What is the purest number?

Answered by Willie Powers

The concept of a “pure” number can be a bit abstract, but it generally refers to a number that is fundamental and independent of any specific units or physical quantities. In other words, it is a mathematical constant that remains the same regardless of the context in which it is used.

One of the most fascinating examples of a pure number is the famous constant 137. This number, also known as the fine-structure constant or alpha, has captivated the minds of physicists for decades. It appears in various fundamental equations of physics and is deeply intertwined with the nature of our universe.

Richard Feynman, a renowned physicist, once said that if he could only pass on one number to the next generation, it would be 137. This statement speaks to the profound significance of this seemingly simple number.

The value of 137 is approximately 1/137 or 0.0073, but its real significance lies in its pure, dimensionless nature. Unlike most physical quantities, such as speed or mass, which depend on the chosen units of measurement, 137 is independent of any specific units. It remains the same regardless of whether we use meters or feet, seconds or minutes.

Physicist Leon Lederman famously said that 137 “shows up naked all over the place.” What he meant by this is that scientists from any planet in the universe, using any system of units or physical constants specific to their world, would all arrive at the same value of 137. It is a universal constant that transcends the limitations of our human understanding.

The significance of 137 becomes even more apparent when we consider its role in the fundamental forces of nature. For example, in the equation describing the electromagnetic force, the fine-structure constant appears as the ratio of the electron charge squared to the product of the speed of light and Planck’s constant. This connection between the fine-structure constant and the fundamental properties of particles and forces is truly remarkable.

Despite decades of research, the reason behind the value of 137 remains a mystery. Some physicists have proposed various theories and explanations, but none have been universally accepted. The pureness and enigmatic nature of 137 continue to spark curiosity and drive scientific inquiry.

The concept of a pure number refers to a mathematical constant that remains unchanged regardless of the units or physical quantities involved. The number 137, also known as the fine-structure constant, is a prime example of a pure number. It appears in various fundamental equations of physics and shows up in diverse contexts, regardless of the specific units used. The significance and value of 137 in understanding the fundamental nature of our universe remain a topic of ongoing research and fascination among scientists.