22.1 Electromagnetism
Quantum electrodynamics (QED) was the first quantum field theory to be discovered. QED describes the electromagnetic field, which is related to the electromagnetic force, the force that conveys electric charge. All charged particles, including protons and electrons, interact via the electromagnetic force.
The electromagnetic force is about 1039 (10,000, billion, billion, billion, billion) times stronger than the force of gravity, but it doesn’t affect large objects very often. This is because most things have charges that cancel each other out, making them neutral, whereas gravity always affects everything with mass.[1]
22.2 Quantum electrodynamics (QED)
22.2.1 Paul Dirac and antimatter
Paul Dirac coined the term ‘quantum electrodynamics’ in 1927 when he provided a quantum theory of the electromagnetic field that explained how an atom can decay to a lower and therefore less energetic state and still follow the laws of energy conservation.[2]
Dirac showed that the atom does this by emitting the excess energy in the form of a photon. He did this by treating the electromagnetic field as if it's a gas made up of photons that act as harmonic oscillators (discussed in Book I).
Within a year, Dirac published his relativistic theory of the electron, which combined quantum mechanics with Albert Einstein’s theory of special relativity[3] (discussed in Book I). This showed that the electron has a spin of +1/2 or -1/2 and predicted, not only the existence of the antielectron - an electron with a negative energy, and therefore an opposite spin and charge - but that all particles have corresponding antimatter partners.
Matter and antimatter annihilate each other upon contact, and the total mass of the particles is converted to kinetic energy in accordance with special relativity.
In 1932, within four years of Dirac’s prediction, the American physicist Carl David Anderson discovered antielectrons, which he named positrons, from tracks produced by cosmic rays - the name given to extremely high-energy radiation that comes from space - inside of a cloud chamber.[4]
Particle detectors
Detectors are used to detect the energy and charge of high-energy particles. Before the invention of particle accelerators, this included radiation from radioactive elements and cosmic rays.
Cloud chambers
A cloud chamber is composed of a jar of gaseous alcohol that’s cooled at the bottom with dry ice. When a highly energetic charged particle moves through this gas, it removes electrons from the atoms it passes, leaving them positively charged. The neutral atoms in the gas then condense around them and along the path of the charged particle. If a magnetic field is placed across the chamber, then it will deflect the path of charged particles.
The British physicist Charles Thomson Rees Wilson invented the cloud chamber in 1911,[5] and the Austrian physicist Marietta Blau showed how the energy and charge of the particle can be determined from the shape of the track, which could be photographed.[6]
Bubble chambers
The cloud chamber was made somewhat obsolete in 1952 when the American physicist Donald Glaser invented the bubble chamber.[7] Bubble chambers work in the same way as cloud chambers, but here energetic charged particles travel through a superheated liquid - a liquid heated by changing pressure - such as liquid hydrogen, instead of a cold gas, and the liquid begins to boil around the ionised atoms that form along the path of the charged particles.
Proportional counters
Proportional counters were invented by the British physicist Samuel Curran in 1948.[8] These combine a Geiger Müller tube - the sensor used in Geiger counters, which were developed in the 1920s[9] - with an ionisation chamber - which measures the charge of ions created by high-energy charged particles. These were developed in the 19th century.[10]
In proportional counters, high-energy charged particles travel through a gas. This strips electrons from the gases’ atoms, leaving free electrons and positive ions. The free electrons are attracted to the positively charged electrode, the anode, and the positively charged ions are attracted to the negative electrode, the cathode. The movement of these particles creates an avalanche effect, where they ionise other particles until there are enough to create a measurable electric field. The particle’s position can then be determined from the time taken for the negative and positive particles to reach their corresponding electrodes.
Wire chambers
The French physicist Georges Charpak developed the multi-wire proportional chamber, known as the wire chamber, in 1968 while working at CERN.[11] These soon replaced bubble chambers because they could detect particles more quickly, and they could be linked to a computer so that data didn't have to be physically examined in the same way that photographs from bubble chambers were.
