PBS Features Einstein's Famous Equation

porp writes "On Tuesday, October 11th at 8PM EDT, PBS will feature a docudrama about Einstein's discovery of his famous E=mc^2 equation. The program will include details explaining those who came before him and the development of his miracle year. The pinnacle of which according to the program was his discovery that matter and energy are two sides of the same coin. Yahoo summarizes the program details in length." From the article: "Based on David Bodanis' best-seller 'E=mc2: A Biography of the World's Most Famous Equation,' the program explores the lives of the men and women who helped develop concepts behind each term: E for energy; m for mass; c for the speed of light; and 2 for 'squared,' the multiplication of one number by itself."

Comments

But Why Is It So?

[Quantum Jim]

I recently derived the famous equation in my slashdot journal entry. It can be found when starting from the assumptions Einstein had when Special Relativity was first proposed. That is:

• The laws of the universe are valid in all inertial reference frames.
• The strength of electric and magnetic fields are each a certain constant in space.

From the second axiom, you can show that the speed of light only depends on the strength of electric and magnetic fields in space using Maxwell's equations. An interesting derivation that requires vector calculus, so I'll save the pain of it for you. ;-) From the first axiom, you can show that the speed of light violated Galilean Relativity.

Knowing that Galilean Relativity is still useful, Einstein proposed another assumption:

• To fix Relativity you need only a simple linear correction factor.

From that, you can derive the Lorentz Transformations. Then while examining how those transformations affect the conservation of momentum in collisions you can derive a more useful definition of momentum based on the old definition and that correction factor.

Finally using the new equations of Momentum and the Lorentz Transformations, you can redo Young's derivation of Kinetic Energy using the old definitions of velocity, force, and energy. The end result is a mass at rest still has some energy. This energy is called the rest energy and is related by the famous relation. That's what Einstein's equation says (no hokey about relativistic mass please).

Now you know why it was so . :-D