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SOME OF JANNA LEVIN'S SCIENTIFIC RESEARCH
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Black Holes
Black holes are among the most outrageous inhabitants of our universe, as well as the most elusive. Black holes emit no light and reflect no light and so are essentially invisible against the darkness of the sky. While black holes can be seen indirectly if they cannibalize a companion star, the future space-based gravitational wave detector LISA and the Earth-based gravitational wave detector LIGO aim to observe the most extreme remnants of a dead star more directly. As black holes orbit each other, space itself ripples in response to the motion creating gravitational waves. If the black holes are rapidly spinning, then the orbit can be extremely irregular, even chaotic. Chaos imposes a fundamentally new perspective on the merger of black holes, gravitational wave detection, and possibly curved spacetime in general.
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Finite Universe
Our universe appears to stretch nearly thirty billion light years across. As far as the eye can see, there is no visible bound to spacetime. Still the universe may not be infinite. There was once a cultural prejudice that the earth was flat and unconnected, so much so that explorers were feared to have fallen off the edge. The assumption that space must be infinite may represent a similar bias. A tenable possibility is that space itself is not only curved, as Einstein suggested, but that it is also finite. A finite universe, and indeed a finite universe with several extra dimensions, may be a prediction of a theory beyond Einstein’s – the long coveted Theory of Everything. Even as we struggle to understand the universe as drawn by a TOE, recent Astronomical observations may be on the cusp of resolving this age old question: Is the universe infinite?
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Theories of Everything
A physical Theory of Everything is the greatest ambition consuming theoretical physics. Yet last century we were forced to concede that there will never be a mathematical theory of everything. Kurt Gödel, Alan Turing, and Gregory Chaitin proved that our knowledge of numbers themselves is fundamentally incomplete. Most numbers are random, a toss of the coin. There are true relations among the numbers about which we can only prove that we can never prove them.
Many times in the history of physics, theories have been shaped by such profound limits. Einstein proposed a fundamental limit in the speed of light and thereby discovered Relativity. Heisenberg invoked an uncertainty principle in measurements of quantum phenomena and thereby laid a cornerstone for Quantum Mechanics. Alongside these should be listed the profound incompleteness in our knowledge of numbers – there can never be a mathematical theory of everything. The proposal is to define the limits mathematical incompleteness might set on a physical theory of everything. Just as Relativity emerged from the limit of light’s speed and Quantum Theory emerged from the limits of measurement, deep insight into the universe and its origins could emerge by confronting the limit of mathematical incompleteness.
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