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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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May 09, 2025Conclusion: Not only is the unit one second of time the characteristic time of the atom’s proton, which we can derive by a proposal for an equation of its radius founded in the golden ratio, but it is the characteristic time of the wave equation solution to the Earth/Moon/Sun system. The unit of a second further presents itself in the establishment of protons in the Universe at about t=1 second after the Big Bang. This means we not only have some keys to theories in particle physics but in cosmology and the science of planetary formation, if not for a theory bridging the microcosmos to the macrocosmos. The theory may prove very useful for exobiology (or astrobiology) because it may have a great deal to say about what kinds of stars are optimally habitable because it is possible this occurs when the characteristic time of one second for star system solutions of the wave equation is close the characteristic time for the planet day of the habitable planet, as is the case for the Earth/Moon/Sun system. We further find that the Earth’s moon may play a more significant role in the wave solution for the Solar System than we may have suspected. The solar radius in terms of moon units plays the role of Z, the number of protons, in wave solutions of the atom. Interestingly, the theory may have applications in archaeology and archaeoastronomy because the unit of a second came to us from the way the ancient Sumerians divided up the Earth’s rotation using their base 60 counting. This may be because 60 is the smallest integer that divides the consecutive integers 1,2,3,4,5.6 evenly, and we have suggested the physics of our theory may be based on six-fold symmetry, which is a very dynamic number responsible for the carbon atom’s extraordinary stability. We also show our characteristic time of 1 second for the carbon atom, and 6 seconds for the hydrogen atom, may be at the root of a theory for biological systems.
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The Second As A Universal Characteristic Time
Abstract: I present my findings that show a characteristic time of one second is in a wave solution of the Solar System and the atom’s proton in common. As well I show it describes the hydrocarbons, the skeletons of biological life chemistry. I show the unit of a second is not arbitrary, as history would have it, but rather comes from the wise decision of the ancient Sumerians to have developed an Earth day (rotation period) of 24 hours and a base 60 counting system. I also find the characteristic time of 1 second is in the protoplanetary disc and in the formation of the proton in the Big Bang that gave birth to the Universe.
In the expression on the left of the equation:
$$\left(\frac{1}{6\alpha^2}\sqrt{\frac{4\pi h}{Gc}}\right)\cdot\frac{r_p}{m_p}=1second$$
it has units of mass times time divided by the mass of a proton. This means we have divided the mass \(6m_p\) into a mass times a time giving one second. You want it to be like this because I found:
$$\left(\sqrt{\phi\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1second$$
Thus we can equate these two equations to get the radius of a proton:
$$r_p=\phi\frac{h}{cm_p}$$
Where \(\phi=0.618\) is the golden ratio. The most recent value is 0.833E-15m. This is very close to the radius of a proton, and may actually be the radius of a proton because \(\phi=0.618\) is the golden ratio which optimizes things in many systems, and the tendency over the years in measuring the proton's size is that it is getting smaller. The historic value was 0.877E-15m, 4% larger than the current value. That value was measured twice by two different methods a long time ago. I find it can be approximated by introducing the fibonacci ratio of 2/3 that approximates the golden ratio by replacing the golden ratio with it, thus using:
$$r_p=\frac{2}{3}\cdot\frac{h}{cm_p}$$
$$r_p=\frac{2}{3}\cdot\frac{6.62607E-34}{(299,792,458)(1.67262E-27)}=0.88094E-15m$$
The proton is thought not to have a precise radius but rather is changing by small amounts around a central value due to it really being a fuzzy cloud of subatomic particles. Thus
$$\left(\sqrt{\frac{2}{3}\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1second$$
$$\left(\sqrt{\phi\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1second$$
are both close to a second, just the first is a little over a second and the second is just under a second, But let us ask what is
$$\left(\frac{1}{6\alpha^2}\sqrt{\frac{4\pi h}{Gc}}\right)\cdot\frac{r_p}{m_p}=1second$$
It is action \(h\) or energy over time as it occurs due to the nature of space, reduced by G, the pliability of space, and the speed of light, c, the speed at which things interact, for the size of a proton \(r_p\) and its mass \(m_p\). \(4\pi\) is introduced for the surface area of a proton. We find then, this gives the characteristic time for the proton, which happens to be nicely one second, But why the 6 in \(6m_p\)? Well this says six protons give a characteristic time of one second. This means six protons which is carbon, the core element of life, is described by one second. You want that because it has been found carbon is the most stable element in terms of which to study other elements because a configuration of 6 protons, or six electric fields, comes out mathematically stable. This can be thought of loosely as the six sided figure, a regular hexagon, has its sides equal in length to its radii thus resulting in dynamic stability associated with six-fold symmetry. It is why the bee’s honeycomb is tessellated regular hexagons. The same goes for the six electrons orbiting, and attracted to, the six protons. Thus you want the basis unit of our physics, 1 second, associated with carbon, 6 protons. But further, since you want your physics to be based on the six-fold you want six seconds to give the proton, or hydrogen atom, because it is the basis unit of chemistry; 1 proton, 1 electron, which it does. We have
$$\frac{1}{6protons}\cdot\frac{1}{\alpha^2}\cdot\frac{r_p}{m_p}\sqrt{\frac{4\pi h}{Gc}}=1 second$$is carbon (C)
$$\frac{1}{1proton}\cdot\frac{1}{\alpha^2}\cdot\frac{r_p}{m_p}\sqrt{\frac{4\pi h}{Gc}}=6 seconds$$is hydrogen (H)
A very interesting thing here is, 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 life chemistry.
