A Very Brief
Unified Theory
of
The Cosmological Constant
λ
by
Larry McClurg
Come now, I will tell thee... The first, namely, that it is, the other,
namely, that it is not. (Parmenides)
Parmenides was an early 5th century BC Greek
Philosopher.
Numbers
are forms, abstract units, where content follows. A value is “filling up the
number” ἐναρίθμιος, with a value from 0 to ∞ and includes the notions of Plato’s forms, Big and Small, or
math’s "more" and "less" ( + - ). Suspend what you think
you know about the infinity symbol for a moment and accept it as a form, an
abstract unit beyond our ability to comprehend, but not eternal, only
incredibly large. Call it X instead, and you would think it normal. Call it
what you will, but for simplicity’s sake “infinity” is best, and we can use it
in math, because the value of numbers is not what allows us to do math. A2+B2=C2.
Wherefore it is not permitted to what is, to be infinite; for it is in
need of
nothing; while, if it were infinite, it would stand in need of
everything. Wherefore all these things are but the names which mortals have
given, believing them, to be true. (Parmenides).
The Mysterious Greek Hen
The
Greek Hen, ἕν, is an indivisible unity, wholeness
without beginning or end. He is
traditionally interpreted as 1. Because a word can mean something doesn’t mean
it does. ΕΝ
ἦν ἐν ἕν (
Hen was in one) οὐ πρὀς
οὗτος (not with this
one). One is divisible 1/2=.5, and obviously
not an indivisible wholeness without beginning or end. On the other hand, a
ring or a circle or zero has no beginning and no end and has been a symbol of
eternity since ancient Egypt. Zero is
not divisible, is never a fraction, 0/1=0, 0/2=0, etc. Zero satisfies the unity
of Hen. ἕν=0 in ways #1 cannot,
and seems to be a 2600 year old formula relating energy ἐνέργεια and frequency ἐναρίθμιος, “filling up the number”.
Frequency
Lower frequency, like a bass
note, means a longer wavelength, λ, the
distance from A to B, or wave crest to wave crest. Low frequencies suffer less
from energy losses and can travel further away from their sources. Higher frequency,
like a high pitched note from a violin means a shorter wavelength, λ. The sustainability, or frequency ν, is number of times
a string can vibrate in a unit time, and depends on the energy. Frequency is a
function of energy and the result is lambda, the length of a line from A to B,
from wave crest to wave crest.
Zero and Infinity
In
830 AD an Indian mathematician, Mahavira, wrote, a number multiplied by zero is
zero,1x0=0 or (n x 0=0) and a number remains the same when zero is subtracted
from it, 1-0=1 or (n-0=n).
It
implies (n/0
= ∞)= (n = (∞ x 0) = 0), however when n is
every number, every number would be 0, which we know is not true. But it isn’t untrue in one special case, n⇔0, if and only if
n=0, n=(∞ x 0)=0= 0 is true & n/0 = 0 = ∞ is true. When expressing
this idea in mathematics, one must remove the ambiguity of which solution is
meant.
Hen=ἕν=0=∞.
Heraclitus said the path up is the same path down.
In it are very many tokens of what is, what is
uncreated and indestructible, alone, complete, immovable without end, a continuous
one. Nor is it divisible, since it is all alike. (Parmenides)
Circle
and Lambda
Example A
1.
A point A has no other properties except Location, 0
2.
An ellipse has 2 focal points, (A and B).
3.A
circle is a special ellipse in which the two focal points (A and B) are in
the same location.
4.
A sine wave is a smooth repetitive oscillation. A line from (A and B), the
crest of one wave, to the crest of another, is named λ, the
wavelength. At that point Hen=ἕν=0=∞=λ.
The Shape of the Universe
Again,
in this simple geometrical illustration, wavelength Lambda is a line (A and B)
between the centers of two circles and is same line (A and B) between the 2
foci of an ellipse and is the same line (A and B) between 2 wave crests. If the line (A to B) is shortened until the
distance is 0, then λ=0, and the 2 circles will share a common center, 0. The
center of a circle cannot be 1. λ=0. Hen=ἕν=0=∞=λ.
Cosmologists
puzzle over whether the universe is flat or curved. This is proof it is not flat.
Example
A
λ is a line |A-B|.
Two circles have centers A
and B and radius r
r is a constant ρ
1/2λ is a variable ρc
1/2λ can never be greater
than r or λ.
r ≥ 1/2λ ⇒ ρ ≥ ρc
When
r≥(1/2λ) ≥ 0 ⇒ ρ/ρc ≥0⇒λ≥0
thus a spherical universe,
for as long as λ≥0.
