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Presentation: How a Characteristic Time of One Second May Describe Physical and Biological Systems

in General

Ian Beardsley

May 23, 2025

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List of Constants, Variables, And Data In This Paper

(Proton Mass)

(Proton Radius)

(Planck Constant)

(Light Speed)

(Gravitational Constant)

1/137 (Fine Structure Constant)

(Proton Charge)

(Electron Charge)

(Coulomb Constant)

(The Author’s Solar System Planck-Constant)

(Earth Mass)

(Earth Radius)

(Moon Mass)

(Moon Radius)

(Mass of Sun)

(Sun Radius)

(Earth Orbital Radius)

(Moon Orbital Radius)

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:

(Kinetic Energy Moon)

(Kinetic Energy Earth)

: 1.67262E − 27kg

: 0.833E − 15m

h : 6.62607E − 34J ⋅ s

c : 299,792,458m /s

G : 6.67408E − 11N

α :

: 1.6022E − 19C

: 8.988E 9

ℏ

⊙

: 2.8314E 33J ⋅ s

: 5.972E 24kg

: 6.378E6m

: 7.34767309E 22k g

: 1.7374E6m

⊙

: 1.989E 30kg

⊙

: 6.96E 8m

: 1.496E11m = 1AU

: 3.844E 8m

K E

(7.347673E 22k g)(966m /s)

= 3.428E 28J

K E

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

= 2.7396E 33J

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The Presentation: I have found some equations that ﬁt together very accurately and nicely in the context

of a quantum mechanical approach to structuring solutions of Nature, that indeed satisfy such a theoretical

context in a complete sense. The result has solutions at the core of cosmology (the origin and fate of the

universe), star systems mechanics, astrobiology (the study of the habitability of star systems in general),

particle physics (like the atom’s proton), theories showing a common structure between the macrocosmos

and microcosmos, biology, formation of planetary systems from the protoplanetary disc, archaeology,

archaeoastronomy (the study of ancient megalithic (stone) observatories), and SETI (The Search For

Extraterrestrial Intelligence). It is the purpose of this presentation to outline some the key concepts

concisely, and succinctly in the theory.

To begin with, I developed a theory which has a wave solution to the Earth/Moon/Sun system much like

the quantum mechanical solution for the atom. Interestingly, the characteristic time that describes this

system is neatly one second to two places after the decimal. The ground state I found is given by our

Moon orbiting the Earth, and is

is the mass of the Moon. I ﬁnd , which is my Planck-type constant for the Solar System, much like

the Planck constant in quantum mechanics used to describe the atom , in our theory is given by one

second as well, and not just by that, but by the kinetic energy of the our home planet, the Earth, the planet

in our Solar System optimized for the conditions for life. I ﬁnd

where is the orbital kinetic energy of the Earth. I know this value for is accurate because the

solution for the energy of the Earth orbiting around the Sun using this value, much like the solution for

the electron around that atom is 99.5% accurate. It is:

where is the earth orbital number, and is the radius of the Sun, and is the radius of the

Moon, is the mass of the Earth, is the mass of the Moon, and is the universal constant of

gravitation. The radius of the Sun, , plays the role of , the number of protons being orbited by an

electron in an atom, but must be normalized by the radius of the Moon, . This gives it a size of 400

because . So we see the Moon plays an important and central role in the quantum solution

of our solar system, not just in the this equation, but in the ground state equation. It plays such a central

role, that I have suggested the condition for optimal habitability of a planet in the habitable zone is given

by the conditions of a perfect eclipse of the star by its moon as seen from the habitable planet, which is

exactly what we have with our Earth/Moon/Sun system. That condition is:

Where is the orbital radius of the habitable planet (like the Earth), is the orbital radius of the

moon, like the orbital radius of our moon around the Earth, is the radius of the star, like our Sun, and

ℏ

⊙

⋅

= 1secon d

ℏ

⊙

ℏ

⊙

= (1secon d )K E

K E

ℏ

⊙

K E

= n

⊙

⋅

2ℏ

⊙

n = 3

⊙

= 400

planet

moon

star

moon

planet

moon

star

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is the radius of the moon, like the Earth’s moon. I use this in my theory to solve star systems in

general—not just our Solar System— for optimal habitability, because we know our Moon orbiting the

