In Noether's own words, her mathematical treatment can be seen as "the greatest possible group theoretic generalisation of general relativity". Noether's result had such a big impact because it showed how important symmetries are in physics. When conversation laws first appeared they gave physicists another angle from which to investigate physical systems. Noether's result goes a step further. It puts mathematicians' understanding of symmetries, which was well advanced even a hundred years ago, at physicists' disposal.
Modern physicists have taken this idea to an extreme. Rather than formulating a theory first and then looking for its symmetries later, they first decide what symmetries their theory should posses and then see how reality fits in with that.
The approach has had startling success. Several fundamental particles, including the famous Higgs boson , were predicted to exist based on the assumption that certain rather abstract symmetries exist, and only later discovered in experiments. The hope is that symmetry will eventually guide us to the hotly sought after theory of everything you can find out more in this article.
What we have just described is just one of two results proved in Noether's paper Invariante Variationsprobleme "invariant variational problems" — and it doesn't apply to general relativity. The symmetries we alluded to above are global transformations in the sense that they do the same thing to every point in the space they act on. If you shift every point along by a fixed distance in a fixed direction, or rotate it through a fixed angle about a fixed axis, then every point experiences exactly the same thing.
Noether's first theorem only applies to theories whose symmetries are all global. If that's the case, then each of the symmetries corresponds to a conservation law. The symmetries of general relativity, however, aren't global. The theory also remains invariant under local transformations that do different things to different points. In this case Noether's first theorem doesn't apply: for every symmetry there isn't a straight-forward conservation law. To deal with general relativity and other so-called generally covariant theories Noether proved a second theorem — and together with the first, this theorem proves Hilbert right: energy conservation does have a different status in general relativity.
The exact nature of energy conservation in general relativity is tricky, so we will leave it for another time. Einstein, for his part, was impressed by Noether's insight.
A hypothetical hidden symmetry, dubbed supersymmetry because it proposes another level of symmetry in particle physics, posits that each known particle has an elusive heavier partner. Some physicists are beginning to ask if supersymmetry is correct. Perhaps symmetry can only take physicists so far. Despite such disappointments, symmetry maintains its luster in physics at large. One candidate relies on a proposed connection between two types of complementary theories: A quantum theory of particles on a two-dimensional surface without gravity can act as a hologram for a three-dimensional theory of quantum gravity in curved spacetime.
Picture a soda can with a label that describes the size and location of each bubble inside. The label catalogs how those bubbles merge and pop. For physicists, understanding a simpler, 2-D theory can help them comprehend a more complicated mess — namely, quantum gravity — going on inside.
The theory of quantum gravity for which this holographic principle holds is string theory, in which particles are described by wiggling strings. A theory of how particles act in two dimensions can serve as a hologram for quantum gravity in three dimensions. Symmetries in the 2-D quantum theory show up in the 3-D quantum gravity theory in a different context. The conservation laws it implies help to explain waves on the surface of the ocean and air flowing over an airplane wing.
Simulating such systems helps scientists make predictions — about weather patterns, vibrations of bridges or the effects of a nuclear blast, for example. So programmers have to manually add in conservation laws for energy and momentum.
She and colleagues have simulated a person beating a drum inside a simplified Stonehenge, determining how sound waves would wrap around the stone — while automatically conserving energy. Mansfield says her method, which she will present in September in London at a Noether celebration, could eventually be used to create simulations that behave more like the real world.
References to Noetherian rings, Noetherian groups and Noetherian modules are sprinkled throughout current mathematical literature. Eventually, society did awaken. In a lecture she gave about Noether at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, Gregory showed a slide of herself with five female colleagues, then at the center for particle theory at Durham University.
While women in science still face challenges, no one in the group had to struggle to get paid for her work. Subscribers, enter your e-mail address for full access to the Science News archives and digital editions. Not a subscriber? Become one now. Skip to content. Science News Needs You Support nonprofit journalism. By Emily Conover June 12, at am. Tags: Emmy Noether , Neil Turok , slice of pi , women in physics.
Mathematical Physics , Outreach. Mathematical Physics. Why women leave physics. Quantum Gravity , Mathematical Physics. Bridging two roads of physics. Fun Stuff , Outreach. In , the Nazi regime fired all Jewish professors and followed the next year by firing all female professors.
She worked as a visiting professor at Bryn Mawr College, but her time in America was short. She died in at age 53, from complications following surgery. Physicists tend to know her work primarily through her theorem. But mathematicians are familiar with a variety of Noether theorems, Noetherian rings, Noether groups, Noether equations, Noether modules and many more. Over the course of her career, Noether developed much of modern abstract algebra: the grammar and the syntax of math, letting us say what we need to in math and science.
She also contributed to the theory of groups, which is another way to treat symmetries; this work has influenced mathematical side of quantum mechanics and superstring theory. Noetherian symmetries answer questions like these: If you perform an experiment at different times or in different places, what changes and what stays the same?
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