In Example B, the distance
between A and B shortens, the circles overlap. The current interpretation of
the shape of space as flat is biased from data that says no such thing. Space
needs to be flat for photons to propagate in a straight line from a Big Bang.
The ratio r/(1/2λ) works
identically to the ρ/ρc ratio describing the gravitational energy and the
critical mass density of the Universal Constant Lambda, used to determine the
possible fate and shape of the universe. R is constant and (1/2λ) varies with time. By definition when the
ratio is positive the universe is spherical.
Example B
ρ is the
gravitational energy density and is constant.
ρc is the critical mass
density, a variable over time, and what is needed for the universe to be
flat.
ρ/ρc ≡ r/(1/2λ)
the density parameter.
In
Example A, When
r≥(1/2λ)≥0 ⇒ ρ/ρc ≥0⇒λ≥0
thus a spherical universe,
for
as long as λ≥0.
In
Example B,
ρ/ρc = .50/.33=1.5 > 0⇒λ>0
thus still spherical.
The Hubble parameter (ratio)
k/a2 is the rate of expansion of the
universe and the
spatial curvature in any time-slice of
the universe; a is the scale factor, and currently a=1, which means the value
of k by default is the spatial curvature. If ρ/ρc is greater than 0, space
(meaning the universe) is said to be curved and spherical, so say Hubble,
Einstein, Friedmann, Lemaître, Robertson and Walker.
It cannot be denied then that when r
>1/2λ ⇒ ρ > ρc ⇒
K > 0, and k is positive, and the universe is therefore spherical.
Astronomical measurements of both matter-energy density of the universe and
spacetime intervals using supernova events confirm this and constrain the
spatial curvature to be very close to zero, although they do not constrain its
sign. Common sense tells you close to zero means it isn’t zero and space must
be curved according to definition, and not flat.
However, in one special case space can
be said not to be curved, if and only if n=0, that is, (n⇔0)
then n/0 = 0 = ∞ is true. The universe can be imagined as flat at the beginning
and end, and then Hen=ἕν=0=∞=λ,
expressed as
(1/2 λ=0) ≡ (ρ/ρc=0) ≡ (λ=0), or in
English, when (1/2 λ=0) it is logically identical to
ρ/ρc=0, which is logically identical to (λ=0). and ρ/ρc=0 only when ρ is 0,
and then no mass density exists at all in the beginning when the
universe is flat. Zero! It would seem impossible for Lemaître’s primeval atom
to have existed without mass density. The conclusion would be there was no Big
Bang in the beginning! Only when 1/2
λ=r, at the end of the cycle, is the
universe again flat and mass density is at a maximum. Lambda stretches from A
to B. From B to C is a new wave cycle , and 1/2 λ< r. The shape of the
universe is alternately flat and spheroid and unrelated to its end.
The
universe is a standing wave with a high frequency, with a constant radius r and constant
circumference=π whose diameter
=1 λ wavelength. 00=01=0=1= λ. An imaginary trampoline in extremely
fast motion gives a idea of how the universe can appear spherical at one point
in time and flat at another, much as a moving fan blade seems solid.
Where, then, it has its farthest boundary, it is complete on every
side, equally poised from the centre in every direction, like the mass of a
rounded sphere. (Parmenides).
Zero
is the still point center of a circle or sphere. Special Relativity gives the formula, E=mc2 . ἕν describes universal energy, and logically ἕ=mc2. Electromagnetic waves (frequency, ν) move through a
vacuum at the speed of light and ν=c. General relativity predicts that c is also
the speed of gravity g and of gravitational waves, hence g=c=ν. Zero-state vacuum energy is always
negative implying a repulsive gravity field from g, the center. Hen=ἕν=∞=0=λ=g=c. Whether
ἕν=0 or ἕν=∞ depends on
context. 2=$2 if it is a loaf of bread, but 2=$200,000 if it is a house.
Surely it is adjudged, as it needs must be. (Parmenides)
A
shorter distance from A to B (the
wavelength λ) means a larger, higher frequency. Frequency is defined the speed of
light divided by Lambda. (ν=c/λ), but we cannot divide by zero except
in one special case and the answer is always zero or infinity. Zero will not
get us an answer, so we must divide by ∞. We are
to set aside the one way as unthinkable, the other path is real and true, (Parmenides),
(ν=c/λ)= )=(ν=c/0) =(ν=c/∞).
