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Angular Momentum, Quantum Gravity, and Megalithic Sites
By
Ian Beardsley
Copyright © April 14, 2025
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Abstract
It may be that the problem of reconciling gravity with quantum mechanics is an abstract problem, one that
may have already been encountered by our ancient ancestors who erected stone observatories like
Stonehenge (megalithic sites) and it may be that they found the solution in the megalithic yard, a unit of
measurement for aligning stones. Presented here is the author’s earlier theory that provides a wave
solution to the Earth/Moon/Sun system that is solved with a characteristic time of one second that is
shown to solve also the atom’s proton. As such, it is suggested we can look at the Solar System, which is
gravitational, to solve the quantum realm and provide a grand unified theory. It is suggested we might be
able to help find such a solution by looking at ancient megalithic sites.
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Data Used In This Paper
(Proton Mass)
(Planck Constant)
(Proton Radius)
(Gravitational Constant)
(light speed)
(Fine Structure Constant)
Earth day=(24)(60)(60)=86,400 seconds. Using the Moon’s orbital velocity at aphelion, and Earth’s
orbital velocity at perihelion we have:
m
P
: 1.67262 × 10
−27
kg
h : 6.62607 × 10
−34
J ⋅ s
r
p
: 0.833 × 10
−15
m
G: 6.67408 × 10
−11
N
m
2
kg
2
c : 299,792,458m /s
α : 1/137
q
p
= q
e
= 1.6022E − 19cou lom bs
k
e
= 8.988E 9
Nm
2
C
2
K E
moo n
=
1
2
(7.347673E 22kg)(966m /s)
2
= 3.428E 28J
K E
earth
=
1
2
(5.972E 24kg)(30,290m /s)
2
= 2.7396E 33J
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Introduction One can speak of the structure of the long term structure of the solar system. The whole
object of developing a theory for the way planetary systems form is that they meet the following criterion:
They predict the Titius-Bode rule for the distribution of the planets; the distribution gives the planetary
orbital periods from Newton’s Universal Law of Gravitation. The distribution of the planets is chiefly
predicted by three factors: The inward forces of gravity from the parent star, the outward pressure
gradient from the stellar production of radiation, and the outward inertial forces as a cloud collapses into a
flat disc around the central star. These forces separate the flat disc into rings, agglomerations of material,
each ring from which a different planet forms at its central distance from the star (they have widths). In a
theory of planetary formation from a primordial disc, it should predict the Titius-Bode rule for the
distribution of planets today, which was the distribution of the rings from which the planets formed.
Also, the Earth has been in the habitable zone since 4 billion years ago when it was at 0.9 AU. Today it is
at 1AU, and that habitable zone can continue to 1.2 AU. So we can speak of this distance to the Earth over
much time. The Earth and Sun formed about 4.6 billion years ago. As the Sun very slowly loses mass over
millions of years as it burns fuel doing fusion, the Earth slips microscopically further out in its orbit over
long periods of time. The Earth orbit increases by about 0.015 meters per year. The Sun only loses
0.00007% of its mass annually. The Earth is at 1AU=1.496E11m. We have 0.015m/1.496E11m/
AU=1.00267E-13AU. So,
The Earth will only move out one ten thousandth of an AU in a billion years. Anatomically modern
humans have only been around for about three hundred thousand years. Civilization began only about six
thousand years ago.
The unit of a second becomes important in my theory. We got the second from the rotation period of the
Earth at the time the moon came to perfectly eclipse the Sun. The Moon slows the Earth rotation and this
in turn expands the Moon’s orbit, so it is getting larger, the Earth loses energy to the Moon. The Earth day
gets longer by 0.0067 hours per million years, and the Moon’s orbit gets 3.78 cm larger per year.
That is as the Earth’s day gets longer and the lunar orbit grows larger, we got the second at the time that
the Earth day was what it is during the epoch when the Moon perfectly eclipses the Sun, 24 hours.
The near perfect eclipse is a mystery in the sense that it came to happen when anatomically modern
humans arrived on the scene, even before that, perhaps around Homo Erectus and the beginning of the
Stone Age. The Earth day was 18 hours long, long before that, 1.4 billion years ago. Homo Erectus is
around two to three million years ago.