Earth holds the Earth at its tilt to its orbit around the Sun making it optimally habitable because this

prevents temperature extremes and allows for the seasons. Here is where my theory has taken a very nice

turn. The Earth as it rotates, determining the length of its day, loses energy to the Moon, meaning its

rotation is slowing down, but very slowly only noticeably over geologic time, meaning the day length is

lengthening ever so slowly over vast epochs, and that a very long time ago was a little shorter than it is

today. However, to establish the optimal day length, we want it to be what it is today, about 24 hours, and

in order to establish that, the Earth day of 24 hours should produce a characteristic time of one second. I

had found it did close to this in the kinetic energies of the Moon and the Earth in their orbits. I had found

that

There is a range in the answer because the Moon’s orbit is not perfectly circular, though close to it, as

well as that of the Earth. However I wanted this value to be closer to a second. I recently found that it is

because of the obvious adjustment I had failed to make but should have, and that is we must include the

effects of the Earth’s tilt to its orbit, which is 23.5 degrees, so we must include the cosine of this angle to

put the equation in the components of the Earth’s spin in it orbital plane around the Sun. So, we have now

our equation for a 24 hour day can indeed be considered a second in that we now have

But not only are we offering a wave solution for the Solar System like we have with the atoms, but it

turns out we are offering the rudiments of a theory of particle physics, and not just that, a relationship

between the microcosmos, the atom’s protons, and the macrocosmos; planetary systems. I say this

because I found that the same characteristic time of the Earth/Moon/Sun system is characteristic of the

proton and predicts very accurately modern measurements of the radius of the proton. I found

is the proton radius, its mass. is the golden ratio. the ﬁne structure constant. Since the

left sides of these equation are both equal to a second, they are equal to one another. When we set them

equal to one another, we ﬁnd they very accurately yield the observed radius of the proton in the most

recent experiments. We ﬁnd the radius of a proton is given by

moon

K E

(Ear th Day) = 1.1 − 1.3secon d s

K E

(Ear th Day)cos(θ ) = 1.0secon d s

(

6 α

4πh

G c

)

⋅

= 1secon d

ϕ ⋅

π r

G m

⋅

= 1secon d

ϕ = 0.618

= ϕ

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But this characteristic time of one second is not just in the Solar System, and atom’s proton, but in the

basis of life chemistry, carbon, and the hydrocarbons, the skeletons of life chemistry. I found

is carbon (C)

is hydrogen (H)

Which is to say that six protons, which is carbon, the basis of life as we know it, has a characteristic time

of one second because in the ﬁrst equation above, we have a mass divided by the mass of a proton, times

seconds, giving six protons times a second (6 proton-seconds) which means 6 protons (carbon, the basis

of life) has a characteristic time of one second. This means that 1 proton, hydrogen, has a characteristic

time of six seconds. Hydrogen is the most fundamental element in the periodic table of the elements

which was theoretically created in the so-called big bang that gave birth to the universe, and is the

element from which all of the other heavier elements were made by stars. This six-fold symmetry that is

in hydrocarbons, the skeletons of biological chemistry, is fundamental to deﬁning the periodic table of the

elements because it has been found that the six protons of carbon and their respective charges, interact

with its six electrons, their respective charges, to balance to make carbon the most stable element

mathematically in which to describe the rest of the atoms in the periodic table. This is no doubt related to

the regular hexagon, a six-sided polygon which tessellates (tiles a surface without leaving gaps) because it

has its radii equal in length to its sides. This hexagonal tessellating property is used by bees to make their

honeycombs. So we see our theory now goes beyond the atom and the solar system. That it goes to

biological chemistry. But, it does not stop there. It seems to go into cosmology, the study of the origin and

fate of the universe. We see this because my equations link proton properties to 1-second, and protons

were ﬁxed in the universe at 1 second after it, meaning we could be seeing a universal clock that has

inﬂuenced everything since the Big Bang.