This high frequency certainly exists,
but is probably undetectable. Moreover, it is immovable in the bonds of
mighty chains without beginning and without end. (Parmenides).
The Value of Infinity
The
speed of light (c) in a vacuum, is 299,792,458 meters per second (ms-1),
which rounds up to 300,000,000 ms-1, which is written as 3 x 108
ms-1. When ν=c and
ἕ=mc2. (ἕν=λ)=(λ/ν=ἕ)= (λ/c=mc2)=(λ=mc3)=(∞=mc3 ). The value of infinity is mc3.
The
mass of the observable universe varies depending on who formulates it. We only
need an approximation 3.35×1054 kg . ∞ = mc3 ≈
(3.35×1054) x
(3 x 108)3 = 30.15 x 1078 the numerical value of infinity.
Frequency, ν=c/λ = (3 x 108)÷( 30.15 x 1078 ) = 9.9502x 10-68
Hz
The Battered Universal Constant
When
Einstein formulated general relativity, he and
his contemporaries believed in a static universe. They thought Lambda was zero,
λ=0. After Hubble published his findings of the redshift,
they were interpreted as the universe is not stationary. Einstein abandoned λ=0 and wrote the cosmological constant was "the
greatest blunder of my life".
The opinions of mortals in which is no true belief at all. (Parmenides)
However
Einstein found that his equations could easily be solved in such a way as to
allow the universe to be expanding now, and to contract in the far future, and
added what he called the cosmological constant, essentially a constant energy density unaffected by
any expansion or contraction, whose role was to offset the effect of gravity on
the universe as a whole in such a way that the universe would remain static.
The original discovery that far away galaxies have higher spectral red shifts
than nearer galaxies (an apparent violation of homogeneity) led to the
discovery of Hubble flow, the metric expansion of space that occurs equally in
all locations, restoring homogeneity.
Galaxies
do not move faster than the speed of light at their present location.
Omega Lambda
In
lieu of λ, the cosmological constant itself,
cosmologists use a ratio, ρ/ρc called the density parameter, referred to as the cosmological constant, ΩΛ=Ω=λ=Λ. The ratio is between the gravitational energy density ρ and the critical mass density ρc ,
what is required for the universe to be flat. The energy density ρ, remains unchanged throughout the history of the universe but the
critical mass density ρc, changes with cosmological time. There is
no current agreement or understanding of the value of λ in the different cosmological
views.
Well it is that thou shouldst learn all things, and the opinions of
mortals in which is no true belief at all. None the less shalt thou learn of
these things also, since thou must judge of the things that are believed by men
as thou goest through thy journey. Thou
shalt know, too, the heavens that surround us, whence they arose.
I tell thee the whole arrangement as it seems to men, in order that no
mortal may surpass thee in knowledge. (Parmenides).
The Unification of Lambda
Hen=ἕν=0=∞=λ=g=c=ΩΛ.
Parmenides-Mnemosyne
Come
now, I will tell thee, the first, namely, that It is, the other, namely, that
It is not. In it are very many tokens that what is, what is uncreated and
indestructible, alone, complete, immovable and without end, a continuous Hen.
Nor is it divisible, since it is all alike. Moreover, it is immovable in the
bonds of mighty chains, without beginning and without end. I tell thee the
whole arrangement as it seems to men, in order that no mortal may surpass thee
in knowledge.
Hen=ἕν=0
Hen=ἕν=0=∞.
Hen=ἕν=0=∞=λ
r is a constant=
ρ,
1/2λ is a variable ρc
1/2λ can never be greater than
r
or λ
ρ is the energy density of the universe.
ρc is the critical density for space to be flat
ρ/ρc = r/(1/2λ) is the density parameter.
In Example A, ρ/ρc = .50/.50=1
r ≥
1/2λ ⇒ ρ ≥ ρc
r≥(1/2λ)≥0 ⇒ ρ/ρc ≥0⇒λ≥0
In Example B, ρ/ρc = .50/.33=1.5
> 0
r >1/2λ ⇒ ρ > ρc ⇒ K > 0,
k is positive, and the universe is
spherical.
if and only if n=0, (n⇔0) then n/0 = 0 = ∞ is true.
(1/2 λ=0) ≡ (ρ/ρc=0) ≡ (λ=0)
The universe is a standing wave with a high frequency,
and has a constant radius r and a constant
circumference=π
whose diameter
=1 λ wavelength.
