This page gives plain-language summaries of physics papers. We draw no link to Dost or to any other text; reading side by side is the reader's own work.
Experiment: measured. Theory: calculated or proved. Interpretation: its meaning is disputed. The labels are our own classification; a paper may have more than one nature.
Main question: How does quantum mechanics combine with special relativity?
In the mid-1920s the Schrödinger equation described atoms very well but did not conform to special relativity: it did not treat time and space equally. The electron's "spin" entered the theory afterwards, as an unexplained addition. The Dirac equation answers this question: can we describe the electron by a single equation that conforms both to quantum mechanics and to relativity? In this paper the notion of spin and the matter of the particle's antiparticle (antimatter) appear as consequences of this equation.
On this page21. The Dirac Equation · Dirac 1928 — The quantum theory of the e · 22. Quantum Electrodynamics (QED) …
Proceedings of the Royal Society A 117, 610-624 theory
Dirac set up a wave equation for the point electron that conforms both to relativity and to the general transformation theory of quantum mechanics.
The paper begins with a shortcoming. The quantum mechanics of the day, with the electron thought of as a point charge, could not fully describe atomic spectra: the number of observed stable states was twice what the theory gave. Goudsmit and Uhlenbeck had met this doubling by giving the electron a model spinning about its own axis and having a magnetic moment; Pauli had placed this in quantum mechanics. Dirac asks why this model is the one nature chose, and thinks the shortcoming may lie elsewhere: the earlier theories did not conform to relativity.
Dirac looks for the simplest Hamiltonian operator that satisfies the conditions both of special relativity and of the general transformation theory of quantum mechanics. The equation he finds depends on time and space in the same way, that is, to first order. For this reason the wave function is not a single number but a four-component object. According to the paper's abstract, this simplest form accounts for the whole of the "doubling" phenomena without any additional assumption. Spin ceases to be something added to the model from outside and comes out of the equation itself.
The abstract says that there is a share of truth in the spinning electron model too, but that the model remains valid as a first approximation. Its greatest failure is that the total orbital angular momentum of an electron in orbit is not constant, as the model expects. That is, Dirac's result is presented not as a model but as a theoretical necessity.
One of the practical consequences of the equation is the fine structure of hydrogen-like atoms: the interaction of spin with orbital motion gives the small splitting of the energy levels spontaneously. Another is that the electron's magnetic moment comes out from the spin and the charge with a definite value; this value was later compared with measurements. The limit of the paper is also seen here: the equation was set up as a wave equation of a single particle and did not by itself describe cases in which particles are created and annihilated.
Afterwards: The equation's negative-energy solutions led Dirac, toward 1931, to propose the existence of the electron's antiparticle; the positron was observed in 1932 by Anderson in cosmic-ray photographs and published in 1933 (source: anderson-1933). It can be said that the equation was a starting point for later theories and that the transition to quantum field theory was made through it.
22. Quantum Electrodynamics (QED)
Main question: How is the interaction of light and matter explained?
Quantum electrodynamics (QED) is the theory that describes the interaction of charged particles (for example electrons) with light, that is, with photons. It is thought of as the quantum counterpart of electromagnetism. In the early 1940s, calculations made with this theory gave infinite results when they came to finer corrections. The question was: is it possible to manage these infinities in a consistent way and reach measurable numbers? The 1948-49 works of Feynman and Schwinger answered this question in two different languages, but producing the same numbers.
Schwinger calculated the first quantum correction to the electron's magnetic moment and compared it with the measured value.
This is a short two-page letter. The Dirac equation said that the electron's magnetic moment would come out at an exactly definite value from its spin and charge. Measurements made in 1947, however, showed that this value was larger by a few parts in a thousand. The question was: could this small deviation be a correction arising from the interaction of the light field with the electron?
Schwinger rearranged quantum electrodynamics so as to gather part of the infinities into the measured mass and charge, and calculated the first-order correction. The result came out finite: the electron's magnetic moment is about (1 + α/2π) times Dirac's value; here α is the fine-structure constant, about 1/137. That is, the correction is roughly of the order of 0.1 percent. This value was consistent with the measurement made at the time.
The importance of the paper lies not in a single number but in the method: the parts of the theory that give infinities are separated from measurable quantities and, "renormalized," give a meaningful result. A more general systematization of this approach was carried out in the following years.
