Oct 29, 2026 · 21 min · 16 segments
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/DonateSPACE Uploaded 21-06-17 Paul Dirac’s insights…
Matt O'DowdHost
Instead of having a two-component spinner up and down, as in powerless theory, He needed four components.

But the resulting equation was so simple and elegant that somehow Dirac knew that he was onto something.

The resulting Dirac equation describes the spacetime evolution of this weird four-component particle wave function represented by the symbol psi.

It contains the marks of both quantum mechanics in the Planck constant and relativity in the speed of light.

The Dirac equation perfectly predicts the motion of electrons at any speed, even in an electromagnetic field.

To begin with, what on earth were those two extra degrees of freedom in the four-component electron? The answer came from trying to calculate the energy of the electron using this equation.

For example, a lone electron moving in an electromagnetic field could keep releasing energy as light infinitely and sink lower and lower to infinite negative energy states.

Imagine an infinitely deep ocean of electrons that exists everywhere in the universe.

These electrons occupy all of the negative energy states, all the way from negative infinity up to zero.

The only time we can actually interact with an electron is when one has a positive energy, which would leave it sitting on top of the sea.

If the energy states of this imaginary ocean are all completely full, then that one extra electron can't lose any more energy.

Instead of having a two-component spinner up and down, as in powerless theory, He needed four components.

But the resulting equation was so simple and elegant that somehow Dirac knew that he was onto something.

The resulting Dirac equation describes the spacetime evolution of this weird four-component particle wave function represented by the symbol psi.

It contains the marks of both quantum mechanics in the Planck constant and relativity in the speed of light.

The Dirac equation perfectly predicts the motion of electrons at any speed, even in an electromagnetic field.

To begin with, what on earth were those two extra degrees of freedom in the four-component electron? The answer came from trying to calculate the energy of the electron using this equation.

For example, a lone electron moving in an electromagnetic field could keep releasing energy as light infinitely and sink lower and lower to infinite negative energy states.

Imagine an infinitely deep ocean of electrons that exists everywhere in the universe.

These electrons occupy all of the negative energy states, all the way from negative infinity up to zero.

The only time we can actually interact with an electron is when one has a positive energy, which would leave it sitting on top of the sea.

If the energy states of this imaginary ocean are all completely full, then that one extra electron can't lose any more energy.
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