2 Particles as Building Blocks of Matter
19
Since Dirac was generalizing this to relativistic energies, he had the same square
root problem as described in the previous paragraph. Dirac pointed out that
if the negative energies are taken to exist like the positive energy states, this
will have disastrous implications. To see this, recall Bohr’s suggestion that in
a hydrogen atom, an electron at a higher level always drops down to a lower
level state and light is emitted. In Dirac’s theory, since there are always negative
energy states which lie lower than the usual positive energy electron states of
atoms, the electrons would drop to the negative energy states and the atoms
would disappear.
For the electron not to disappear into the negative energy states, Dirac
postulated that the negative energy levels must be filled up with electrons
so that Pauli’s exclusion principle will prevent the electron from falling from
a positive energy state to a negative energy state. By this time, Pauli had
enunciated his celebrated principle (he did so in 1925) to explain the pattern
of light emission in atoms. Pauli’s exclusion principle states that two identical
particles with spin half, like electrons or protons, cannot occupy the same point
in space. This simple hypothesis explained a lot about atomic spectra and also
explained why matter is stable and does not collapse into a ball. Pauli received
Nobel Prize for this suggestion in 1945. Application of the Pauli principle
implied that if the negative energy levels were filled by electrons, a positive
energy cannot fall to this state and would go on behaving like a normal electron
without disappearing. The same is supposed to happen for all spin half particles
(say a proton or neutron), etc.
Filling of the negative energy states just to save Dirac’s theory was dubbed
as the Dirac sea, and as an idea, it looked pretty contrived. However, once
Quantum Field Theory was invented, the Dirac sea was reinterpreted to mean
that there is a new kind of matter (called anti-matter) which has exactly
opposite property to matter. For example, an unoccupied negative energy
state for electron would mean that it is its anti-particle with a positive charge
(opposite to the electron charge) and with positive energy. That would be
an electron’s anti-matter. This particle is known as the positron and was
discovered by Carl Anderson in 1932 while he was analyzing the cosmic rays in
a cloud chamber. He found an electron-like particle which bent in the opposite
direction to the electron in a magnetic field, proving that it had opposite charge
to the electron but same mass. That was a major discovery for which Anderson
got Nobel Prize in 1936, at the very young age of 31.
19
Since Dirac was generalizing this to relativistic energies, he had the same square
root problem as described in the previous paragraph. Dirac pointed out that
if the negative energies are taken to exist like the positive energy states, this
will have disastrous implications. To see this, recall Bohr’s suggestion that in
a hydrogen atom, an electron at a higher level always drops down to a lower
level state and light is emitted. In Dirac’s theory, since there are always negative
energy states which lie lower than the usual positive energy electron states of
atoms, the electrons would drop to the negative energy states and the atoms
would disappear.
For the electron not to disappear into the negative energy states, Dirac
postulated that the negative energy levels must be filled up with electrons
so that Pauli’s exclusion principle will prevent the electron from falling from
a positive energy state to a negative energy state. By this time, Pauli had
enunciated his celebrated principle (he did so in 1925) to explain the pattern
of light emission in atoms. Pauli’s exclusion principle states that two identical
particles with spin half, like electrons or protons, cannot occupy the same point
in space. This simple hypothesis explained a lot about atomic spectra and also
explained why matter is stable and does not collapse into a ball. Pauli received
Nobel Prize for this suggestion in 1945. Application of the Pauli principle
implied that if the negative energy levels were filled by electrons, a positive
energy cannot fall to this state and would go on behaving like a normal electron
without disappearing. The same is supposed to happen for all spin half particles
(say a proton or neutron), etc.
Filling of the negative energy states just to save Dirac’s theory was dubbed
as the Dirac sea, and as an idea, it looked pretty contrived. However, once
Quantum Field Theory was invented, the Dirac sea was reinterpreted to mean
that there is a new kind of matter (called anti-matter) which has exactly
opposite property to matter. For example, an unoccupied negative energy
state for electron would mean that it is its anti-particle with a positive charge
(opposite to the electron charge) and with positive energy. That would be
an electron’s anti-matter. This particle is known as the positron and was
discovered by Carl Anderson in 1932 while he was analyzing the cosmic rays in
a cloud chamber. He found an electron-like particle which bent in the opposite
direction to the electron in a magnetic field, proving that it had opposite charge
to the electron but same mass. That was a major discovery for which Anderson
got Nobel Prize in 1936, at the very young age of 31.