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Space-time Invariance and Quantum Gravity Space-time Invariance and Quantum Gravity Madness By Dr. Harold WilliamsDr. Harold Williams of Montgomery College PlanetariumMontgomeryCollegePlanetarium
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Space-time Invariance and Gravity: only c and G General Relativity 1915, continuous Real Numbers Dr. Harold Alden Williams, Montgomery College Planetarium at the Takoma Park/Silver Spring Campus
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Space-time Invariance and Quantum Gravity: or How c, G, and h create the fabric of time- space (reality)! Dr. Harold Alden Williams, Montgomery College Planetarium at the Takoma Park/Silver Spring Campus
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World Lines t for timetime x for distancedistance dx/dt speeddx/dtspeed
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Space-time At least one space dimension not shown space dimension
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Special Relativity http://en.wikipedia.org/wiki/Special_relativity http://en.wikipedia.org/wiki/Special_relativity_for_beginners “Nothing but Relativity” by Palash B. Pal shows that only Galilean and Einstein Relativity are even possible with the “Principle of Relativity” “Principle of Relativity” ≡ “Physical laws appear the same to any inertial observer.”inertial
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Speed of light, fastest speed c=by definition=299795458 (exact) metes/second There is a fastest speed because we leave in a causal universe. (if the principle of sufficient cause” is valid)principle of sufficient cause
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There is a Fastest Speed What ever that fastest speed is nothing can move faster than fastest. c is the fastest speed. Experimentally this, c, is the speed of light, electromagnetic radiation, in a vacuum.speed of light v is the speed, this formula actually is only correct when v 1 and v 2 are in the same direction collinear, velocity addition formulae.velocity addition formulae
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A Paradox of Non-Relativistic Thinking If speed of light were not absolute, you would see the car coming toward you reach the collision point before the car it struck No paradox if light speed is same for everyone
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Michelson–Morley experiment Same geometry as the previous diagram. History of special relativityHistory of special relativity
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Luminiferous aether Quantum Foam
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Test Relativity for Yourself If speed of light were not absolute, binary stars would not look like two distinct points of light You can verify relativity by simply looking through a telescope at a binary star system
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Correct velocity addition formulae for non-colinear velocities http://en.wikipedia.org/wiki/Addition_of_ Velocities_Formula
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Newton’s Universal Law of Gravity F 12 is the force on object 2 due to object 1. G is the gravitational constant.gravitational constant m 1 and m 2 are respectively the masses of objects 1 and 2. r 21 = |r 2 − r 1 | is the distance between objects 2 and 1. is the unit vector from object 1 to 2.unit vector
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G, Newtonian constant of gravitation G=6.673(10) × 10 -11 m 3 kg -1 s -2 measured in SI units. G=4π 2 AU 3 /(yr 2 M )
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Max Planck the man
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Max Planck 1918
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Max Planck latter
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History of Planck length, time, and mass In 1899 a year before he formulated blackbody radiation in December of 1900 in Prussian Academy of Sciences, Max Planck: 'Über irreversible Strahlungsvorgänge'. Sitzungsberichte der Preußischen Akademie der Wissenschaften, vol. 5, p. 440-479-480 (1899). Just used dimensional analysis.Max Planck440479480
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(Gh/(2πc 5 )) 1/2 =√G ħ/ c 5 =t P =5.3905x10 - 44 seconds the Planck time, a chronon, smallest time, quanta of time, when! Time is quantitized at this level, so called “third quantitization.”Planck time (Gh/(2πc 3 )) 1/2 =√G ħ/ c 3 =l P =1.6160x10 - 35 meters the Planck length, an extention, smallest length, quanta of distance, where! Space is quantitized at this level, so called “third quantitization.”Planck length
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(ch/(2πG)) 1/2 =√c ħ/ G=M P =2.1761x10 - 8 kilograms=21µ grams the Planck mass, the minimum mass of a clock capable of measuring time. The value of this mass is comparable to the mass of a flea egg. Pages 62-81 in Eugene P. Wigner’s book Symmetries and Reflections Scientific Essays Chapter 5, Relativistic Invariance and Quantum Phenomena in the section titled “Quantum Limitations of the Concepts of General Relativity.”Planck mass
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Einstein’s General Theory of Relativity, a theory of GravityGeneral Theory of Relativityravity
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Spherically Symmetric Vacuum Solution to General Relativity Invariant ds 2 in spherical coordinates
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BlackBlack Hole Radius, Schwartzshield Radius Schwartzshield Radius R s Schwartzshield Radius G Newtonian Gravitational Constant M Mass causing curvature c speed of light
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Einstein’s Energy Mass relationship E is the energy, M is the mass, and c the speed of light
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Speed = frequency wavelength tautology λ is the wavelength f is the frequency c is the wave speed, speed of light in a vacuum here.
