A large numbers coincidence

Sahil Gupta
5 min readNov 29, 2021

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I found a precise, extreme, and symmetric coincidence involving all the fundamental physical constants, which led to a series of questions, which led to a realization that the Big Bang cosmological model is false.

FYI

Coincidence hunting is not science. But assuming that the fundamental constants are related is consistent with the idea that the universe is a connected structure describable with shapes and numbers. Coincidences have sparked physic equations before, from those of planet orbit period and radius (Kepler) to units of charge and the speed of light (Weber) to wavelengths of hydrogen emission (Balmer). Similarly, the occurrence of ~ 10⁴⁰ in cosmic and atomic ratios has sparked Large Numbers Hypotheses (Weyl, Dirac) (Dinculescu, Kritov), of which this coincidence is an iteration.

The Big Bang LCDM model is considered fact in modern academic science, but modest scrutiny reveals serious issues, such as claims that “galaxies move faster than the speed of light” or that “space expands faster than the speed of light”, and the inability to explain recent observations of mature galaxies in the distant universe (XMM-2599, SPT0418-47, MRG-M2129).

The coincidence with Planck’s constant

c is the speed of light.
h is Planck’s constant, the ratio of a photon’s energy to its frequency (E=hf).

A coincidence is
h proton mass * proton charge radius * c * π/2.

import math

c = 2.99792458 * 10**8 # meters / second
h = 6.62607004 * 10**-34 # meter^2 * kilogram / second

proton_mass = 1.6726219 * 10**-27 # kilograms
electron_mass = 9.1093837 * 10**-31 # kilograms

# measured in the lab https://physics.nist.gov/cgi-bin/cuu/Value?rp
proton_charge_radius_lab = 8.414 * 10**-16 # meters

h_maybe = proton_mass * proton_charge_radius_lab * c * math.pi/2
print(str(h_maybe) + ' meter^2 * kilogram / second')
>> 6.62736464226731e-34 meter^2 * kilogram / second

~ 6.627 * 10^-34 m^2*kg/s! Almost exact!

The coincidence is likely true, because the expression pries open Planck’s constant with properties of the proton, which exists at the scale of what Planck’s constant describes. (The π/2 may be mappable to an arc-radius ratio, and is worth investigation.)

Then, I applied the possible expression for the proton charge radius to Dirac’s large numbers hypothesis.

The coincidence with Hubble’s constant

H is Hubble’s constant, the cosmological rate of redshift.
G is the gravitational constant.

A coincidence is
1/H * cthe radius of an electron mass photon * the radius of a proton charge
/ the radius of a proton mass black hole.

G = 6.67430 * 10**-11                    # meter^3 / kilogram / second^2

electron_mass_photon_radius = h / (electron_mass * c * 2*math.pi)
proton_charge_radius_maybe = h / (proton_mass * c * math.pi/2)
proton_mass_black_hole_radius = 2 * G / c**2 * proton_mass

VALUE = electron_mass_photon_radius * proton_charge_radius_maybe / proton_mass_black_hole_radius
print(str(VALUE) + ' meters')
>> 1.3076515309253237e+26 meters
H_maybe = c / VALUE
print(str(H_maybe) + ' 1/second')

# H in the "Standard Model" Doppler interpretation of redshift
conversion_to_km_s_mpc = 3.08570 * 10**19
print(str(H_maybe * conversion_to_km_s_mpc) + ' kilometer / second / megaparsec')
>> 2.292602049629079e-18 1/second
>> 70.74282144540449 kilometer / second / megaparsec
hubble_time_maybe = 1/H_maybe
print(str(hubble_time_maybe) + ' seconds')
conversion_to_billion_years = 1 / 3600 / 24 / 365 / 10**9
print(str(hubble_time_maybe * conversion_to_billion_years) + ' billion years')
>> 4.3618559974758394e+17 seconds
>> 13.831354634309486 billion years

~ 13.8 billion years! This is within bounds of recent measurements https://arxiv.org/abs/2106.15656!

Discussion

How does one evaluate this considering the commonly accepted notion that 13.8 billion years is an “age”?

How can a constant be an age? Don’t ages go up?

Does that make this coincidence temporary? Maybe H varies, and 13.8 billion years is the “age of the universe”.

Or H is a constant, and 13.8 billion years is not an age. And the universe has no age.

Meanwhile, what about the other constants? Does G change? A “time-varying-G”? What would that be like? Earth formed 4.5 billion years ago. Would that be gravity changing by some 4.5/13.8 ≈ 30%?? More likely is gravity was the same strength and G is a constant.

Returning to the meaning of H, where does it come from? A measure of redshift.

The big bang model claims the redshift is caused by galaxies receding or “space expanding”, so if one imagines time in reverse, everything was coming closer together, and 13.8 billion years ago everything was at a single point.

But what if galaxies are not receding? The Doppler effect is real and galaxies do drift, but galaxies drifting and their minor redshift and blueshift is different from the cosmic redshift. What if the Doppler interpretation of cosmic redshift is false? What if “space expanding” is false?

Hubble’s raw experimental measurement was photon redshift, a measure of photon energy loss. What if photons simply lose energy traveling in intergalactic space?

Excursion

I tested this idea against all redshift data from the NASA extragalactic database.

Blue points are raw data. Red points are the model of photons losing energy. Orange points are the model of galaxies receding.

https://docs.google.com/spreadsheets/d/1HI61-pDIzzSItw48K0gar1pEt2xsA9cfF9EOy511G8w

Photons continuously losing energy while traveling is a better fit than galaxies receding from the Milky Way.

This simple test supports the idea that the cosmic redshift is continuous photon decay, where 1/(13.8 billion years) is the best fit coefficient. An emitted photon moves in intergalactic space and loses energy as e^-x. Specifically, after a photon travels for t time or d distance,
E_observed / E_emitted = e^(-Ht) = e^(-d/(c/H)).

What causes the photon energy loss? There will be room for many verbal explanations. Here are a few. All the matter in space is gravitationally connected, and there is a cost forging through it. The photon continuously cools. It takes work to move. The photon imparts motion to its surroundings, and energy is conserved.

This is the essence of Zwicky’s and Nernst’s light fatigue model, which was pejored as tired light and then straw-manned. The common criticisms (supernovae light curves, cosmic microwave radiation, no blurriness) can be rebutted (supernovae studies introduced bias when calibrating data (SALT2), ambient microwave radiation was actually predicted by non-big-bang models decades before Penzias and Wilson, that photons losing energy must cause a blurry image is a false precept).

Maybe it’s time for a new term for this model of cosmic redshift, photon hubbling.

The photon gets hubbled as it moves.

Conclusion

All the fundamental constants can be equated in a way that a cosmic photon length / an electron photon length = a proton charge length / a proton gravity length.

In other words, a ratio of photon extremes = a ratio of proton extremes.

Precise, extreme, and symmetric, with not a fundamental constant absent.

This gives a reason to think 1/H (~ 13.8 billion years) is derivable from c G h m_electron and m_proton, 13.8 billion years is a constant and not an age, and the universe has no age.

Sahil Gupta
Big Circus Model
bigcircusmodel.org

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