The Functional

Paul Adrien Maurice Dirac

It worked.  It served its function.

Actually, to be technical about it, it was a functional, not a function. Big distinction. Never mind why.  It’s works.————  ?

Dirac’s Equation

But Why?

What did it imply?  Well, something very profound.  They didn’t want to believe it at first.

“Where is my Dirac?” — Albert Einstein

Human calculator: P. A. M. Dirac was regarded by many in the world of science as Albert Einstein’s only real equal.

Moreover, given Paul Dirac‘s apparent lack of interest in his fellow humans, where even Einstein found him a tad bit difficult to communicate with personally, most his colleagues were surprised at the singular event in 1937. They were for a bit of a shock when, in 1934, he met a chatty Hungarian divorcee called Manci Balazs and three years later married her.

Dirac’s Delta Function

There was the time when a visiting American academic, pink with excitement at the thought of sitting next to the great Dirac during a college dinner, was greeted with two courses of utter silence. Eventually, the poor American ventured: ‘Are you going anywhere nice on holiday this year?’ After 35 minutes more silence and the arrival of the cheese course, Dirac finally responded: ‘Why do you ask?’

He turned down a knighthood because he didn’t want people using his first name.  Why?  Why not. ———- Why not?

There is a logical problem here.

Structure versus Function — Structure and Function.  Which is it?  How about both.

“The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible.”  — Paul Dirac

Dirac himself blamed his oddness on terrible childhood bullying at the hands of his Swiss father. Charles Dirac was intense, peculiar and insisted on eating alone with his youngest son in the dining room while his wife and Dirac’s brother and sister ate in the kitchen. Charles also insisted on speaking only French and would refuse Paul permission to leave the table ‘if he had made a linguistic error’.  It was an utter nightmare for the young Dirac, who had terrible problems with his digestion and several times a week would be forced to vomit his dinner back up onto his plate.

Where is my Dirac?

Paul Dirac and Richard Feynman
“I have an equation. Do you have one too?”

Paul Adrien Maurice Dirac ( /dɪˈræk/ di-rak; 8 August 1902 – 20 October 1984) was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. [Wikipedia]

Nobody understands Quantum Mechanics
Richard Feynman

Einstein used to keep a copy of Dirac’s book on quantum mechanics by his bed, apparently mumbling  ‘Where’s my Dirac?’ when he came upon a particularly knotty problem.

Dirac Delta Functional Re-presentation

Every homeomorphism is open, closed, and continuous.  Oops.  How can something be opened and closed at the same time?

There you go man, keep as cool as you can
Face piles and piles of trials with smiles,
It riles them to believe that you perceive the web they weave,
And keep on thinking free.
— Moody Blues

Dirac established the most general theory of quantum mechanics and discovered the relativistic equation for the electron, which now bears his name. The remarkable notion of an antiparticle to each particle – i.e. the positron as antiparticle to the electron – stems from his equation. He was the first to develop quantum field theory, which underlies all theoretical work on sub-atomic or “elementary” particles today, work that is fundamental to our understanding of the forces of nature. He proposed and investigated the concept of a magnetic monopole, an object not yet known empirically, as a means of bringing even greater symmetry to Maxwell’s equations of electromagnetism. He quantized the gravitational field, and developed a general theory of quantum field theories with dynamical constraints, which forms the basis of the gauge theories and superstring theories of today. The influence and importance of his work has increased with the decades, and physicists daily use the concepts and equations that he developed. [Wikipedia]

Manci was his functional opposite: where Paul hardly spoke, she never stopped; he found sympathy difficult, she had friends coming out of her ears.   He was attentive, very abstract and logical to a fault — an Architect Rational (INTP); she was very expressive, subjective and passionate — a Provider Guardian (ESFJ).  Both very bright in their own way.

Dirac’s quantum electrodynamics made predictions that were – more often than not – infinite and therefore unacceptable. A workaround known as renormalization was developed, but Dirac never accepted this. “I must say that I am very dissatisfied with the situation,” he said in 1975, “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!” His refusal to accept renormalization resulted in his work on the subject moving increasingly out of the mainstream. [Wikipedia, revised]

You never know he might be right, after all, consensus science is never a science.

Needless to say, it was she, Manci, who was forced to woo him, but somehow it worked. As a friend once put it: “He gave her status and she gave him a life.”  A year after their marriage, he wrote Manci a lovely letter saying: “You have made me human. I shall be able to live happily with you even if I have no more success in my work.”  They were married for 50 years and had two children.

In 1928, building on 2×2 spin matrices which he discovered independently of Wolfgang Pauli‘s work on non-relativistic spin systems, (Abraham Pais quoted Dirac as saying “I believe I got these (matrices) independently of Pauli and possibly Pauli got these independently of me”) he proposed the Dirac equation as a relativistic equation of motion for the wavefunction of the electron. This work led Dirac to predict the existence of the positron, the electron’s antiparticle, which he interpreted in terms of what came to be called the Dirac sea. The positron was observed by Carl Anderson in 1932. Dirac’s equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon. [Wikipedia, revised]

Yes it worked.  It was Functional. Not just Structural.  Functional and Structural.  Dynamic and Stable.  Big Difference.

You see the Proton and the Electron both are Fermions, which have Fermi-Dirac statistics, opposite in the charge, different in their masses.  As a pair they form Hydrogen, the simplest atom, a dynamic and stable form that forms a visible basis of the our universe.

“Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else.” — YS Kim

Without structure, you have no function.
Without function, you have no structure.

Well, our friend Dirac, too, has a religion, and its guiding principle is “God does not exist and Dirac is His prophet” — Wolfgang Pauli.

No, the Higgs Boson, the so-called God Particle, does not answer all of our questions.

It seems clear that the present quantum mechanics is not in its final form. — Paul Dirac

8 thoughts on “The Functional

  1. Timothy David Andersen August 22, 2012 / 7:49 pm

    Weird isn’t it? The Dirac delta function, combined with an integral and a function, is a functional. We sometimes just call it a distribution or a generalized function. It is the limit of a sequence of functions but not a function itself.


  2. goodrumo August 23, 2012 / 12:24 am

    Loved reading about the science, the relationships and temperament, also enjoying the YS Kim page too.


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