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One of the evident facts about the world is the stability of empty space-time. In classical general relativity we can explain this as a consequence of the positive energy theorem... the positive energy theorem must extend in some suitable form to any viable quantum theory of gravity.
Lee Smolin
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Some of the effects predicted by the theory [of loop quantum gravity] appear to be in conflict with one of the principles of Einstein's special theory of relativity... that the speed of light is a universal constant.... Photons of higher energy travel slightly slower than low-energy photons.... the principle of [general] relativity is preserved but Einstein's special theory of relativity requires modification.... A photon can have an energy-dependent speed without violating the principle of [general] relativity!
Lee Smolin
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The suggestion was that a positive energy proof for general relativity could be gotten by restricting supergravity to its bosonic sector, which is general relativity.
Lee Smolin
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The positive energy theorem was for half a century or more an open challenge to relativists. Many attempts were made to prove flat spacetime was stable, but none completely succeeded completely until a majestic tour de force of geometric reasoning of Shoen and Yau. This was followed two years later by a proof of Witten, which was as elegant as it was short. It is this proof of Witten's that we take as a template here for the quantum theory.
Lee Smolin
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Calculation establishes that a quantum positive energy theorem may be possible using a representation based on the Ashtekar connection. Left open is a key question of whether this use of the Ashtekar connection is necessary or whether a positive quantum energy result can be achieved for representations based on other connections, i. e., for [other] values of the Immirzi parameter.
Lee Smolin
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We show that some known classical results have particularly simple derivations within the Ashtekar formalism. These include Witten's positive energy theorem...
Lee Smolin
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There is a smallest unit of space. Its minimum value is given by the cube of the Planck length... If you take a volume of space and measure it to a very fine precision... It has to fall into some discrete series of numbers, just like the energy of an electron in an atom.... we can calculate the discrete areas and volumes from the theory.
Lee Smolin
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In string theory one studies strings moving in a fixed classical spacetime.... what we call a background-dependent approach.... One of the fundamental discoveries of Einstein is that there is no fixed background. The very geometry of space and time is a dynamical system that evolves in time. The experimental observations that energy leaks from binary pulsars in the form of gravitational waves—at the rate predicted by general relativity to the... accuracy of eleven decimal places—tell us that there is no more a fixed background of spacetime geometry than there are fixed crystal spheres holding the planets up.
Lee Smolin
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In quantum theory, distance is inverse to energy, because you need particles of very high energy to probe very short distances. The inverse of the Planck energy is the Planck length.
Lee Smolin
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Accustom yourself continually to make many acts of love, for they enkindle and melt the soul.
Teresa of Ávila
Lee Smolin
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Born:
June 6, 1955
(age 69)
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