of 1 65

Ancient Aliens, UFOs, and Spacetime Operators

By!

Ian Beardsley!

of 2 65

Introduction

This book consists of three papers, two dealing with extraterrestrials and UFO’s, and one a

theory for reality that plays a role in the papers about extraterrestrials and UFO’s."

of 3 65

Contents

Interconnections In UFOlogy…………………………………………..4

Ancient Sumerians, Ancient Aliens, And UFO’s Today……………24

Solving the Atom and Earth/Moon/Sun System

with Spacetime Operators in Common…………………………..42

of 4 65

Interconnections In UFOlogy

Ian Beardsley

of 5 65

Even though my case number 67958 was concluded by MUFON to be not a UFO but a “bat” or

“bug” (Which I now agree with) does not matter, because something interesting unfolded that

does suggest the existence of an intriguing mystery. The latitude plus 40 degrees on earth may

be a gateway to the future. This is the path traveled by the star Vega.

of 6 65

She had seen flying saucers, real ones, and their sub-craft and captains; she had even seen

great holes in the earth where the rest of us see nothing but solid ground.

Two Dogs, Grandma Crow

of 7 65

The Mathematical Construct

This project lay dormant for several years, but upon watching the movie Stargate last night, I

solved it.

of 8 65

On the early evening of July 9, 2015 in Claremont, California I stood in my backyard and

pointed the camera nearly due west about 25 or 30 degrees high. As I was filming I noticed the

brief appearance of a black spot. I brought my camcorder into the house and downloaded the

footage to my computer and found the spot, for which I removed a frame, and dropped it on my

desktop for analysis. I thought it could best be described as a “black orb”, and I reported the

image to MUFON (The Mutual UFO Network). To my amazement, the number assigned to my

case was 67958. That is, my case was the sixty-seven thousand nine-hundred and fifty-eighth

case to be reported. This interested me because those digits could be arranged as the consecutive

integers 5, 6, 7, 8, 9. Thinking about it now I realize those are the perfect consecutive integers

for an ET to use in communicating, because they contain the integers of alpha squared. Alpha is

the fine structure constant, which is 1/137 a number scientists find to mysteriously occur again

and again in the their mathematical formulations of Nature. Alpha squared is

The fine structure constant squared is the ratio of the potential energy of an electron in the first

circular orbit to the energy given by the mass of an electron in the Bohr model times the speed of

light squared:

It is only missing the five in the consecutive integers 5,6,7,8,9.

= 1/18769

of 9 65

I immediately decided that case 67958 being a long-shot number to receive, that whoever was

assigned the case number 56789, the numbers for my case arranged in successive order, had

experienced an even more unlikely occurrence than myself. Since MUFON makes their cases

available to the public, I looked up that case number. It was at 10:17 PM in Utah. As a person

who has worked in astronomy, and is familiar with the famous SETI Wow! Signal, I recognized

that the time of sighting case number 56789 was at the same time. The SETI Wow signal was a

signal intercepted by SETI (The Search For Extraterrestrial Intelligence) that had all of the

earmarks of being of non-human intelligent origins. I then looked at a map of Utah and to my

amazement noticed that the center of that state was a city called Nephi. I knew that Nephi meant

Nephilim, and, that Nephilim was Hebrew for Anunnaki which translates as “Those who came

from above” in the Hebrew bible and Anuannaki is the beings spoken of in ancient

Mesopotamian (Sumerian) Cuneiform clay tablets who the Sumerians said in these most ancient

human writings, gave us mathematics, schools, government, and agriculture.

of 10 65

The Certificate For My Case, Case 67958

Case 56789 as it Appears in The MUFON Files

of 11 65

In the Bible “Nephilim” is actually translated as “Giants” It was Zecharia Zitchin who when

when he was a student in Russia in Bible class raised his hand and said doesn’t Nephilim

actually translate as “Those who came from above.” I resolved this by asking a Yiddish scholar

why it was translated like this. He told me because those who came from above were giants.

Zecharia Sitchin went on when he grew up to translate Sumerian cuneiform and write the book

“The Twelfth Planet” where he said Nephilim in the Bible came from Annunaki in the Sumerian

cuneiform tablets of Mesopotamia. The Sumerians there are credited with being the first to

settle down from wandering, gathering, and hunting and invent agriculture, science, and

writing. It is believed the idea spread out from there, Sitchin says they were taught these

sciences by the Annunaki who came from the sky.

I then noticed some interesting things about the city of Nephi at the center of Utah. That to the

right of it was Wyoming, which has in it Devils Tower which is where in the movie “Close

Encounters of the Third Kind” humans make contact for the first time with extraterrestrials.

Devils Tower is a national monument, a mountain of rock that is flat on top making it perfect for

the landing pad of extraterrestrial spacecraft. To the left of Nephi is Nevada where the secret

military base Area 51 is where people have long believed houses extraterrestrials and a program

where we are working with them to back-engineer their craft. Below Nephi is Roswell New

Mexico, where it was purported that a UFO crashed in 1947 and three alien bodies were found

about three feet tall each. It was later believed to be covered-up by the military as the debris of a

weather balloon. However, the military official holding the weather balloon in the newspaper

photo was holding a note in his hand that with the advent of modern computers much later,

people were able to enlarge and read some of, which did mention a crashed disc and and three

bodies about three feet tall. Later around 2012 to 2014, because of the freedom of information

act, a memo was released to the public, and it did say there were three bodies about three feet

tall and the debris of a crashed disc. I remember when that came out in mainstream media and I

find it strange that today, even though there has been full disclosure, that Roswell is spoken of

only as a theory by UFO enthusiasts. I then placed stars at these locations and found it made a

cross with the top portion missing. I calculated the top portion of the cross formed by using the

golden ratio and found it to be around the Oregon-Idaho border in a place where the three

major rivers of the Northwest converge, called Treasure Valley near the city of Nyssa. I had the

following map:

of 12 65

As you can see I placed a star at the center of Wyoming because Wyoming is where Devils Tower

is. But we can place a star exactly where Devils Tower is, which is in the North-East corner of the

the state. We can also place a star to the East of Area 51 in California at the largest city, which is

Los Angeles, and we get an expanded cross as pictured below…

of 13 65

Interestingly we see that that the Nephi-Roswell axis points to NASA’s mission control in Texas,

as pictured below….

of 14 65

of 15 65

For the longest time this project remained dormant because I couldn’t figure out the significance

of a cross, since 2009, but just last night I solved it when I was watching the movie Stargate. At

the beginning of that movie, an archaeologist solves the mystery of the six symbols plus one on

the Stargate. He explains that a location in space requires six points, each at the center of the

face of a cube, to specify it, and a seventh point to specify a destination. The six-points make a

cross that intersects at the location of the stargate and the seventh point is the destination where

you want to go, as pictured below..

Thus all I had to do was take the center of the cross as Nephi, get the coordinates of the city of

Nephi which are +39.7102 degrees North, 111.8363 degrees West and project the +39.7102

degrees north on to the sky, the seventh point, or destination. Positions of the stars are given

like this as projections of latitude onto the sky and longitude onto the sky, lattitude projected

onto the sky is called declination. It is fixed, but longitude onto the sky changes as the earth

rotates and is measured in right ascension (RA) which is in hours, minutes, and seconds. 1 hour

of right ascension is 15 degrees because the earth rotates through 15 degrees in one hour. Thus

we have a scenario where we have a latitude on the sky of declination approximately plus 40

degrees, and stars moving along it over the course of the night. Constellations that exist at or

near this declination are Aurigae, Cygnus, and the Summer Triangle to name a few. For our

drawing we will consider the Summer Triangle because it has the very bright star Vega the

brightest star at this declination. It is the brightest star in the constellation Lyrae with the

designation alpha-Lyrae, and is the fifth brightest star in sky, the missing number 5 in our fine

structure constant squared (alpha squared) that we talked about at the beginning of this paper.

We have the following drawing…

of 16 65

Vega: +38deg 47min 01sec

18hrs. 36min. 56 sec

of 17 65

Nephi couldn’t point to a more special star than Vega.

Vega is the fifth brightest star and the second brightest star in the Northern Celestial

Hemisphere after Arcturus. By astronomers it is called the next most important star after the

Sun. It was the pole star in 12,000 BCE and will be again in 13,727 due to the precession of the

Earth’s spin axis with a period of 25,770 years. Vega, being close and bright has been the

standard with which to compare other stars, it was the first star to have its distance determined

with the Ancient Greek method of parallax, and serves as the baseline for calibrating the

photometric brightness scale and was used to to define the zero point for the UBV photometric

system, a system used in astronomy to study brightness of stars, or variations in brightness.

