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Mathematical Universe Cambridge 2013

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One may say the eternal mystery of the world is its COMPREHENSIBILIY

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On 25th of November 1915, after a period of pain and struggle, Einstein finally writes down the final form of his gravitational field equations.

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Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, Sitsungsberichte der Preussischen Akad. d. Wissenschaften, 1, 1917, 142-152.

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= 0 1922 1924 1927

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Λ > 0 1931

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1929

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Einsteins equations new that much earlier

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Supernova in NGC 4526

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Acceleration of the Universe

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Schwarzschild, K. (1916). "Über das Gravitationsfeld eines Massenpunktes nach der Einstein'schen Theorie". Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften 1: 189–196.

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The simplest kind of black hole in theory but one that could never occur in the real universe. A Schwarschild black hole doesn't rotate, has no electric charge, and exists in a spacetime with no other masses. There exist more realistic solutions to Einsteins equations describing black holes (Kerr – rotates, no charge, Reissner-Nordstrom – charge, no rotation)

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NGC 4261

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NGC 7052 How did equations know about that?

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Gravitational waves are ripples in the curvature of spave-time which propagate as a wave travelling outward from the source. Einstein, A., "Über Gravitationswellen." Sitzungsberichte, Preussische Akademie der Wissenschaften, 154, (1918). Two-dimensional representation of gravitational waves generated by two neutron stars orbiting each other.

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AURIGA is the Antenna Ultracriogenica Risonante per l'Indagine Gravitazionale Astronomica, or "ultra-cryogenic resonant antenna for gravitational- wave astronomy." The detector consists of an aluminum cylinder 3 meters in length and weighing approximately 2.3 tons. LIGO: laser interferometer

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The Binary Pulsar PSR 1913+16 In 1993, the Nobel Prize in Physics was awarded to Russell Hulse and Joseph Taylor of Princeton University for their 1974 discovery of a pulsar, designated PSR1913+16, in a binary system, in orbit with another star around a common center of mass. Using the Arecibo 305m antenna, Hulse and Taylor detected pulsed radio emission and thus identified the source as a rapidly rotating, highly magnetized neutron star. The neutron star rotates on its axis 17 times per second; thus the pulse period is 59 milliseconds. The Vela Pulsar and its surrounding pulsar wind nebula.

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What equations did know before it has been detected? We have discussed: 1.Expansion of the universe 2.Acceleration of the universe – cosmological constant – dark energy (?) 3.Gravitational collapse – black holes 4.Gravitational waves There are more such wonders: 1.Three classical tests: bending of light, perihelion motion, gravitational red shift 2.CMB – a window into the early history of the universe 3.Origin of chemical elements in the universe 4.Evolution of massive stars 5.............. 6.............. In predicting some of these effects equations from various branches of physics had to be combined

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Hertz once said of Maxwell's equations, "One cannot escape the feeling that... they have an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them." Hinrich Hertz James Clerk Maxwell

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WHAT DOES IT MEAN THAT THAT THE UNIVERSE IS MATHEMATICAL?

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Common sense view: Mathematics is a purely formal science; mathematical structures are lacking causal powers. The role of matheatics in physics is purely descriptive. There is a physical world, and it just happens that some mathematical structures descibe it correctly (up to a certain approximation) Let us take a look at the current practice of physicists...

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The theory of weak interactions tells us that that this happens because the down quark, being a part of a neutron, transforms into the up quark, emitting an intermediating boson W- which, in turn, decays into an electron and antineutrino. Is it a description ?

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Listen To The Sunset Listen to the sunset, Hear its silent sigh As it falls down the horisen Warning, the moon is nigh Listen to the sunset Hear its silent threat That darkness will be upon us It makes everyone upset Listen to the sunset The vanity of its words How beautiful this sunset is With its colour, and birds Katniss Everdeen

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However, physicists, in their practice, treat this process in a radically different way. Elementary particles are but places within the mathematical structure and outside of this structure have no meaning at all. Physical nature of elementary particles, and their interactions with other particles, is entirely determined by the mathematical structure. The beta minus decay is not described by mathematics; it is prescribed by it. Analogy with hardwere and softwere.

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Einstein has given us new worlds

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Gotfried Wilhelm Leibniz in the margin of his Dialogue: When God calculates and thinks things through, the world is made.

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