Dimensional Analysis Demystified

EasyChair Preprint 11182, version 3

Abstract

This exploration delves into the world of dimensional analysis, a fundamental tool in mathematics and physics. Dimensions, such as length, width, height, and time, are the basic attributes that define our physical reality. The powers of these dimensions play a pivotal role in understanding how various physical quantities are interrelated. This study introduces the concept of dimensional transitions, both from lower to higher dimensions and vice versa, shedding light on how new dimensions and powers are introduced, presenting mathematical challenges, and deepening our comprehension of the physical world.

The study showcases mathematical equations central to quantum mechanics and quantum gravity, elucidating the intricate relationship between energy, length scales, and fundamental constants. Of particular interest is the interplay of dimensions and powers in equations that encompass spatial and temporal dimensions, emphasizing the influence of the fourth dimension, often associated with time. This analysis demonstrates that by following this method, dimensional analysis becomes a powerful tool for exploring the relationships between dimensions in the physical world and their role in mathematical and physical equations.

In summary, this work unravels the complexities of dimensional analysis and its applications, offering insights into how it contributes to our understanding of the fundamental laws of physics.

Keyphrases: Planck Equation, Powers of Dimensions, conceptual framework, dimensional analysis, fundamental constants, quantum gravity, quantum mechanics

@booklet{EasyChair:11182,
  author    = {Soumendra Nath Thakur},
  title     = {Dimensional Analysis Demystified},
  howpublished = {EasyChair Preprint 11182},
  year      = {EasyChair, 2023}}