The important thing here is that Vega is the polestar every 25,700 years which means it is the

star the Earth’s spin axis points to, which makes it useful for navigation, and the other

important thing is how often it does this because it was the pole star around 12,000 BC and

earlier meaning it had the important position during the time when the Ancient Sumerians

settled down from following the herds and inventing agriculture, science, mathematics, writing,

and architecture, which, as we said some theories believe this knowledge was given to them by

ancient aliens.

Polaris is the current pole star, meaning the Earth’s spin axis points to it. Like Vega, it is the

brightest star in its constellation Ursa Minor meaning it has the same alpha designation for its

catalog name Alpha Ursae Minoris, the same alpha that belongs to Vega, the same alpha of the

the Greek letter , that is the natural constant constant the has the numbers of our UFO

MUFON case number 56789. As well like Vega it is very studied for the same reason: it defines

the standard for studying other stars. Just like Vega is a standard for the Ancient Greek method

of determining distances, parallax, Polaris is used to measure distances by the method of

cepheid variables, as it is the closest cepheid variable to us, which is a star that varies in

brightness with a regular period due to radial pulsations. The brightness of this star is reported

to have changed a hundred times since it was first measured by the Ancient Greek astronomer

Ptolemy, which means in astronomy this star goes against everything we know about stars of

this type. The fact that it switches roles with our Nephi star as pole star and that something

unusual is going on with it physically might be a clue as to why it is so important with respect to

our work here.

The most important thing we want to accentuate here is that Vega and Polaris switch places with

one another as pole star every 25,722 years, and that the transition for Vega to Polaris in this

role was at the time hunters following the herds settled down to create civilization.

Whether or not Area 51 is back-engineering extraterrestrial craft, or whether it was a flying disc

that crashed in Roswell or a weather balloon doesn’t matter; the events that unfolded lead to a

very elegant construct so unlikely that one should be easily inclined to think that something is

happening here, though we just can’t say what.

of 18 65

I would like to note here that just as Vega passes over Nephi, and travels along the 40 degree

latitude projected onto the sky, that it also then passes through other countries and cities at or

around the 4o degree North latitude. In Europe these are Madrid, the capitol of Spain, Rome,

the capitol of Italy, and Athens the Capitol of Greece. See the illustration below…

We can make a broad historical sweep to see what this means; Geometry and Astronomy are

founded in Ancient Greece around 300 BC. These thinkers surmise the Earth is round, and even

develop a method to determine its circumference. This obscure knowledge makes its way into

the hands of an Italian explorer, Christopher Columbus some 1600 hears later. He suggests if

the Earth is round then we can establish a Westerly route to India as another option for a trade

route with the country. He needs the funding for such a voyage, and this is given to him in Spain

by Queen Isabella and he lands in the Bahamas in October 1492 calling it San Salvador, and the

New World was discovered. He thought he had landed in India and that is how the natives of the

New World got the name Indians.

Now we are not just an ocean faring civilization, but a spacefaring civilization. The astronomer

Carl Sagan wrote in Cosmos:

The surface of the Earth is the shore of the cosmic ocean

From it we have learned most of what we know

Some part of our being knows this is from where we came

We long to return

These aspirations I think are not irreverent

Though they may trouble whatever Gods may be

Now we have the Wow! Signal, founded on a method of search for the frequency of 1420

megahertz or the 21-centimeter spectral line in other words because it is naturally emitted by

hydrogen. The equation is the Rydberg equation for hydrogen:

But our message in this paper comes from hydrogen as well, from alpha squared, the fine

structure constant squared, The fine structure constant squared is the ratio of the potential

energy of an electron in the first circular orbit of a hydrogen atom to the energy given by the

mass of an electron in the Bohr model times the speed of light squared:

= R

(

−

)

of 19 65

Gobekli Tepe

The world’s oldest megalithic site is Gobekli Tepe in South Eastern Anatolia, Turkey it marks the

oldest known human settlement. Gobekli Tepe first noted in a survey in 1963 was designated a

UNESCO World Heritage site in 2018 the year the movie Stargate was released. We have said

that astronomy and geometry start in Ancient Greece, at our 40 degree latitude and that this

knowledge travels West 1600 years later to Italy at the same latitude sparking a voyage funded

by Madrid, Spain which leads again to the same latitude, the Vega latittude, at Nephi, United

States of our message involving the next great adventure, space voyages; we landed on the

Moon in 1969. It turns out Anatolia is at the same latittude. This seems to be one of the regions

where settling down from wandering and gathering and living in settlements began. Vega passes

overhead here and takes the idea to Greece, then Italy, then Madrid, then Nephi, Unites States.

Gobeckli Tepe dates back to 9500 BCE to 8000 BCE, the so-called Neolithic.

The megalithic structures at Gobekli Tepe includes stone pillars with anthropomorphic symbols

Apparently, the first known written word for God appears at Gobekli Tepe according to a 2019

paper by Manu Seyfzadeh and Robert Schock titled “World’s First Known Written Word at

Gobekli Tepe on T-Shaped Pillar 18 Means God”. Apparently the Luwians adopted symbols from

Anatolian iconography and they have an identical symbol for God. At Gobekli Tepe there is also

a symbol for Gate that is the same as the Luwian symbol for the same. The interesting thing is

that the word for God and the word for Gate look almost the same (Howard Barry Schatz, 2022).

We might venture to think then, that the Gate for humanity is along the 40 degree latitude

traveled by Vega that takes us from Anatolia to Greece to Italy to Spain to Nephi United States.

The Symbol for Gate is two parallel vertical lines with a horizontal line between them and

semicircles on either side, while the one for God does not have the horizontal line, as if to depict

an “Open” gate (Howard Barry Schatz, 2022). Here I have done sketches:

= 1/18769

of 20 65

The Initial Cause

We have said that astronomy and geometry start in Ancient Greece, at our 40 degree latitude

and that this knowledge travels West 1600 years later to Italy at the same latitude sparking a

voyage funded by Madrid, Spain which leads again to the same latitude, the Vega latitude, at

Nephi, United States of our message involving the next great adventure, space voyages; The

United States landed on the Moon in 1969. It turns out Anatolia is at the same latitude. This

seems to be one of the regions where settling down from wandering and gathering and living in

settlements began. Vega passes overhead here and takes the idea to Greece, then Italy, then

Madrid, then Nephi, Unites States. We have said that megalithic structures at Gobekli Tepe

include stone pillars with anthropomorphic symbols, the first known written word for God. That

the word for God and the word for Gate look almost the same. That, the first known written

word for God appears at Gobekli Tepe, that the Gate for humanity is along the 40 degree latitude

traveled by Vega that takes us from Anatolia to Greece to Italy to Spain to Nephi, United States.

We can now go further; we can look for the cause of this effort by the Italians, funded by Spain,

brought about by Greece to find a Westerly route to India. It actually began in China, as we will

now show…

The Silk Road was a network of trade routes used from 200 BCE until the mid 15th century

joining the East and West, spanning 6,400 kilometers (4,000 miles).

The network (also called the Silk Routes) began with the Han dynasty’s expansion into Central

Asia around 114 BCE. It began when the envoy Zhang Qian was commissioned to explore the

unknown lands beyond to establish trading partners and allies.

The bridge between the East and west came with the Parthian Empire (Persian tribes) stretching

from Anatolia (in Turkey) to what is today Afghanistan. By 100 BCE Chinese silk was sought by

Rome, Egypt, and Greece as well as tea, dyes, perfumes, and porcelain. Western exports were

horses, camels, honey, wine, and gold. Few people travelled the entire route but rather relied on

a succession of middlemen stationed along the routes. An exchange of ideas in religion

(particularly Buddhism) and in the sciences came with the trade.

The Silk Road abruptly ended with the rise of the Ottoman Empire in 1453 severing the trade

between the East and the West. This resulted in what became known as the Age of Discovery,

European Colonialism, and globalization efforts. Thus we see our path of Vega that traces our

gateway to the future began with the Silk Road which arose from the desire for business and

trade between the East and West, arguably centered around silk and tea.

of 21 65

The Extended Map

As we said, Vega, the most important star in the sky passes over Turkey at the site of Gobekli

Tepe where we have the oldest written word for God found and is certainly one of the oldest

references to God, which happens to be similar to a reference there for gate. Vega continues to

Greece one of the places where astronomy and mathematics originates with the knowledge of a

round earth that makes its way to Italy 500 years later and inspires Columbus to find a westerly

route to India, who gets funded by Spain, also on the path of Vega, which ultimately goes to the

New World in Nephi, of the New World where Columbus actually lands discovering it, and

Nephi means those who came from above in the Old Testament. Now in our story we continue

along the path of Vega across the Pacific and we land in Japan, a leader in technology, and from

there Vega goes to China, which has one of the most ambitious space programs in the world.

