Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM

Juan Francisco González Hernández

doi:doi:10.11648/j.ajmp.20251403.11

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Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM

Juan Francisco González Hernández^*

Published in American Journal of Modern Physics (Volume 14, Issue 3)

Received: 23 April 2025 Accepted: 6 May 2025 Published: 3 June 2025

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Abstract

Despite their undeniable experimental success, General Relativity (GR) and the Standard Model (SM) are still regarded as effective field theories (EFTs), only valid up to a certain energy scale or length threshold, beyond which new physics is anticipated. These foundational theories, while extremely precise within their respective domains¡agravitation for GR and quantum fields for the SM¡aremain fundamentally incompatible and incomplete when attempting a unified description of nature.In this work, we present and review the framework of Extended Relativity (ER) within the mathematical setting of Clifford spaces (C-spaces), which generalize Minkowskian spacetime by incorporating multivectorial (polyvector) coordinates. This formalism offers a natural extension of spacetime geometry capable of encoding extended objects and higher-order geometric degrees of freedom. The ER approach aims to provide a geometric and algebraic platform potentially capable of bridging the divide between quantum theory and gravity.Beyond reviewing concepts, methods, and selected results from ER in C-spaces, we also highlight its theoretical connections with other generalized relativities (OR), including Born reciprocity, multitemporal relativity, and recent frameworks inspired by emergent spacetime and quantum entanglement (QE). These connections may shed light on phenomena such as the emergence of spacetime, dark energy, or the role of maximal acceleration and higher-derivative symmetries.Finally, we explore the compelling possibility that ER is only a step toward a more fundamental theory, which we term Beyond Extended Relativity (BER). This leads us to propose a broader framework, perhaps governed by new symmetry principles and limits, capable of addressing the unresolved challenges of unification, quantum gravity, and the ultimate structure of spacetime.

Published in	American Journal of Modern Physics (Volume 14, Issue 3)
DOI	10.11648/j.ajmp.20251403.11
Page(s)	130-139
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

Quantum Gravity, Clifford Spaces, C-spaces, Polyvectors, Extended Relativity, Beyond Standard Model, Beyond General Relativity

References

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Hernández, J. F. G. (2025). Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM. American Journal of Modern Physics, 14(3), 130-139. https://doi.org/10.11648/j.ajmp.20251403.11

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Hernández, J. F. G. Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM. Am. J. Mod. Phys. 2025, 14(3), 130-139. doi: 10.11648/j.ajmp.20251403.11

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AMA Style

Hernández JFG. Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM. Am J Mod Phys. 2025;14(3):130-139. doi: 10.11648/j.ajmp.20251403.11

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@article{10.11648/j.ajmp.20251403.11,
  author = {Juan Francisco González Hernández},
  title = {Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM},
  journal = {American Journal of Modern Physics},
  volume = {14},
  number = {3},
  pages = {130-139},
  doi = {10.11648/j.ajmp.20251403.11},
  url = {https://doi.org/10.11648/j.ajmp.20251403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20251403.11},
  abstract = {Despite their undeniable experimental success, General Relativity (GR) and the Standard Model (SM) are still regarded as effective field theories (EFTs), only valid up to a certain energy scale or length threshold, beyond which new physics is anticipated. These foundational theories, while extremely precise within their respective domains¡agravitation for GR and quantum fields for the SM¡aremain fundamentally incompatible and incomplete when attempting a unified description of nature.In this work, we present and review the framework of Extended Relativity (ER) within the mathematical setting of Clifford spaces (C-spaces), which generalize Minkowskian spacetime by incorporating multivectorial (polyvector) coordinates. This formalism offers a natural extension of spacetime geometry capable of encoding extended objects and higher-order geometric degrees of freedom. The ER approach aims to provide a geometric and algebraic platform potentially capable of bridging the divide between quantum theory and gravity.Beyond reviewing concepts, methods, and selected results from ER in C-spaces, we also highlight its theoretical connections with other generalized relativities (OR), including Born reciprocity, multitemporal relativity, and recent frameworks inspired by emergent spacetime and quantum entanglement (QE). These connections may shed light on phenomena such as the emergence of spacetime, dark energy, or the role of maximal acceleration and higher-derivative symmetries.Finally, we explore the compelling possibility that ER is only a step toward a more fundamental theory, which we term Beyond Extended Relativity (BER). This leads us to propose a broader framework, perhaps governed by new symmetry principles and limits, capable of addressing the unresolved challenges of unification, quantum gravity, and the ultimate structure of spacetime. },
 year = {2025}
}

