Frank Wilczek, Fantastic Realities, 2006 ✓

[…] the material world is constructed from vast numbers of identical copies of a relatively small number of building blocks — electrons, photons, protons and neutrons — that come in stereotyped units, having the same properties […]. They are described by waves […]. But the waves in question have the odd interpretation that their absolute square governs the probability for finding particles.

Together, these two ideas underlie the modern picture of atoms. An atom is a pattern of definite form, determined by minimizing the energy of electron waves bound to a small, positively charged nucleus (where protons and neutrons accumulate) by electrical attraction. A quantum-mechanical atom, unlike the Newtonian Solar System, has its size, shape and structure determined uniquely by the laws of physics.

This atomic model […] provides the ultimate foundation for chemistry, materials science and physiology. But it begs the question of what holds the nuclei together. The pursuit of this question […] revealed several new worlds of subnuclear phenomena. These included two new fundamental interactions, supplementing gravitation and electromagnetism, and a totally unexpected cornucopia of additional building blocks.

Truly satisfactory understanding came only after a long series of ingenious experiments and theoretical investigations, culminating in the so-called Standard Model. […]

It became clear early on that the proton and neutron are subject to additional forces, beyond gravity or electromagnetism, and more powerful than either, but acting only over short distances. Systematic study of the newly-named strong interaction suggested great complexity: the strong forces between protons and neutrons depend on the distances between the particles, their relative velocities, and even the relative orientation their spins. Nevertheless, they could be measured and they were used to create a of working quantum model of atomic nuclei that was comparable in power, if not in elegance, to the successful quantum model of atoms. Nor could complex details obscure the most fundamental point, that the rules of quantum dynamics still apply within the atomic nucleus, and that when applied to protons and neutrons subject to the strong interaction, they produce well-defined nuclei with unique structures.

Now we understand that the apparent complexity of the strong interaction occurs because protons and neutrons are composite objects. They are composed of quarks and gluons, whose mutual interactions are governed by beautifully simple (but hard to solve!) equations.

A second, new sort of interaction first revealed itself in processes that turn neutrons into protons (together with other particles), or vice versa. Such processes, when they occur within an atomic nucleus, change the chemical nature of the atom involved. Further investigation of comparatively feeble — that is, slow — processes whereby various otherwise-stable particles change into one another revealed many systematic patterns, and blossomed into the concept of a fourth fundamental interaction, the weak interaction.

The development of weak-interaction theory began a process whereby classic atomism, involving stable individual objects, has been replaced by a more sophisticated and accurate picture. In this new scenario, individual particles are not permanent. Rather they appear as excitations of universal quantum fields. These fields provide, in contemporary physics, the primary, permanent elements of reality.

It is only with the development of quantum-field theory that the first aspect of quantum mechanics became fully integrated into physical theory. Two electrons anywhere in the Universe, whatever their origin, have exactly the same properties. We understand this as a consequence of both being excitations of the same underlying feature, the electron field. The same logic, of course, applies to photons, quarks or gluons.

The field concept came to dominate physics starting with the work of Faraday in the mid-nineteenth century. Its conceptual advantage over the earlier Newtonian program of physics, to formulate the fundamental laws in terms of forces among atomic particles, emerges when we take into account the circumstance, unknown to Newton (or, for that matter, Faraday) but fundamental in special relativity, that influences travel no faster than a finite limiting speed. For then the force on a given particle at a given time cannot be deduced from the positions of other particles at that time, but must be deduced in a complicated way from their previous positions. Faraday’s intuition that the fundamental laws of electromagnetism could be expressed most simply in terms of fields filling space and time was of course brilliantly vindicated by Maxwell’s mathematical theory.

The concept of locality, in the crude form that one can predict the behavior of nearby objects without reference to distant ones, is basic to scientific practice. Practical experimenters — if not astrologers — confidently expect, on the basis of much successful experience, that after reasonable (generally quite modest) precautions to isolate their experiments they will obtain reproducible results. Direct quantitative tests of locality, or rather of its close cousin causality, are afforded by dispersion relations.