The latitude of +40 degrees through which Vega passes in the center of China near Xining, the

capital of Qinghai Province. Xining was a commercial hub along the Northern Silk Road’s Hexi

Corridor for 2000 years, it has a history of over 2,100 years. It also is a site of religious

significance to Muslims and Buddhists with Mosques and Monasteries and is the home of

Qunhai University, a Double first class University.

The +40 degree latitude also is the Island of Honshu, Japan, Japan’s largest and most populous

island where the capitol of Tokyo is. Humans first arrived here 60,000 years ago.

The latitude of +40 degrees through which Vega passes in the center of China near Xining, the

capital of Qinghai Province. Xining was a commercial hub along the Northern Silk Road’s Hexi

Corridor for 2000 years, it has a history of over 2,100 years. It also is a site of religious

significance to Muslims and Buddhists with Mosques and Monasteries and is the home of

Qunhai University, a Double first class University.

The +40 degree latitude also is the Island of Honshu, Japan, Japan’s largest and most populous

island where the capitol of Tokyo is. Humans first arrived here 60,000 years ago.

of 22 65

A great deal has unfolded for me regarding Roswell and Area 51. I just learned about

Rendlesham, and how it was the European Roswell (UFO event). Interestingly my work

Contacting ET continues now looking at Rendlesham. If you draw a line from Rendlesham by

connecting it with Stonehenge the ancient Druid Observatory and continue it West at the slope

provided by these two points, the line goes straight through Roswell. See the maps below:

of 23 65

I solved the riddle, the following drawing explains it:

of 24 65

Ancient Sumerians, Ancient Aliens, And UFO’s Today

By!

Ian Beardsley!

of 25 65

Abstract

After developing a a single theory for atomic systems and planetary systems, I have found that

the unit of a second for measuring time, which ultimately came to us from the Ancient

Sumerians, who ﬁrst settled down from following the herds and hunting with stone spearpoint to

invent writing, mathematics, agriculture and metallurgy along the Tigris and Euphrates rivers of

Mesopotamia, is a Natural constant.

There has been some suggestion by many scholars that, since this invention of civilization by

the Sumerians happened mysteriously almost overnight on an archaeological time scale, that

they were given knowledge by Ancient Aliens.

I am able to suggest that traces of such Aliens may exist in ancient records and contemporary

UFO sightings, and that the two are connected. I show this connection may be rooted in the

idea of the unit of a second for measuring time as a Natural constant, that it is a basis unit for

describing atomic systems, planetary systems, and biological systems in common.

of 26 65

Introduction !

I developed a theory that solves both the atom and the solar system in terms of a base unit of

1 second and quantization of the system with the Earth’s moon. When working out the theory

the base unit of time came out to be 1 second, and I thought that was rather incredible

because the second came to us ultimately from the Ancient Sumerians who mysteriously

settled down from hunting with stone spearpoint and inventing agriculture, mathematics, and

astronomy, but we would hazard to guess they didn’t know about a wave equation solution for

the solar system or the radius and mass of the atom’s proton, let alone of the proton itself, that

all came much later with modern science.!

What was even more compelling was that this unit of a second occurred in many forms in

terms of many diﬀerent things in the theory. I found:!

Where is the kinetic energy of the Moon, is the kinetic energy of the Earth, is the

ﬁne structure constant is 1/137, is the rotation period of the Earth 24 hours, is

Planck’s constant, is the universal constant of gravitation, is the speed of light, is the

radius of the proton, is the mass of a proton, is a wavelength associated with the

Moon in the theory, is the mass of the Moon, is the mass of the Earth, is the mass

of the Sun, is the diameter of the Earth’s orbit, is the orbital velocity of the Moon, and

is the orbital velocity of the Earth, 3 is the Earth orbital number.!

I will leave how I arrived at all that and the theory for that to my paper “Solving the Atom and

Earth/Moon/Sun System with Spacetime Operators in Common” which is the third part of this

book. For now I would like to go into the theory that we may have ultimately got our unit of a

second for measuring time from ancient aliens who may have given it to the Ancient Sumerians

1secon d =

(Ear th Day)

(

6α

4πh

)

⋅

= 1secon d

⋅

πr

⋅

= 1secon d

moon

= 1secon d

1secon d = d

⊙

Ear th Day

moon

⊙

of 27 65

who started civilization, the Ancient Sumerians from whom we got writing, mathematics, and

agriculture.!

We have the unit of a second today because the Ancient Sumerians had a base 60 system of

counting (sexagesimal it is called). The Sumerians divided the day into 12 hours, evenly

divisible into 60, and so from sunrise to sunrise was 24 hours, and from sunset to sunset was

24 hours. They multiplied 60 by 6, to get 360 degrees in a circle. Since the Earth does one

orbit around the Sun in 365 days, which is a year, the Earth goes through about 1 degree a day.

The Babylonians got that from them, and further divided the hour into 60 minutes, and the

minute into 60 seconds, though hours were in their sun dials, they only used minutes and

seconds for astronomy. The West, the Europeans, got their sun dials from the Babylonians but

did not incorporate minutes and seconds into their mechanical clocks until the 17th century,

but it all came from the Sumerians, who settled down from hunting with stone spearpoint and

started agriculture, writing, mathematics, and civilization in general. Sun dials were used in

Egypt as well and had 12 divisions throughout the day as well for hours. A sun dial simply tells

time by the angle of a shadow cast by the Sun as the sun rises and sets, its position measuring

time.!

The interesting thing is that we have the duration of a second is what it is not because we were

attempting to find some base unit of time for Nature, but rather we have the duration of a

second from ancient times that came to us over many years of dividing the rotation of the Earth

into hours, minutes, and seconds in such a way that we ended up with it. However we may have

had some sort of a thought going into it that was six-fold in Nature that lead it to being natural if

we consider:

And that thought may be was in a six-fold pattern that the motions of the Earth/Moon/Sun

system had in it approximately which we inadvertently characterized in the calendar:

Which can be written

Where there are 360 degrees in a circle and as such the Earth approximately moves through one

degree per day around the Sun. We achieved this because the ancients of Sumeria and Babylonia

from which the ancient Greeks received their counting system used base 60, sexagesimal

because 60 is evenly divisible by so much, that is by

1,2,3,4,5,6, 10, 12, 15, 20, 30,…

My Guess That Panned Out

I thought we might want to look for clues in present times for the possibility of aliens who may

still be coming here, in the reports of UFO’s.

1secon d =

365.25

⋅

= 0.0000000316881year

(

360d a ys

year

)(

24h ours

d a y

)(

60min

h our

)(

60sec

min

)

= 31104000secon d s /year

(

60d a ys

year

)(

1h our

d a y

)(

60min

h our

)(

60sec

min

)

of 28 65

I have undertaken this, and thought what a better way than to look at how we measure the

ancient second with modern clocks. The ancients did it with the position of the Sun in the sky

which comes from the rotation of the Earth, that turns once in 24 hours giving us the length of

the day, but that is not a very precise way to do it because the rotation of the Earth can waver in

its period due to gravitational influences from other bodies in the solar system, like the Moon,

the Sun, and the planets.

We started with sun dials in ancient times, moved to gear ratios for clocks in medieval and

renaissance Europe, but in contemporary times we moved to oscillators, like the quartz crystal

oscillators in digital wrist watches, which is much more accurate. After that we got more

accurate with atomic clocks that make use of cesium. Quartz crystals and Cesium both occur in

Nature, and we mine them for making clocks.

In the 1980s the advent of solid-state digital electronics allowed for quartz timekeepers and

these are the mostly widely used today in most clocks and watches. If a quartz crystal is

appropriately shaped it will oscillate at a frequency of 32768 Hz, that is, 32768= oscillations

per second. Thus we began to define the second as that many oscillations of a quartz crystal.

Of course, over a year, a watch made from quartz crystals might lose a second or two over a year,

and more accurate is an atomic clock using cesium 133, the only stable isotope of cesium. The

second is now defined by 9,192,631,770 cycles of oscillations of the cesium atom.

Thus the first place I looked in hopes of finding clues to the existence of extraterrestrials,

extraterrestrials who may have given us the second in ancient times, was where cesium is found

and mined. It turns out it is a rare element and its most abundant deposits are in the province of

Manitoba in Canada, a place called Bernic Lake, in its South East corner. I then looked for UFO

sightings in Manitoba, and to my surprise found the most well documented UFO sighting in

Canada was there at Falcon Lake near the capitol Winnipeg which is right near Bernic Lake

where Cesium for clocks to define the second is primarily mined.

