Statistical mathematics can be used in virtually every field of study. Whether you are a sports orator or a historian; a customer service representative or a legal consultant, statistics plays a role. I was surprised to discover my usage of statistics in science was a pivotal and essential skill in understanding “the big picture”.
A Journey into Statistical Physics
The science of physics is defined as, “the science that deals with matter and energy such as light, motion, sound, heat, electricity, or force, and the laws that govern them”. Every sensory perception we experience actually results from changes of atoms or particles that happen at a microscopic level. The way these interact at this tiny level, inevitably compounds upon itself to form the macroscopic results we experience. It relates by taking the individual properties of atoms and producing statistical probablitities of the macrostates of everyday life. To put this plainly, physics often studies a property of a single atom or its components. This is essential in order to understand the relationship of everything around us. Statistics is able to take the data of a state of these atomic properties and and help to produce, through probabilities, results we are able to observe with our senses.
The average kinetic energy of atoms can be used to describe temperatue. The same information can be used to determine entropy by determining the changes from nonequalibrium states to eqalibrium states. This statistical information gives us understanding in the laws of thermodynamics. Thermodynamics; thusly, draws on the probabillity of a large amount of the same kind of particals’ average behavior. One statistical result we observe from this is that particles at high energies become more random whereas their counterpart low energy particles have a higher probability of occurring. James Clerk Maxwell and Ludwig Boltzman are accredited to establishing the fundamental principles of statistical mechanics as they apply to thermodynamics. Their publication The Motions and Collisions of Perfectly Elastic Spheres (1)In 1860 details their work in the field of thermodynamics and details a wide range of statistical data.
Over the years statistics have been used in many other studies of physics.Statistical mechanics is used to supplement Shrodinger’s Cat theory in quantum physics. It is also used in studies and theories such as superconductivity as well as Brownian motion and polymer field theory.
These statistical analysis help us to understand the way things work around us. By studying these elements at the smallest levels, we are able to then begin to grasp how their relationships result in our perceptions of the world and its components. I am certain statistics is going to continue to play a pivotal role in our understanding physics for generations to come.