00=01=0=1= λ.
Hen=ἕν=∞=0=λ=g=c
ν=c and ἕ=mc2
(ἕν=λ)=(λ/ν=ἕ)= (λ/c=mc2)=(λ=mc3)=(∞=mc3 )
∞= mc3 ≈
(3.35×1054) x
(3 x 108)3 = 30.15 x 1078
Frequency, ν=c/λ = (3 x 108)÷( 30.15 x 1078 ) = 9.9502x 10-68
Hz
Hen=ἕν=0=∞=λ=g=c=ΩΛ
Space is
Transcendental
The mind can see beyond walls or
the past or future horizon in space
as thru a window or door of perception.
(c) 2011
About the Author
I
am a singer/songwriter of the Mind Garage, a Rock n’ Roll Band formed in 1967.
Our very first record, Asphalt Mother, has become an underground cult classic.
But the story of the Mind Garage is much more than how a group of musicians
worked their way out of the backwater to find success in the music business
with RCA, the largest recording company
in the world at the time. The story is about the Electric Liturgy which
ultimately influenced and paved the way for an entirely new genre of rock
music, Christian rock, now in it’s many varieties as CCM, Contemporary
Christian Music, and how that music is incorporated into the worship services
of Christian churches today. The Electric Liturgy idea came from the
extraordinary Reverend Michael J Paine.
He was at that time a campus minister at West Virginia University who
challenged the band to write original rock and roll, “tavern music”, with
religious content in the tradition of Bach.
In doing so he changed the world.
The
ideas in this book came from Michael Paine’s views on philosophy and science.
Michael began writing to me about these things in 1996. At first I thought he
simply wanted his handwritten notes typed up.
But during the process Michael became my mentor, whether he planned it
or not. For the next 15 years, he wrote to me of pre-Socratic philosophers,
Parmenides, Plato and his teachers and students, and the Classical Greek
language, the philosophies and science of the Enlightenment, and from Einstein,
Planck and Bohr, to quantum physics, the Big Bang and String Theory.
I
used some of Michael’s ideas for poems and songs, and was eventually inspired
to investigate the “One”, the Greek Hen, ἕν, an indivisible wholeness without beginning or end. It
normally means the number one. One morning on my birthday, I wrote down these
personal revelations. . In practical
matters, when an ancient Greek needed a horse for his field, zero horse would
never do, and by necessity ἕν=1, And
it dawned on me that 0, a number Ancient Greeks didn’t use normally, was the
only number that could really be Hen in a philosophical , quantum and a
cosmological way. Was it an ancient Greek secret reserved for the wise? Everything the Goddess Memory
said to Parmenides in 500 BC, scattered throughout these pages, is Theoretical
Quantum Physics. Michael was right, λ=0.
Parmenides
pointed out that the endless variety and eternal changes were just an illusion;
the universe was stationary, not expanding and not infinite. We have to
distrust our senses and rely solely on our intellect. We must always follow the
path which IS. We must not
bother ourselves with the confusions of trying to figure out what IS NOT.
In Transcendent matters, ἕν=0. When
it is called for we must use ∞ or 0, or v or c, or what must from need, be.
Larry
McClurg April 26, 2011
A note from Mary Ann:
Larry McClurg has become a friend to me in many ways, but mostly in his patient, nurturing encouraging manner to help me understand not only the brilliance of his insights, such as what is published here, but in his incredible musical talent, his zest for life, his love and respect for all things living, and his vision which resounds with truth that hunger, homelessness, etc. are easily remedied situations if people would implement a few simple principles and some proven techniques of self-sustaining food production.
His band, Mind Garage, changed the course of Rock and Roll by becoming the first Christian Rock Band. Wherever they played, crowds of people of ALL faiths and of NO faith jammed blocks and blocks around the location, trying to hear this epic new form of rock.
Larry, you continue to amaze me. Thank you for all you do, and for being who you are. You have made the world a better place and I thank you, not only for myself but for my children and her children. God bless.
http://en.wikipedia.org/wiki/Mind_Garage
His band, Mind Garage, changed the course of Rock and Roll by becoming the first Christian Rock Band. Wherever they played, crowds of people of ALL faiths and of NO faith jammed blocks and blocks around the location, trying to hear this epic new form of rock.
Larry, you continue to amaze me. Thank you for all you do, and for being who you are. You have made the world a better place and I thank you, not only for myself but for my children and her children. God bless.
http://en.wikipedia.org/wiki/Mind_Garage
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