Can the Boltzmann and Bohr Magneton Constants Be Expressed as Nucleotide Bases via Quantum Superposition? ()

Tahir Ölmez^{}

Social Sciences Department, Selçuk University, Selcuklu, Turkey.

**DOI: **10.4236/oalib.1109653
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Social Sciences Department, Selçuk University, Selcuklu, Turkey.

This paper attempts to express the Boltzmann and the Bohr magneton constants with nucleotide bases (A T, G, C and U) as regards to Quantum Perspective Model. At first, if you take the exact value of Boltzmann and the Bohr magneton constants after the comma, you can convert this decimal base numbers to binary number base system. Secondly, after converting process of this numbers, you should sequence this numbers as decimal number base system again. Thirdly, sum this decimal base numbers respectively. Fourthly, total adding processes correspond to genetic codes [Adenine (A), Thymine (T) Guanine (G), Cytosine (C) and Uracil (U)]. Fifthly, the result explanations of Boltzmann and the Bohr magneton constants can be defined like this: [as the Boltzmann constant equals to Guanine (G): 78 and the Bohr magneton approximately equals to “66” Thymine (T)]. Sixthly, the dual explanation of Einstein’s mass energy equivalence can be stemmed from *Quantum Superposition*, since the Einstein’s mass energy equivalence can be sequenced as both “GAUCUAUCAAUC” and “GAUCUAUCTAUC” too. Seventhly, approximately the total atomic weight of nucleotide bases (A T, G, C and U) can be also expressed as the value of “Kelvin” temperature. Eighthly, let alone this result, the calculated total atomic weight of proton, neutron and electron also can be expressed as nucleotide bases (A T, G, C and U) “CTAGATATTTAGATAT”. Lastly, the NCBI (The National Center for Biotechnology Information) search results of this sequences are very interesting model organism consequence just like as “*Drosophila albomicans*” (*Fruit Fly*) which is also very similar genetic genes to human genes. As a result, the expression of Boltzmann and the Bohr magneton constants with genetic codes reach meaningful consequences to shed lights on novel research method between Quantum Physics and Biochemistry.

Keywords

Biochemistry, Quantum Superposition, Quantum Physics, Nucleotide Bases, Fruit Fly (Drosophia Albomicans), Binary Number Base Systems, Quantum Perspective Model, The Boltzmann Constant, The Bohr Magneton Constant, Einstein’s Mass Energy Equivalence

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Ölmez, T. (2023) Can the Boltzmann and Bohr Magneton Constants Be Expressed as Nucleotide Bases via Quantum Superposition?. *Open Access Library Journal*, **10**, 1-10. doi: 10.4236/oalib.1109653.

1. Introduction

The relationship between the nucleotide bases (also named as genetic codes) and some irrational numbers and some universal constant numbers were researched with Quantum Perspective Model by Kevser Köklü and Tahir Ölmez. Before this article, with respect to Quantum Perspective Model, Kevser Köklü researched the relationship between the velocity of light numbers and genetic codes [1]. Secondly, the relation with Pi numbers [2] and nucleotide bases was also explained by Kevser Köklü too. Thirdly, not only the link between the Planck’s constant numbers [3] and genetic codes but also the link between some irrational numbers and genetic codes were researched by Tahir Ölmez [4]. Fourthly, the calculated expression of the atomic weight of proton, neutron and electron with nucleotide bases was also researched by Tahir Ölmez. Fifthly, the atomic weight of Avogardo’s number can be also expressed as “Uracil (U)” nucleotide base [5].

Some other constant numbers are the Boltzmann and the Bohr magneton constants. At first, Boltzmann constant defines the relation between absolute temperature and the kinetic energy [6]. The other one is the Bohr Magneton [7] that expresses the electron magnetic moment caused by its orbital or spin [8]. However, the scope of this research article is searching the relations between the Boltzmann constant, the Bohr magneton constant and chemical formulas of nucleotide bases.