And indeed for our solar system the characteristic time is one second as well. The Planck type constant \(\hbar_\odot\) for the solar system I found is is given by the Earth orbit meaning the Earth quantizes angular momentum for the system
$$\hbar_\odot=(1second)KE_e$$
That is, it is 1 second times the kinetic energy of the Earth. But, the ground state is given by the Moon orbiting the Earth$$\frac{\hbar_{\odot}^2}{GM_m^3}\cdot\frac{1}{c}=1second$$
Where \(M_m\) is the mass of the Moon. That is,
$$\frac{\hbar_\odot^2}{GM_m^3}=\frac{(2.8314E33)^2}{(6.67408E-11)(7.34763E22kg)^3}=3.0281E8m$$
is the analogy to the ground state of the hydrogen atom:
$$r_1=\frac{\hbar^2}{ke^2m_e}$$ $$r_1\approx0.529E-10m$$We know our Planck constant for the Solar System is correct, \(\hbar_\odot\), because we have
$$KE_e=\sqrt{n}\frac{R_\odot}{R_m}\cdot\frac{G^2M_e^2M_m^3}{2\hbar_\odot^2}$$
Is 99.5% accurate. n=3 is Earth orbit, \(R_\odot\) the radius of the Sun, \(R_m\) the radius of the Moon:
$$E_n=\sqrt{n}\frac{R_\odot}{R_m}\frac{G^2M_e^2M_m^3}{2\hbar_\odot^2}$$
$$\frac{R_\odot}{R_m}=\frac{6.96E8m}{1737400m}=400.5986$$$$E_3=(1.732)(400.5986)\frac{(6.67408E-11)^2(5.972E24kg)^2(7.347673E22kg)^3}{2(2.8314E33)^2}$$
==2.727E33J
The kinetic energy of the Earth is
$$KE_e=\frac{1}{2}(5.972E24kg)(30,290m/s)^2=2.7396E33J$$ $$\frac{2.727E33J}{2.7396E33J}100=99.5\%$$ Which is very good, about 100% accuracy for all practical purposes. $$\frac{R_\odot}{R_m}\rightarrow Z^2$$
The radius of the Sun in lunar radii, plays the role of the number of protons, Z, for the atom. That is for the atom:
$$E_n=-\frac{Z^2(k_ee^2)^2m_e}{2\hbar^2n^2}$$
The characteristic time of about one second gives us, as well, the rotation period of the Earth, 24 hours, in terms of the kinetic energies of the Moon and the Earth:
$$\frac{KE_m}{KE_e}(EarthDay)= 1.1-1.3 seconds$$
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:
$$KE_{moon}=\frac{1}{2}(7.347673E22kg)(966m/s)^2=3.428E28J$$
$$KE_{earth}=\frac{1}{2}(5.972E24kg)(30,290m/s)^2=2.7396E33J$$
Even though the second came to us historically because the ancient Sumerians divided the Earth day (rotation period) into 24 hours, and because each hour and minute got further divisions by 60 because of their base 60 counting system by the ancient Babylonians that inherited it from the ancient Sumerians, the division is not arbitrary, and hence neither is the second, because I have found this system is given by the rotational angular momentum of the Earth in terms the solar system Planck-type constant:
$$\frac{L_{earth}}{\hbar_\odot}24=60$$
$$L_{earth}=\frac{4}{5}\pi M_ef_eR_e^2$$ Where the 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 by modeling our Solar System is found to be the exponent in the pressure gradient for the protoplanetary disc from which our Solar System formed. That is I found$$P(R)=P_0\left(\frac{R}{R_0}\right)^{-\frac{L_{earth}}{\hbar_\odot}}$$
the pressure of the disc as a function of radius. Which suggests that the structure of the protoplanetary disc could be governed by the same fundamental time of one second in the Earth’s rotation and that the Earth’s formation process may be encoded in the same number we developed since ancient times to describe time (24, 60). 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. It is the pressure gradient of the disc in radial equilibrium balancing the inward gravity and outward centripetal force. 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 it is good for life chemistry. 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 $$M_\star=1.06(1.9891E30kg)=2.108446E30kg$$ $$R_\star=1.100(6.9634E8m)=7.65974E8m$$ $$r_p=\sqrt{1.35L_\odot}AU=1.161895AU(1.496E11m/AU)=1.7382E11m$$ $$R_p=\frac{2R_\star^2}{r_p}=2\frac{7.65974E8m)^2}{1.7382E11m}=\frac{6.751E6m}{6.378E6m}=1.05848EarthRadii$$
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.
