Research Article
Extended Relativity in Clifford Spaces: An Alternative Approach to Unification Beyond GR and SM
Juan Francisco González Hernández*
Issue:
Volume 14, Issue 3, June 2025
Pages:
130-139
Received:
23 April 2025
Accepted:
6 May 2025
Published:
3 June 2025
DOI:
10.11648/j.ajmp.20251403.11
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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.
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¡agravitat...
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