The brevity of the letter is a limit: the detailed derivation and higher orders were left to other papers. Moreover, this first correction is a single number; for testing the theory, higher orders and other measurements are needed. Even so, the fact that the calculation came out finite showed concretely for the first time that a measurable prediction could be obtained from a theory that had until then given infinite results.
This summary was written without looking at the paper's own abstract or text, relying on a known account; it should be checked against the source.
Afterwards: The electron's magnetic moment was calculated and measured to far higher orders in the following decades; it is said that QED is one of the most precisely tested theories. For this work Schwinger shared the 1965 Nobel Prize in Physics with Feynman and Tomonaga.
Feynman rebuilt QED over spacetime, in the language of the paths particles follow, and gave the rules that simplify the calculations.
Feynman's paper is another way of presenting QED. In quantum mechanics the probability of a particle going from one point to another is found by adding up the contributions of all possible paths; Feynman applies this to the electromagnetic interaction. Electrons and photons are treated as objects that send and receive one another, like light, in spacetime, and each interaction corresponds by a rule to a definite contribution.
These rules are shown with drawings later called "Feynman diagrams": a line is the path of a particle, and a vertex is an interaction. The diagrams are not just pictures; a mathematical expression to be written down corresponds to each of them. In this way long and error-prone calculations become orderly by counting which diagrams can be drawn.
The paper also shows how to handle the part of the interaction of light and matter that comes out infinite. The infinities are separated off by being redefined with the measured mass and charge; what remains is a finite, comparable result. This part gives the same numbers as Schwinger's work of the same years.
The paper's strength is in convenience, but it also has a limit: the method rests on an irregular series expansion, that is, on the sequence of diagrams that can be drawn, and this series does not work when the interaction is very strong. In QED, since the coupling constant is small, about 1/137, a few diagrams often give sufficient accuracy.
This summary was written without looking at the paper's own abstract or text, relying on a known account; it should be checked against the source.
Afterwards: In 1949 Dyson showed that the formulations of Feynman, Schwinger and Tomonaga were different presentations of the same theory. Feynman diagrams then became the standard calculational tool not only in QED but in the rest of particle physics.
23. Renormalization
Main question: Why do the infinities in quantum field theory arise?
In quantum field theory, when calculating a particle's interaction with its own field, one must also sum over very short distances and very high energies; the sum can go to infinity. Renormalization is the way of getting finite results by absorbing these infinities into the measured quantities. Wilson's 1971 work looked at the subject anew as a matter of scale: if we examine a system by "zooming" to different sizes, how do the parameters change? The question concerns both the source of the infinities and why this method works.
Wilson combined the renormalization group, which describes scale change in critical phenomena, with Kadanoff's scaling picture.
At first sight the paper is concerned not with field theory but with critical phenomena. When a fluid approaches its critical point or a magnet reaches the Curie temperature, the system's behavior begins to look similar at every scale and the measured quantities follow power laws carrying definite exponents. Kadanoff had proposed an idea to explain this: grouping neighboring spins into blocks and thinking of the block as a new "single spin".
Wilson turns this idea into a systematic theory. As the scale is changed with each block, one looks at how the parameters describing the system (such as coupling constants) change; this change can be thought of as a kind of "flow". Some points stay fixed in this flow (fixed points), and critical behavior is determined around these fixed points. Thus the reason for power laws and for universality (very different systems sharing the same exponents) can be understood as the details losing their importance as the scale shrinks.
This work does not by itself answer the problem of infinities, but it brings to field theory this view: the theory can be regarded as an effective description valid up to a certain energy, and the details of high energies are absorbed into the parameters at low energy.
The limit of the paper is its direct field of application: the subject treated here is critical phenomena; its application to quantum field theory is the carrying of the same idea to another field with similar mathematics. The question of how parameters change with scale is today worked on in both solid-state physics and particle physics, in a common language.
This summary was written without looking at the paper's own abstract or text, relying on a known account; it should be checked against the source.
Afterwards: For these works Wilson received the 1982 Nobel Prize in Physics. The effective-theory view gained wide acceptance in field theory; however, what the infinities "really" mean remains a philosophically debated subject.