The deep and ancient historic roots of the field and locality concepts provide no guarantee that these concepts remain relevant or valid when extrapolated far beyond their origins in experience, into the subatomic and quantum domain. This extrapolation must be judged by its fruits. That brings us, naturally, to our second question.

Undoubtedly the single most profound fact about Nature that quantum field theory uniquely explains is the existence of different, yet indistinguishable, copies of elementary particles. Two electrons anywhere in the Universe, whatever their origin or history, are observed to have exactly the same properties. We understand this as a consequence of the fact that both are excitations of the same underlying ur-stuff, the electron field. The electron field is thus the primary reality. The same logic, of course, applies to photons or quarks, or even to composite objects such as atomic nuclei, atoms, or molecules. […]

The existence of classes of indistinguishable particles is the necessary logical prerequisite to a second profound insight from quantum field theory: the assignment of unique quantum statistics to each class. […] Quantum field theory not only explains the existence of indistinguishable particles and the invariance of their interactions under interchange, but also constrains the symmetry of the solutions. For bosons only the identity representation is physical (symmetric wave functions), for fermions only the one-dimensional odd representation is physical (antisymmetric wave functions). One also has the spin-statistics theorem, according to which objects with integer spin are bosons, whereas objects with half odd integer spin are fermions. […] The fermion character of electrons, in particular, underlies the stability of matter and the structure of the periodic table.

A third profound general insight from quantum field theory is the existence of antiparticles. […]

The three outstanding facts we have discussed so far: the existence of indistinguishable particles, the phenomenon of quantum statistics, and the existence of antiparticles, are all essentially consequences of free quantum field theory. When one incorporates interactions into quantum field theory, two additional features of the world emerge.

The first of these is the ubiquity of particle creation and destruction processes. Local interactions involve products of field operators at a point. When the fields are expanded into creation and annihilation operators multiplying modes, we see that these interactions correspond to processes wherein particles can be created, annihilated, or changed into different kinds of particles. […] Just because the emission and absorption of light is such a common experience, and electrodynamics such a special and familiar classical field theory, this correspondence between formalism and reality did not initially make a big impression. The first conscious exploitation of the potential for quantum field theory to describe processes of transformation was Fermi’s theory of beta decay. He turned the procedure around, inferring from the observed processes of particle transformation the nature of the underlying local interaction of fields. Fermi’s theory involved creation and annihilation not of photons, but of atomic nuclei and electrons (as well as neutrinos) — the ingredients of ‘matter’. It began the process whereby classic atomism, involving stable individual objects, was replaced by a more sophisticated and accurate picture. In this picture it is only the fields, and not the individual objects they create and destroy, that are permanent.

The second is the association of forces and interactions with particle exchange. When Maxwell completed the equations of electrodynamics, he found that they supported source-free electromagnetic waves. The classical electric and magnetic fields thus took on a life of their own. Electric and magnetic forces between charged particles are explained as due to one particle acting as a source for electric and magnetic fields, which then influence others. With the correspondence of fields and particles, as it arises in quantum field theory, Maxwell’s discovery of electromagnetic waves corresponds to the existence of real photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual photons. The association of forces (or, more generally, interactions) with exchange of particles is a general feature of quantum field theory. […]

The greatest lesson, however, is a moral and philosophical one. It is truly awesome to discover, by example, that we humans can come to comprehend Nature’s deepest principles, even when they are hidden in remote and alien realms. Our minds were not created for this task, nor were appropriate tools ready at hand. Understanding was achieved through a vast international effort involving thousands of people working hard for decades, competing in the small but cooperating in the large, abiding by rules of openness and honesty. Using these methods — which do not come to us effortlessly, but require nurture and vigilance — we can accomplish wonders.