2. Methods

According to Quantum Perspective Model, the representation of nucleotide bases (A T, G, C and U) was explained by chemical formulas. Regarding these chemical formulas, it was calculated based on the atomic masses of the elements. However, this article aims to investigate not only the relationship between the Boltzmann constant and nucleotide bases, but also the relationships between the Bohr magneton constant calculated as nucleotide bases. In sum, the aim of this research article is searching the relations between the atomic weight of basic atomic particles, number base systems and chemical formulas of nucleotide bases.

The chemical structures of nucleotide bases consist of Carbon (C), Nitrogen (N), Oxygen (O) and Hydrogen (H) [9]. For the representation of nucleotide bases (A, T, C, G and U) in chemical atoms (see Table 1).

2.1. The Calculation of the Boltzmann Constant Value as Nucleotide Bases

The value of the Boltzmann constant is 1.380649 × 10^{−23} J∙K^{−1}

1.380649 × 10^{−23} J∙K^{−1}

0.1380649 × 10^{−24} J∙K^{−1} [6].

At first, Please take the value of the Boltzmann constant after comma (0, 13 80 64 9). Secondly,convert this decimal numbers to binary number base (see Table 2). Thirdly, after writing this binary numbers one by one, convert this binary numbers to decimal numbers again partially.For instance [13:11 01; 80:101 0000; 64:1000000; 9:100 1]. Fourthly, sum the partial numbers respectively..For instance [(13 = 3 + 1 = 4); (80 = 5 + 0 = 5); (64 = 64) and (9 = 4 + 1 = 5)]. Fifthly, add the total partial decimal numbers (4 + 5 + 64 + 5 = 78). Finally, see Table 2 for the equivalents of this number “78” Guanine (G).

2.2. The Calculation of the Bohr Magneton Constant Value as Nucleotide Bases

9.2740100783 × 10^{−24} J∙T^{−1 }

0.92740100783 × 10^{−25} J∙T^{−1} [7] [8].

At first, Please take the Bohr magneton constant value after comma (0, 92 74 01 00 78 3). Secondly,convert this decimal numbers to binary number base (see Table 3). Thirdly, after writing this binary numbers one by one, convert this

Table 1. Representation of nucleotide bases (A, T, C, G and U) in chemical atoms.

Table 2. Representation of decimal numbers in binary base for the value of the Boltzmann constant after comma.

Table 3. Representation of decimal numbers in binary base for the value of the Bohr magneton constant after comma.

binary numbers to decimal numbers again partially. For instance [(92:10,11100); (74:100,1010); (01:1); (00:0); (78:100,1110) and (3:3)]. Fourthly, sum the partial numbers respectively..For instance [(92 = 2 + 28 = 30); (74 = 4 + 10 = 14); (01 = 1); (00 = 0);(78 = 4 + 14 = 18); and (3 = 3)].Fifthly, add the total partial decimal numbers (30 + 14 + 1 + 0 + 18 + 3 = 66). Finally, see Table 1 for the equivalents of this number “66” Thymine (T).

2.3. The Calculation of Einstein’s Mass Energy Equivalence Value as Nucleotide Bases (Table 4)

*E* = *m ** *c*^{2} [10].

In sum, as regards to Quantum Perspective Model, after the expression of The Boltzmann constant and the Bohr magneton constant numbers as nucleotide bases, some important consequences were reached by this article. This result will be put forth in next pages.

3. Results

At first, the calculation of the Boltzmann constant value as nucleotide base can be expressed with Guanine (G) nucleotide base. Secondly, the calculation of the Bohr magneton constant value as nucleotide base can be expressed with Thymine (T) nucleotide base. Thirdly, the energy equivalence for the atomic weight of proton value as nucleotide bases can be expressed with “GAUC” [Guanine (G), Adenine (A), Uracil (U) and Cytosine (C)] nucleotide bases. Fourthly, the energy equivalence for the atomic weight of electron value as nucleotide bases can be expressed with “UAUC” [Uracil (U) Adenine (A), Uracil (U) and Cytosine (C)] nucleotide bases. Fifthly, not only the energy equivalence for the atomic weight of neutron value as nucleotide bases is “AAUC” but also “TAUC” too. Sixthly, the calculated total energy equivalence of elementary atomic particles is either “GAUC UAUC AAUC” or “GAUC UAUC TAUC”. Lastly, the pair of calculated

Table 4. The calculation of Einstein’s mass energy equivalence value as nucleotide bases.

total energy equivalence of elementary atomic particles is “CTAGATATTTAG” or “CTAGATATATAT”. Can this sequence be a novel expression of some constant numbers?

