4000.6.  Derivation of General Formula for Constants of Cosmology and Quantum Mechanics — Part I

Author: Andrew Joseph Yanthar-Wasilik
Website: luxdeluce.com

Original date: 22 September 2017 AD, Feast of St Maurice
Edited: 11 September 2026, Feast of Sts. Protus & Hyacinth; St. Adelphus; St. Paphnutius

Dedication

This article is dedicated to Lord Jesus Christ, the Creator of the Universe and Beyond.

Abstract

This article derives general formulae for the components of an exponent expression used in calculations of cosmological and quantum-mechanical constants. The derivation is based on integer formulae for the dimensionless coupling constants of the electromagnetic, weak, and strong nuclear forces.

The principal expression is:

ExpM = (A / B)^C

The three constituent parts, A, B, and C, are derived as functions of the constant number, represented by .

1. Introduction

The general formulae in this article are developed from equations presented in the previous work:

Book 5 — Integer Formula for Dimensionless Coupling Constants of Fundamental Forces.

All coupling constants use the same underlying equations, from which their values may be calculated.

The integer formulae for selected coupling constants are:

Constant	Description	Integer Formula
	Fine-structure constant; electromagnetic force
	Weak force; force of decays
	Strong nuclear force; quarks and nucleons

From this partial sequence, a complete sequence may be obtained.

2. General Form of the Expression

The main exponent is defined as:

ExpM = (A / B)^C

where:

• A is derived from a linear sequence of exponents.
• B is derived from a related exponent sequence and a power-base function.
• C is derived from the constant sequence and a third exponent sequence.

Part A — Derivation of Ax

3. Exponent Sequence for Part A

At , there is an asymptote. The axis at  separates real and complex values, as shown by graphs of the function. This occurs when the denominator is 24.

At , the numerator equals zero.

	11	12	13	14	15	16	17
							—

The constant difference is:

This is the slope of the linear function:

Therefore:

The y-intercept occurs at :

Thus, the exponent may be expressed as:

4. Formula for Part A

The formula for Part A is:

Equation A

Part B — Derivation of Bx

5. Initial Examples

The sequence for Part B includes:

The exponent sequence in Part B is the exponent sequence from Part A multiplied by a factor of 11.

6. Exponent Sequence for Part B

	6	7	8	9	10	11
						—

The slope is:

The y-intercept is:

Therefore, the exponent for Part B is:

7. Base of the Power in Part B

The base sequence includes the expressions:

The term  in the expression  is the reciprocal of the exponent in Part A:

The remaining sequence is:

 

Therefore, the base of the power is:

 

Its reciprocal is:

8. Constant Function

The constant  is defined as:

Equation I

9. Formula for Part B

The formula for Part B is:

Equation B

Part C — Derivation of

10. Exponents in Part C

Examples of the exponent sequence are:

The sequence:

is one-third of the first exponent sequence:

Therefore:

Using the constant function from Equation I:

the exponent for Part C becomes:

Equation C

Editorial note: In the source text, the term  is used temporarily to distinguish this intermediate constant expression from the final .

11. Final Expression

The main exponent is:

Equation EM

where:

Substitution of Equations A, B, and C into Equation EM produces the full general expression.

 

12. Conclusion

This article has derived the component formulae A, B, and C used in the expression:

Part II will derive the general formula for any value of the constant alpha and for constants similar to alpha.

References

1. Brian Kell, Carnegie Mellon University (CMU).
   Reference cited in connection with methods for finding formulae for sequences.

Next Article

Book 6 — Derivation of General Formula for Constants of Cosmology and Quantum Mechanics — Part II