The idea is that neutrino decoupling (neutrinos stop interacting with one another) happens when the

reaction rate of weak interactions falls below the Hubble parameter, the expansion rate of the universe

. The reaction rate per particles is given by

is the Fermi constant is about , and is the temperature of the Universe. The

expansion rate of the universe is given by

Where is the Plank mass is about 1.22E19GeV. and have units of inverse time ( ). Neutrino

decoupling happens when

6proton s

⋅

4πh

G c

= 1secon d

1proton

⋅

4πh

G c

= 6secon d s

Γ ≈ G

1.166E − 5G eV

−2

H ≈

−1

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This is when the number of protons in the universe was set in place which, as it would turn out, is close to

one second in rough estimate.

The expansion rate of the Universe is governed by the Friedmann equation

Where is the energy density of the Universe. It is

The Hubble expansion rate is

Since

we have

We said protons and neutrons are set in the universe when it has cooled in its expansion to about 1MeV.

We have

This was done in Planck units where time can be expressed in inverse energy. Since in Planck units

we have

This theory seems, then, to have applications at the core of cosmology, astrobiology (the study of life in

the universe in general), solar system mechanics, particle physics, theories of common structure between

micro-scales and macro-scales, and biology . But, as we will see now, has applications at the core of star

system formations from protoplanetary discs, and in archaeology and archaeoastronomy (the study of

8π G

ρ ∝ T

H ∝

≈ 2.4E18GeV

t ∝

2.4E18G eV

(1E − 3G eV )

= 2.4E 24GeV

−1

1G eV

−1

= 5.39E − 25s

t ≈ (2.4E 24)(5.39E − 25)

t ≈ 1.3secon d s

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ancient stone observatories, for example). We see this because I have found that the pressure gradient of

the protopanetary disc, as a function of radius, that gave birth to our solar system, is given by:

Where the rotational angular momentum, , is given by the mass of the Earth, the size of the Earth,

and its rotation frequency. The value is 2.5, which is 60/24, by modeling our solar system is found in the

theory of solar system formation to be the exponent in the pressure gradient for the protoplanetary disc

from which our solar system formed. This is the solution to:

The protoplanetary disc that evolves into the planets has two forces that balance its pressure, the

centripetal force of the gas disc due to its rotation around the protostar and the inward gravitational

force on the disc from the protostar , and these are related by the density of the gas that makes

up the disc.

I can use this to solve not just star systems in general, but to provide a theory for optimally habitable star

systems.

In order to apply this to other star systems, we have to be able to predict the radius of the habitable planet,

presumably in the n=3 orbit. I found the answer to be in the Vedic literature of India. They noticed that the

diameter of the Sun is about 108 times the diameter of the Earth and that the average distance from the

Sun to the Earth is about 108 solar diameters, with 108 being a signiﬁcant number in Yoga. So I wrote the

equivalent:

The surprising result I found was, after applying it to the stars of many spectral types, with their different

radii and luminosities (the luminosities determine , the distances to the habitable zones), that the

radius of the planet always came out about the same, about the radius of the Earth. This may suggest

optimally habitable planets are not just a function of the distance from the star, which determines their

temperature, but are functions of their size and mass probably because they are good for life chemistry

atmospheric composition, and gravity. Here are just a few examples using the data for several spectral

types:

…

P(R) = P

(

)

−

earth

ℏ

⊙

earth

ℏ

⊙

24 = 60

earth

π M

earth

d P

= − ρ

(

⋆

−

)

⋆

planet

= 2

⋆

planet

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F8V Star

Mass: 1.18

Radius: 1.221

Luminosity: 1.95

F9V Star

Mass: 1.13

Radius: 1.167

Luminosity: 1.66

G0V Star

Mass: 1.06

Radius: 1.100

Luminosity: 1.35

G1V Star

Mass: 1.03

Radius: 1.060

Luminosity: 1.20

As you can see we consistently get about 1 Earth radius for the radius of every planet in the habitable

zone of each type of star. It might be that radius is right for life in terms of gravity and densities for the

elements. I got these results for the stars from spectral types F5V to K3V. It probably goes beyond that.

