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<p>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 <i>G</i>, <i>c</i>, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\hbar \)</EquationSource> </InlineEquation> and <i>e</i>. 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月8日

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  • Robi Banerjee

摘要

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, \(\hbar \) 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.