On the Physics of Heaven and Hell 2.1.0

In Manichaeism, a religion founded by the Persian Mani in the third century, both light and dark, and good and evil, are eternal principles involved in an eternal struggle. The idea is an old one – Heraclitus born 535 BC says for example that “the path up and down are one and the same”. In The Marriage of Heaven Hell, William Blake illustrates the Manichean view that these principles are mutually dependant:

Without Contraries there is no progression. Attraction and Repulsion, Reason and Energy, Love and Hate are necessary to Human existence. From these contraries spring what the religious call Good & Evil. Good is the passive that obeys Reason. Evil is the active springing from Energy. Good is Heaven. Evil is Hell.

Blake is right to say that “Without Contraries there is no progression”, but there is no need for -nor any possibility of- progress unless one exists in an imperfect state…

These religious/philosophical ideas can be re-cast in the language of mathematical-physics, and in such a way as to reveal their falsity, to reveal that that darkness and evil are, not an eternal principle, but a finite disturbance of an eternal principle, not an eternal principle in themselves, but a privation of an eternal principle. To do so we use the equation

\lim_{x\to \infty } \left(e^{(s+1) \left(\zeta (s)-\frac{1}{s-1}\right)} \left(\left(\frac{1}{\exp \left((s+1) \left(\sum _{n=1}^x \frac{1}{n^s}-\int_1^x \frac{1}{n^s} \, dn\right)\right)}\right){}^{\frac{1}{s+1}}\right){}^{s+1}\right)=1

which is an extension of gamma, the zeta function, and the traditional equation for the area of an area-unit-circle

\pi \sqrt{\frac{1}{\pi }}^2=1

But, unlike its predecessor, the extended version allows for a potentially infinite hierarchy of energy levels arising from a singularity of light. From here we get:

\left(\frac{e^{2 \gamma } \left(e^{\frac{1}{s-1}-\zeta (s)}\right)^2}{e^{2 \gamma } \left(e^{\frac{1}{s-1}-\zeta (s)}\right)^2-e^{2 \gamma } \left(\exp \left(-\left(\sum _{n=1}^x \frac{1}{n^s}-\int_1^x \frac{1}{n^s} \, dn\right)\right)\right){}^2}\right){}^{1/s}

If and only if s = 1 then

\left(\frac{e^{2 \gamma } \left(e^{\frac{1}{s-1}-\zeta (s)}\right)^2}{e^{2 \gamma } \left(e^{\frac{1}{s-1}-\zeta (s)}\right)^2-e^{2 \gamma } \left(\exp \left(-\left(\sum _{n=1}^x \frac{1}{n^s}-\int_1^x \frac{1}{n^s} \, dn\right)\right)\right){}^2}\right){}^{1/s}=\frac{1}{1-e^{2 \gamma } \left(e^{-\left(\sum _{n=1}^x \frac{1}{n}-\int_1^x \frac{1}{n} \, dn\right)}\right){}^2}

This extension buys us a way to distort pi (in the sense of the ratio of the circumference to the diameter of a circle, not some particular number). If pi becomes larger than e^{2 \gamma } (s is a positive real number > 1), the result is a form of curvature in which light predominates over space, and if pi becomes smaller than e^{2 \gamma } (s is a positive real number < 1) the result is a form of curvature in which space predominates over light.  It also buys a universe in which there are distinct epochs, each of which is associated to a different set of fundamental physical constants.

Let s = 12, and let

\left(\frac{e^{2 \gamma } \left(e^{\frac{1}{s-1}-\zeta (s)}\right)^2}{\hbar =e^{2 \gamma } \left(e^{\frac{1}{s-1}-\zeta (s)}\right)^2-e^{2 \gamma } \left(\exp \left(-\left(\sum _{n=1}^7 \frac{1}{n^s}-\int_1^7 \frac{1}{n^s} \, dn\right)\right)\right){}^2}\right){}^{1/s} = the critical line/radius on the right hand side of which  curvature in the direction of light is non-classical. Then

Let s = 0.9, and let

\left(\frac{e^{2 \gamma } \left(e^{-\left(\zeta (s)-\frac{1}{s-1}\right)}\right)^2}{\sigma }\right)^{1/s} = the critical line on the right hand side of which curvature in the direction of space- gravitational curvature- is non-classical:

Polar plots of

e^{2 \gamma } \left(e^{-\left(\zeta (12)-\frac{1}{12-1}\right)}\right)^2-e^{2 \gamma } \left(\exp \left(-\left(\sum _{n=1}^{p_x} \frac{1}{n^{12}}-\int_1^{p_x} \frac{1}{n^{12}} \, dn\right)\right)\right){}^2


e^{2 \gamma } \left(e^{-\left(\zeta (0.9)-\frac{1}{0.9\, -1}\right)}\right)^2-e^{2 \gamma } \left(\exp \left(-\left(\sum _{n=1}^{p_x} \frac{1}{n^{0.9}}-\int_1^{p_x} \frac{1}{n^{0.9}} \, dn\right)\right)\right){}^2

 on the non-classical side of the critical line:

There is in this model a state of infinite light-density associated to the heavenly realm, and an arrow of time that points out of heaven and -without intervention from outside- leads irreversibly to hell. The Manichean view is that there is a marriage of heaven and hell, i.e. that light and darkness are mutually dependant. If Manichaeism is true -if Blake’s ideas expressed in The Marriage of Heaven and Hell are valid– then there would be no origin of our universe, a balance of light and dark, and no arrow of time. The universe would have the character implied by the Heraclitean principle of The Unity of Opposites, Nietzsche’s Doctrine of Eternal Recurrence, and expressed in mathematical more so than philosophical terms terms by the Steady State Theory, and by Roger Penrose’s Conformal Cyclic Cosmology. Instead however there unquestionably is an origin in pure light to which there can be no natural return, darkness dominates, and this dominance is rising.

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(1) Manichaeism, Encyclopædia Britannica

(2) Patrick, G trans. (2013), The Fragments of Heraclitus

(3) Blake (1790), The Marriage of Heaven and Hell

(4) McGill, V (1948), The Unity of Opposites: A Dialectical Principle

(5) Kierkegaard and Nietzsche (2007), Repetition and Notes on the Eternal Recurrence

(6) Bondi and Gold (1948), The Steady State Theory of the Expanding Universe

(7) Penrose, R (2010), Cycles of Time: An Extraordinary New View of the Universe