Politics is for the present, but an equation is for eternity.

– Albert Einstein

You are surfing the internet, reading about 7 equations that changed the world with the help of those equations themself.

You wouldn’t be able to read this text if the electronic components of your device didn’t work. Your device works with the help of the quantum theory of solids leading to semiconductors and computer chips. Of course, satellites are involved in making internet-work too. As the satellites move with speed of around 14,000 km/hr and are 20,000 km above the earth, the clocks on satellites work faster than the clocks here on earth. Without the help of Einstein’s Equation, the clocks on satellites wouldn’t work as they should.

You see, equations govern our daily lives. Many equations are helping us to change the way we interact with nature. From refrigerator that works using the Second Law of Thermodynamics, to air navigation using Pythagorean Theorem – Our life is governed by Equations.

Here you have a list of 7 equations that completely changed the world – changed the way we interact with the laws of nature. These are some of the most important equations ever found.

## Table Of Contents

**Issac Newton’s Law of Universal Gravitation**

Newton’s Law of Universal Gravitation says that everything in the universe attracts every other thing in the universe with a force. The force increases as the mass of attracting body increases and decreases as the distance between objects increases. Mathematically, Gravitational Force= Product of Mass of Attracting Bodies/Square of Distance between the centres of Attracting Bodies

Mathematically writing,

Where G means Newton’s Universal Gravitational Constant, whose value is about 6.67430×10^{−}^{11} N⋅m^{2}/kg^{2}.

This law explains why earth with other planets revolve around the sun as they do. Although this equation isn’t accurate and Einstein’s Theory of Relativity replaced it, this equation is still used in many places.

*Fun Fact: Scientists are still working on a field of theoretical physics named Quantum Gravity. It is supposed to describe Gravity in accordance with Quantum Mechanics.*

**Mass–Energy Equivalence**

Albert Einstein, at the age of 26, published a 3-page long paper. The paper mentioned, “If a body gives off the energy L in the form of radiation, its mass diminishes by L/c^{2}“.

This statement is generally known as the equation E=mc^{2}.

In the equation,

- E means Energy
- m means Mass
- and c means the speed of light whose value of c is 299,792,458 m/s.

E=mc^{2} is the most famous equation in all of physics. It’s hard to find persons who don’t know this equation. Wikipedia defines it as ” Mass-energy equivalence is the principle that anything having mass has an equivalent amount of energy and vice versa.”

If we have 1 kg of mass. Then applying E=mc^{2},

E= (1 kg)* (3*10^{8} m/s)^{2}

= 9*10^{16} kgm^{2}/s^{2
}= 9*10^{16} Joules

It implies 1 kg of mass has energy equivalent to about 90,000,000,000,000,000 joules of energy. That’s a huge amount of energy. So even a small amount of mass has a huge amount of equivalent energy. This is how Nuclear bombs and Nuclear Power Plants Work. They release energy that’s in atoms. And even if the change in mass during the nuclear process is small, the energy liberated is huge enough to destroy a city in seconds or to power a city for a long time. It depends on us, humans, if we use that energy for good or for bad.

You can see the following video where Albert Einstein himself talks about his most famous equation, E=mc^{2}.

httpv://youtu.be/pRAJkWVAXLw

**The Pythagorean Theorem**

The Pythagorean Theorem says that the square of the longest side of a right-angled triangle is equal to the sum of squares of the other two sides of the same triangle.

This may sound simple, but beyond its simplicity lies its importance. Our math professor at college told us that this is one of the most important theorems in all of the math. It is not only used to find the length of a side of a triangle when other’s two are known; it actually defines length i:e distance in math. It is the base of trigonometry and is also used in other fields like Physics and Engineering.

**Maxwell’s Equation**

In the beginning, God said that the four-dimensional divergence of an antisymmetric second rank tensor equals zero and there was light.

– Dr. Michio Kaku

The equations are named after James Clerk Maxwell, who published the equations between 1861 and 1862 A.D. Maxwell’s Equations are compared to Newton’s Laws of Motion and Universal Laws of Gravitation in terms of usefulness. It explains how electric field and magnetic fields arise, are related to, and impact each other.

On working through Maxwell’s Equations, it was found that electric and magnetic fields could exist together.

Where,

- μ
_{0 }means magnetic permeability in a classical vacuum whose value is 1.256 * 10^{−6}H/m. - ϵ
_{0}means dielectric permittivity of classical vacuum whose value is 8.85 * 10^{−12}F/m

And yeah, this is the speed of light. Hence it was understood that light is an electromagnetic wave. You shall thank Maxwell for providing these magnificent four equations. Without them, you couldn’t be reading here at PhysicsDB.com as data transmission from our server to your device includes electromagnetic waves.

**The Second Law Of Thermodynamics**

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible.

According to the Second Law of Thermodynamics, If we have a hot body and a cold body in thermal contact, heat flows from a hotter body to a colder body. If we want to make heat flow from a colder body to a hotter body, then we need to perform some work on the system.

For example, We do work (electricity does) on a refrigerator to cool down objects to a temperature less than that of surrounding, and the body will never cool down if we don’t do work on the refrigerator.

To explain this, entropy was introduced. Entropy basically means disorder. Higher the entropy of a system, Lesser the heat energy can be used to do work. Second Law of Thermodynamics says entropy of an isolated system never decreases. Replacing “entropy” by “disorder”, the disorder of an isolated system never decreases.

If you make your room messy, you can’t expect it to clean itself.

There are various statements on the Second Law of Thermodynamics. Most known and important classical statements about the Second Law being:

Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.

– Rudolf Clausius

It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature.

– Lord Kelvin

**Logarithms**

Logarithms, generally denoted by log gives the power to which the base must be raised to get a certain number. log to base 10 of 1000 gives 3 because you need to raise 10 by 3 to get 1000. Similarly, log to base 2 of 32 gives 5 because 2^5=32.

It was introduced in 1614 by Jhon Napier and quickly became famous among scientists, engineers etc, because it could transform complicated calculations to an easier one.

If you have two large numbers, and you need to multiply them, you can do the calculations easily using logarithms because multiplication can be converted to addition using logarithms. Similarly, a division can be converted to subtraction using logarithms.

as, log(x*y)=log(x)+log(y) and log (x/y)=logx-logy

This eased early scientists and engineers heavily with their calculations when modern calculating devices weren’t available.

**Calculus**

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

– John von Neumann

Calculus is the mathematical study of change and, if you see around you, you can see how everything is changing. Nothing is static. This makes calculus a very important part of Physics and Mathematics. If you are a student of Physics, you already know how important calculus is. We rarely find theorems that don’t directly use calculus.

Calculus has two main branches: Differential Calculus and Integral Calculus. Differential calculus is used to know how fast something is changing while Integral Calculus is used to know how much something is accumulating. Differential and Integral are opposite to each other.

Suppose you have data about the position of a body and want to find the velocity of the related body.

What do you do? You take the first derivative of position function with respect to time. Doing this, you will know how fast the position is changing.

Suppose you want to find acceleration. You will take a derivative of velocity function with respect to time. Doing it, you will get – how fast velocity is changing i:e acceleration.

*Fun Fact: The derivative(rate of change) of acceleration is called JERK.*

Isaac Newton and Gottfried Wilhelm Leibniz separately developed calculus. Sir Issac Newton used calculus to develop his theory of gravitation too. Hence, we think it is reasonable to include the first principle of calculus in this list.

This equation defines derivative as a rate of change and is also the base of calculus.

What do you think about this list? Do you know some equations that should have been on the list? Or you want to say something?

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