Negative energy in Dirac equation

[kahoomann]

When Dirac solved his equation for electron, he found out there are negative energy states.
My question is why electrons won't jump from positive energy state to negative energy states and release energy as photon?

Dirac proposed that all negative energy states have been filled so electrons can't jump to negative energy states. It's clearly contrived

 

[ismaili]

When Dirac solved his equation for electron, he found out there are negative energy states.
My question is why electrons won't jump from positive energy state to negative energy states and release energy as photon?

Dirac proposed that all negative energy states have been filled so electrons can't jump to negative energy states. It's clearly contrived

Yep. You can say that the Dirac sea picture is kinda artificial, but, anyway, it's a successful phenomenological model.
Actually, Dirac only solved the negative probability problem manifestly. However, the Dirac equation still has negative energy solution. This motivates the discovery of anti-particles.

Yet the complete exact solution is given by QFT where the field solutions for the equation of motion are no longer interpreted as the wavefunctions. That is, $$\psi^*\psi$$ is not probability anymore. The wavefunctions become fields which are recognized as operators. And the problems disappear naturally.

BTW, I remember that I see somewhere an article saying that the Dirac sea picture is somehow can be thought of as an aether. (I'm not very clear about this.)

 

[denian]

argument.

I would respond by explaining that the concept of negative energy in the Dirac equation is a mathematical representation and does not necessarily have a physical interpretation. In other words, it is a theoretical concept that helps us understand the behavior of particles at the quantum level, but it does not necessarily mean that negative energy states actually exist in the physical world.

Furthermore, the concept of energy is relative and can only be measured in relation to a reference point. In the case of the Dirac equation, the reference point is the vacuum, which has a zero energy state. This means that the negative energy states in the Dirac equation are actually lower in energy than the vacuum state, but they are still positive in relation to other energy states.

In addition, the Pauli exclusion principle states that no two particles can occupy the same quantum state simultaneously. This means that all negative energy states are already occupied by other particles, so electrons cannot jump into them.

Moreover, the release of energy as photons occurs when an electron transitions from a higher energy state to a lower energy state. Since the negative energy states in the Dirac equation are already lower in energy than the positive energy states, there is no energy difference for the electron to release as a photon.

In summary, the concept of negative energy in the Dirac equation is a mathematical construct that helps us understand the behavior of particles at the quantum level. It does not have a physical interpretation and is not a valid explanation for the behavior of electrons in terms of energy states and photon emission.