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:
$$r_{planet}=\sqrt{\frac{L_\star}{L_\odot}}AU$$
Also, the theory utilizes the fact that the Moon as seen from the Earth perfectly eclipses the Sun as a possible condition for optimal habitability of the planet, which is
$$\frac{r_{planet}}{r_{moon}}=\frac{R_{star}}{R_{moon}}$$
Orbital radius of the planet to that of the moon is radius of the star to that of the moon. It is known that the Moon has a lot to do with the conditions for life on Earth being good because its orbit holds the Earth at its inclination to the Sun its orbit preventing temperature extremes and allowing for the seasons. It may be the ancient Sumerians accidentally gave us the second, which turns out to be Natural, not arbitrary, because they chose base 60 as their counting system because it was evenly divisible by the first six integers1, 2, 3, 4, 5, 6, the smallest number that does this, and this is to introduce six-fold symmetry that is a heart of stable dynamics.
How we derive the solar system Planck-type constant:
$$\hbar_\odot=(hC)KE_e$$
$$hC=1second $$
Where
$$C=\frac{1}{3}\cdot\frac{1}{\alpha^2c}\sqrt{\frac{2}{3}\cdot\frac{\pi r_p}{Gm_p^3}}$$$$C=\frac{1}{3}\cdot\frac{1}{\alpha^2c}\sqrt{\frac{1}{3}\cdot\frac{2\pi r_p}{Gm_p^3}}$$=
$$\frac{1}{3}\cdot\frac{18769}{299792458}\sqrt{\frac{1}{3}\cdot\frac{2\pi(0.833E-15)}{(6.67408E-11)(1.67262E-27)^3}}$$
=$$1.55976565E33$$
=$$\frac{s}{m}\sqrt{\frac{m}{kg^3}\cdot\frac{s^2kg}{m^3}}=\frac{s}{m}\sqrt{\frac{s^2}{kg^2m^2}}=\frac{s}{m}\cdot\frac{s}{kg\cdot m}=\frac{1}{kg}\cdot\frac{s^2}{m^2}$$
$$\frac{1}{C}=kg\frac{m^2}{s^2}=\frac{1}{2}mv^2=energy$$$$hC=(6.62607E-34)(1.55976565E33)=1.03351seconds\approx1.0seconds$$
$$hC=\left(kg\frac{m}{s^2}\cdot m\cdot s\right)\left(\frac{1}{kg}\cdot\frac{s^2}{m^2}\right)$$
=$$\left(kg\frac{m^2}{s}\right)\left(\frac{1}{kg}\cdot\frac{s^2}{m^2}\right)=seconds$$
$$KE_{earth}=\frac{1}{2}(5.972E24kg)(30,290m/s)^2=2.7396E33J$$
$$\hbar_\odot=(hC)KE_{earth}=(1.03351s)(2.7396E33J)=2.8314E33J\cdot s$$
I find we can write a solution for the kinetic energy not in terms of the Moon and the Earth, but in terms of the Sun and the Earth, which is
$$KE_e=\frac{R_\odot}{R_m}\cdot\frac{G^2M_e^4M_\odot}{2L_p^2}$$
To do this we have to use the condition of a perfect eclipse:
$$\frac{R_\odot}{R_m}=\frac{r_e}{r_m}$$
And, use the orbital velocity of the Earth given by
$$v_m^2=\frac{GM_e}{r_m}$$
And, redefining \(\hbar_\odot\) as
$$\hbar_\odot=9.13E38J\cdot s$$
which would come from
$$L_p=r_ev_mM_e=(1.496E11m)(1022m/s)(5.972E24kg)=9.13E38kg\cdot\frac{m^2}{s}$$
$$L_p\rightarrow\hbar_\odot$$
This gives the two different Planck-type constants for the solar system are related by
$$L_p=\sqrt{\frac{M_e^2M_\odot}{M_m^3\sqrt{3}}}\cdot\hbar_\odot$$
However, this again yields the characteristic time of one second by using \(\hbar_\odot=1sec(1/2)M_ev_e^2\):
$$1second=2r_p\frac{v_m}{v_e^2}\sqrt{\frac{M_m^3\sqrt{3}}{M_e^2M_\odot}}$$
Where the square root of 3 is the square root of the Earth orbital number.
