Relativity Calculator
"If my theory of relativity is proven successful, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew." - Albert Einstein ( 1879 - 1955 )
§ Listen to Albert Einstein giving a short lecture about e=mc2: 
"It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing -- a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to m c-squared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned above. This was demonstrated by Cockcroft and Walton in 1932, experimentally." - Prof. Albert Einstein ( excerpts from 1947 film, "Atomic Physics" )
source: American Institute of Physics ( http://www.aip.org/history/einstein/ )
Special Relativity was first published in 1905 by Albert Einstein at age 26 working quietly in the Swiss Patent Office, Bern, Switzerland, under the title 
"On The Electrodynamics Of Moving Bodies", translated from "Zur Elektrodynamik bewegter Körper", Annalen der Physik, volume 17: 891, 1905, a downloadable copy of which is available here in pdf.
Also read "On The Relativity Principle And The Conclusions Drawn From It", by A. Einstein, translated from Jahrbuch der Radioaktivität und Elektronik volume 4 (1907): 411-462
And, "Does the Inertia of a Body Depend upon its Energy-Content?", by A. Einstein, Annalen der Physik volume 18: 639, 1905
§ Define:
§ Some Derivations:
1).
.
2).
§ The Problem:
However the entire classical Newtonian physics derived above is predicated upon the concept of mass as an invariant constant. But we now know differently, namely that mass, m, is a variable quantity owing to the Addition of Relativistic Velocities, where
is the relationship between rest mass undergoing velocity and its equivalent dilated mass.
§ The Solution:
But, whoa! Look,
§ More Simple Algebraic Derivation:
note: see another quick and dirty matheamtical derivation
§ Einstein's Interpretation:
The interpretation that Einstein therefore applied is as follows:
Nevertheless it still should always be remembered that
On the other hand, applying a relativistic kinetic energy concept, we can arrive at the following:
§ The Law of Inertia of Energy:
Or,
is the equation for matter in the form of inertial ( dilated ) mass which can be derived from a given amount of energy E whose capability for performing work is given by
.
§ Derivation of classical Newtonian kinetic energy:
§ Derivation of relativistic energy:
However for 
, relativistic mass dilation as a function of velocity,
where 
is rest mass ( proper mass ) within a given inertial frame of reference, we still have
However using a dummy variable trick for integrating,
And therefore,
§ 2nd Derivation of relativistic energy:
§ Derivation of classical kinetic energy:
§ Here we now have these important energy definitions:
Therefore,
§ Derive the law of conservation of total energy, relativistic and non - relativistic:
Finally, using the binomial series to derive the law of conservation of total energy, relativistic and non - relativistic:
§ Deriving mass dilation using Richard Fehnman's suggested equations from his "Lectures on Physics - Vol. I " ( although this derivation is somewhat recursive ):
"Imagination is more important than knowledge" - Albert Einstein ( 1879 - 1955 )
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