of Oppenheimer Prize". Physics Today. American Institute of Physics. April 1972. doi:10.1063/1.3070824. Retrieved 1 March 2015.

Further reading

  • Hoddeson, Lillian; Henriksen, Paul W.; Meade, Roger A.; Westfall, Catherine L. (12 February 2004). Critical Assembly: A Technical History of Los Alamos During the Oppenheimer Years, 1943-1945. Cambridge University Press. ISBN 978-0-521-54117-6.

External links

https://en.wikipedia.org/wiki/Robert_Serber

 

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1 hour ago, AdamSmith said:

Robert Serber

From Wikipedia, the free encyclopedia
 
Robert Serber
Robert Serber ID badge.png
Robert Serber ID badge photo from Los Alamos.
Born March 14, 1909
Philadelphia, USA
Died June 1, 1997 (aged 88)
New York City, USA
Alma mater Lehigh University
University of Wisconsin–Madison
Scientific career
Doctoral advisor John Hasbrouck Van Vleck
Doctoral students Leon Cooper
Influences Eugene Wigner
J. Robert Oppenheimer

Robert Serber (March 14, 1909 – June 1, 1997) was an American physicist who participated in the Manhattan Project. Serber's lectures explaining the basic principles and goals of the project were printed and supplied to all incoming scientific staff, and became known as The Los Alamos Primer. The New York Times called him “the intellectual midwife at the birth of the atomic bomb.”[1]

 

Contents

 

Early life and education

He was born in Philadelphia as the eldest son of David Serber and Rose Frankel in a Jewish family.[2] He married Charlotte Leof (26 Jul 1911 – 1967) in 1933, the daughter of his stepmother's uncle.[3] Rose Serber died in 1922 and David married Charlotte's cousin Frances Leof in 1928. He earned his B.S. in Engineering Physics from Lehigh University in 1930 and earned his PhD from the University of Wisconsin–Madison with John Van Vleck in 1934, after which he was initially going to begin postdoctorate work at Princeton University with Eugene Wigner. He changed his plans and went to work with J. Robert Oppenheimer at the University of California, Berkeley (and shuttled with Oppenheimer between Berkeley and the California Institute of Technology). In 1938 he took a job at the University of Illinois at Urbana–Champaign where he stayed until he was recruited for the Manhattan Project. He later became a professor and chair of the physics department at Columbia University.

Manhattan Project

He was recruited for the Manhattan Project in 1941, and was in Project Alberta on the dropping of the bomb. When the Los Alamos National Laboratory was first organized, Oppenheimer decided not to compartmentalize the technical information among different departments. This increased the effectiveness of the technical workers in problem solving, and emphasized the urgency of the project in their minds, now they knew what they were working on. So it fell to Serber to give a series of lectures explaining the basic principles and goals of the project. These lectures were printed and supplied to all incoming scientific staff, and became known as The Los Alamos Primer, LA-1. It was declassified in 1965, and is available at this Wikipedia page. Serber developed the first good theory of bomb disassembly hydrodynamics.

325px-Agnew_RobertSerber.jpg
 
Serber on Tinian in 1945, just before the bombings of Hiroshima and Nagasaki

Serber's wife Charlotte was appointed by Oppenheimer to head the technical library at Los Alamos, where she was the only wartime female section leader.[4]

Serber created the code-names for all three design projects, the "Little Boy" (uranium gun), "Thin Man" (plutonium gun), and "Fat Man" (plutonium implosion), according to his reminiscences (1998). The names were based on their design shapes; the "Thin Man" would be a very long device, and the name came from the Dashiell Hammett detective novel and series of movies of the same name; the "Fat Man" bomb would be round and fat and was named after Sydney Greenstreet's character in The Maltese Falcon (from Hammett's novel). "Little Boy" would come last and be named only to contrast to the "Thin Man" bomb. This differs from the unsupported theory, now abandoned, that "Fat Man" was named after Churchill and "Thin Man" after Roosevelt (see Links).

Serber was to go on the camera plane for the Nagasaki mission, "Big Stink", but it left without him when Major Hopkins ordered him off the plane as he had forgotten his parachute, reportedly after the B-29 had already taxied onto the runway. Since Serber was the only crew member who knew how to operate the high-speed camera, Hopkins had to be instructed by radio from Tinian on its use. Serber was with the first American team to enter Hiroshima and Nagasaki to assess the results of the atomic bombing of the two cities.

Post-war work

In 1948 Serber had to defend himself against anonymous accusations of disloyalty, mostly because his wife Charlotte's family were Jewish intellectuals with Socialist leanings, and also because he tried to remove politics from discussions of the feasibility of the fusion bomb, leading to arguments with Edward Teller.[5] Serber went on to be consultant to numerous labs, businesses, and commissions.

In 1972 Serber was awarded the J. Robert Oppenheimer Memorial Prize.[6][7]

Robert Serber is interviewed in the Oscar-nominated documentary, The Day After Trinity (1980). In the 1989 movie dramatization of the Manhattan Project, Fat Man and Little Boy, the role of Robert Serber is played by Dr. H. David Politzer, a professor of theoretical physics at Caltech. Politzer was awarded the Nobel Prize in Physics in 2004.

Serber died June 1, 1997 at his home in Manhattan from complications following surgery for brain cancer.[1]

Bibliography

References

  1.  
  1. "Serber is recipient of Oppenheimer Prize". Physics Today. American Institute of Physics. April 1972. doi:10.1063/1.3070824. Retrieved 1 March 2015.

Further reading

  • Hoddeson, Lillian; Henriksen, Paul W.; Meade, Roger A.; Westfall, Catherine L. (12 February 2004). Critical Assembly: A Technical History of Los Alamos During the Oppenheimer Years, 1943-1945. Cambridge University Press. ISBN 978-0-521-54117-6.

External links

https://en.wikipedia.org/wiki/Robert_Serber

 

This is a very under-explored  interest of mine only due to The fact that when I was first introduced to it and then subsequently watched the film I was already beyond accepting the “pass” of what was being handed to me at the time. :o I have a keen interest in this subject matter and I pledge to contribute more to it now that I no longer have Such access to that “passing” 

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It’s so challenging being agnostic, when some ( most) of the most beautiful music performed is from an organ in a church. I’m sure someday I’ll understand.

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