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May 10, 2026Foundations of Physics0 citationsOpen Access

Gravity, Fine-Structure Constant and Natural Units – Some Thoughts Based on Dimensional Analysis –

RBRobi Banerjee

Key Points

  • The aim is to explore links between fundamental dimensions and natural constants using dimensional analysis.
  • Utilized dimensional analysis based on fundamental physics dimensions: length, time, and mass.
  • Examined the relationships of constants G, c, ☏, and e using Maxwell's equations.
  • Discussed various unit systems informed by dimensional analysis.
  • Demonstrated that the fine-structure constant arises directly from the links between dimensions and constants.
  • Highlighted the difficulties in quantizing gravity, distinguishing it from quantum mechanics.
  • Outlined different unit systems that can be developed through dimensional analysis.

Abstract

Abstract Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis based on Maxwell’s dimensions length (L), time (T) and mass (M) as well as the constants G, c, and e. We find that the form of the fine-structure constant is a direct consequence of this connection. Additionally, our approach emphasises that gravity is a quite distinct area of physics which is not yet successfully quantised, i. e. not yet combined with quantum mechanics. We also discuss different unit systems based on dimensional analysis and natural constants.

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Cite This Study

Robi Banerjee (2026) studied this question.

synapsesocial.com/papers/6a002191c8f74e3340f9c78ehttps://doi.org/10.1007/s10701-026-00929-7
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Zero Degrees of Freedom: The Geometric Unification of Gravity, Time Dilation, and the Fine-Structure Constant (α)2026
  2. 2Dimensional Analysis in General Theory of Relativity2024
  3. 3Derivation of Fundamental Constants from the (6+2)-Dimensional Structure of Spacetime2026
  4. 4Natural Constants Determined to High Precision from Boltzmann’s Constant and Avogadro’s Number—A Challenge to Experiments and Astrophysical Observations to Match the Precision of the Results2025
  5. 5Natural Constants Determined to High Precision from Boltzmann’s Constant and Avogadro’s Number — A Challenge to Experiments and Astrophysical Observations to Match the Precision of the Results2025 · 2 citations