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Dirac, Einstein, and Mathematical Beauty
Choose from these words to fill the blanks below:
equations, mathematically, Occam, simple, contemporaneous, beauty, quantum, successful, symmetric, astray, predicts, essense, balance
"make things as              as possible, but not simpler"
          's Razor
we don't want to multiply hypotheses unnecessarily
strike a                between explanatory power and over-complexity
"Our experience hitherto justifies us in trusting that nature is the realization of the simplest that is                              conceivable."
how is it that mathematics is so                      in describing the physical reality and nature, especially in the field of physics
Einstein believes that examining things mathematically, by thinking mathematically, we can get at the                of nature
others looked for the              in mathematics
Paul Dirac
the generation after Einstein
although they were                               
applied relativity to the new theory of                mechanics
famous for always saying that he looked for beauty in his                   , that how he knows they are true
but there are many cases when beauty can lead one             
you may find beautiful, very                    equations, which, however, do not match reality
there is room for debate here
quantum electrodynamics
1930s - 1940s
theory                  certain values to 8 or 9 decimal places
experiments verify this


Paul Dirac (1902-1984)
English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics, and predicted the existence of antimatter
  • among other discoveries, he formulated the Dirac equation, which describes the behavior of fermions (quarks and leptons [electrons])
  • also did work that forms the basis of modern attempts to reconcile general relativity with quantum mechanics
  • 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 that was not yet known empirically, as a means of bringing even greater symmetry to James Clerk Maxwell's equations of electromagnetism

Spelling Corrections:


Ideas and Concepts:

Dirac on Oppenheimer via tonight's Understanding Einstein class: "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."
Via this afternoon's Understanding Einstein class, Paul Dirac on religion: "If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards in heaven if not on earth all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins."
Direc on Math and God via this morning's Understanding Einstein class: "It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder:Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better."
From the getting-to-know-your-quantum-theories department via this morning's Understanding Einstein department: "In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. Although near the end of his life, Richard Feynman gave a series of lectures on QED intended for the lay public, it is important not to over-interpret his diagrams as representing reality. Nothing is implied about how a particle gets from one point to another. The diagrams do not imply that the particles are moving in straight or curved lines. They do not imply that the particles are moving with fixed speeds. The fact that the photon is often represented, by convention, by a wavy line and not a straight one does not imply that it is thought that it is more wavelike than is an electron. The images are just symbols to represent the actions:photons and electrons do, somehow, move from point to point and electrons, somehow, emit and absorb photons. We do not know how these things happen, but the theory tells us about the probabilities of these things happening."
On the use of Einstein quotes in our culture, via this morning's Understanding Einstein class: "One other quotation here, "To punish me for my contempt of authority, fate has made me an authority myself." This is good reminder that all those quotations you see floating around that are attributed to Einstein may or may not actually be anything that Einstein ever said, but because our culture tends to see Einstein as an authority figure, everything he has purportedly said is made out to be authoritatively true in some sense, even in areas where he wasn't an authority at all such as religion. This is, of course, a cheap use of Einstein's name and a classic fallacy called appeal to authority. But let's continue on in our study of the more substantial content on which Einstein actually was an authority:the electrodynamics of moving bodies."#einsteinquote2"
Pre-Einstein Physics up to 1905
Einstein's Life Up To 1905
The Annus Mirabilis Papers of 1905
Dirac, Einstein, and Mathematical Beauty
Events, Clocks, and Observers