Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics

Bhushan Poojary

doi:doi:10.11648/j.ajtas.20251404.14

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Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics

Bhushan Poojary^*

Published in American Journal of Theoretical and Applied Statistics (Volume 14, Issue 4)

Received: 14 July 2025 Accepted: 24 July 2025 Published: 11 August 2025

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Abstract

We propose a novel theoretical framework in which energy is generalized to a bicomplex quantity, significantly extending previous formalisms that treated energy as a complex number. In this bicomplex approach, energy comprises two distinct imaginary components arranged orthogonally, providing a richer algebraic structure. By carefully defining arithmetic operations within this bicomplex space, we demonstrate that division naturally introduces a geometric scaling factor identified explicitly as the fine-structure constant α. The emergence of α within this algebraic structure provides new insights into its fundamental geometric interpretation and underscores its role as a universal scaling factor connecting quantum-scale interactions to larger-scale phenomena. We present rigorous algebraic derivations and systematically define the arithmetic rules governing bicomplex quantities. Additionally, we clarify how these algebraic properties facilitate novel connections across various domains, including quantum mechanics, holographic theories, and theoretical physics frameworks aimed at unification. Specifically, the introduction of bicomplex energy allows us to interpret quantum mechanical processes and holographic projections in a unified mathematical context, offering fresh perspectives on longstanding theoretical challenges. The proposed framework not only deepens theoretical understanding but also generates experimentally testable predictions. These include unique signatures that could manifest in high-precision quantum electrodynamics experiments, as well as potential observable effects in advanced holographic or quantum-gravity-inspired setups. The framework invites further exploration into how higher-dimensional algebraic structures might underlie physical constants and fundamental interactions, providing a robust mathematical foundation for future theoretical and experimental investigations.

Published in	American Journal of Theoretical and Applied Statistics (Volume 14, Issue 4)
DOI	10.11648/j.ajtas.20251404.14
Page(s)	155-159
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Bicomplex Energy, Fine-Structure Constant, Quantum Mechanics, Holography, Theoretical Physics, Algebraic Structure, Quantum Electrodynamics, Experimental Predictions

References

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[4]	B. Poojary. Certainty Principle Using Complex Plane. International Journal of Applied Physics and Mathematics. 2014, 4(5), 332-335. https://doi.org/10.7763/IJAPM.2014.V4.303
[5]	C. Segre. Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici. Mathematische Annalen. 1892, 40, 413-467. https://doi.org/10.1007/BF01443559
[6]	G. B. Price. Introduction to Multicomplex Spaces and Functions. Marcel Dekker, New York, 1991.
[7]	R. Penrose. Twistor Algebra. Journal of Mathematical Physics. 1967, 8(2), 345-366. https://doi.org/10.1063/1.1705200
[8]	J. Cockle. On Certain Functions Resembling Quaternions, and on a New Imaginary in Algebra. Philosophical Magazine. 1848, 33(3), 435-439. https://doi.org/10.1080/14786444808646110
[9]	D. Rochon. A Bicomplex Riemann Zeta Function. Advances in Applied Clifford Algebras. 2004, 14(2), 231-248. https://doi.org/10.1007/s00006-004-0008-y
[10]	S. Olariu. Hyperbolic Complex Numbers in Relativity. Elsevier, Amsterdam, 2002.
[11]	B. Poojary. Holographic Address Space: A Framework for Unifying Quantum Mechanics and General Relativity. TSI Journals. 2025, 20(1), 101-115. URL: https://www.tsijournals.com/articles/holographic-address-space-a-framework-for-unifying-quantum-mechanics-and-general-relativity.pdf
[12]	W. Pauli. Zur Quantenmechanik des magnetischen Elektrons. Zeitschrift für Physik. 1927, 43, 601-623. https://doi.org/10.1007/BF01397326
[13]	A. Einstein. Zur Elektrodynamik bewegter Körper. Annalen der Physik. 1905, 322(10), 891-921. https://doi.org/10.1002/andp.19053221004
[14]	J. Maldacena. The Large N Limit of Superconformal Field Theories and Supergravity. Advances in Theoretical and Mathematical Physics. 1998, 2, 231-252. https://doi.org/10.4310/ATMP.1998.v2.n2.a1
[15]	L. Susskind. The World as a Hologram. Journal of Mathematical Physics. 1995, 36(11), 6377-6396. https://doi.org/10.1063/1.531249
[16]	A. Zeilinger. Experiment and the Foundations of Quantum Physics. Reviews of Modern Physics. 1999, 71(2), S288-S297. https://doi.org/10.1103/RevModPhys.71.S288
[17]	H. Bethe. The Electromagnetic Shift of Energy Levels. Physical Review. 1947, 72(4), 339-341. https://doi.org/10.1103/PhysRev.72.339