As a result, these dual consequences can be stemmed from “Quantum Physics” named as “Quantum superposition” In sum, after searching these sequences at NCBI (The National Center for Biotechnology Information) database, the consequences are many living organisms. These are bacteria, insects, snakes, moths, fishes, cattle and in particularly fruit flies “Drosophia albomicans” [11] (see Figures 1-3). Could this relationship be a sign of the relations between the Universal Genetic Code Table, some Universal constant numbers and the chemical Periodic Table?

4. Discussion

According to Quantum Perspective Model, prior to this article, the relationship between Planck’s constant numbers [3] and genetic codes were studied by T. Ölmez. The consequence of this article can be expression of Planck’s constant numbers as both Adenine (A) and Thymine (T) nucleotide bases. This twin result may be explained by Quantum Superposition. But also the link between some irrational numbers and genetic codes were researched by Tahir Ölmez, too (see Table 5).

As for this article, according to Einstein’s mass energy equivalence, at first, Please take The square of the speed of light (c²), then sequence (multiply) the atomic weight of proton, neutron and electron respectively. Secondly, the result of this process is written by Table 4. For example, the calculated the energy equivalence for the atomic weight of proton value as nucleotide bases is “GAUC”.

Figure 1. The NCBI Blast Result “CTAGATATTTAGATAT” of Nucleotide Bases [20].

Figure 2. The NCBI Distance Tree of result for “Drosophila albomicans” [20].

Figure 3. The NCBI Gene Search Result for “Drosophila albomicans” [20].

Table 5. The summary of some irrational numbers and genetic sequences.

Thirdly, the calculated the energy equivalence for the atomic weight of electron value as nucleotide bases are “UAUC”. Fourthly, the calculated the energy equivalence for the atomic weight of neutron value as nucleotide bases “AAUC or TAUC”. Fifthly, the calculated total energy equivalence of elementary atomic particle is “GAUC UAUC AAUC” or “GAUC UAUC TAUC”. At the calculation of Einstein’s mass energy equivalence, nucleotide bases were sequenced side by side. Because in mathematics, it can be expressed that exponents are added in the multiplication operation of exponential numbers. So, in calculations nucleotide bases were written just like as in “GAUC UAUC AAUC” or “GAUC UAUC TAUC”.

At the calculated representation of decimal numbers in binary base for the value of the Bohr magneton constant after comma, “0000” and “00” regarded as “zero”. Please, see Table 3.

This two digit of disregarded value “00” can be stemmed from “Adenine (A) and Thymine (T) pairs with two (2) hydrogen bonds” [20]. Besides, binary encoding systems consist of binary information from all data in a computer system that includes only two possible value: 0 and 1. If current passes through the transistor (switch on), this represents one (1). If current doesn’t pass (switch off) that means zero (0). That’s why; it can be the reason of zero’s disregard [1].

5. Conclusion

This paper tries to shed lights on the relationships between some constant numbers just like as both the Boltzmann constant and the Bohr magneton constant and nucleotide bases [Adenine (A), Thymine (T) Guanine (G), Cytosine (C) and Uracil (U)]. According to Quantum Perspective Model, the chemical formulas of nucleotide bases [Adenine (A), Thymine (T) Guanine (G), Cytosine (C) and

Table 6. The summary of some constant numbers and nucleotide bases.

Uracil (U)] consist of Carbon(C), Nitrogen (N), Oxygen (O) and Hydrogen (H).

