Transcript The REAL OCCULT: - Montgomery College

Space-time Invariance
and Quantum Gravity
Madness
By Dr. Harold Williams
of Montgomery College Planetarium
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
Space-time Invariance and Quantum Gravity:
or How c, G, and h create the fabric of timespace (reality)!
Dr. Harold Alden Williams, Montgomery College Planetarium at the
Takoma Park/Silver Spring Campus
World Lines
• t for time
• x for distance
• dx/dt speed
Space-time
• At least one
space
dimension not
shown
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.”
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)
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 1  v2
v 1 v2 
2
1  v 1 v2 c
v is the speed, this formula actually is
only correct when v1 and v2 are in the same
direction collinear, velocity addition formulae.
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
Michelson–Morley experiment
• Same geometry as
the previous
diagram.
• History of special
relativity
Luminiferous aether
• Quantum Foam
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
Correct velocity addition formulae
for non-colinear velocities
http://en.wikipedia.org/wiki/Addition_of_
Velocities_Formula
Newton’s 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.
G, Newtonian constant of gravitation
G=6.673(10) × 10-11 m3 kg-1 s-2
measured in SI units.
G=4π2 AU3/(yr2 M)
Max Planck the man
Max Planck 1918
Max Planck latter
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.
(Gh/(2πc5))1/2 =√Għ/c5=tP =5.3905x1044seconds the Planck time, a chronon,
smallest time, quanta of time, when!
Time is quantitized at this level, so called
“third quantitization.”
(Gh/(2πc3))1/2=√Għ/c3=lP =1.6160x1035meters the Planck length, an extention,
smallest length, quanta of distance, where!
Space is quantitized at this level, so called
“third quantitization.”
(ch/(2πG))1/2 =√cħ/G=MP =2.1761x108kilograms=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.”
Einstein’s General Theory of
Relativity, a theory of Gravity
Spherically Symmetric Vacuum
Solution to General Relativity
• Invariant ds2 in spherical coordinates
Black Hole Radius,
Schwartzshield Radius
2GM
Rs  2
c
Rs Schwartzshield Radius
G Newtonian Gravitational Constant
M Mass causing curvature
c speed of light
Einstein’s Energy Mass
relationship
E  Mc  M  E / c
2
2
E is the energy, M is the
mass, and c the speed of light
Speed = frequency wavelength
tautology
c   f  f  c  or   c / f
c is the wave speed, speed of light in a
vacuum here.
λ is the wavelength
f is the frequency
Planck’s Law
Quantum Mechanics
E  hf  E  hc 
h is Planck’s constant, energy time
h, Planck constant
• h=6.62606876(52)×10-34 J s (measured)
• J=Joules = kg m2 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
Substituting things and solving for
the wavelength
2GE / c
2G hc  / c
  Rs  2    Rs 
2
c
c
2
1/ 2
2Gh
 2Gh 
  3   3 
c
 c 
2
2
Substituting things and solving for
the frequency
2
2GE / c
2Ghf / c
  c / f  Rs 

2
2
c
c
f
2
1/ 2
 c 
c

 f 

2Gh
 2Gh 
5
5
1/ 2
 2Gh 
f  1/ T  T  1/ f   5 
 c 
T is the period of oscillation
2
Now we can actually derive the
Planck time, length, and mass
The Universe we live in
• Had a beginning!
• Is expanding,
getting larger with
time.
• Is accelerating now,
the rate of
expansion is
increasing, too.
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; 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:
13.7x109 years/tP*4π/3*(46x109 light-years/lP)3
=6.6x10245.
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!
Wikipedia Resources
•
•
•
•
•
Cosmic Background Radiation
Quantum Gravity
General Relativity
Planck Time
Planck Units
Wikipedia Cosmological Resources
• Cosmic Inflation
• Cosmological Constant
(hc5/(2πG))1/2=eP=MP c2=1.95x109 joules
the Planck Energy
eP=1.28x(1028 eV or 1019GeV or 1016TeV
e0=0.467 tons of TNT
Possible Madness
• http://www.digitalphilosophy.org/
• Edward Fredkin
End
Sort of
Hubble Parameter
• H0 ≈ 70 km/sec 1/Mpc =2.3x10-18 sec-1
• H0 ≈1/4.4x1017sec=1/13.9x109years
• 1/ H0 is the age of the universe (somewhat
model dependent)
• H0 ≈10-33eV
Cosmological Relativity
the Special and General Theories for the Structure of the Universe
by Moshe Carmeli (the man)
• ds2=dx2+dy2+dz2-c2dt2-τ2dυ2
• 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/ H0
• υ, recessional velocity (of the galaxy)
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
Planck Mass, MP,
relative to some other masses
• MP=2.1761x10-8kilograms=21µ grams
• me = 9.10938188(72) × 10-31 kg electron
mass
• Σ i=1 to 3 Δmνi = 0.7eV= 1.2 × 10-36 kg
neutrino masses reference
World lines, sheets, and volumes
of 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.
End for now!