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Poojary, B. (2025). Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics. American Journal of Theoretical and Applied Statistics, 14(4), 155-159. https://doi.org/10.11648/j.ajtas.20251404.14

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ACS Style

Poojary, B. Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics. Am. J. Theor. Appl. Stat. 2025, 14(4), 155-159. doi: 10.11648/j.ajtas.20251404.14

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AMA Style

Poojary B. Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics. Am J Theor Appl Stat. 2025;14(4):155-159. doi: 10.11648/j.ajtas.20251404.14

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@article{10.11648/j.ajtas.20251404.14,
  author = {Bhushan Poojary},
  title = {Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics
},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {14},
  number = {4},
  pages = {155-159},
  doi = {10.11648/j.ajtas.20251404.14},
  url = {https://doi.org/10.11648/j.ajtas.20251404.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20251404.14},
  abstract = {We propose a novel theoretical framework in which energy is generalized to a bicomplex quantity, significantly extending previous formalisms that treated energy as a complex number. In this bicomplex approach, energy comprises two distinct imaginary components arranged orthogonally, providing a richer algebraic structure. By carefully defining arithmetic operations within this bicomplex space, we demonstrate that division naturally introduces a geometric scaling factor identified explicitly as the fine-structure constant α. The emergence of α within this algebraic structure provides new insights into its fundamental geometric interpretation and underscores its role as a universal scaling factor connecting quantum-scale interactions to larger-scale phenomena. We present rigorous algebraic derivations and systematically define the arithmetic rules governing bicomplex quantities. Additionally, we clarify how these algebraic properties facilitate novel connections across various domains, including quantum mechanics, holographic theories, and theoretical physics frameworks aimed at unification. Specifically, the introduction of bicomplex energy allows us to interpret quantum mechanical processes and holographic projections in a unified mathematical context, offering fresh perspectives on longstanding theoretical challenges. The proposed framework not only deepens theoretical understanding but also generates experimentally testable predictions. These include unique signatures that could manifest in high-precision quantum electrodynamics experiments, as well as potential observable effects in advanced holographic or quantum-gravity-inspired setups. The framework invites further exploration into how higher-dimensional algebraic structures might underlie physical constants and fundamental interactions, providing a robust mathematical foundation for future theoretical and experimental investigations.},
 year = {2025}
}

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TY  - JOUR
T1  - Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics

AU  - Bhushan Poojary
Y1  - 2025/08/11
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DO  - 10.11648/j.ajtas.20251404.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
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UR  - https://doi.org/10.11648/j.ajtas.20251404.14
AB  - We propose a novel theoretical framework in which energy is generalized to a bicomplex quantity, significantly extending previous formalisms that treated energy as a complex number. In this bicomplex approach, energy comprises two distinct imaginary components arranged orthogonally, providing a richer algebraic structure. By carefully defining arithmetic operations within this bicomplex space, we demonstrate that division naturally introduces a geometric scaling factor identified explicitly as the fine-structure constant α. The emergence of α within this algebraic structure provides new insights into its fundamental geometric interpretation and underscores its role as a universal scaling factor connecting quantum-scale interactions to larger-scale phenomena. We present rigorous algebraic derivations and systematically define the arithmetic rules governing bicomplex quantities. Additionally, we clarify how these algebraic properties facilitate novel connections across various domains, including quantum mechanics, holographic theories, and theoretical physics frameworks aimed at unification. Specifically, the introduction of bicomplex energy allows us to interpret quantum mechanical processes and holographic projections in a unified mathematical context, offering fresh perspectives on longstanding theoretical challenges. The proposed framework not only deepens theoretical understanding but also generates experimentally testable predictions. These include unique signatures that could manifest in high-precision quantum electrodynamics experiments, as well as potential observable effects in advanced holographic or quantum-gravity-inspired setups. The framework invites further exploration into how higher-dimensional algebraic structures might underlie physical constants and fundamental interactions, providing a robust mathematical foundation for future theoretical and experimental investigations.
VL  - 14
IS  - 4
ER  -

