18. Lesson 18:
Special Relativity, 4

Einstein’s Mass and Energy

  What’s Coming:

Here we go. The T-shirt equation. Nothing is the same after this fourth of Einstein’s 1905 papers…that one that said \(m=\dfrac{E}{c^2}\). We’ll develop it without calculus (although if you want to see a full derivation, it’s included for those with that background). Energy now simplifies! Mass becomes interesting! Particle collisions become understandable! Matter gets made! And I get my white board on the Big Bang Theory!

The implications again, are surprising and consequential. The conservation of energy and momentum will take on a whole new meaning and we’ll see that there really are only two kinds of energy! All of the varieties of energy you learned about? They boil down to just two.

Finally, spacetime. What the “S” stands for in QS&BB. Our modern intepretation doesn’t come from Einstein, but from one of his former professors who so disliked him, that he called him a lazy dog as a student since Einstein always cut classes. Then that professor put Relativity on a firm, mathematically sophisticated foundation that we wll now use.

  Goals of this lesson:

Understanding, Appreciation, and Familiarity

I’d like you to Understand:

• What the simple, but far-reaching T-shirt equation, \(E=mc^2\) actually means and how to use it.

• How energy and momentum conservation come together and make a strange, but beautiful reality.

I’d like you to Appreciate:

• How energy and mass are the same thing…not one converting into the other.

• Einstein’s life is so fraught with myth so I’d like you to appreciate what he did and what he didn’t do.

I’d like you to become Familiar With:

• The idea of invariance as a fundamental concept in physics

• How relativity makes particle physics and nuclear physics work. And nuclear energy and chemistry!

• How we learned to trust Relativity and what experimental confirmations have led us there.

• How the geometry of spacetime is so unlike what you’d expect. Hyperbolic??