What is the most beautiful physics or math equation?
Beauty is obviously a subjective metric, but that has not stopped many scientific publications, including Cosmos, from attempting to rank great equations by their sheer jaw-dropping beauty.
A more comfortable and familiar mode of ranking for scientifically minded people is the notion of “elegance.”
An “elegant” equation is one that captures an abundance of complex information and describes it in a relatively simple way.
Science history books will sometimes describe the long reflections and intellectual twists and turns that great thinkers like Einstein labored through as they tried to solve the problems they saw around them, and to describe the processes of the physical world.
When the equation finally came to a person like Einstein or Newton, it was tight and tidy, like a gleaming mineral extracted from a dark mine of confusion. It was all the more impressive because many thinkers had descended into that mine and emerged empty-handed.
Trimmed of superfluous elements through the liberal application of Occam’s razor, the great physics equations are pregnant with complex possibilities and hidden mysteries, like wild and zany children’s toys wrapped in the most subdued, understated gift paper.
Every physics student quickly learns that it’s only when you use an equation to solve problems — or figure out how to prove it — that its complexity and subtlety will show itself. Like the child who unwraps the zany toy, the young physicist sees how much there really is hidden behind the gift paper. We have a chance to glimpse the dark mine that Einstein and Newton descended into alone.
Here are some of the equations reporters have selected as the “most beautiful” over the years.
The Pythagorean Theorem
Business Insider chose a simple equation, familiar to most people who have graduated high school. The Pythagorean Theorem will help you answer pretty much all your edge and angle-related queries, as long as you can break everything down into triangles and as long as there is a right angle in there somewhere.
The equation is at the core of much of geometry, links it with algebra, and is the foundation of trigonometry. Without it, accurate surveying, map-making, and navigation would be impossible.
Newton’s Second Law Of Motion
Cosmos ventured into vector territory, declaring F = ma their favorite equation.
Force equals mass times acceleration. In other words… It’s easier to push an empty shopping cart than a full one.
Newton’s formulation was critical in allowing us to develop much of the technology that exploded after his illustrious career ended. F = ma is used “in almost every calculation which involves using force to cause movement.”
It tells you how powerful an engine needs to be to power a car, how much lift an aircraft needs to take-off, how much thrust to lift a rocket, how far a cannonball flies.
Einstein’s General Relativity Equation
Livescience asked some astronomers and mathematicians for their favorite equations of all time and received this response.
Einstein’s incredible equation describes the relationship between the energy-momentum tensor Tμν, which encodes exactly how matter is distributed in the universe, and the curvature of space-time, expressed in terms of a series of Ricci tensors and Ricci scalars.
Even more intriguingly, matter here is understood in the broad sense associated with Einstein, i.e. any energy-carrying medium counts as “matter.”
Space Telescope Science Institute astrophysicist Mario Livio nominated the general relativity equation as his favorite, saying, “It is still amazing to me that one such mathematical equation can describe what space-time is all about. All of Einstein’s true genius is embodied in this equation.”
“The right-hand side of this equation describes the energy contents of our universe (including the ‘dark energy’ that propels the current cosmic acceleration). The left-hand side describes the geometry of space-time. The equality reflects the fact that in Einstein’s general relativity, mass and energy determine the geometry, and concomitantly the curvature, which is a manifestation of what we call gravity.”
The Schrodinger Equation
New Scientist gave a nod to the equation that opened up the quantum world.
In 1927 Erwin Schrödinger wrote down an equation for quantum waves. It fitted experiments beautifully while painting a picture of a very strange world, in which fundamental particles like the electron are not well-defined objects, but probability clouds.
The Schrodinger equation describes how a wave function evolves over time. is the time-dependent wave function, and V(x) is the potential that the particle is subjected to.
“In plain language, the Schrodinger equation means ‘total energy equals kinetic energy plus potential energy.'”
Normally what will be known initially is the value of the Hamiltonian (far right term), which accounts for the total kinetic and potential energy of the particles in the system.
This H value is set. The Schrodinger equation then becomes a simple partial differential equation. The PDE is solved for the wave function , which contains valuable information about the system.
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