Charpak’s multi-wire proportional chamber was composed of many thin wires placed next to each other. He showed that each wire behaves as a proportional counter. This means that the wire chamber can be used to detect hundreds of particles a second, which led to more accurate measurements of the position of particles.
22.2.2 Early quantum electrodynamics
Other physicists, including Wolfgang Pauli,[12] Eugene Wigner,[13] Pascual Jordan,[14] Max Born, Werner Heisenberg,[15], and Enrico Fermi[16], helped extend Dirac’s idea to form the basis of modern QED theory.
While photons can be thought of as both particles and waves, QED treats photons as particles that ‘carry’ the electromagnetic force. Charged particles interact by emitting and absorbing photons. Photons do not experience the electromagnetic force themselves, and so they do not interact with each other, but the effects of electromagnetism are produced by the energy and momentum they carry.[17]
The photons that carry force are known as ‘virtual’ particles. Virtual particles are created the instant a particle emits or absorbs a photon, the total energy and momentum of the system is the same before and after, but Heisenberg’s uncertainty principle allows ‘extra’ energy to exist in the form of a particle for a very brief period of time.[18] Each virtual particle can be thought of as a harmonic oscillator, where the strength of the field is given by the displacement from its rest position.
Virtual particles exist for such a short time that they are essentially invisible and can only be detected by the effect they have on the particle that emits or absorbs them. Force-carrying photons are therefore different from photons produced by other means, like nuclear fusion, which could potentially exist forever.[19]
The possible ways in which charged particles can interact by exchanging virtual photons are represented by Feynman diagrams. These were devised by Richard Feynman in the 1940s and 1950s.[20] Feynman diagrams show a plot of time and space with straight lines used to depict fermions, like electrons, and wavy lines to depict bosons, like virtual photons. Antiparticles are represented as normal particles that are moving backwards in time.
Figure 22.1 |
A Feynman diagram showing how an electron changes trajectory when it emits a photon. |
Figure 22.2 |
A Feynman diagram showing one electron emitting a photon, and a second electron absorbing it. |
In 1932, the British physicist Patrick Blackett and the Italian physicist Giuseppe “Beppo” Occhialini showed that photons can produce positrons and electrons in pairs if they are energetic enough.[21] They did this by improving the efficiency of cloud chamber records by linking the chamber to Geiger counters that trigger a camera when a particle arrives.
22.2.3 Problems with early quantum electrodynamics
By 1939, the American physicist Robert Oppenheimer,[22] the Swiss physicist Felix Bloch and the American physicist Arnold Nordsieck,[23] and the Austrian-American physicist Victor Weisskopf[24] had all shown that this version of QED couldn’t be entirely correct. This is because it led to the prediction that the energy, mass, and charge of a single electron are all infinite, which obviously doesn't match our observations.
The American physicists Willis Lamb and Robert Retherford found another problem with QED in 1947.[25] Lamb and Retherford measured hydrogen lines in the microwave spectrum to study the difference in energy between the ℓ = 0 and ℓ = 1 states (discussed in Chapter 11). It was predicted that the two states should have equal energies but a magnetic field could induce an energy difference between them.
Lamb and Retherford measured this difference and then calculated what the difference would be if there was no magnetic field. To their surprise, it was not zero. The two states did not have equal energies after all. This difference is known as the Lamb shift, and it couldn’t currently be explained with QED.
22.2.4 Renormalisation
At the 1947 Shelter Island Conference on Quantum Mechanics, which took place in Long Island, New York, over 20 physicists - including Lamb, Oppenheimer, Feynman, Hans Bethe, and American physicists Julian Schwinger and David Bohm - discussed how they could solve these problems.[26]
On the train ride home, Bethe realised that the infinite values could be removed in a process known as renormalisation, where the infinities cancel out, leaving just the measured values.[27] This theory was developed by Schwinger,[28,29] Feynman,[20,30] and the Japanese physicist Sin’ichirō Tomonaga[31,32] in the late 1940s. The American physicist Freeman Dyson later showed that all of these approaches are equivalent.[33]
The problem of Lamb shift was solved with the realisation that different corrections were needed for ℓ = 0 and ℓ = 1 states as they differ in their average distance from the nucleus.