(1.00267E − 13AU/year)(1E 9years) = 0.0001AU
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Angular Momentum, Quantum Gravity, And Ancient Megalithic Sites
At the heart of a grand unified field theory which would bridge general relativity with quantum
mechanics, is the concept of angular momentum; Planck’s constant, which is at the core of quantum
mechanics, has units of angular momentum. This is an active area in theoretical physics for developing a
theory for quantum gravity. This is because gravity is an inverse square law and moment of inertia has r
squared dependence, which suggests that spacetime curvature (gravity) may coupled to quantum spin.
I find it is possible that this basic problem may be encoded in ancient megalithic structures, like
Stonehenge, which are ancient observatories. They are stones placed with alignments for the Moon and
the Sun due to the Earth’s rotation and orbit around the Sun. I find I can quite simply explain why I
believe in this connection of quantum gravity to ancient stone monuments.The rotational velocity of the
Earth at its equator which determines how far things on the Earth surface travel over time, is:
1.
Where is the Earth’s radius and is its rotational frequency. We can write this
2.
3.
Because
4.
This means that
5.
because the rotational angular momentum of the Earth is given by
6.
Which is derived from the moment of inertia, :
7.
8.
9.
v
rot
= (2 π R
e
)( f
e
)
R
e
f
e
v
rot
=
M
e
R
e
M
e
R
e
(2 π R
e
)( f
e
)
v
rot
=
(4/5)π M
e
F
e
R
2
e
M
e
R
e
⋅
60
24
4
5
⋅
60
24
= 2
v
rot
=
L
earth
M
e
R
e
⋅
60
24
L
earth
= (4/5)π M
e
F
e
R
2
e
I
I =
2
5
MR
2
L = Iω
ω = 2π f
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This is interesting in equation 5 having the ratio 60/24 because it suggests we use the ancient Sumerian
method of dividing-up the rotation of the Earth to measure time, and this method gives us the unit of a
second we have today which I will show is the characteristic time of a wave solution for the solar system
and the atom’s proton. Our base unit of time that we have today came from the ancient Sumerians having
divided the Earth’s rotation period (an earth day) into 24 units that we today call hours. The ancient
Babylonians further used the the ancient Sumerian’s system of base 60 counting to divide the hour into 60
minutes, and each minute into 60 seconds, giving us the duration of our base unit of a second that we have
today. It is further interesting that
10.
This is important because 2.5 megalithic yards (MY) are recurrent throughout Stonehenge and other
megalithic sites in Europe. The megalithic yard is a proposed ancient unit of measurement, approximately
0.829 meters that was suggested by the Scottish engineer Alexander Thom in the 1960’s. He derived it
from his survey of Neolithic stone circles, standing stones, and other megalithic structures in Britain and
Brittany. Also, 2.5 occurs in the moment of inertia, , which is the rotational analog to linear mass. For a
solid sphere it is equation 7:
And it is the reason that the 2 in 4/5 commutes to the giving the circumference of the Earth in the
above equations 2 and 3 for the velocity at the surface of the Earth equator leaving 2/5 which is the 24/60
of the Sumerian counting that gave us a second. This connects ancient megalithic sites (2.5 MY) to the
idea that there is a connection between gravity
11.
and rotational resistance
12.
I have found that one second is the characteristic time that describes the solar system and proton in
common in a wave solution for the the Earth/Moon/Sun system. Let’s go into that a little bit, then pick
this up again…
The Theory
We begin with the characteristic time for our solution is one second and is given by the mass of the moon,
, cubed:
13.
Yes, it does happen to be one second, our base unit of time we have today, ultimately given to us by the
ancient Sumerians when they invented mathematics thousands of years ago. This becomes important, as
we will see. The other extraordinary thing we find is that the Planck-type constant for our solar system
60
24
=
5
2
= 2.5
I
I =
2
5
MR
2
π
2 π R
e
F ∝
1
r
2
I ∝ r
2
M
m
ℏ
2
⊙
GM
3
m
⋅
1
c
= 1secon d
ℏ
⊙
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is given by the kinetic energy of the Earth, the third planet where life is extraordinarily abundant,
multiplied by one second.
14.
We find our equations hold so well when the Earth day is about what it is today (24 hours long) giving a
characteristic time of close to one second in terms of the kinetic energy of the Moon and the Earth:
15.
I also find that this characteristic time of one second is characteristic of the proton, the most fundamental
unit that makes up matter, predicting its radius:
16.
17.
Where and are the radius and mass of a proton. Equating these two gives about the radius of a
proton:
18.
This is very close to the value upon which the proton radius converged historically by two independent
methods which was 0.877E-15m. The result from our theory is
19.