The Protoplanetary Disc
If the characteristic time for both the solar system
$$\frac{\hbar_{\odot}^2}{GM_m^3}\cdot\frac{1}{c}=1second$$
and the proton
$$\left(\frac{1}{6\alpha^2}\sqrt{\frac{4\pi h}{Gc}}\right)\cdot\frac{r_p}{m_p}=1second$$
$$\left(\sqrt{\frac{2}{3}\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1second$$
are 1 second, then the characteristic time of 1 second should be in the protoplanetary disc from which the planets formed. I would guess it would be in the time between collisions of particles in the protoplanetary disc. Ultimately, the planets form from these collisions. The time between collisions in the protoplanetary disc are given byParticle number density n ( the number of particles per unit volume).
Relative velocity between particles \(v_{rel}\).
Particle cross-section (related to particle size).
For micron to millimeter sized grains in a dense inner region of the protoplanetary disc (like about 1 AU from the star, which is the Earth orbit) the range of these values are:\(n\approx10^{10}-10^{15}\)particles per meter cubed (from disc models)
Particles sizes are \(r\approx10^{-6}-10^{-3}\)meters.
Relative velocities of particles are \(v_{rel}\approx1-10m/s\) as driven by Brownian motion, turbulence, and gas drag.
We can imagine a scenario where this yields 1 second by using typical values:$$t_c\approx\frac{1}{(0.32\times10^{12}m^{-3})(\pi (10^{-6}m)^2(1m/s)}=1second$$
Our equation$$\left(\frac{1}{6\alpha^2}\sqrt{\frac{4\pi h}{Gc}}\right)\cdot\frac{r_p}{m_p}=1second$$
suggests that the proton’s fundamental structure encodes a natural unit of time, the presence of G, h, and c may emerge from a balance between gravity, quantum mechanics, and relativistic effects. Since the equation for the characteristic time of the solar system$$\frac{\hbar_{\odot}^2}{GM_m^3}\cdot\frac{1}{c}=1second$$
indicates that the solar system is quantized by planetary formation processes in a way that maintains a fundamental unit of periodicity of 1 second. So we are connecting the formation of entire planetary systems to the fundamental structure of matter itself (the protons). A micron-sized dust grain at about 10E-12 grams, has about 10E11 protons, a millimeter sized dust grain, about 10E-6 grams, has about 10E17 protons. But where did these dust grains come from? They formed in the protoplanetary gas cloud from elements, mostly hydrogen and helium, and elements like C, O, Si, and Fe, that formed from hydrogen and helium in stars by nucleosynthesis. The heavier elements are made from hydrogen and helium in stars then later expelled into space by supernovae. But where did the hydrogen (and some of the helium) come from? They were made in the Big Bang, so we should be able to track the characteristic time of the solar system, and proton back to the Big Bang and the formation of the Universe.
