8 Famous Scientific Equations That Changed the World

 

Isaac Newton's Law of Universal Gravitation

In the parameters of a universal constant, G, the masses of the two objects, m1 and m2, and the separation between the objects, r, Newton's law of gravitation explains the force of gravity between two things, F.

 The astonishing scientific discovery of Newton's law provides an almost perfect explanation for why the planets travel the way they do. This applies to gravity everywhere in the universe, not just on Earth or in our solar system, which makes it even more astonishing. For two hundred years, Newton's theory of gravity held up very well, and it wouldn't be updated until Einstein's theory of general relativity.

Albert Einstein’s Theory of Relativity

With his special and general theories of relativity, Einstein fundamentally changed the course of science. According to the famous equation E = mc2, matter and energy are equivalent. The theory of special relativity introduced concepts like the speed of light serving as a universal speed limit and time passing differently for objects traveling at various speeds.

The first significant alteration to our understanding of gravity since Newton's law was brought about by general relativity, which depicts gravity as a folding and bending of space and time themselves. Our comprehension of the universe's beginnings, structure, and ultimate destiny depends on general relativity.

The Pythagorean Theorem

This theorem is fundamental to how we comprehend geometry. When you square the lengths of the short sides, a, and b, and put them together, you obtain the square of the length of the long side, c, which illustrates how the sides of a right triangle relate to one another on a flat plane. 

In some aspects, this connection truly distinguishes between curved, non-Euclidean geometry and our typical, flat Euclidean geometry. A right triangle is drawn on the surface of a sphere, for instance, does not necessarily have to adhere to the Pythagorean theorem.

The Second Law of Thermodynamics

According to this, entropy (S) is constantly constant or rising in a closed system. Roughly stated, thermodynamic entropy represents the degree of chaos in a system. Heat will always tend to flow from the hot area to the cold area until the system is evenly distributed. For example, a system that begins in an ordered, uneven state, say, a hot region next to a cold region, will always tend to even out.

One of the few instances in physics where time plays such a significant role in the second law of thermodynamics. The majority of physical processes are reversible; thus, we can solve the equations in reverse without causing any problems. However, the second law only applies in this manner. We never witness the coffee freeze when we place an ice cube in a cup of hot coffee because the ice cube always melts.

Maxwell's Equations 

This set of four differential equations defines the behavior of and link between electricity (E) and magnetism (H) (H).

The basis of our understanding of how electromagnetism functions daily are Maxwell's equations, which are to classical electromagnetism what Newton's laws of motion and law of universal gravitation are to classical mechanics. However, as we will see, electromagnetism is explained by a quantum mechanical theory in current physics, and it is now obvious that these beautiful equations are only an approximation that works well on human scales.

Logarithms

The inverses of exponential functions are called logarithms. A logarithm for a given base reveals what power you must increase that base to obtain a number. The base 10 logarithm of 1 is, for instance, log(1) = 0, log(10) = 1, and log(100) = 2, respectively, since 1 = 100 and 10 = 101.

One of the most beneficial uses of logarithms is their ability to convert multiplication into addition, as shown by the equation log(ab) = log(a) + log(b) in the diagram.

This was the most popular method for swiftly multiplying huge numbers until the advent of the digital computer, which vastly accelerated calculations in physics, astronomy, and engineering.

Calculus

The calculus definition of the derivative is provided in this formula. The derivative calculates the rate of change of a quantity. For example, we can conceive of velocity, or speed, as being the derivative of position - if you are walking at 3 miles per hour, then every hour, you have changed your location by 3 miles.

The derivative and the integral, the other calculus foundation, are central to how scientists and mathematicians both understand change. This makes sense because a large portion of science is interested in understanding how things change.

Schrõdinger's Equation

The fundamental equation of quantum mechanics is this one. This equation determines how atoms and subatomic particles behave, and general relativity describes our cosmos at its biggest scales.

The two most successful scientific theories in history are modern quantum mechanics and general relativity, and all of the experimental findings to date are perfectly consistent with their predictions. The majority of contemporary technology also depends on quantum mechanics; lasers, semiconductor-based computers, and nuclear power all depend on quantum phenomena.

Written By- Aasis Kaur 

Edited by - Rumela