Interestingly, the Falcon Lake UFO sighting was in 1967 (May 20), the year we defined the

second with the cesium atomic clock, and was right near Bernic Lake where the cesium is

primarily mined. It involved a ship landing and a geologist that saw it, and approached it, Stefan

Michalak, who was hiking there looking for quartz deposits of all things, to stake a mining claim.

I thought perhaps the extraterrestrials were in the area looking for cesium, or quartz (which

occurs there as well) for their ship clocks.

To see the proximity of Falcon Lake of the UfO sighting, and Bernic Lake where Cesium is

primarily mined, to one another, and with the capitol of the province of Manitoba, go to the

maps on the next page…

of 29 65

The Falcon Lake UFO Incident

Just how did the Falcon Lake UFO incident unfold? Steve Michalak was out inspecting a quartz

vein when he he saw two objects hovering 45 meters (150 ft) away from him glowing red. One

of the objects landed nearby and took on a disk shape. The other craft ﬂew off. Before

approaching the craft Steve sat and drew it for half an hour. He noticed the craft lacked any

seams and had no insignias, and looked like smooth metal. It was 10.5 meters (34 ft) in

diameter, and 4.5 meters in height (15 ft).

He noticed a door was open with light coming out, and heard voices of people talking. He

attempted to communicate with them in English to offer mechanical support, but they did not

respond and he tried in Polish, Russian, and German to no avail. He touched the craft and the

ﬁngertips of his gloves melted, it was so hot.

of 30 65

The craft then rotated revealing a grid of holes that emitted a blast of heated gas that hit him in

the chest, setting his clothes a ﬁre, which he took off and the craft ﬂew away. After returning

home he sought medical attention at Misericordia Health Center for his injuries and nausia

where he was admitted to the emergency room. His injuries were conﬁrmed by the doctors, with

gridline burns on his chest and stomach. It was conﬁrmed he had radiation poisoning. He was

never convinced he saw a UFO that was alien but rather an experimental aircraft. The incident

was investigated by the Royal Canadian Mounted Police, the Royal Canadian Air Force, The

Department of Health, Department of National Defense, and American authorities the Aerial

Phenomena Research Organization and the United States Air Force as a part of the Condon

Committee. That is just a brief synopsis so I will leave the detailed story to books on the subject.

Cesium Clocks And the Ancient Constant of Nineveh

All that remains to be done now is to connect the Ancient Sumerians with modern cesium

atomic clocks that now deﬁne the unit of a second. It may seem a daunting task, but it can be

done.

The Ancient Sumerians who settled down in the Middle East (Mesopotamia) from following the

herds and hunting with stone spearpoints, to invent agriculture, mathematics, writing,

government, and metallurgy, did so almost overnight on an archaeological timescale and it has

been a mystery of archaeology just what caused this to happen.

Apparently, in their writing, cuneiform, which presses symbols into clay tablets with a stylus, the

Sumerians say they got their knowledge from “the Anunaki, those who came from above”.

According to Zecharia Sitchin, the word Nephilim in the Bible came from the Sumerians. Even

mainstream archaeology today says that the stories of the Bible had their origins in Sumerian

stories. Nephilim is Hebrew for “Those who came from above”, but it is translated as giants. I

asked a yiddish scholar why this is and he said it is because those who came from above were

giants.

Moving on, with the unearthing by archaeologists of the Assyrian civilization in current day Iraq,

and discovery of the palace and library of King Assurbanipal in Nineveh, we now had access to

some 30,000 Sumerian cuneiform tablets. Some of what was in them years later found their way

to NASA scientist, Maurice Chatelain, who oversaw the communications systems of the Apollo

missions to the Moon.

The language of Sumerian was decoded in 1846 by an Englishman, Henry Rawlinson, using

tablets with the same text inscribed in three different languages, thus breaking the code. In 1872

they were ﬁnally translated by the English Assyriologist, George Smith. Chatelain writes in his

book “Our Cosmic Ancestors”:

Among the tablets translated by Smith was a certain quantity that contained nothing but numbers,

fantastically huge numbers, apparently derived from complicated calculations…

I have not been able to ﬁnd out to this day when and where somebody decided to study these

mathematical tablets again, but the translation into our decimal system was ﬁnally published a few years

ago, and one number stood out. It consisted of ﬁfteen digits: 195,995,200,000,000…

I personally discovered the existence of the number in 1955,…

of 31 65

One day I remembered that the Sumerians, who were the ancestors of the Babylonians, who were in turn

invaded by the Assyrians, used calculations based on multiples of 60 more than 3,000 years ago. We still

do not know for sure who the Sumerians were and where they came from but we have found out that they

were truly great astronomers who knew the revolution periods of all the planets of the solar system,

including Uranus and Neptune…

They were the ones who divided the day into 86,400 seconds with 24 hours of 60 minutes of 60 seconds

each. Immediately the realization came to me that the number of Nineveh represented a very, very long

long period of time expressed in seconds!…

The thought ﬂashed into my mind that the clever Sumerians were familiar, among other things

astronomical, with the precession of the equinoxes — the turning of the terrestrial axis of rotation around

the pole of the ecliptic. This movement has a cycle of 9.540 million days or about 26,000 years.

…When I divided the Nineveh number by the cycle of the precession of the equinoxes, also called The

Big Year, I had the greatest surprise of my life! The sacred number of Nineveh divided exactly into 240 Big

Years of 9.450 million days each…

Then came my conclusion that this enormous number of Nineveh could very well be the long lost magic

number called the ‘great constant of the solar system’ the number that alchemists, astrologers, and

astronomers had been looking for for a very long time, while their ancestors were familiar with it more

than 3,000 years ago…

To put it short, Chatelain tested this and found the Nineveh constant was exact multiples of the

conjunction periods of all the planets.

This constant was the number I needed to suggest that the Ancient Sumerians got the unit of a

second, which came from their sexagesimal counting system, from extraterrestrials. I suggest

extraterrestrials, because the second I ﬁnd is a base unit that describes a quantum mechanical

solution of the solar system and the atom’s proton in common, as in the equations presented at

the beginning of this paper. In other words, the second might not be arbitrary, but a natural

constant. I can suggest this because we now deﬁne the second not with dividing up the rotation

period of the Earth, but with cesium atomic clocks, which started in 1967 the year Canada’s

most famous and well documented UFO landing was sighted, and that was sighted in one of the

only reserves of the rare element cesium that makes atomic clocks possible.

Here is how we do it. The Nineveh constant is 1.959552E14 seconds/cycle. The second is now

deﬁned as 9,192,631,770 cycles of the cesium atom per second. We have

A day has 86,400 seconds:

NinevehConstant

CesiumOscillations

1.959552E14

9,192,631,770

= 21,316.5507

sec

c ycle

21,316.55057

sec

c ycle

= 146.0018855

sec

c ycle

≈ 146

sec

c ycle

(

86,400

sec

day

)(

c ycle

146sec

)

= 591.7808

c ycle

day

≈ 592

c ycle

day

of 32 65

A year is 365.25 days, but this is a cycle of the Earth around the Sun so we have:

It is the golden ratio. But we have to take the square root to get the right units. A particular

approximation we have to is found in Ancient Egypt. While the Sumerians started civilization

that spread throughout the world, the Ancient Egyptians did the same at the same time

independently, but they were isolated by ocean mountains and desert so no one invaded them,

like Semitic tribes with the Sumerians. However, they did much similar to the Sumerians, like

dividing the day into 12 hours as well. And, there has been much theorizing that Ancient Aliens

gave them a great deal, like the pyramids, whose construction cannot be explained. Questions

remain how such large, heavy stones were cut, moved, and stacked to make them.

In Maurice Chatelain’s book “Our Cosmic Ancestors” Chatelain suggests the pyramids were

landing beacons for alien craft because they were polished, and reﬂective, and were ﬂat on top.