The 0.877fm was challenged in 2010 by a third experiment making it 4% smaller and was 0.842E-15m. I
suggest it may be that the radius of a proton is actually
20.
utilizing an optimization characteristic of the golden ratio, as Nature often does, where is the
golden ratio. The most recent value is 0.833E-15m. In this case we say
21.
Where equation 17
ℏ
⊙
= (1secon d )K E
e
K E
m
K E
e
(Ear th Da y) = 1.1 − 1.3secon d s
(
1
6 α
2
4πh
G c
)
⋅
r
p
m
p
= 1secon d
2
3
⋅
π r
p
α
4
G m
3
p
1
3
⋅
h
c
= 1secon d
r
p
m
p
r
p
=
2
3
⋅
h
cm
p
r
p
=
2
3
⋅
6.62607E − 34
(299,792,458)(1.67262E − 27)
= 0.88094E − 15m
r
p
= ϕ ⋅
h
cm
p
= 0.816632E − 15m
ϕ = 0.618
ϕ ⋅
π r
p
α
4
G m
3
p
1
3
⋅
h
c
= 1secon d
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is a little over a second, and 21
is a little under a second. The proton doesn’t have a precise size, but is fuzzy like a cloud of subatomic
particles. It can have a functional radius depending on the Nature of the problem, which determines the
definition of what its radius is.
The ancient Sumerians were responsible for giving us the unit of a second because they divided the
earth’s rotation period, its day, into 24 hours, and the ancient Babylonians divided each hour into 60
minutes, and each minute into 60 seconds from the ancient Sumerians base 60 mathematics. Perhaps the
most exciting equation in our theory is:
22.
Where is the rotational angular momentum of the Earth. This specifies not only that the rotation
period of the Earth is best measured by dividing the day into 24 units and 60 units, but that such an
optimization includes the mass and radius of the Earth. Another exciting equation in our theory is that
during the time in the Earth’s history when the day is about 24 hours which specifies close to a second
from the kinetic energies of the Earth and Moon, the Moon perfectly eclipsing the Sun as seen from the
Earth, holds:
23.
is the orbital radius of the Earth, is the orbital radius of the Moon, is the radius of the
Sun, and is the radius of the Moon. The Moon makes life so successful on Earth because it holds
the Earth at its inclination to its orbit around the Sun, preventing temperature extremes and allowing for
the seasons.
The Schrödinger Wave Equation must be solved to determine the energies and orbitals of the electron in
the hydrogen atom. In spherical coordinates it is
24.
It has the solutions
2
3
⋅
π r
p
α
4
G m
3
p
1
3
⋅
h
c
= 1secon d
ϕ ⋅
π r
p
α
4
G m
3
p
1
3
⋅
h
c
= 1secon d
L
earth
ℏ
⊙
24 = 60
L
earth
r
planet
r
moo n
=
R
star
R
moo n
r
planet
r
moo n
R
star
R
moo n
−
ℏ
2
2 m
[
1
r
2
∂
∂r
(
r
2
∂
∂r
)
+
1
r
2
sinθ
∂
∂θ
(
sinθ
∂
∂θ
)
+
1
r
2
sin
2
θ
∂
2
∂ ϕ
2
]
ψ + V(r)ψ = E ψ
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25.
26.
I find the solutions are for the Earth orbiting the Sun are:
27.
28.
is the solar radius, that of the Moon. For Earth , third planet. Because these have accuracies
close to 100% accurate we know that our equation for the solar system Planck constant is correct,
equation 14:
The Value of the Solar System Planck Constant
Let us now compute the value of and show that the units work…
Where from equation 17
Where is the radius of a proton, is the mass of a proton, is the speed of light, and is the fine
structure constant. We found this gives the characteristic time of one second in terms of a proton. We
guess the planetary scale is connected to the proton scale because the planets formed from the
protoplanetary disc and it is made of different combinations of protons. We derive the value of our solar
Planck constant:
=
E
n
= −
Z
2
(k
e
e
2
)
2
m
e
2ℏ
2
n
2
r
n
=
n
2
ℏ
2
Z k
e
e
2
m
e
K E
e
= n
R
⊙
R
m
⋅
G
2
M
2
e
M
3
m
2ℏ
2
⊙
r
n
=
2ℏ
2
⊙
GM
3
m
⋅
R
⊙
R
m
⋅
1
n
R
⊙
R
m
n = 3
ℏ
⊙
= (1secon d )K E
e
ℏ
⊙
ℏ
⊙
= (hC )K E
e
hC = 1secon d
C =
1
3
⋅
1
α
2
c
2
3
⋅
π r
p
G m
3
p
r
p
m
p
c
α
C =
1
3
⋅
1
α
2
c
1
3
⋅
2 π r
p
G m
3
p
1
3
⋅
18769
299792458
1
3
⋅
2 π (0.833E − 15)
(6.67408E − 11)(1.67262E − 27)
3
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=
=
=
Returning To Angular Momentum, Quantum Gravity, And Ancient Megalithic Sites
The outer circle of the ancient stone observatory, Stonehenge, is 110 meters in diameter. If the velocity of
the Earth at its equatorial surface is
24.
