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

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