The Big Bang: In other words, if the planetary system inherits a characteristic time of 1 second from the dust grains in the protoplanetary disc, and the dust grains inherit a characteristic time of 1 second from the elements, and elements inherit the characteristic time of 1 second from the proton, then we would guess that the proton inherits the characteristic time of 1 second from its origins in the Big Bang that gave birth to the Universe. And, indeed it does:
Big Bang
(time=1second)
Around one second after the Big Bang, the universe had cooled enough that neutrinos decoupled, and protons and neutrons were forming in equilibrium, this is the moment when baryons (protons/neutrons) become stable, linking the 1-second time unit to matter itself. (time=1-3 minutes) At this time the first atomic nuclei (H, He, Li) form. Thus the 1-second time unit marks when the proton’s number became fixed in the Universe, given by our equations$$\left(\frac{1}{6\alpha^2}\sqrt{\frac{4\pi h}{Gc}}\right)\cdot\frac{r_p}{m_p}=1second$$
$$\left(\sqrt{\frac{2}{3}\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1second$$
which give the radius of a proton when set equal to one another$$r_p=\frac{2}{3}\cdot\frac{h}{cm_p}$$
Or,$$r_p=\phi\frac{h}{cm_p}$$
Where we say$$\left(\sqrt{\phi\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1second$$
Where$$\left(\sqrt{\frac{2}{3}\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1second$$
is a little over a second, and$$\left(\sqrt{\phi\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1second$$
is a little under a second. These equations contain the fundamental constants related to gravity (G), quantum mechanics (h), relativity (c), and electromagnetism (\(\alpha\)), constants that cover the fundamental forces that shaped the early Universe. G, h, c, and control the rate of interaction in the early universe, including weak interactions, and gravity, which govern proton stability and neutrino decoupling. Thus, our equations describe the fundamental physics at t=1 second, confirming that this time is deeply embedded in the structure of the Universe. This means the 1-second characteristic time was imprinted at the birth of the Universe then inherited by the proton through fundamental constants, planetary systems (through particles interactions in the protoplanetary discs), galaxies and cosmic evolution because protons make up most of the universe’s baryonic matter. My equations link proton properties to 1-second, and protons were fixed in the Universe at 1 second, meaning we could be seeing a universal clock that has influenced everything since the Big Bang. How is it figured that the protons and neutrons stopped converting into one another and their numbers in the Universe became set? 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$$G_F^2T^5=\frac{T^2}{M_{Pl}}$$
$$T_{decoupling}=(G_F^2M_{Pl})^{-1/3}$$
This happens when the temperature of the universe is \(T=1MeV\) which occurs at 1 second after the Big Bang. We know this because temperature evolves with time as$$T\propto t^{-1/2}$$
Meaning that the universe had cooled to 1MeV after 1 second. Before decoupling, the universe was so dense that protons and neutrons were constantly interconverting but because weak interaction stops maintaining neutron-proton equilibrium at 1 second, the proton to neutron ratio freezes in. Neutrons are unstable and decay with a half life of about 10 minutes, however when a few minutes after the bang they start forming, with protons, helium-4 nuclei, they become stable. The protons don’t decay rapidly so you end up with, after freezing, 6 times more protons than neutrons in the Universe, this explains why 25% of mass of the universe is helium. It is about 75% hydrogen. 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 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$$t\approx(2.4E24)(5.39E-25)$$
$$t\approx 1.3 seconds$$
Click here to read The Second As A Universal Characteristic Time
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April 14 2025Click 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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The Search For The Galactic Codex
I have found that our Solar System has a fascinating mathematical structure underlying it. Our planet is an extraordinary example of a life bearing world. The mathematical structure I have found in my wave solution of the Solar system for the Earth/Moon/System could be taken as characteristic of a star like our Sun. Naturally, in discovering something about our solar system we would wonder if other star systems have a dynamic mathematical construction as well. As such, we would want to go to other star systems and survey their characteristics, and any ancient history of how other civilizations measured time and made calendars based on their observations of celestial motions like we did with ours. We might guess that other civilizations in the universe might discover such incredible mathematical structure underlying their planetary systems as well and would, once they could achieve interstellar travel, begin a survey of the mathematical structure behind star systems of other life bearing worlds and create a collection of them done throughout the galaxy, and they may have worked with other civilizations throughout the galaxy and compiled, if you will, a Galactic Codex. Some may even have achieved intergalactic travel and found the thumbprints not just characteristic of star-types but of galaxy-types. Let us look at what I have found our first entries could be in a galactic codex, which would be for the star system we know best, our Solar System. We begin with the characteristic time for our solution is one second and is given by the mass of the moon, \(M_m\), cubed:
$$\frac{\hbar_{\odot}^2}{GM_m^3}\cdot\frac{1}{c}=1\text{ second}$$
Yes, it does happen to be one second, our base unit of time we have today, ultimately given to us by the ancient Sumerians when they invented mathematics thousands of years ago. This becomes important, as we will see. The other extraordinary thing we find is that the Planck-type constant for our solar system is given by the kinetic energy of the Earth, the third planet where life is extraordinarily abundant, multiplied by one second.
