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Infinity of Cosmology Ben Anderson and Kevin Liang Discovering Infinity

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“ T HE most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age.” - H.P. Lovecraft, “The Call of Cthulu”

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Astronomy: The Second Oldest Profession - For centuries, humans have turned their eyes to the skies - Early models of the universe differed on the question of finite size - Finite size, infinite time?

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The Structure of the Universe - Early astronomers pondered the structure of the heavens - Thales of Miletus: The Earth is a flat disk floating in an atmosphere of vapor that held the planets and stars - Anaximander placed the heavens in tiered shells around the Earth - The lack of parallax was the “proof” of this model

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The Persistence of Geometry - Most early models claimed a geometry inherent to the Universe. - Copernicus removed the Earth from the center of his model - Kepler used the geometry of the five regular solids

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Olbers’s Paradox Infinite and eternal static universe – Infinite stars → Completely bright night sky?

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The Start of it all(?) - The Big Bang, the currently accepted model - ~13.8 billion years ago - Inflation: the first seconds after the Big Bang. - The four forces start as one - As the universe began to cool, baryonic matter formed

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Forces of Nature The gravitational and electromagnetic forces, in principle, stretch to infinity. But not the weak or strong forces. – So is the strong force eventually infinite in magnitude? – Resolved with color confinement.

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Nucleosynthesis - High energy required - Explains prevalence of lighter elements

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It’s All Relative - Einstein’s theory of relativity radically shifts the way we view the universe - The speed of light, c, becomes a sort of universal speed limit - Many strange things result, including the Doppler effect for light - z = (λ obsv – λ emit ) / λ emit

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Hubble and Expansion - Expansion rate measured by observing distant galaxies - Assumption: - Isotropic - Homogenous - v(t) = H(t)d

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Math! - E = K + U - M r = (4/3)πr 3 (t)ρ(t) - ρ o = ρ(t o )R 3 (t) - K = (½)mv 2 - U = (GMm)/r - ω = r(t o ) - r(t) = R(t) ω

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The Future of Expansion - Open, closed or flat? - As is often the case in physics, we use simplified models!

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Fate of the Cosmos The universe’s ultimate fate depends on the mass/energy ratio, its average density, and rate of expansion. – Also a question of how much dark energy do we have in our universe Three possibilities from the curvature of space: flat, open, or closed.

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Fate of the Cosmos Flat universe – Without dark energy The universe will expand forever at a continuously decreasing rate (asymptotically approaching zero) – With dark energy Initially, the universe will expand at a decreasing rate, then increases. – Ultimate fate Big Freeze, Big Rip, Heat Death

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Fate of the Cosmos Open universe – Without dark energy The universe continues to expand at a constant rate. Gravity hardly does anything to stop it. – With dark energy The universe expands at an accelerating rate. – Ultimate fate Big Freeze, Big Rip, Heat Death

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Fate of the Cosmos Closed Universe – Without dark energy Expansion eventually stops and the universe contracts by way of gravity. – With (enough) dark energy Expansion can continue indefinitely. – Ultimate fate A cyclical universe? Is this cycle infinite?

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Fate of the Cosmos Recent experimental data suggests that our universe is of the flat variety (with a small margin of error)

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Black Holes Regions of infinite space-time curvature. – Regions of infinite density. -If you were travelling with a buddy near a black hole, and your buddy accidentally passes beyond the event horizon, then said buddy is gone forever. -However, you can take solace in the fact that you will see your buddy falling into the black hole for an infinite amount of time

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Infinity of the Physical Continuum Multiverse theories – A universe infinite in space and time …

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Infinity of the Physical Continuum Multiverse theories – Bubble universes -Our universe is one of many “holes” in a block of Swiss cheese -Vacuum fluctuations of an inflation field

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Infinity of the Physical Continuum Multiverse theories – Many worlds interpretation of quantum mechanics Do our decisions create new universes?

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Infinity of the Physical Continuum Multiverse theories – Brane worlds -Each universe (a brane) is like a slice of bread -The entire loaf is the multiverse -Between each loaf of bread is hyperspace -Explains weakness of gravity? -Cyclical universes?

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Infinity of the Physical Continuum Multiverse theories – Simulated universes →… → -Is our universe a computer simulation being run by someone else in the “real” universe? -Is that “real” universe actually also a simulation? -There are ongoing research projects trying to resolve this problem (attempting to locate the “pixel” of our universe)

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Infinity of the Physical Continuum How small can you go? – Molecules → atoms → protons → quarks → anymore? – Planck length: the shortest measurable length (no improvements in measurement do better) Planck time: the time it takes light to travel a Planck length. Zeno’s paradoxes?

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Works Cited Einstein, Albert, and Leopold Infeld. The Evolution of Physics. London: Scientific Book Club, Print. Greene, Brian. The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos. Random House, Inc Print. Luminet, Jean-Pierre. Black Holes. Press Syndicate of the University of Cambridge Print. Maor, Eli. "Cosmological Infinity." To Infinity and Beyond: A Cultural History of the Infinite. Boston: Birkhäuser, Print. Poe, Edgar Allen. Eureka: A Prose Poem Web. 26 Jan Schombert, James. "History of Cosmology." History of Cosmology. University of Oregon, Web. 27 Jan "The Start of Scientific Cosmology (Cosmology: Ideas)." The Start of Scientific Cosmology (Cosmology: Ideas). American Institute of Physics, n.d. Web. 27 Jan “Will the Universe expand forever?” Universe 101: Our Universe. National Aeronautics and Space Administration, n.d. Web. 26 Jan

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