At first, the calculation of the Boltzmann constant value “78” is defined as Guanine (G) nucleotide base. Secondly, the calculation of the Bohr magneton constant value “66” can be defined with Thymine (T) nucleotide base. Even, thirdly, after searching the pair of calculated total energy equivalence of elementary atomic sequences “CTAGATAT TTAG or CTAGATATATAT “at NCBI (The National Center for Biotechnology Information) database, the striking consequence can be especially fruit flies “Drosophia albomicans” (see Table 4 and Figures 1-3). Not only the relations between some irrational numbers and bony fishes, but also the relations between some constant numbers and fruit flies were explained by NCBI database as regards to Quantum Perspective Model [15]. They have similar human genes and are a special type of insect model organisms used in molecular and genetic research to understand human genes [21]. Fourthly, the dual explanation of Einstein’s mass-energy equivalence can be deduced from Quantum Superposition, since Einstein’s mass-energy equivalence can be listed as both “GAUCUAUCAAUC” and “GAUCUAUCTAUC”. Fifthly, the pair of calculated total energy equivalence of elementary atomic particles is “CTAGATATTTAG or CTAGATATATAT”. Sixthly, Even the sum of the atomic weights of DNA “272” consisting of the nucleotide bases Cytosine (C), Adenine (A), Thymine (T) and Guanine (G) is very close to the numerical value of the “Kelvin” temperature “273”, which is almost “absolute zero”. At the calculation of sum of the atomic weights of DNA, the lack of one “1” can be stemmed from minus value of Kelvin “273” [22]. Seventhly, some constant numbers can be defined as nucleotide bases just like as in Table 6. Lastly, Let alone the previous results, not only the Boltzmann constant numbers are related to nucleotide bases but also the Bohr magneton constant numbers are related to nucleotide bases, too (see Table 6). As a result, not only some constant numbers are related to genetic codes but also the golden ratio numbers [19] and Fibonacci sequence [23] are related to genetic codes, too. In sum, using some physical and chemical constants [8], can the relationships between both Biochemistry and Quantum Physics be explained by genetic codes?

Conflicts of Interest

The author declares no conflicts of interest.

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[14] | Ölmez, T. (2021) Can Irrational Numbers (Such as Square Root of the Number Five) Be Reached by Analysis of Genetic Sequences? Open Access Library Journal, 8, e7104. https://doi.org/10.4236/oalib.1107104 |

[15] | Ölmez, T. (2022) Are Irrational Numbers (Like the Square Root of the Number Seven) Applicable to Genetic Sequences? Open Access Library Journal, 9, e8513. https://doi.org/10.4236/oalib.1108513 |

[16] | Ölmez T. (2021) According to Quantum Perspective Model, Are the Numbers of Pi Also Meaningful in Biochemistry? International Journal of Natural Sciences: Current and Future Research Trends (IJNSCFRT), 11, 1-10. |

[17] | Ölmez, T. (2021) According to Quantum Perspective Model, Is Euler’s Identity Also Meaningful in Biochemistry? International Journal of Natural Sciences: Current and Future Research Trends, 9, 23-28. https://ijnscfrtjournal.isrra.org/index.php/Natural_Sciences_Journal/article/view/1037/15 |

[18] | Ölmez, T. (2020) With Respect to Quantum Perspective Model, Can Euler Numbers Be Related to Biochemistry? Global Journal of Science Frontier Research, 20, 7-14. https://doi.org/10.34257/GJSFRFVOL20IS9PG7 |

[19] | Ölmez, T. (2020) Is There an Aesthetics in Golden Ratio as Regards to the Common Cis-Regulatory Elements versus to Atomic Numbers of Elements with Respect to Quantum Perspective Model? Neurology and Neuroscience Reports, 3, 1-4. https://doi.org/10.15761/NNR.1000119 |

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[21] | Fruit Fly Lab. https://www.nasa.gov/ames/fruit-fly-lab |

[22] | Kelvin. https://en.wikipedia.org/wiki/Kelvin |

[23] | Ölmez, T. (2021) Is There a Similarity between Fibonacci Sequence and Euler’s Number with Respect to Quantum Perspective Model? Global Journal of Science Frontier Research, 20, 33. https://doi.org/10.34257/GJSFRFVOL20IS9PG35 |

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