Equations That Changed The World: Top 5

Equations played a very important role on the development of today’s technology. All the technology we have today is a reflection of nature. For example, computers, medical devices, nuclear weapons, etc. So how did this process develop? Scientists or philosophers wanted to understand nature first. Then they created a universal language to express it. Of course, that language is math. Later, they derived equations expressing the equilibria of the universe. So, what are the 5 most important equations that change all perceptions about the workings of the universe?

Newton’s Law of Universal Gravitation

Newton's universal gravity law

Sir Isaac Newton was an English physicist who lived from 1642-1727. If you want to learn briefly about Newton’s life, you can access it here. Newton first published the universal gravitational force in his Principia in 1687 and hypothesized this law. He expressed this law in his own words as follows;

“I stated that the forces that hold the planets in the spheres must be the squares of their mutual distances from the centers around them, and so they compared the force required to keep the moon in the Orb, and they almost completely found the answer with the gravitational force on Earth.”

Issac Newton
The law of universal gravity

Albert Einstein’s The Theory of Relativity

E: Energy, m: mass, c: speed of light

Albert Einstein developed the General Theory of Relativity in 1915. Einstein explained how a geometric gravity works within the framework of modern physics. It replaced Newton’s Theory of Gravity.

The General Theory of relativity has this name because it generalizes the Special theory of relativity. This theory says: The universe has a convoluted fabric of spacetime. This texture is shaped by the amount of mass and energy found in any part of the universe. So what is the spacetime fabric?

2D rubber-sheet model of a curved spacetime according to the Einstein field equations. Positive mass (blue) and negative mass (red) share the same single “side” of a 4D hypersurface. The positive mass creates a positive curvature with an attractive gravitational potential (gravity well) while a negative mass produces a negative curvature with a repulsive gravitational potential (gravity hill). In this case, positive masses would attract anything, while negative masses would repel anything (including other negative masses).

The space-time fabric of the universe:

According to the Euclidean approach; Time is a fourth dimension of space. That is, time is accepted as unchanging and universal, independent of the movement of the observer. The relativity approach, on the other hand, cannot be considered separately from the 3 dimensions of time-space. This approach is called the ‘space-time continuum’. The reason for this approach is related to the vector (directional) velocity of an object, the speed of light field and the strength of the gravitational field. These areas can slow the progress of time. At the same time, time also depends on the movement of the observer, so in any case time is not universal.

Returning to the general theory of relativity, the universe has a unique texture and is related to the amount of mass and energy in any part of the universe. Albert Einstein expressed this relationship with a set of differential equations. These are Albert Einstein’s field equations.

Einstein and Eddington is a film about Einstein’s work. I enjoyed it, I recommend it to you too…

Einstein and Eddington
Einstein and Eddington, 2008, Historical Drama

The Pythagorean Theory

The pythgorean theorem
The Pythgorean Theory

In mathematics, the Pythagorean theorem is the relationship between the three sides of a right triangle. It applies to a right triangle with one angle of ninety degrees. According to this theorem, let each side of a right triangle be any side of a square. The side ninety degrees opposite the triangle is the hypotenuse. So it’s the longest side. The area of the square forming the hypotenuse is the sum of the areas of the squares forming the other sides. This theory is an excellent discovery for triangles.

The Greek Philosopher Pythagoras developed this theorem and named it theorem. Pythagoras was born in 570 BC. This theorem has been proven many times in different ways. The same conclusion was reached each time.

Pythagoras. Etching by F. L. D. Ciartres after (C. V.).
Pythagoras. Etching by F. L. D. Ciartres after (C. V.).

Maxwell’s Equations

maxwell equation

Maxwell’s equations are a set of combined partial differential equations. The Lorentz force law forms the basis of classical electromagnetism, classical optics and electrical circuits. With this equation; It provides a mathematical model for fields such as electricity generation, electric motors, wireless communication, lenses, radar. Electric and magnetic fields are produced by the change of charge, current and field. Maxwell’s equations show how this happens. Maxwell first used the equations to prove that light is an electromagnetic phenomenon.

The Second Law of Thermodynamics

increase in entropy (dS) from heat transfer (δQ) to temperature in a closed system (T)

The second of thermodynamics states that the entropy of isolated systems will not decrease (more on Entropy here). He explains the reason for this by the unexpected formation of isolated systems from thermodynamic equilibrium (maximum entropy stage).

Carnot Machine

The French scientist Sadi Carnot wrote the first formulation in 1824. The Carnot machine that Carnot developed is the basic principle of the second law of thermodynamics. Carnot machine; It provides a continuous heat and work transfer. In this way, it maintains the heat and energy balance of the system.

Carnot’s machine was introduced before the 1st Law of thermodynamics and the mathematical definition of entropy. It has facilitated the interpretation of the 1st Law and the understanding of the 2nd Rule. It is still valid today.

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