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Author Information

Bhushan Poojary

NIMS University, BSC Physics, Jaipur, India

Contact Email

http://orcid.org/0000-0002-5122-0236

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APA Style

Poojary, B. (2025). Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics. American Journal of Theoretical and Applied Statistics, 14(4), 155-159. https://doi.org/10.11648/j.ajtas.20251404.14

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ACS Style

Poojary, B. Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics. Am. J. Theor. Appl. Stat. 2025, 14(4), 155-159. doi: 10.11648/j.ajtas.20251404.14

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AMA Style

Poojary B. Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics. Am J Theor Appl Stat. 2025;14(4):155-159. doi: 10.11648/j.ajtas.20251404.14

Copy | Download

@article{10.11648/j.ajtas.20251404.14,
  author = {Bhushan Poojary},
  title = {Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics
},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {14},
  number = {4},
  pages = {155-159},
  doi = {10.11648/j.ajtas.20251404.14},
  url = {https://doi.org/10.11648/j.ajtas.20251404.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20251404.14},
  abstract = {We propose a novel theoretical framework in which energy is generalized to a bicomplex quantity, significantly extending previous formalisms that treated energy as a complex number. In this bicomplex approach, energy comprises two distinct imaginary components arranged orthogonally, providing a richer algebraic structure. By carefully defining arithmetic operations within this bicomplex space, we demonstrate that division naturally introduces a geometric scaling factor identified explicitly as the fine-structure constant α. The emergence of α within this algebraic structure provides new insights into its fundamental geometric interpretation and underscores its role as a universal scaling factor connecting quantum-scale interactions to larger-scale phenomena. We present rigorous algebraic derivations and systematically define the arithmetic rules governing bicomplex quantities. Additionally, we clarify how these algebraic properties facilitate novel connections across various domains, including quantum mechanics, holographic theories, and theoretical physics frameworks aimed at unification. Specifically, the introduction of bicomplex energy allows us to interpret quantum mechanical processes and holographic projections in a unified mathematical context, offering fresh perspectives on longstanding theoretical challenges. The proposed framework not only deepens theoretical understanding but also generates experimentally testable predictions. These include unique signatures that could manifest in high-precision quantum electrodynamics experiments, as well as potential observable effects in advanced holographic or quantum-gravity-inspired setups. The framework invites further exploration into how higher-dimensional algebraic structures might underlie physical constants and fundamental interactions, providing a robust mathematical foundation for future theoretical and experimental investigations.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Energy as a Bicomplex Quantity: Fine-Structure Constant as a Geometric Scaling Factor in Holographic Quantum Mechanics

AU  - Bhushan Poojary
Y1  - 2025/08/11
PY  - 2025
N1  - https://doi.org/10.11648/j.ajtas.20251404.14
DO  - 10.11648/j.ajtas.20251404.14
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 155
EP  - 159
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20251404.14
AB  - We propose a novel theoretical framework in which energy is generalized to a bicomplex quantity, significantly extending previous formalisms that treated energy as a complex number. In this bicomplex approach, energy comprises two distinct imaginary components arranged orthogonally, providing a richer algebraic structure. By carefully defining arithmetic operations within this bicomplex space, we demonstrate that division naturally introduces a geometric scaling factor identified explicitly as the fine-structure constant α. The emergence of α within this algebraic structure provides new insights into its fundamental geometric interpretation and underscores its role as a universal scaling factor connecting quantum-scale interactions to larger-scale phenomena. We present rigorous algebraic derivations and systematically define the arithmetic rules governing bicomplex quantities. Additionally, we clarify how these algebraic properties facilitate novel connections across various domains, including quantum mechanics, holographic theories, and theoretical physics frameworks aimed at unification. Specifically, the introduction of bicomplex energy allows us to interpret quantum mechanical processes and holographic projections in a unified mathematical context, offering fresh perspectives on longstanding theoretical challenges. The proposed framework not only deepens theoretical understanding but also generates experimentally testable predictions. These include unique signatures that could manifest in high-precision quantum electrodynamics experiments, as well as potential observable effects in advanced holographic or quantum-gravity-inspired setups. The framework invites further exploration into how higher-dimensional algebraic structures might underlie physical constants and fundamental interactions, providing a robust mathematical foundation for future theoretical and experimental investigations.
VL  - 14
IS  - 4
ER  -

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