The Most Famous Equation

Examining the most famous equation of all time.

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Albert Einstein's contributions to our understanding of the universe, and his ability to convert concepts into symbols and language which could be shared are unparalleled by any other individual in human history.   His contributions were inspired by previous thinkers, and one can make the case that his theories and hypothesis were built on the shoulders of giants, dating back to Newton, Copernicus, Maxwell, Lorentz, and other collaborators in his time.   

Einstein's most famous equation is an interesting one:   E = mc²

The core meaning of the equation is that energy and 3D matter are fundamentally interconnected - Or you could say that matter/mass is really just a measurement of energy.  Mass, in this equation is a super-concentrated form of potential energy.   Further, to measure the exact mass of an object, you must include its rest mass, plus any additional potential or kinetic energy that exists in the object.  

Energy and matter are two sides of a coin, and can be converted from one to another.  This idea, and its encapsulation into such an elegant formula changed our entire world, and its meaning, and related ideas in relativism have lead to revolutionizing science, technology and the world as we know it.  

In the equation:   (using metric measurements)
Eis Energy (measured in joules, J)
mis mass  (measured in kilograms, kg)
c²is the speed of light, squared (measured in meters per second, m/s, squared)

The concept of "The Speed of Light" is the most mysterious aspect of the equation, and the most abstract to most people.   A number has been given to this constant, which is 299,792,458 meters per second, or 186,000 miles per second.    Let's not worry about the specific numbers for now though, or the ridiculous quantity of squaring them.   The specific numbers of distance per time are arbitrary anyways, based on the fact that we have decided on an distance called a meter or yard or foot or mile - and our measurement of time is an arbitrarily chosen measurement as well.

The more important part of this equation is understanding the nature of the variable units, and the meaning of squaring "c".   Speed is a measurement that can only exist where there is Time.   It's a measurement of motion - distance through time.   Energy or matter moving through 3D space in 4D time.    Speed requires the dimension of time, and in this equation, the dimensional promotion aspect is what's important conceptually.   Furthermore, the variable of "c" is squared, which is a mathematical way to dimensionally promote a value.   So the  "c²" is a description of a dimensional promotion, related to the conversion from matter to energy and vice-versa.  

http://www.physics.brocku.ca/PPLATO/interactive-mathematics/dimensions.html
Dimensional analysis is a way of checking that equations might be true.  Dimensional analysis tells us that E = mc³ makes no sense.  

https://www.scienceforums.net/topic/72525-emc2-and-dimensional-analysis/

The equation is telling us that a dimensional conversion takes place when converting 3D matter into energy.  

We can also write the equation as:

E = mcc

When we convert the form of the equation we can solve for m or c², which gives additional perspective.

c² = E/m

cc = E/m

The speed of light squared equal energy divided by mass.

m = E/c²   

m = E/cc

Mass equals energy divided by the speed of light squared. 

Interestingly, when Einstein first published this most famous equation, he wrote solving for Mass:  m = E/c²   

 

Does the Inertia of a Body Depend upon its Energy-Content?   (Einstein's 1905 Paper)
http://www.ConscioCentric.com/images/einstein-1905-emc2.pdf

https://www.youtube.com/watch?time_continue=3&v=msVuCEs8Ydo

https://en.wikipedia.org/wiki/Geodesics_in_general_relativity

https://www.quora.com/Could-Einsteins-famous-mass-energy-equivalence-equation-have-been-derived-earlier-using-dimensional-analysis

There was already an equation which the same dimensional analysis satisfied -:

T = 1/2 m.v^2

where T is the Kinetic Energy, m is mass and v is velocity

But why would anyone imagine that the v could be replaced by 'c', the speed of light to give the mass energy of a body? Why not any other speed? Maybe it did strike someone, but without any theoretical or experimental basis it would just be a flight of fancy. Einstein was the first one to derive the equation. I don't think he imagined it from a dimensional analysis and then went about somehow proving it.

https://study.com/academy/lesson/using-dimensional-analysis-to-check-an-equations-correctness.html

https://www.quora.com/What-is-the-significance-of-Einsteins-equation-E-mc-2