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## Distance Scales in the Universe II

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**Physics X**Extraordinary Concepts in Physics Distance Scales in the Universe II taught by: Robert J. Nemiroff**Physics X: About This Course**• Pronounced "Fiziks Ecks" • Reviews the coolest concepts in physics • Being taught for credit at Michigan Tech • Michigan Tech course PH4999 • Aimed at upper level physics majors • Light on math, heavy on concepts • Anyone anywhere is welcome • No textbook required • Wikipedia, web links, and lectures only**Scales of the Universe: Motion: Distance over Time**• Velocity: dx/dt • minimum: zero • minimum predictable: Δp Δx > h; v ~ Δv > (h/m) Δx • maximum: c (speed of light) • Acceleration: d2x/dt2 • minimum: zero • maximum: unknown • Higher orders of motion • Must be nonzero for an object at rest to move • Jerk: d3x/dt3; Jounce: d4x/dt4 • Even higher orders. Is there a limit?**Universe: Analog or Digital?**• Analog Principle • Everything is fuzzy if you look close enough • A line on a page appears crisp only from afar • Uncertainty principle • Digital Principle • Everything is discrete if you look close enough • Seemingly fuzzy patterns are made of discrete dots • Quanta, string theory • Which is more correct?**Planck Units**• Unitless measures of length, mass, time, and charge to which measured quantities can be normalized • Composed of fundamental constants • c, G, h, ε0 • More basic than length, time, mass, and charge? • c => m/s • G => m3/kg/s2 • h (angular momentum) => m2 kg/s • ε0 => C2 s2 /kg/m3**Planck Length**• ~1020 times smaller than the radius of a proton • Never been imaged • Significance experimentally unknown • Black holes: lp2 ~ minimum area of an event horizon (possibly) • String theory & Loop quantum gravity: lp2 ~ minimum area that a single bit of information might occupy.**Planck Mass**• ~2 x 10-8 kg • Defined by when the Compton wavelength (h/mc) is equal to the Schwarzschild radius (2Gm/c2) for a particle • Not minuscule: a flea can have a mass of several Planck masses**Planck Time**• The time it takes for light to travel one Planck length. • Before this time near the Big Bang, the universe was so dense that quantum effects will dominate general relativistic (GR) gravitational effects.**Interactive Universe Zoom**Secret Worlds: The Universe Within**Movies and Interactive Web Sites**• Powers of Ten • 1977 movie version of 1957 book "Cosmic View" • Earlier version: 1968 Cosmic Zoom