The science fair:
President Obama Tours the 2015 White House Science Fair Exhibits
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President Obama welcomed young scientists and engineers from across the country to showcase their inventions, robots, and discoveries at the 2015 White House Science Fair!
Hosted by President Obama, the Fair features innovative projects, designs, and experiments from students all across America. With students from a broad range of science, technology, engineering, and math (STEM) competitions, this year’s Fair also included a specific focus on girls and women who are excelling in STEM and inspiring the next generation with their work. This year’s Fair – the 5th ever – featured dozens of innovative projects, designs, and experiments from students across America who are excelling in science, technology, engineering, and math (STEM).
“As a society, we have to celebrate outstanding work by young people in science at least as much as we do Super Bowl winners. Because superstar biologists and engineers and rocket scientists and robot-builders… they’re what’s going to transform our society. They’re the folks who are going to come up with cures for diseases and new sources of energy, and help us build healthier, more successful societies.” –President Obama at the 2014 White House Science Fair
2015 Science Fair Exhibitors
The White House Science Fair features extraordinary science projects and experiments from some of America’s most innovative students. Find out more about the students participating in this year’s Science Fair with this fact sheet.
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https://www.whitehouse.gov/science-fair
Emmy Noether:
E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws
Nina Byers
Physics Department
University of California at Los Angeles
Los Angeles, CA. 90095
Abstract
Emmy Noether proved two deep theorems, and their converses, on the connection between symmetries and conservation laws. Because these theorems are not in the mainstream of her scholarly work, which was the development of modern abstract algebra, it is of some historical interest to examine how she came to make these discoveries. The present paper is an historical account of the circumstances in which she discovered and proved these theorems which physicists refer to collectively as Noether's Theorem. The work was done soon after Hilbert's discovery of the variational principle which gives the field equations of general relativity. The failure of local energy conservation in the general theory was a problem that concerned people at that time, among them David Hilbert, Felix Klein, and Albert Einstein. Noether's theorems solved this problem. With her characteristically deep insight and thorough analysis, in solving that problem she discovered very general theorems that have profoundly influenced modern physics.
I. Introduction
Emmy Noether's paper "Invariante Varlationsprobleme" [1], hereafter referred to as I.V., profoundly influenced 20th century physics. It was presented to the July 16, 1918 meeting of the Könighche Gesellschaft der Wissenschaften zu Göttingen by Felix Klein presumably because Noether was not a member of the Gesellschaft1. One wonders if she was even present when the paper was read. The paper proved two theorems and their converses which revealed the general connection between symmetries and conservation laws in physics. They led to a deeper understanding of laws such as the principles of conservation of energy, angular momentum, etc., and also were instrumental in the great discoveries of gauge field symmetries of the 20th century. [2]
Remarkably these theorems are something of a departure from the main line of Noether's mathematical research, which was the development of modern abstract algebra. An examination of the historical circumstances in which she made these discoveries sheds light on how she came to do this work. The work followed upon David Hilbert's discovery of the variational principle from which he derived the field equations of general relativity. At this time David Hilbert, Felix Klein and others in Göttingen were intensely interested in the recently completed general theory of relativity. There were unresolved issues regarding the question of energy conservation in the theory. Published correspondence [3] between Hilbert and Klein regarding this indicates that Noether's help was requested by Hilbert to clarify these issues, and that she then did the work whose results are published a few years later in I.V.. The discussion and proofs of the two theorems in I.V. clarified and resolved the issues regarding energy conservation, as Hilbert acknowledged in his 1924 Grundlagen der Physik article [4]. From her Collected Works [5], it would seem that after this and some additional work on differential invariants in general relativity [6], Noether returned to the main line of her mathematical research.
Here I will present first a chronology of events leading up to Noether's publication of the I.V. paper; then a discussion of some rather difficult issues regarding energy conservation in general relativity which her work resolved; and finally a description and discussion of the two theorems in the I.V. paper.
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http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html
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