Can somebody further explain this excerpt from Michio Kaku's Physics of the Impossible? It looks like he's missing a step.
>In developing his new equation for the electron, Dirac realized that Einstein’s celebrated equation, E = mc2, was not quite right. Although it is splattered over Madison Avenue ads, children’s T-shirts, cartoons, and even the costumes of superheroes, Einstein’s equation is only partially correct. The correct equation is actually E = ± mc2. (This minus sign arises because we have to take the square root of a certain quantity. Taking the square root of a quantity always introduces a plus or minus ambiguity.)
>But physicists abhor negative energy. There is an axiom of physics that states that objects always tend to the state of lowest energy (this is the reason that water always seeks the lowest level, sea level). Since matter always drops down to its lowest energy state, the prospect of negative energy was potentially disastrous. It meant that all electrons would eventually tumble down to infinite negative energy, hence Dirac’s theory would be unstable. So Dirac invented the concept of the “Dirac sea.” He envisioned that all negative energy states were already filled up, and hence an electron could not tumble down into negative energy. Hence the universe was stable.
Where did he get negative energy? Negative mc times negative mc should still equal positive energy.
>In developing his new equation for the electron, Dirac realized that Einstein’s celebrated equation, E = mc2, was not quite right. Although it is splattered over Madison Avenue ads, children’s T-shirts, cartoons, and even the costumes of superheroes, Einstein’s equation is only partially correct. The correct equation is actually E = ± mc2. (This minus sign arises because we have to take the square root of a certain quantity. Taking the square root of a quantity always introduces a plus or minus ambiguity.)
>But physicists abhor negative energy. There is an axiom of physics that states that objects always tend to the state of lowest energy (this is the reason that water always seeks the lowest level, sea level). Since matter always drops down to its lowest energy state, the prospect of negative energy was potentially disastrous. It meant that all electrons would eventually tumble down to infinite negative energy, hence Dirac’s theory would be unstable. So Dirac invented the concept of the “Dirac sea.” He envisioned that all negative energy states were already filled up, and hence an electron could not tumble down into negative energy. Hence the universe was stable.
Where did he get negative energy? Negative mc times negative mc should still equal positive energy.