22.3 Zero-point energy and the Casimir effect
Quantum field theories state that all fundamental fields must be quantised at each point in space. This means that virtual particles are constantly coming into and out of existence almost everywhere. The temporary change of energy at a point in spacetime is known as a quantum fluctuation. The excess energy is known as zero-point energy or vacuum energy.[34] This excess energy should add to the energy density of the universe (discussed in Book I).
If spacetime is infinitely divisible, then it should produce an infinite amount of energy, yet this does not seem to be the case. We will probably not understand how vacuum energy affects the energy density of the universe until we have developed a quantum field theory of gravity (discussed in Chapter 25).
In 1948, the Dutch physicists Hendrik Casimir and Dirk Polder discovered the Casimir effect, which demonstrates measurable forces, possibly arising from vacuum energy.[35] Casimir and Polder showed that if two uncharged metal plates are placed close enough together in a vacuum, and are then pushed together slightly, they will start to attract each other.
This is because the vacuum energy between the plates contains contributions from all whole wavelengths that fit in the gap between the plates. As they are pushed together, more wavelengths are excluded, and the radiation pressure between the plates decreases, pulling the plates together.
This effect becomes dominant if the plates are less than a micrometre (one-thousandth of a millimetre) apart and was first demonstrated by the physicist Steve Lamoreaux in 1997.[36]
Figure 22.3 |
An illustration of the Casimir effect, which causes metal plates to attract each other. |
In 1961, the Russian physicists Igor Ekhiel’evich Dzyaloshinskii, Evgeny Lifshitz, and Lev Pitaevskii predicted that if the medium between the two plates is not a vacuum, then some materials can be made to repel each other via the Casimir effect.[37] This was shown experimentally in 2009.[38]
Some argue that the Casimir effect does not provide evidence for vacuum energy, as it can also be explained in terms of relativistic van der Waals forces.[39] These are the forces between neutral atoms, which were given a quantum description by the German physicist Fritz London in 1930.[40]
Quantum van der Waals forces occur because the negative charges of the electrons in an atom and the positive charge of the nucleus are not always in the same place relative to each other. The fluctuation of charge can result in attractive forces between atoms, in this case, the atoms that make up the metal plates.
In 1981, the Russian physicists Viatcheslav Mukhanov and Gennady Chibisov showed that quantum fluctuations were present during the inflationary epoch of the early universe[41] (discussed in Book I). These fluctuations expanded during inflation, and this can explain the asymmetry in spacetime that led objects to become gravitationally bound, creating structure in the universe.
22.3.1 Black holes and Hawking radiation
Virtual particles are usually created with an antimatter partner, and they annihilate each other almost instantly. A virtual particle can become ‘real’, however, if it’s removed from its anti-partner and it gains the required amount of energy from an outside source. In 1974, the British physicist Stephen Hawking showed that this is what happens at the edge of black holes[42] (discussed in Book I).
To an observer on either side, the constant production of particles would make it seem as if the black hole was emitting radiation, and so this effect is known as Hawking radiation. Hawking showed that black holes will start to evaporate, and eventually disappear when they contain more Hawking radiation than matter and energy.
22.3.2 The black hole information paradox
Black holes only have mass, and sometimes charge and angular momentum, but they retain no information about the matter that formed them. If black holes existed forever, then this information would be thought of as existing within the black hole. If they evaporate by emitting Hawking radiation, then this information appears to be lost forever.
In quantum mechanics, information loss violates unitarity, which is another way of saying that it violates the conservation of probability because it makes the sum of probabilities of all possible quantum outcomes different from one. This may mean breaking the laws of energy conservation and is known as the black hole information paradox[43,44] (discussed in Chapter 25).