Space-time Invariance and Quantum Gravity

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Space-time Invariance and Quantum Gravity

• By Dr. Harold Williams
• of Montgomery College Planetarium

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World Lines

• t for time
• x for distance
• dx/dt speed

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Space-time

• At least one space dimension not shown

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World lines, sheets, and volumesof particles,
strings, and branes

• We know we live in a universe with at least 3
  space dimensions that we have some freedom in.
• Maybe more elaborate structures exist, but we do
  not as yet perceive them.

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Special Relativity

• http//en.wikipedia.org/wiki/Special_relativity
• http//en.wikipedia.org/wiki/Special_relativity_fo
  r_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.

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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.

v is the speed, this formula actually is only
correct when v1 and v2 are in the same direction,
velocity addition formulae.
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Speed of light, fastest speed

• cby definition299795458 (exact) m/s

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Correct velocity addition formulae for
non-colinear velocities
http//en.wikipedia.org/wiki/Addition_of_Velocitie
s_Formula
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Newtons Universal Law of Gravity
F12 is the force on object 2 due to object 1.
G is the gravitational constant.
m1 and m2 are respectively the masses of objects
1 and 2.
r21 r2 - r1 is the distance between objects 2
and 1.
is the unit vector from object 1 to 2.
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G, Newtonian constant of gravitation
G6.673(10) 10-11 m3 kg-1 s-2 measured
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Einsteins General Theory of Relativity, a theory
of gravity
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Spherically Symmetric Vacuum Solution to General
Relativity

• Invariant ds2 in spherical coordinates

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Black Hole Radius, Schwartzshield Radius
Rs Schwartzshield Radius
G Newtonian Gravitational Constant
M Mass causing curvature
c speed of light
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Einsteins 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
c is the wave speed, speed of light in a vacuum
here.
? is the wavelength
f is the frequency
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Plancks Law
Quantum Mechanics
h is Plancks constant, energy time
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h, Planck constant

• h6.62606876(52)10-34 J s (measured)
• JJoules kg m2 s-2 (Energy SI unit)
• hh/(2p)1.054571596(82)10-34 J s some times
  called the Dirac 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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(Gh/(2?c5))1/25.3905x10-44s?tP the Planck time,
a chronon, smallest time, quanta of time, when!
Time is quantitized at this level, so called
third quantitization. (Gh/(2?c3))1/21.6160x10-3
5m?lP the Planck length, an extention, smallest
length, quanta of distance, where! Space is
quantitized at this level, so called third
quantitization.
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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).
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46x109 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 its 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 13.7x109
years/tP4?/3(46x109 light-years/lP)3
6.6x10245.
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Wikipedia Resources

• Cosmic Background Radiation
• Quantum Gravity
• General Relativity
• Planck Time
• Planck Units

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Wikipedia Cosmological Resources

• Cosmic Inflation
• Cosmological Constant

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(hc5/(2?G))1/21.95x109 jouleseP the Planck
Energy eP1.28x(1028 eV or 1019GeV or
1016TeV e00.467 tons of TNT Planck mass
eP/c2mP2.17x10-8 kg
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Meaning of the Planck Mass, mP

• me 9.10938188(72) 10-31 kg
• S i1 to 3 ?m?i 0.7eV 1.2 10-36 kg
  reference

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End

• Sort of

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Hubble Parameter

• H0 70 km/sec 1/Mpc 2.3x10-18 sec-1
• H0 1/4.4x1017sec1/13.9x109years
• 1/ H0 is the age of the universe (somewhat model
  dependent)
• H0 10-33eV

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Cosmological Relativitythe Special and General
Theories for the Structure of the Universeby
Moshe Carmeli (the man)

• ds2dx2dy2dz2-c2dt2-t2d?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
• t, age of the universe1/ H0
• ?, 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 Hartnett
• Preface finished by Moshe Carmeli
• Also in this text Gianluca Gemelli
• 5-dimensional special relativistic hydrodynamics
  and cosmology by Gianluca Gemelli

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End for now!