⋆

= 1.18(1.9891E 30kg) = 2.347E 30kg

⋆

= 1.221(6.9634E 8m) = 8.5023E 8m

= 1.95L

⊙

AU = 1.3964AU(1.496E11m /AU ) = 2.08905E11m

⋆

= 2

(8.5023E 8m)

2.08905E11m

6.92076E6m

6.378E6m

= 1.0851Ear th R a dii

⋆

= 1.13(1.9891E 30kg) = 2.247683E 30kg

⋆

= 1.167(6.9634E 8m) = 8.1262878E8m

= 1.66L

⊙

AU = 1.28841AU(1.496E11m /AU ) = 1.92746E11m

⋆

= 2

(8.1262878E 8m)

1.92746E11m

6.852184E6m

6.378E6m

= 1.0743468Ear th Ra dii

⋆

= 1.06(1.9891E 30k g) = 2.108446E 30kg

⋆

= 1.100(6.9634E 8m) = 7.65974E 8m

= 1.35L

⊙

AU = 1.161895AU(1.496E11m /AU ) = 1.7382E11m

⋆

= 2

7.65974E 8m)

1.7382E11m

6.751E6m

6.378E6m

= 1.05848Ear th Ra dii

⋆

= 1.03(1.9891E 30kg) = 2.11E 30kg

⋆

= 1.060(6.9634E 8m) = 7.381E 8m

= 1.20L

⊙

AU = 1.0954AU(1.496E11m /AU ) = 1.63878589E11m

⋆

= 2

7.3812E 8m)

1.63878589E11m

6.6491E6m

6.378E6m

= 1.0425Ear th R a dii

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In order to get , the distance of the habitable planet from the star, we use the inverse square law for

luminosity of the star. If the Earth is in the habitable zone, and if the star is one hundred times brighter

than the Sun, then by the inverse square law the distance to the habitable zone of the planet is 10 times

that of what the Earth is from the Sun. Thus we have in astronomical units the habitable zone of a star is

given by:

We see our theory has applications to archaeology because the second came to us historically from the

ancient Sumerians because they divided the Earth day (rotation period) into 24 hours, and, because each

hour and minute got further divisions by 60 because their base 60 counting system was inherited by the

ancient Babylonians who were the ultimate source of dividing the hour into minutes and the minutes into

seconds. I have found this system is given by the rotational angular momentum of the Earth in terms the

solar system Planck-type constant, because, as I already pointed out:

This base 60 counting combined with dividing the day into 24 units is mathematically optimal because

the rotational angular momentum incorporates not just the day (rotation period of the Earth) but the mass

and size of the Earth. And, as I said, we are touching on archaeoastronomy, as well. This is because

60/24=2.5 and the Scottish engineer, Alexander Thom, found ancient megalithic (stone) observatories

throughout Europe may have been based on a unit of length he called the megalithic yard and that the

separations between stones, that align with celestial positions and cycles, are recurrently separated by 2.5

megalithic yards. Like in Stonehenge.

Finally, this has applications in SETI (The Search For Extraterrestrial Intelligence) because we have

found that the unit of one second may be a universal constant, and, as such, alien civilizations might use

it. As such in sending us a radio message to let us know that they are there may be encoded, for example,

or pulsed, in intervals of a second, aside from the fact that the theory has to do with habitable star systems

in general, perhaps giving us an idea of what to look for in ﬁnding them, and in understanding them.

I have computed my Planck-type constant, , as such:

Where

planet

⋆

⊙

earth

ℏ

⊙

24 = 60

earth

π M

ℏ

⊙

ℏ

⊙

= (hC )K E

hC = 1secon d

C =

⋅

π r

G m

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Conclusion: We live in a mysterious and enigmatic universe where a great deal deﬁes explanation.

Through the characteristic time of one second we may be able to describe a great deal of it in a uniﬁed

perspective that has applications across various disciplines from the physical to the biological and the

astrobiological. Here, we have laid out the basis set for a complete theory, in simple terms, but a great

deal remains to be done in opening it up with more sophisticated mathematics and computer modeling

than I have been able to do. We need to do this with various specializations in many ﬁelds that no one

person can understand in their entirety.

ℏ

⊙

= (hC )K E

earth

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