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Planck’s Law h is Planck’s constant, energy time Quantum Mechanics
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h, Planck constant h=6.62606876(52)×10 -34 J s (measured) J=Joules = kg m 2 s -2 (Energy SI unit) ħ=h/(2π)=1.054571596(82)×10 -34 J s some times called the Dirac’s Constant or the reduce Planck’s Constant
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Substituting things and solving for the wavelength
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Substituting things and solving for the frequency T is the period of oscillation
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Now we can actually derive the Planck time, length, and mass
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The Universe we live inUniverse Had a beginning!beginning Is expanding, getting larger with time.expanding Is accelerating now, the rate of expansion is increasing, too.accelerating
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46x10 9 light-years radius of the universe, so an estimate of the current information content, pixels, of the universe, since creation could be made. So here it is the current estimate of the information content of the universe, which is an always increasing number, because time is advancing; we get older and not younger; it’s a one way trip; no time travel allowed (you can not kill your mother before you were conceived); and the observable universe is expanding and accelerating since the creation event:universeobservable universe 13.7x10 9 years/t P *4π/3*(46x10 9 light-years/l P ) 3 =6.6x10 245.
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Some modest Conclusions No infinity in ticks or tocks yet or ever! No infinitesimals! Expansion drives order in our cosmos! Just because we can imagine it does not make it real or realizable! Enjoy uncertainty and the increasing container that you are in! We no longer have to fear the irrational numbers like the Pythagoreans, since they are not part of physics!
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WikipediaWikipedia Resources Cosmic Background Radiation Quantum Gravity General Relativity Planck Time Planck Units
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WikipediaWikipedia Cosmological ResourcesCosmological Cosmic Inflation Cosmological Constant
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(h c 5 /(2π G )) 1/2 =e P =M P c 2 =1.95x10 9 joules the Planck Energy e P =1.28x(10 28 eV or 10 19 GeV or 10 16 TeV e 0 =0.467 tons of TNT
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Possible Madness http://www.digitalphilosophy.org/ Edward Fredkin
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End Sort of
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Hubble Parameter H 0 ≈ 70 km/sec 1/Mpc =2.3x10 -18 sec -1 H 0 ≈1/4.4x10 17 sec=1/13.9x10 9 years 1/ H 0 is the age of the universe (somewhat model dependent) H 0 ≈10 -33 eV
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Cosmological Relativity Cosmological Relativity the Special and General Theories for the Structure of the Universe by Moshe Carmeli (the man)Special and General Theories for the Structure of the UniverseMoshe Carmelithe man ds 2 =dx 2 +dy 2 +dz 2 -c 2 dt 2 -τ 2 dυ 2 x, y, z usual meaning lengths in space c, maximum speed in the universe, speed of light in a vacuum t, time, what good clocks keep τ, age of the universe=1/ H 0 υ, recessional velocity (of the galaxy)
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Relativity: Modern Large-Scale Spacetime Structure of the Cosmos Moshe Carmeli editor Probably his last book Finished by John HartnettJohn Hartnett Preface finished by Moshe Carmeli Also in this text Gianluca Gemelli 5-dimensional special relativistic hydrodynamics and cosmology by Gianluca Gemelli5-dimensional special relativistic hydrodynamics and cosmology
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Planck Mass, M P, relative to some other masses M P =2.1761x10 -8 kilograms=21µ grams m e = 9.10938188(72) × 10 -31 kg electron mass Σ i=1 to 3 Δm ν i = 0.7eV= 1.2 × 10 -36 kg neutrino masses referencereference
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World lines, sheets, and volumes of particles, strings, and branesbranes We know we live in a universe with at least 3 space dimensions that we have some freedom in. universe Maybe more elaborate structures exist, but we do not as yet perceive them.
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End for now!
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