Feynman's perspective on negative energy states and pair creation

[kahoomann]

Dirac's theory of the electron predicted that there were identical particles of equal mass but of negative energy.

He appealed to the Pauli exclusion principle and proposed that there was a negative energy 'sea' of electrons that was full up to -2mc^2 in order to answer critics that positive energy electrons described by the Dirac electron theory would simply decay down to -infinity.
With this description pair creation is described by absortion of a photon (where the energy of the photon E_p > 2mc^2) by a negative energy electron that scatters up to a poitive energy state leaving behind a hole.

This hole is the negative energy 'sea' has equal but opposite charge to the electron and is commonly known as a positron.

I believe that this description is somewhat old hat and not used anymore in modern QFT circles. Can anybody give me a not too technical explanation to why the 'old hat' qualitative explanation is unsatisfactory and how Feynman's resolution works, i.e. negative-energy particles can only travel backward in time.

 

[eljose79]

Thank you for bringing up this interesting topic about Dirac's theory of the electron. While it is true that Dirac's theory proposed the existence of negative energy particles, modern quantum field theory has moved beyond this concept and uses Feynman's resolution to explain the phenomenon of pair creation.

One of the main issues with Dirac's theory was the concept of the negative energy 'sea' of electrons. This idea was necessary to avoid the problem of positive energy electrons decaying into negative infinity. However, it was a somewhat ad hoc solution and did not have a solid theoretical basis.

Feynman's resolution, on the other hand, is based on the concept of antiparticles. According to this theory, every particle has an antiparticle with opposite charge and spin. When a high-energy photon interacts with an electron, it can create a pair of particles – one with positive energy and one with negative energy. This is known as pair creation.

The key difference between Feynman's resolution and Dirac's theory is the concept of negative energy particles traveling backward in time. In Feynman's theory, the negative energy particles are actually antiparticles traveling forward in time. This may seem counterintuitive, but it is consistent with the principles of quantum mechanics.

In summary, while Dirac's theory was groundbreaking and revolutionary in its time, modern quantum field theory has moved beyond it and uses Feynman's resolution to explain the phenomenon of pair creation. I hope this helps to clarify the difference between these two theories.

 

[denian]

I can provide some insight into Feynman's perspective on negative energy states and pair creation. Feynman was a renowned physicist who made significant contributions to the development of quantum electrodynamics (QED).

Feynman's perspective on negative energy states and pair creation was based on his understanding of QED, which is a quantum field theory that describes the interactions between charged particles and the electromagnetic field. In QED, particles are represented as excitations of quantum fields, and interactions between particles are described as exchanges of virtual particles.

Dirac's theory of the electron, which predicted the existence of negative energy states, was a significant breakthrough in physics. However, it faced some criticisms, one of which was the concern that positive energy electrons would simply decay into negative energy states and disappear. To address this issue, Dirac proposed the concept of a "sea" of negative energy electrons that filled all possible energy states up to -2mc^2, where m is the mass of the electron and c is the speed of light.

Feynman's perspective on this concept was that it was an unsatisfactory explanation because it relied on the idea of a negative energy "sea" that could not be observed or measured. Instead, Feynman proposed a different explanation for pair creation, which involves the absorption of a photon with energy greater than 2mc^2 by a negative energy electron. This interaction results in the electron gaining positive energy and becoming a real particle, while the excess energy is converted into a positron (the antiparticle of the electron) that travels backward in time.

This explanation is in line with Feynman's interpretation of quantum mechanics, which states that particles can also be described as waves and can travel backward in time. This concept, known as Feynman's "sum over histories," is a fundamental aspect of his formulation of QED and has been successful in predicting and explaining various phenomena in particle physics.

In summary, Feynman's resolution of the issue of negative energy states and pair creation is based on his view of particles as waves and his interpretation of quantum mechanics. This explanation is considered more satisfactory than Dirac's concept of a negative energy sea, as it does not rely on unobservable or unmeasurable entities. However, it should be noted that both Dirac's and Feynman's explanations are still used and studied in modern QFT circles, as they both provide valuable insights into the behavior of