$$\hbar_\odot=(1\text{ second})KE_e$$
We find life occurs so successfully when the Earth day is about what it is today (24 hours long) giving a characteristic time of close to one second in terms of the kinetic energy of the Moon and the Earth:
$$\frac{KE_m}{KE_e}(\text{EarthDay})= 1.1 - 1.3 \text{ seconds}$$
I also find that this characteristic time of one second is characteristic of the proton, the most fundamental unit that makes up matter, predicting its radius:
$$\left(\frac{1}{6\alpha^2}\sqrt{\frac{4\pi h}{Gc}}\right)\cdot\frac{r_p}{m_p}=1\text{ second}$$
$$\left(\sqrt{\frac{2}{3}\cdot\frac{\pi r_p}{\alpha^4Gm_p^3}}\right)\frac{1}{3}\cdot\frac{h}{c}=1\text{ second}$$
Where \(r_p\) and \(m_p\) are the radius and mass of a proton. Equating these two gives about the radius of a proton:
$$r_p=\frac{2}{3}\cdot\frac{h}{cm_p}$$
The ancient Sumerians were responsible for giving us the unit of a second because they divided the earth’s rotation period, its day, into 24 hours, and the ancient Babylonians divided each hour into 60 minutes, and each minute into 60 seconds, from the ancient Sumerians base 60 mathematics. Perhaps the most exciting entry in our galactic codex is:
$$\frac{L_{earth}}{\hbar_\odot}24=60$$
Where \(L_{earth}\) is the rotational angular momentum of the Earth. This specifies not only is the rotation period of the Earth best measured by dividing the day into 24 units and 60 units, but that such an optimization includes the mass and radius of the Earth. Another exciting entry in our galactic codex is that during the time in the Earth’s history when the day is about 24 hours which specifies close to a second from the kinetic energies of the Earth and Moon, the Moon perfectly eclipsing the Sun as seen from the Earth, holds:
$$\frac{r_{planet}}{r_{moon}}=\frac{R_{star}}{R_{moon}}$$
\(r_{planet}\) is the orbital radius of the Earth, \(r_{moon}\) is the orbital radius of the Moon, \(R_{star}\) is the radius of the Sun, and \(R_{moon}\) is the radius of the Moon. There is a lot more that we will find in the course of this paper regarding the exciting entries to be made in this Galactic Codex. We will even find, with astronomy being what it is today, that we can begin to make entries in the codex for other star systems. But of course, to really understand such star systems, we want to go to them, and survey them not just physically, but archaeologically.
Perhaps, in our radio astronomy search for extraterrestrial intelligence (SETI) one of the transmissions we might receive might be not just the physical characteristics for their star and planet, but a Galactic Codex for many star systems. We even may be able to find traces of a galactic codex here on earth now, left in the ruins of archaeological sites. Such examples could be in clay Sumerian cuneiform tablets or in the megalithic yard which was perhaps a standard length used to construct megalithic sites, like Stonehenge. We will look at that, too, in this paper.
Click here to read The Search For The Galactic Codex
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Feb 2 2025 (updated March 11 2025)At the end of the paper we suggest that the one second characteristic time was created in The Big Bang and inherited by the protoplanetary disc.
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Does A Prebiotic Path To Life On Earth Exist
I have waded through the literature and the limiting factor is phosphate compounds.
In order to have life you need the 20 genetically encoded amino acids. DNA and RNA synthesize these into the proteins life needs. Miller and Urey simulated a hypothetical early Earth with the constituents water, methane, ammonia, and hydrogen mixing them together in a bottle and passing a current. They produced 11 of the genetically encoded amino acids, but not all of them.
Life also needs DNA and RNA. To have this you need the sugar ribose, phosphates, and the nucleobases adenine, cytosine, guanine, thymine, and uracil. Prebiotic paths, paths before life existed, to these nucleobases, exist, but they have to combine with ribose to make nucleosides, and these have to combine with phosphates to make nucleotides. There exist prebiotic paths to nucleotides, but they have to polymerize into long chains and the reactions required to do this use phosphate compounds that we know did not exist on early Earth. This is the main problem in trying to explain life on Earth. Phosphates are rare on Earth, life needs them for nutrients, and they are the limiting factor in Earth ecosystems that determine life density.
One could suggest life arose on planets that were rich in phosphates, evolved into intelligence, and polymerized nucleotides in a laboratory and put them on Earth.
The problem also that arises though, is the sequencing of the nucleobases into a complex set of instructions for synthesizing amino acids into the proteins life needs. We don’t know how such a set of instructions, the genetic code, could evolve into existence.
Further problems arise in the fats, or lipids; they make up a big part of the cells that make make up life that house the DNA and RNA.