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TY  - JOUR
T1  - Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM
AU  - Juan Francisco González Hernández
Y1  - 2025/06/03
PY  - 2025
N1  - https://doi.org/10.11648/j.ajmp.20251403.11
DO  - 10.11648/j.ajmp.20251403.11
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 130
EP  - 139
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20251403.11
AB  - Despite their undeniable experimental success, General Relativity (GR) and the Standard Model (SM) are still regarded as effective field theories (EFTs), only valid up to a certain energy scale or length threshold, beyond which new physics is anticipated. These foundational theories, while extremely precise within their respective domains¡agravitation for GR and quantum fields for the SM¡aremain fundamentally incompatible and incomplete when attempting a unified description of nature.In this work, we present and review the framework of Extended Relativity (ER) within the mathematical setting of Clifford spaces (C-spaces), which generalize Minkowskian spacetime by incorporating multivectorial (polyvector) coordinates. This formalism offers a natural extension of spacetime geometry capable of encoding extended objects and higher-order geometric degrees of freedom. The ER approach aims to provide a geometric and algebraic platform potentially capable of bridging the divide between quantum theory and gravity.Beyond reviewing concepts, methods, and selected results from ER in C-spaces, we also highlight its theoretical connections with other generalized relativities (OR), including Born reciprocity, multitemporal relativity, and recent frameworks inspired by emergent spacetime and quantum entanglement (QE). These connections may shed light on phenomena such as the emergence of spacetime, dark energy, or the role of maximal acceleration and higher-derivative symmetries.Finally, we explore the compelling possibility that ER is only a step toward a more fundamental theory, which we term Beyond Extended Relativity (BER). This leads us to propose a broader framework, perhaps governed by new symmetry principles and limits, capable of addressing the unresolved challenges of unification, quantum gravity, and the ultimate structure of spacetime. 
VL  - 14
IS  - 3
ER  -

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Juan Francisco González Hernández

Department of Physics and Chemistry, IES Humanejos, Parla, Spain

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Hernández, J. F. G. (2025). Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM. American Journal of Modern Physics, 14(3), 130-139. https://doi.org/10.11648/j.ajmp.20251403.11

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Hernández, J. F. G. Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM. Am. J. Mod. Phys. 2025, 14(3), 130-139. doi: 10.11648/j.ajmp.20251403.11

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Hernández JFG. Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM. Am J Mod Phys. 2025;14(3):130-139. doi: 10.11648/j.ajmp.20251403.11

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@article{10.11648/j.ajmp.20251403.11,
  author = {Juan Francisco González Hernández},
  title = {Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM},
  journal = {American Journal of Modern Physics},
  volume = {14},
  number = {3},
  pages = {130-139},
  doi = {10.11648/j.ajmp.20251403.11},
  url = {https://doi.org/10.11648/j.ajmp.20251403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20251403.11},
  abstract = {Despite their undeniable experimental success, General Relativity (GR) and the Standard Model (SM) are still regarded as effective field theories (EFTs), only valid up to a certain energy scale or length threshold, beyond which new physics is anticipated. These foundational theories, while extremely precise within their respective domains¡agravitation for GR and quantum fields for the SM¡aremain fundamentally incompatible and incomplete when attempting a unified description of nature.In this work, we present and review the framework of Extended Relativity (ER) within the mathematical setting of Clifford spaces (C-spaces), which generalize Minkowskian spacetime by incorporating multivectorial (polyvector) coordinates. This formalism offers a natural extension of spacetime geometry capable of encoding extended objects and higher-order geometric degrees of freedom. The ER approach aims to provide a geometric and algebraic platform potentially capable of bridging the divide between quantum theory and gravity.Beyond reviewing concepts, methods, and selected results from ER in C-spaces, we also highlight its theoretical connections with other generalized relativities (OR), including Born reciprocity, multitemporal relativity, and recent frameworks inspired by emergent spacetime and quantum entanglement (QE). These connections may shed light on phenomena such as the emergence of spacetime, dark energy, or the role of maximal acceleration and higher-derivative symmetries.Finally, we explore the compelling possibility that ER is only a step toward a more fundamental theory, which we term Beyond Extended Relativity (BER). This leads us to propose a broader framework, perhaps governed by new symmetry principles and limits, capable of addressing the unresolved challenges of unification, quantum gravity, and the ultimate structure of spacetime. },
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM
AU  - Juan Francisco González Hernández
Y1  - 2025/06/03
PY  - 2025
N1  - https://doi.org/10.11648/j.ajmp.20251403.11
DO  - 10.11648/j.ajmp.20251403.11
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 130
EP  - 139
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20251403.11
AB  - Despite their undeniable experimental success, General Relativity (GR) and the Standard Model (SM) are still regarded as effective field theories (EFTs), only valid up to a certain energy scale or length threshold, beyond which new physics is anticipated. These foundational theories, while extremely precise within their respective domains¡agravitation for GR and quantum fields for the SM¡aremain fundamentally incompatible and incomplete when attempting a unified description of nature.In this work, we present and review the framework of Extended Relativity (ER) within the mathematical setting of Clifford spaces (C-spaces), which generalize Minkowskian spacetime by incorporating multivectorial (polyvector) coordinates. This formalism offers a natural extension of spacetime geometry capable of encoding extended objects and higher-order geometric degrees of freedom. The ER approach aims to provide a geometric and algebraic platform potentially capable of bridging the divide between quantum theory and gravity.Beyond reviewing concepts, methods, and selected results from ER in C-spaces, we also highlight its theoretical connections with other generalized relativities (OR), including Born reciprocity, multitemporal relativity, and recent frameworks inspired by emergent spacetime and quantum entanglement (QE). These connections may shed light on phenomena such as the emergence of spacetime, dark energy, or the role of maximal acceleration and higher-derivative symmetries.Finally, we explore the compelling possibility that ER is only a step toward a more fundamental theory, which we term Beyond Extended Relativity (BER). This leads us to propose a broader framework, perhaps governed by new symmetry principles and limits, capable of addressing the unresolved challenges of unification, quantum gravity, and the ultimate structure of spacetime. 
VL  - 14
IS  - 3
ER  -

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