$$\left(\frac{1}{6\alpha^2}\sqrt{\frac{4\pi h}{Gc}}\right)\cdot\frac{r_p}{m_p}=1second$$

13.

$$\frac{Gm_p^2}{r_p^2}=\frac{h}{c}\cdot\frac{1}{t_1^2}\cdot\frac{4\pi}{36\alpha^4}$$

14.

$$F_{pp}=F_n\cdot\frac{4\pi}{36\alpha^4}$$

15.

$$\left(\frac{1}{9}\cdot\frac{\phi\pi}{\alpha^4}\right)\left(\frac{r_p}{Gm_p^2}\right)\left(\frac{h^2}{c^2}\cdot\frac{1}{m_p}\cdot\frac{1}{t_1^2}\right)=1$$

16.

$$\left(\frac{1}{U_{pp}}\right)\left(U_n\right)\left(\frac{1}{9}\cdot\frac{\phi\pi}{\alpha^4}\right)=1$$

$$U_n=\left(\frac{h^2}{c^2}\cdot\frac{1}{m_p}\cdot\frac{1}{t_1^2}\right)$$

17.

$$\frac{\frac{4\pi}{36\alpha^4}}{\frac{1}{9}\frac{\phi\pi}{\alpha^4}}=\Phi$$

18.

$$\frac{F_{pp}}{F_n}=\Phi\frac{U_n}{U_{pp}}$$

19.

$$\left(F_{pp}\right)\left(U_{pp}\right)=\left(F_n\right)\left(U_n\right)\Phi$$

$$\frac{2.7E-34N}{2.21E-42N}\cdot\frac{2.92E-57J}{2.24E-49J}=1.6=\Phi$$

Click here to read A Theory For The Property Of Inertia (mass) Looking At The Proton

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

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 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

$$\frac{\hbar_{\odot}^2}{GM_m^3}\cdot\frac{1}{c}=1second$$

\(M_m\) is the mass of the Moon. I find \(\hbar_\odot\), which is my Planck-type constant for the Solar System, much like the Planck constant in quantum mechanics used to describe the atom \(\hbar\), 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

$$\hbar_\odot=(1second)KE_e$$

where \(KE_e\)is the orbital kinetic energy of the Earth. I know this value for \(\hbar_\odot\) is accurate because the solution for the energy of the Earth orbiting around the Sun using this value, which is much like the solution for the electron around the proton in an atom, is 99.5% accurate. It is:

$$KE_e=\sqrt{n}\frac{R_\odot}{R_m}\cdot\frac{G^2M_e^2M_m^3}{2\hbar_\odot^2}$$

where \(n=3\) is the earth orbital number, and \(R_\odot\) is the radius of the Sun, and \(R_m\) is the radius of the Moon, \(M_e\) is the mass of the Earth, \(M_m\) is the mass of the Moon, and \(G\) is the universal constant of gravitation. The radius of the Sun,\(R_\odot\) , plays the role of \(Z\), the number of protons being orbited by an electron in an atom, but must be normalized by the radius of the Moon, \(R_m\). This gives it a size of 400 because \(R_\odot/R_m=400\). 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:

$$\frac{r_{planet}}{r_{moon}}=\frac{R_{star}}{R_{moon}}$$

Where \(r_{planet}\) is the orbital radius of the habitable planet (like the Earth), \(r_{moon}\) is the orbital radius of the moon, like the orbital radius of our moon around the Earth, \(R_{star}\) is the radius of the star, like our Sun, and \(R_{moon}\) 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

$$\frac{KE_m}{KE_e}(EarthDay)= 1.1-1.3 seconds$$

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

$$\frac{KE_m}{KE_e}(EarthDay)cos(\theta)= 1.0seconds$$

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

$$\left(\frac{1}{6\alpha^2}\sqrt{\frac{4\pi h}{Gc}}\right)\cdot\frac{r_p}{m_p}=1second$$

$$\left(\sqrt{\phi\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1second$$

\(r_p\) is the proton radius, \(r_m\) its mass. \(\phi=0.618\) is the golden ratio. \(\alpha\) 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

$$r_p=\phi\frac{h}{cm_p}$$

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

$$\frac{1}{6protons}\cdot\frac{1}{\alpha^2}\cdot\frac{r_p}{m_p}\sqrt{\frac{4\pi h}{Gc}}=1 second$$

$$\frac{1}{1proton}\cdot\frac{1}{\alpha^2}\cdot\frac{r_p}{m_p}\sqrt{\frac{4\pi h}{Gc}}=6 seconds$$

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 \(\Gamma \) falls below the Hubble parameter, the expansion rate of the universe \(H\). The reaction rate per particles is given by

$$\Gamma\approx G_F^2T^5$$

\(G_F\) is the Fermi constant is about \(1.166E-5GeV^{-2}\), and \(T\) is the temperature of the Universe. The expansion rate of the universe is given by

$$H\approx\frac{T^2}{M_{Pl}}$$

Where \(M_{Pl}\) is the Plank mass is about 1.22E19GeV. \(\Gamma\) and \(H\) have units of inverse time (\(s^{-1}\). Neutrino decoupling happens when

$$G_F^2T^5=\frac{T^2}{M_{Pl}}$$

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

$$H^2=\frac{8\pi G}{3}\rho$$

Where \(\rho\) is the energy density of the Universe. It is

$$\rho\propto T^4$$

The Hubble expansion rate is

$$H\propto \frac{T^2}{M_{Pl}}$$

$$M_{Pl}\approx2.4E18GeV$$

Since

$$t\propto\frac{1}{H}$$

we have

$$t\propto\frac{M_{Pl}}{T^2}$$

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

$$t\propto\frac{2.4E18GeV}{(1E-3GeV)^2}=2.4E24GeV^{-1}$$

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

$$1GeV^{-1}=5.39E-{25s}$$

we have

$$t\approx(2.4E24)(5.39E-25)$$

$$t\approx 1.3 seconds$$

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 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:

$$P(R)=P_0\left(\frac{R}{R_0}\right)^{-\frac{L_{earth}}{\hbar_\odot}}$$

$$\frac{L_{earth}}{\hbar_\odot}24=60$$

$$L_{earth}=\frac{4}{5}\pi M_ef_eR_e^2$$

Where the rotational angular momentum, \(L_{earth}\), 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:

$$\frac{dP}{dr}=-\rho\left(\frac{GM_\star}{r^2}-\frac{v_\phi^2}{r}\right)$$

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 \(v_\phi^2/r\) and the inward gravitational force on the disc from the protostar \(GM_\star/r^2\), and these are related by \(\rho\) 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:

$$R_{planet}=2\frac{R_\star^2}{r_{planet}}$$

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 \(r_{planet}\), 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:

…

F8V Star

Mass: 1.18

Radius: 1.221

Luminosity: 1.95

$$M_\star=1.18(1.9891E30kg)=2.347E30kg$$

$$R_\star=1.221(6.9634E8m)=8.5023E8m$$

$$r_p=\sqrt{1.95L_\odot}AU=1.3964AU(1.496E11m/AU)=2.08905E11m$$

$$R_p=\frac{2R_\star^2}{r_p}=2\frac{(8.5023E8m)^2}{2.08905E11m}=\frac{6.92076E6m}{6.378E6m}=1.0851EarthRadii$$

F9V Star

Mass: 1.13

Radius: 1.167

Luminosity: 1.66

$$M_\star=1.13(1.9891E30kg)=2.247683E30kg$$

$$R_\star=1.167(6.9634E8m)=8.1262878E8m$$

$$r_p=\sqrt{1.66L_\odot}AU=1.28841AU(1.496E11m/AU)=1.92746E11m$$

$$R_p=\frac{2R_\star^2}{r_p}=2\frac{(8.1262878E8m)^2}{1.92746E11m}=\frac{6.852184E6m}{6.378E6m}=1.0743468EarthRadii$$

G0V Star

Mass: 1.06

Radius: 1.100

Luminosity: 1.35,

$$M_\star=1.06(1.9891E30kg)=2.108446E30kg$$

$$R_\star=1.100(6.9634E8m)=7.65974E8m$$

$$r_p=\sqrt{1.35L_\odot}AU=1.161895AU(1.496E11m/AU)=1.7382E11m$$

$$R_p=\frac{2R_\star^2}{r_p}=2\frac{7.65974E8m)^2}{1.7382E11m}=\frac{6.751E6m}{6.378E6m}=1.05848EarthRadii$$

G1V Star

Mass: 1.03

Radius: 1.060

Luminosity: 1.20

$$M_\star=1.03(1.9891E30kg)=2.11E30kg$$

$$R_\star=1.060(6.9634E8m)=7.381E8m$$

$$r_p=\sqrt{1.20L_\odot}AU=1.0954AU(1.496E11m/AU)=1.63878589E11m$$

$$R_p=\frac{2R_\star^2}{r_p}=2\frac{7.3812E8m)^2}{1.63878589E11m}=\frac{6.6491E6m}{6.378E6m}=1.0425EarthRadii$$

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.

In order to get \(r_{planet}\), 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:

$$r_{planet}=\sqrt{\frac{L_\star}{L_\odot}}AU$$

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:

$$\frac{L_{earth}}{\hbar_\odot}24=60$$

$$L_{earth}=\frac{4}{5}\pi M_ef_eR_e^2$$

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, \(\hbar_\odot\), as such:

$$\hbar_\odot=(hC)KE_e$$

$$hC=1second$$

Where

$$C=\frac{1}{3}\cdot\frac{1}{\alpha^2c}\sqrt{\frac{2}{3}\cdot\frac{\pi r_p}{Gm_p^3}}$$

$$\hbar_\odot=(hC)KE_{earth}=(1.03351s)(2.7396E33J)=2.8314E33J\cdot s$$

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.

Click here to read Presentation: How a Characteristic Time of One Second May Describe Physical and Biological Systems in General

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Click here to read Angular Momentum, Quantum Gravity, and Megalithic Sites

It may be that the problem of reconciling gravity with quantum mechanics is an abstract problem, one that may have already been encountered by our ancient ancestors who erected stone observatories like Stonehenge (megalithic sites) and it may be that they found the solution in the megalithic yard, a unit of measurement for aligning stones. Presented here is the author’s earlier theory that provides a wave solution to the Earth/Moon/Sun system that is solved with a characteristic time of one second that is shown to solve also the atom’s proton. As such, it is suggested we can look at the Solar System, which is gravitational, to solve the quantum realm and provide a grand unified theory. It is suggested we might be able to help find such a solution by looking at ancient megalithic sites.

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Click here to read Does A Prebiotic Path To Life Exist?

If you have read my work in astronomy theories, you know it provides a theory that applies to the physical problem of habitable planets and star systems in general, so, naturally I am interested in the biological problem of a prebiotic path to life, even though I am not a biologist. Luckily I can read the textbooks on astrobiology (also called exobiology) which frames the question of life not just in terms of the Earth, but in terms of star systems in general, and I can read them because with training in physics I know enough chemistry to follow it, biology mostly being chemistry. Here is what I found the main stumbling blocks were, with the major ones seeming to be in a lack of phosphorus on Earth, followed by Chat GPT’s analysis of these paragraphs..."

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