But, I would like to point out when Chatelain solves the mathematical proportions of the

pyramids he suggests it is because the ancient Egyptians approximated the golden ratio, ,

above in our cesium clocks and the constant of Nineveh, as and the pi ( ) the ratio of the

circumference of a circle to its diameter as . In the pyramids Chatelain had to reconcile

and with one another, which don’t reconcile exept in the Egyptian approximations to these

values above if we take the square root of , as we have to do above with . We

have for our cesium clocks with respect to the Nineveh constant as Chatelain suggests we have

for the pyramids:

So this all has to do with the number

So the Nineveh constant that the ancient Sumerians wrote down thousands of years ago at the

dawn of civilization not only describes the periodic motion of the planets, planets that during the

18th century at the birth of modern science we did not even know existed, which Maurice

Chatelain said divide evenly into it to four places after the decimal, not only does it do that, it

describes the oscillations of a cesium atom in its ground state that deﬁne a second, a second

that I have shown in theory is a natural constant at the basis of describing the planets and the

592

cycle

day

365.25

day

cycle

= 1.62

c ycle

day

≈ 1.618 = Φ

c ycle

day

196

121

c ycle

day

Φ ≈

196

121

= 4

Φ ≈

= 1.272727...

of 33 65

atom in common. And, it does so via the relationship between the golden ratio and pi that the

Ancient Egyptians used to construct their pyramids. In turn, this cesium, which is ideal for

making such clocks was in the end used to deﬁne the second more accurately and made the

standard in 1967 when one of the most well documented UFO landings was reported in detail,

with much evidence to back it up, near Winnipeg, the capitol of the Manitoba providence where

most of the Cesium is mined for making such clocks. The Ancient Sumerians have been a

mystery to archaeology, how they settled down from hunting with stone spearpoints to invent

writing, mathematics, metallurgy, and agriculture. Also mysterious are the ancient Egyptians,

who invented mathematics, writing and agriculture around the the same time as the ancient

Sumerians independently and separately, especially their enormous stone pyramids stacked

with enormous stone blocks to precise Mathematical dimensions that we cannot even ﬁgure

today how they could have been cut, transported, and lifted. Did the ancient Sumerians and

Egyptians get their start in inventing civilization from visitors from another world more advanced

than ourselves? Can we ﬁnd indications of the presence of such visitors in ancient and

contemporary times, and are there clues that show them to be the same people?

I also found that UFOs are prominent in Canada, and are most abundant in the Manitoba

providence where the cesium is mined. In fact most of their sightings are around the capital of

Manitoba, Canada Winnipeg near the cesium mines and the Falcon Lake UFO incident. A

Manitoba news station did a story on it saying Manitoba is a UFO hotspot, with most of the

sightings in Winnipeg, significantly. They reported the numbers of sightings in cities in

Manitoba up to 2016 when the story was released. They are:

Winnipeg 767, Carman 53, Brandon 45, Thompson 40, Sperling 36

I immediately knew to look to Manitoba, Canada after I learned cesium was abundant there

because Todd, who goes by the name of “Taken by the Greys”, said on Canadian radio that he

was abducted by grey aliens at lake Manitoba, and by a secret people in Black Suits. He said he

was the one who ﬁrst said there were men in black suits, and that it is from him that they got the

idea for the ﬁlm “Men in Black”, a science ﬁction movie about men and women who wear black

suits and oversee our relationships with extraterrestrials on Earth. Todd has a Youtube channel

where he has documented his abduction at Lake Manitoba, it goes by the name of Taken by the

Greys.

I have found that the basis unit of one second is not just a Natural constant for physical systems

like the atom and the planets around the Sun, but for the basis of biological life, that it is in the

sixfold Nature of the chemical skeletons from which life built, the hydrocarbons.

We return to a couple of the equations at the beginning of this paper…

The first can be written:

1secon d =

6α

⋅

4πh

1secon d =

K E

(Ear th Da y)

of 34 65

14)

15)

From which instead of saying the left sides of these equations are seconds, we say they are

proton-seconds by not letting the units of cancel with the bodies of these equations on the

left, which are in units of mass, but rather divide into them, giving us a number of protons. I say

this is the biological because these are the hydrocarbons the backbones of biological chemistry.

We see they display sixfold symmetry. I can generate integer numbers of protons from the time

values from these equations for all of the elements with a computer program. Some results are:

A very interesting thing here is looking at the values generated by the program, the smallest

integer value 1 second produces 6 protons (carbon) and the largest integer value 6 seconds

produces one proton (hydrogen). Beyond six seconds you have fractional protons, and the rest of

the elements heavier than carbon are formed by fractional seconds. These are the hydrocarbons

the backbones of biological chemistry. And carbon is the core element of life. We see the

duration of the base unit of measuring time, 1 second, given to us by the ancients, is perfect for

the mathematical formulation of life chemistry. Here is the code for the program, it finds integer

solutions for time values, incremented by the program at the discretion of the user:

h 4π r

= 6proton ⋅ secon d s = carbon(C )

h 4π r

= 1proton ⋅ 6secon d s = h ydrogen(H )

of 35 65

#include <stdio.h>

#include <math.h>

int main(int argc, const char * argv[]) {

int n;

float value=0, increment,t=0, p=1.67262E-27, h=6.62607E-34,G=6.67408E-11,

c=299792458,protons[100],r=0.833E-15;

{

printf("By what value would you like to increment?: ");

scanf("%f", &increment);

printf("How many values would you like to calculate for t in equation 1 (no more than 100?): ");

scanf("%i", &n);

}

while (n>=101);

{

for (int i=0; i<n;i++)

{

protons[i]=((137*137)/(t*p))*sqrt(h*4*(3.14159)*(r*r)/(G*c));

int intpart=(int)protons[i];

float decpart=protons[i]-intpart;

t=t+increment;

if (decpart<0.25)

{ printf("%.4f protons %f seconds %f decpart \n", protons[i], t-increment, decpart);

}}}}

The Geographic Layout For UFOs and Cesium Mines

Interestingly, a straight line south from Falcon Lake where the UFO sighting was connects with

Houston, NASA’s location of mission control for space flights. I thought perhaps I was looking at

extraterrestrial navigation routes. The line of Falcon Lake to Houston, connects with Baja

Mexico, and that with Seattle, Washington a hub of tech Industry, where Microsoft is. A square

is made that encloses the United States nicely whose center is Denver, Colorado and Boulder

Colorado, Denver a so-called Beta World City, which means it is a primary node in the global

economic Network. Boulder Colorado maintains one of our Cesium atomic clocks that we use to

keep track of time accurately for science and caldendars. It is a one of a handful of laboratories

that does this. See the maps and drawings below:

of 36 65

of 37 65

of 38 65

The green square in the south-east corner just south-east of Winnipeg is Falcon Lake, the grey

circle just north of there (Just north-east of Winnipeg is Bernic Lake). They are very close to one

another.

of 39 65

Closing Statement

We are at a time in our history when we have built telescopes that we have been able to put in

space. They have enabled us to detect some of the tiny specks orbiting other stars that are

planets, tiny specks that we always guessed should exist if our theory was right that planets

orbiting other stars are common place. Some of these planets that we have found have turned

out to be like the Earth, solid and at the right distance from their star to not be to hot for water

to vaporize, or too far for it to freeze, but for it exist in its liquid phase, a condition we believe to

be necessary for life to happen as we understand it.

We are further at a time in our development where we can leave the Earth and explore some of

the planets orbiting our star, the Sun. Our technology in the realm of computing power, as

achieved with solid state technology and integrated circuitry in our computers has taken off into

beyond what we ever dreamed it would reach so early on. It has enabled us make robotic landers

and send them to Mars to send back information about its terrain, whether it has water and can

be colonized, a necessity for us to do because resources on Earth are finite, and our survival in

the end depends on us being able to expand out into space.

But these are interplanetary missions, and in the end we need to travel between the stars. While

the planets orbiting our Sun are accessible — it takes about a year with current technology to get

to Mars — the distances between the stars are immense, with current technology it would take

thousands of years to reach the nearest one. Space is inhospitable: its is cold and devoid of air, it

is a major undertaking just to leave the Earth and go to the Moon that takes months of planning;

we can’t just press a button and take off and go their at anytime we wish.

But computers are not just making developments in the physical and biological sciences, giving

us an idea or our origins, where we going, and what we are about, they are making

advancements in our ability to engineer better ones of them, themselves; the ability to make

more complex computations quicker and store information in smaller and smaller volumes.

With such computing power we may be able to develop a way to not just travel to the planets of

our star system, but to travel to the planets of other star systems.

This I believe is important to do. Especially in light of this study. Because, through it, we see the

solar system and the atom have a profound structure mathematically that is connected, and we

have to ask, why our solar system has this apparent design, and the Earth has such favorable

conditions to support life over the billions years needed for life to develop into something as

sophisticated as the human, that can alter its environment in it favor to such a degree that no

other animal has ever achieved.

We have to ask if this not just true of our star system, but of other star systems; there are many

kinds of stars, big hot ones, and small cool ones. If our solar system in its mathematical

structure reveals so much about us, what does the mathematical structure of other star systems

reveal about the inhabitants of their planets? Are the different star systems related but different,

and if so what would that tell us about our purpose in life, or its meaning?

