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snoopies622

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- TL;DR Summary
- Seeking a basic understanding of how non-zero values of these components manifest themselves in experiments.

Forgive me if you've heard this song before, but I don't understand how to interpret the [itex] \psi_3 [/itex] and [itex] \psi_4 [/itex] components of the Dirac equation. For instance, at 8:27 of this video

we see that while an electron at rest can be in a state like [1,0,0,0], the same electron as viewed from a reference frame moving along the x-axis would be seen in the state [1, 0, 0, [itex] p_x / (E+m) [/itex]].

Does this mean that in the moving reference frame, there is a non-zero probability of observing a positron instead of (or in addition to) an electron? Somehow the [itex] \psi_3 [/itex] and [itex] \psi_4 [/itex] components are associated with both positrons and negative energy, which itself confuses me since positrons have positive energy.

I'm also wondering how the Dirac equation is normalized (if that's the right word). When using the Schrodinger equation for a particle, at any given moment [itex] \int |{\psi}|^2 =1 [/itex] for all of space because it is certain that the particle will be found somewhere. What is the parallel relation for the Dirac equation? Is it [itex] \int (|{\psi_1}| ^2 + |{\psi_2}|^2 + |{\psi_3}|^2 + |{\psi_4}|^2) =1 [/itex] for all of spacetime?

Thanks.

we see that while an electron at rest can be in a state like [1,0,0,0], the same electron as viewed from a reference frame moving along the x-axis would be seen in the state [1, 0, 0, [itex] p_x / (E+m) [/itex]].

Does this mean that in the moving reference frame, there is a non-zero probability of observing a positron instead of (or in addition to) an electron? Somehow the [itex] \psi_3 [/itex] and [itex] \psi_4 [/itex] components are associated with both positrons and negative energy, which itself confuses me since positrons have positive energy.

I'm also wondering how the Dirac equation is normalized (if that's the right word). When using the Schrodinger equation for a particle, at any given moment [itex] \int |{\psi}|^2 =1 [/itex] for all of space because it is certain that the particle will be found somewhere. What is the parallel relation for the Dirac equation? Is it [itex] \int (|{\psi_1}| ^2 + |{\psi_2}|^2 + |{\psi_3}|^2 + |{\psi_4}|^2) =1 [/itex] for all of spacetime?

Thanks.

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