Then, at Stonehenge it is
25.
since Stonehenge is at a latitude of 51 degrees. This is the velocity at which the stones at Stonehenge
move with the rotation of the Earth that determines the position of the Sun in the sky. Divide this by the
110 meter diameter of Stonehenge and we have
26.
is the number of megalithic yards recurrent throughout Stonehenge. The ancients could have measured
the second with their heart beat, which is about 1 second. And a pendulum, with length of one megalithic
yard does one swing in about a second.
The Planck constant has units of angular momentum ( ) and in quantum
mechanics the orbital angular momentum is where n is the orbital number, meaning it is
1.55976565E 33
s
m
m
kg
3
⋅
s
2
kg
m
3
=
s
m
s
2
kg
2
m
2
=
s
m
⋅
s
kg ⋅ m
=
1
kg
⋅
s
2
m
2
1
C
= kg
m
2
s
2
=
1
2
mv
2
= en erg y
hC = (6.62607E − 34)(1.55976565E 33) = 1.03351secon d s ≈ 1.0secon d s
hC =
(
kg
m
s
2
⋅ m ⋅ s
)
(
1
kg
⋅
s
2
m
2
)
(
kg
m
2
s
)(
1
kg
⋅
s
2
m
2
)
= secon d s
K E
earth
=
1
2
(5.972E 24kg)(30,290m /s)
2
= 2.7396E 33J
ℏ
⊙
= (hC )K E
earth
= (1.03351s)(2.7396E 33J ) = 2.8314E33J ⋅ s
v
rot
=
L
earth
M
e
R
e
⋅
60
24
= 464.5975m /s
v
rot
= (465m /s)cos(51
∘
) = 292.38m /s
292.38m /s
110m
(1secon d ) = 2.65 ≈ 2.5
ℏ
Joule ⋅ s = k g ⋅ m
2
/s
L = mvr = nℏ
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quantized in terms of integer multiples of and fundamental particles have spin, like that of an electron is
which means that angular momentum is fundamental to quantum structure just as gravity is
fundamental to spacetime. At the Planck length , quantum gravity effects dominate, since
this is described in terms of of angular momentum in quantum mechanics, G of gravity, and c of
relativity we say at this length spacetime may have a granular, quantized structure, so it follows spin
networks could define spacetime geometry for a unified field theory. This one is called Loop Quantum
Gravity. If spacetime has a moment of inertia it is said that
Where
is the the Planck frequency. No complete theory yet reconciles general relativity with quantum mechanics
but the duality is a hint. Experiments like GINGER are aiming to test this but it is thought angular
momentum is the missing link between quantum mechanics and gravity. I think from my wave solution
we may be able to find what I found about the Solar System (governed by gravity), like
might tell us something about quanta, like the atom’s proton in
It may be that this is an abstract problem that exists in both the problems between quantum mechanics and
gravity and the problems between stone alignments in ancient observatories such as at Stonehenge and
that our ancient ancestors solved with the 2.5 megalithic yards. I say this because we found in this paper
that
Where
ℏ
(1/2)ℏ
l
p
= ℏG /c
3
ℏ
I
spacetime
∼ ℏ/ω
Planc k
ω
Planc k
∼ c
5
/ℏ
5
G
r
2
ℏ
2
⊙
GM
3
m
⋅
1
c
= 1secon d
ℏ
⊙
= (1secon d )K E
e
(
1
6 α
2
4πh
G c
)
⋅
r
p
m
p
= 1secon d
ϕ ⋅
π r
p
α
4
G m
3
p
1
3
⋅
h
c
= 1secon d
v
rot
=
L
earth
M
e
R
e
⋅
60
24
L
earth
ℏ
⊙
24 = 60
60
24
= 2.5
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The Author