In order to to make the jump to the stars, we have to undergo an expansion of consciousness to

adapt to space travel and its implications. It may be we will soon find that there is already a

social structure for the different worlds in common that allows for the different space faring

civilizations to function together, and that Earth might be invited to join such an intergalactic

community. I leave this paraphrasing a poem by the astronomer Carl Sagan:

The surface of the Earth is the shore of cosmic ocean

From it we have learned most of what we know

Some part of our being knows this is from where we came

of 40 65

Recently, we have waded out to sea, enough to wet our toes

Some part of our being knows this is from where we came

We long to return

These aspirations, I think, are not irreverent

Though they may trouble whatever Gods may be.

of 41 65

The Data For Verifying The Equations

You can verify my equation for the second as a basis unit of nature with the following data. You

will ﬁnd if you do the dimensional analysis that they all have the correct units.

(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:

The equation at the beginning of the paper that gives one second as a basis unit from using a

wavelength associated with the Moon in its ground state is derived from my Planck

constant for the planets . You can verify it as such:

: 1.67262 × 10

−27

h : 6.62607 × 10

−34

J ⋅ s

: 0.833 × 10

−15

G: 6.67408 × 10

−11

c : 299,792,458m /s

α : 1/137

= q

= 1.6022E − 19coulom bs

= 8.988E 9

K E

moon

(7.347673E 22kg)(966m /s)

= 3.428E 28J

K E

earth

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

moon

ℏ

⊙

moon

ℏ

⊙

= 3.0281E8m

moon

ℏ

⊙

⋅

= 1.0secon d s

ℏ

⊙

K E

ℏ

⊙

ℏ

⊙

(

6α

⋅

4πh

)

K E

of 42 65

Solving the Atom and Earth/Moon/Sun System with Spacetime Operators in

Common

Ian Beardsley

of 43 65

Efforts today are to make a theory of everything (TOE) which for some is a grand unified field

theory. For others it should include all aspects of the physics of the Universe. It seems most of

the effort is in a grand unified field theory. Here I formulate spacetime operators that solve the

atom and Earth/Moon/Sun System in common. It may be that they solve more than that, but

that is where I have applied them here. It may be many more operators are needed for solutions

of everything. The operators are in kilograms/meters/seconds because space and time (meters

and seconds) define matter (kilograms) and everything, or most everything seems to be a

relationship between mass, space, and time.

of 44 65

Preface

You can speak of the structure of the solar system even though it changes with time. This is

important to understand when I refer to sizes of the Moon and the planets, and their orbital

distances.

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 (it has a thickness). In a theory of planetary

formation from a primordial disc, it should predict the Titius-Bode rule for the distribution of

planets.

of 45 65

The Spacetime Operators

In my paper The Solar System As A Solution To The Wave Equation (Beardsley, 2024) I

showed that I could solve the solar system, like we do with the atom, with the quantum

mechanical Schrödinger wave equation and that the result is done in terms of the Moon and a

base unit of one second. The solar system is as such connected to the proton of the atom. As a

result I found that

Where is the radius of a proton, is the mass of a proton, is the fine structure constant,

is Planck’s constant, is the constant of gravitation, and is the speed of light. We see this by

considering

Where . The units

describe the Nature of space and time. We say 2E-12 of it are the degree to which space acts on

the size and mass of a proton to give it a characteristic time of one second:

We see that same unit of time is in the orbital energies (kinetic energies) of the Earth and the

Moon in terms of the Earth’s spin, its day, or period of rotation which is

1secon d =

6α

⋅

4πh

6α

4πh

(3128.167)

4π (6.62607E − 34)

(6.67408E − 11)(299,792,458)

2.018E − 12

kg ⋅ s

≈ 2E − 12

kg ⋅ s

α = 1/137

kg ⋅ s

0.833E − 15m

1.67262E − 27kg

= 4.9802E11

≈ 5E11

6α

4πh

⋅

(

5E11

kg ⋅ s

)(

2E − 12

)

= 1secon d

(Ear th Da y) = (24hrs)(60mi n)(60sec) = 86400secon d s

of 46 65

That is the solar day, the rotation of the Earth with respect to the Sun. It makes little difference

whether we use it or, the sidereal day, the rotation of the Earth with respect to the stars. We

have

Where we have used the orbital velocity of the Moon at aphelion, and that of the Earth at

perihelion, though it makes little difference on how you do it because the orbits are close to

circular. We get

Where KE means kinetic energy and subscripts m and e are moon and earth respectively.

Why does the basis of our counting system, 1 second, happen to be the basis unit of time for our

solution of the solar system and the atom. I don’t know, but I can say how we ended-up with that

unit for the basis of our counting.

The interesting thing is that we have the duration of a second is what it is not because we were

attempting to find some base unit of time for Nature, but rather we have the duration of a

second from ancient times that came to us over many years of dividing the rotation of the Earth

into hours, minutes, and seconds in such a way that we ended up with it. However we may have

had some sort of a thought going into it that was six-fold in Nature that lead it to being natural if

we consider:

And that thought may be was in a six-fold pattern that the motions of the Earth/Moon/Sun

system had in it approximately which we inadvertently characterized in the calendar:

Which can be written

Where there are 360 degrees in a circle and as such the Earth approximately moves through one

degree per day around the Sun. We achieved this because the ancients of Sumeria and Babylonia

from which the ancient Greeks received their counting system used base 60, sexagesimal

because 60 is evenly divisible by so much, that is by

9) 1,2,3,4,5,6, 10, 12, 15, 20, 30,…

1secon d =

K E

(Ear th Da y)

K E

(7.347673E 22kg)(966m /s)

= 3.428E 28J

K E

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

1secon d =

365.25

⋅

= 0.0000000316881year

(

360d a ys

year

)(

24h ours

d a y

)(

60min

h our

)(

60sec

min

)

= 31104000secon d s /year

(

60d a ys

year

)(

1h our

d a y

)(

60min

h our

)(

60sec

min

)

of 47 65

The Sumerians divided the day into 12 hours, evenly divisible into 60, and so from sunrise to

sunrise was 24 hours, and from sunset to sunset was 24 hours. They multiplied 60 by 6, to get

360 degrees in a circle. Since the Earth does one orbit around the Sun in 365 days, which is a

year, the Earth goes through about 1 degree a day. The Babylonians got that from them, and

further divided the hour into 60 minutes, and the minute into 60 seconds, though hours were in

their sun dials, they only used minutes and seconds for astronomy. The West, the Europeans,

got their sun dials from the Babylonians but did not incorporate minutes and seconds into their

mechanical clocks until the 17th century, but it all came from the Sumerians, who settled down

from hunting with stone spearpoint and started agriculture, writing, mathematics, and

civilization in general. Sun dials were used in Egypt as well and had 12 divisions throughout the

day as well for hours. A sun dial simply tells time by the angle of a shadow cast by the Sun as the

sun rises and sets, its position measuring time.

We have one second in equations 1, and 5:

Equation 5 can be written

10)

Since orbital velocities are given by

We have equation 10 is

11)

It can be made more accurate using aphelions and perihelions appropriately. It is an amazing

fact that the Moon as seen from the Earth near perfectly eclipses the Sun. To say that

mathematically is to write

12)

1secon d =

6α

⋅

4πh

1secon d =

K E

(Ear th Da y)

(Ear th Da y) = 1secon d

= G

⊙

⋅

(Ear th Da y) = 1secon d

7.347673E 22kg

1.989E 30kg

⋅

1.496E11m

3.84E8m

(86,400s) = 1.243secon d s

⊙

of 48 65

That is, the earth orbital radius to that of the Moon is equal to the radius of the Sun to the radius

of the Moon. Putting that into equation 11 yields:

13)

Let us look at equation 4 and write it:

14)

And write 13 as

15)

So that we see ( means corresponds to)

⊙

⋅

⊙

(Ear th Da y) = 1secon d

7.347675E 22kg

1.989E 30kg

⋅

6.96E8m

1,737,400m

(86,400s) = 1.2786secon d s

(

6α

4πh

)

⋅

= 1secon d

(

(Ear th Da y)

)

⋅

⊙

= 1secon d

≜

of 49 65

And

So, we have

16)

17)

Thus the spacetime operator for the Earth-Moon system is on the order of 1.5E33 times greater

than that for the atom, and the radius of the proton to the mass of the proton is on the order

order of 1.5E33 times greater than that of the radius of the Sun to its mass. Thus the two

systems, that of the atom and that of the Earth and Moon nearly balance with C1/C2 about equal

to one.

It is worth noting here, while the Moon near perfectly eclipses the Sun, and that this was seen by

prehistoric man that hunted with stone spearpoint, the ratio of the the radius of the Sun to the

orbital radius of the Moon is about 9/5=1.8, which the ratio of the molar mass of gold to the

molar mass of silver, that is it is the mass of a gold atom to a silver atom. This is interesting

because gold and silver have been the primary metals used since ancient times for ceremonial

jewelry, gold yellow like the Sun, silver, silver like the Moon. We have

is the radius of the Sun, is the orbital radius of the Moon, Au, is gold and Ag is silver.

So, not only did the Sumerians of Mesopotamia, who created writing, mathematics, and

agriculture, divide the day into 12 units called hours, so did the Ancient Egyptians. They both

measured hours with sun dials, simply a stick that casts a shadow from the Sun that moves as

(

6α

4πh

)

= 2.018E − 12

kg ⋅ s

≜

(

(Ear th Da y)

)

= 3.654E 21

kg ⋅ s

= 4.98E11

≜

⊙

= 3.5E − 22

(

6α

4πh

)

(

(Ear th Da y)

)

= C

⊙

3.654E 21

2.018E − 12

= 1.8107E 33

4.98E11

3.5E − 22

= 1.423E 33

= 1.27245

⊙

of 50 65

the Sun moves, rising in the East and setting in the West. As the shadow moves it passes

through twelve lines each line representing the hour of a day. We see from equation 8

that gives the seconds per year, that the 1 hour day exists naturally in a base 60 counting. The

Sumerians also used base 12, because it divides evenly into 60 and is an abundant number, full

of divisors, 1, 2, 3, 4, 6 all divide evenly into it and add up to 16, which greater than 12. It makes

computing very easy.

We have spacetime operators operating on radius to mass of a proton and operating on radius to

mass of the the Sun, equations 14 and 15:

The operator for the proton is in units of

But we can also make a spacetime operator in which acts not on but on to

give a characteristic time of one second as well. It is

18)

It acts on

19)

We have

(

60d a ys

year

)(

1h our

d a y

)(

60min

h our

)(

60sec

min

)

= secon d s /year

(

6α

4πh

)

⋅

= 1secon d

(

(Ear th Da y)

)

⋅

⊙

= 1secon d

(

6α

4πh

)

kg ⋅ s

m ⋅ kg

m /kg

kg ⋅ m

⋅

π r

G m

m ⋅ kg

⋅

= kg ⋅ m

⋅

π r

G m

⋅

(352275361)π (0.833E − 15m)

(6.67408E − 11)(1.67262E − 27kg)

= 1.402818E42

m ⋅ kg

⋅

6.62607E − 34

299,792,458

= 7.3674E − 43kg ⋅ m

of 51 65

We have

So we have equations 20, and 14:

20)

14)

We have that

And

Solving The Atom

We see the spacetime operators solve the atom by giving us the radius of a proton. We set

equation 20 equal to equation 14

20)

14).

These two yield

(

1.402818E42

m ⋅ kg

)

(

7.3674E − 43kg ⋅ m

)

= 1.0335secon d s = 1.0secon d s

⋅

π r

G m

⋅

= 1secon d

(

6α

4πh

)

⋅

= 1secon d

(

6α

4πh

)

= 2.018E − 12

kg ⋅ s

≈ 2E − 12

kg ⋅ s

= 4.9802E11

≈ 5E11

⋅

π r

G m

= 1.402818E42

m ⋅ kg

⋅

= 7.3674E − 43kg ⋅ m

⋅

π r

G m

⋅

= 1secon d

(

6α

4πh

)

⋅

= 1secon d

of 52 65

21).

We can arrive at this radius of a proton another way, energy is given by Planck’s constant and

frequency

We have

We take the rest energy of the mass of a proton :

The frequency of a proton is

This gives

The radius of a proton is then

This is close to the CODATA value for the proton radius around 2018 (0.842E-15m). The result

We find it may be that the radius of a proton is actually

22)

⋅

E = h f

f = 1/s, h = J ⋅ s, h f = (J ⋅ s)(1/s) = J

E = J = J oules = en erg y

E = m

⋅

≈ ϕ =

⋅

6.62607E − 34

(299,792,458)(1.67262E − 27)

= 0.88094E − 15m

= ϕ ⋅

= 0.816632E − 15m

of 53 65

Where is the golden ratio constant (0.618…). This is more along the lines of more recent

measurements. Thus we have solved the atom with our spacetime operators by producing the

radius of a proton.

Solving The Earth Orbit

Looking at equations 14 and 15

14)

15)

They seem to suggest that the Earth orbit might by quantized in terms of the Moon and a base

unit of one second.

We say there is a Planck constant for the solar system. We do it with a base unit of one second

because equations 14 and 15 suggest we should . We suggest it is such that it is given by the

standard Planck constant for the atom, , times some constant, , and the Kinetic energy of the

Earth.

23)

24)

Where

25).

Where equation 25 comes from equation 20

20).

We derive the value of our solar Planck constant

(

6α

4πh

)

⋅

= 1secon d

(

(Ear th Da y)

)

⋅

⊙

= 1secon d

ℏ

⊙

= (hC )KE

hC = 1secon d

C =

⋅

π r

G m

⋅

π r

G m

⋅

= 1secon d

C =

⋅

2π r

G m

⋅

18769

299792458

⋅

2π (0.833E − 15)

(6.67408E − 11)(1.67262E − 27)

of 54 65

Now we show that our Planck constant for the solar system gives the base unit of one second for

the quantization. We call our solar Planck constant and find the wavelength for the Moon

which is the ground state for the solar system:

26)

Then wavelength associated with the Moon divided by the speed of light should be 1 second if

our planetary system is quantized in terms of the Moon and a base unit of one second. We have

27)

And we see it is, so we have

28).

The solution for the orbit of the Earth around Sun with the Schrödinger wave equation can be

inferred from the solution for an electron around a proton in the a hydrogen atom with the

Schrödinger wave equation. The Schrödinger wave equation is, in spherical coordinates

1.55976565E 33

⋅

kg ⋅ m

⋅

= kg

= energ y

hC = (6.62607E − 34)(1.55976565E 33) = 1.03351secon d s ≈ 1.0secon d s

hC =

(

⋅ m ⋅ s

)

(

⋅

)

(

)(

⋅

)

= secon d s

K E

earth

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

ℏ

⊙

= (hC )KE

earth

= (1.03351s)(2.7396E 33J ) = 2.8314E 33J ⋅ s

ℏ

⊙

moon

ℏ

⊙

(2.8314E 33)

(6.67408E − 11)(7.34763E 22kg)

= 3.0281E8m

moon

3.0281E8m

299,792,458m /s

= 1.010secon d s

moon

= 1secon d

of 55 65

29)

Its solution for the atom is

30)

31)

is the energy for an electron orbiting protons and , is the orbital shell for an electron with

protons, the orbital number. I find the solution for the Earth around the Sun utilizes the

Moon around the Earth. This is different than with the atom because planets and moons are not

all the same size and mass like electrons and protons are, and they don’t jump from orbit to

orbit like electrons do. I find that for the Earth around the Sun

32)

33)

is the kinetic energy of the Earth, and is the planet’s orbit. is the radius of the Sun,

is the radius of the Moon’s orbit, is the mass of the Earth, is the mass of the Moon, is

the orbit number of the Earth which is 3 and is the Planck constant for the solar system.

Instead of having protons, we have the radius of the Sun normalized by the radius of

the Moon. It is has always been an amazing fact the the sizes of the Moon and the Sun are such

that given their orbital distances, the Moon as seen from the Earth perfectly eclipses the Sun.

This becomes part of the theory and we suggest it is a condition for sophisticated planets that

harbor life by writing it:

34)

That is the orbital radius of the planet (Earth) to the orbital radius of its moon (The Moon) is

about equal to the the radius of the star (The Sun) to the radius of its moon (The Moon). We say

the system is quantized by the Moon and the base unit of one second. It is a fact that the Moon

orbiting the Earth optimizes the conditions for life on Earth because it holds the Earth at its

inclination to its orbit around the Sun allowing for the seasons, preventing extreme hot and

extreme cold. Let us now see if our solar Planck constant works…

35).

−

ℏ

[

∂

∂r

(

∂

∂r

)

sinθ

∂

∂θ

(

sinθ

∂

∂θ

)

sin

∂

∂ϕ

]

ψ + V(r)ψ = E ψ

E = −

)

2ℏ

ℏ

Z k

K E

= n

⊙

⋅

2ℏ

⊙

2ℏ

⊙

⋅

⊙

⋅

K E

⊙

ℏ

⊙

planet

moon

≈

star

moon

⊙

6.96E8m

1737400m

= 400.5986

of 56 65

=2.727E36J

The kinetic energy of the Earth is

The accuracy of our equation is:

Which is very good. Thus we have solved the Earth/Moon/Sun System with our spacetime

operators by using them to find a Planck constant for the solar system.

The Basis Set For The Solar System

We want the basis set of equations for the solar system. We have equation 26

26)

We have from equation 27

36).

We have equations 23, and 24

23)

24)

We have equations 20, 14, and 5

20)

14)

K E

= (1.732)(400.5986)

(6.67408E − 11)

(5.972E 24kg)

(7.347673E 22kg)

2(2.8314E 33)

K E

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

2.727E 36J

2.7396E 33J

100 = 99.5 %

moon

ℏ

⊙

= 3.0281E8m

moon

ℏ

⊙

⋅

= 1.0secon d s

ℏ

⊙

= (hC )KE

hC = 1secon d

⋅

π r

G m

⋅

= 1secon d

(

6α

4πh

)

⋅

= 1secon d

1secon d =

K E

(Ear th Da y)

of 57 65

From these it becomes clear that

37)

38)

39).

The Solar Formulation

Our solution of the wave equation for the planets gives the kinetic energy of the Earth from the

mass of the Moon orbiting the Earth, but you could formulate based on the Earth orbiting the

Sun. In our lunar formulation we had:

40)

We remember the Moon perfectly eclipses the Sun which is to say

41)

Thus equation 40 becomes

42)

The kinetic energy of the Earth is

43)

Putting this in equation 42 gives the mass of the Sun:

44)

We recognize that the orbital velocity of the Moon is

45)

So equation 44 becomes

ℏ

⊙

K E

ℏ

⊙

ℏ

⊙

(

6α

⋅

4πh

)

K E

= 3

⊙

⋅

2ℏ

⊙

K E

= 3

⋅

2ℏ

⊙

K E

⋅

⊙

= 3r

⋅

ℏ

⊙

of 58 65

46)

This gives the mass of the Moon is

47)

Putting this in equation 40 yields

48)

We now multiply through by and we have

49)

Thus the Planck constant for the Sun, , in this the case the star is the Sun, is angular

momentum quantized as Bohr discovered for the atom by The angular

momentum we will call , the subscript for Planck. We have

We write for the solution of the Earth/Sun system:

50)

Let us compare this to that of an atom:

51)

We notice that in equation 50

; ; ; ;

is really . We can write 50 as

⊙

= 3r

⋅ v

⋅

ℏ

⊙

ℏ

⊙

K E

⊙

⋅

⊙

K E

⊙

⋅

⊙

ℏ

⊙

h /2,2h /2,3h /2,...

= r

= (1.496E11m)(1022m /s)(5.972E 24 kg) = 9.13E 38kg ⋅

= r

= 7.4483E 77J ⋅ m

⋅ kg = 8.3367E 77kg

⋅

K E

⊙

⋅

⊙

E = −

⋅

2ℏ

→

⊙

→ G

→ M

⊙

ℏ

→ L

ℏ

⊙

of 59 65

52)

We say. . That is

Let us see how accurate our equation is:

We have that the kinetic energy of the Earth is

Our equation has an accuracy of

Which is very good.

We call the same in our solar solution. But we now want our solution for the solar

formulation. is the mass of the Earth and is the mass of the Sun. We have our solution

might be!

53) !

Where is !

K E

⊙

⋅

⊙

2ℏ

⊙

ℏ

⊙

= ℏ

⊙

/2π

ℏ

⊙

= 9.13E 38J ⋅ s

⊙

= 2π ℏ

⊙

= 5.7365E 39J ⋅ s

K E

⊙

⋅

⊙

2ℏ

⊙

(6.67408E − 11)

(5.972E 24kg)

(1.9891E 30kg)

2(8.3367E 77kg

⋅

)

⊙

(6.759E 30J )

⊙

6.957E8m

1737400m

= 400.426

K E

= 2.70655E 33J

K E

earth

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

2.70655E 33J

2.7396E 33J

= 98.79 %

ℏ

⊙

ℏ

⊙

⋅

⊙

of 60 65

We have

54)

This has an accuracy of

Thus the solutions to the wave equation!

for the solar formulations are!

52)

53)

Equating The Lunar And Solar Formulations Yield Our 1 Second Base Unit

Let us equate equation 32 with equation 52:

32)

52)

This gives:

ℏ

⊙

= 9.13E 38J ⋅ s

(9.13E 38)

(6.67408E − 11)(5.972E 24kg)

⋅

400.5986

= 1.4638E11m

1.4638E11m

1.496E11m

100 = 97.85 %

−

ℏ

[

∂

∂r

(

∂

∂r

)

sinθ

∂

∂θ

(

sinθ

∂

∂θ

)

sin

∂

∂ϕ

]

ψ + V(r)ψ = E ψ

K E

⊙

⋅

⊙

2ℏ

⊙

ℏ

⊙

⋅

⊙

ℏ

⊙

= 9.13E 38J ⋅ s

⊙

= 2π ℏ

⊙

= 5.7365E 39J ⋅ s

K E

= n

⊙

⋅

2ℏ

⊙

K E

⊙

⋅

⊙

2ℏ

⊙

⋅

2ℏ

⊙

⋅

⊙

of 61 65

55)

We remember that

This gives

56)

We have

57)

This equates the orbital velocity of the Moon with the centripetal acceleration of the Earth in

terms of one second by way of the mass of the Earth, the mass of the Sun, the mass of the Moon,

and the orbital number of the Earth. Let us compute

58)

Let us see how well equation 57 works. at aphelion is 966 m/s and .

. We have

That is an accuracy of

⊙

⋅ ℏ

⊙

ℏ

⊙

= (hC )KE

hC = 1secon d

C =

⋅

2π r

G m

6α

h 4π r

= 1.004996352secon d s

6α

⋅

h 4π

⋅

⊙

(1secon d )

⊙

(5.972E 24kg)

(1.9891E 30kg)

(7.34763E 22kg)

(1.732)

= 321,331.459 ≈ 321,331

= 29,800m /s

= 1AU = 1.496E11m

2(966m /s) =

(29,800m /s)

1.496E11m

(1sec)(321,331.459)

1,907m /s = 1,932m /s

of 62 65

Equation 57 can be written:

59)

From equation 1:

We have

60)

Since , the diameter of the Earth orbit, we have

61)

And we see the Earth/Moon/Sun system determines the radius and mass of the proton and vice

versa. We basically have

62)

Where is the Earth orbital number. We have

1907

1932

= 98.7 %

1secon d = 2r

⊙

6α

h 4π r

= 1.004996352secon d s

6α

⋅

h 4π

= 2r

⋅

⊙

= d

6α

⋅

h 4π

= d

⋅

⊙

1secon d = 2v

⊙

1secon d =

K E

moon

K E

earth

Ear th Da y

1secon d =

Ear th Da y

Ear th Da y =

⊙

n = 3

of 63 65

= 7.83436E4seconds

EarthDay=(24)(60)(60)=86400 seconds,

accuracy

This last equation, equation 62, we can use to find the rotation period, or the length of the day,

of an earth-like planet in the habitable zone of any star system, so it would be very useful.

We want to turn our attention to equation 59 and write it

63)

We see equating solar and lunar formulations for energy yield the base unit of one second.

Equating the lunar and solar solutions for orbitals instead of the for energies, which we just did,

we have

Yields

64)

Where . The accuracy of this is

Thus the energy equations gave the equation 55:

Ear th Da y =

2(1.496E11m)

966m /s

7.34763E 22kg

1.9891E 30kg

1.732

7.834E4s

86,400s

100 = 90.675 %

1secon d = d

⊙

2ℏ

⊙

⋅

⊙

⋅

⊙

ℏ

⊙

3/2 = cos(π /6)

(2.8314E 33)

(5.972E 24)

(7.34763E 22)

= (0.866)(9.13E 38)

(1737400)

(6.96E8)

4.29059E 72 = 4.5005E 72

4.29059E 72

4.5005E 72

100 = 95.3 %

of 64 65

55) !

And equating the orbital equations gives

65)

These last two yield

66)

The accuracy is

Is 98% accuracy. The important thing that comes out of this is our base unit of a second because

we see it is also a function lunar, solar, and earth masses.

63)

⊙

⋅ ℏ

⊙

2 3

⋅

⊙

⋅ ℏ

⊙

= 1

(400.5986)

5.972E 24kg

1.9891E 30kg

= 1

0.98 = 1

1secon d = d

⊙

of 65 65

The Author