Theoretical physics is a branch of physics that uses mathematical models and abstractions of physical objects and systems to explain and predict natural phenomena. It is, in the broadest sense, the attempt to say why things happen the way they do, not merely to record that they do. This is in contrast to experimental physics, which tests and refines those explanations through direct measurement and observation. In practice, the two feed each other constantly: a theoretical prediction suggests an experiment, and an unexpected experimental result sends theorists back to the drawing board.
The scope of theoretical physics is enormous. It ranges from the behaviour of quarks and elementary particles at scales far smaller than an atom to the large-scale structure of the universe itself. Where direct experimentation is impossible or simply not yet feasible, theoretical physics advances understanding through mathematical reasoning and thought experiments. This is perhaps the thing that surprises people most about the field: some of its most important results have come from pure reasoning, long before any instrument could test them. General relativity, quantum mechanics, and the Standard Model of particle physics each originated primarily as theoretical constructions, only later confirmed by experiment.
A physical theory is, at its core, a mathematical model of some set of physical phenomena. It gets judged on two main grounds: how well its predictions match what we already observe, and whether it can successfully predict new things that can then be tested. A theory that explains everything after the fact, but predicts nothing in advance, is unsatisfactory. Karl Popper made this point sharply in The Logic of Scientific Discovery: a scientific theory must be capable of being shown to be false by some possible observation. If no conceivable experiment could contradict it, it is not science in any meaningful sense.
There is also a question of elegance, or economy. When two competing theories account for the same phenomena equally well, physicists generally prefer the simpler one. This instinct goes by the name Occam's razor, and while it is not a law of nature, it has a remarkable track record. Theories that unify large numbers of apparently separate phenomena under a single framework tend to be regarded as especially powerful. James Clerk Maxwell's demonstration in the nineteenth century that electricity, magnetism, and light are all manifestations of a single electromagnetic field is probably the clearest historical example of what unification looks like when it actually works.
When a new theory supersedes an older one, it almost always contains the older theory as a limiting case. This is sometimes called the correspondence principle. The predictions of special relativity, for instance, reduce to those of Newtonian mechanics when velocities are small compared to the speed of light. Newton's laws are not wrong, exactly; they are a very good approximation within a certain domain. The older theory retains its practical usefulness long after it has been subsumed by something broader and more accurate.
It is also worth being clear about what a physical theory is not. A mathematical proof establishes the truth of a conclusion given certain axioms, and that is that. A physical theory, however well-supported, remains permanently open to revision by future observations. That is not a weakness. It is the defining feature of a science that is actually trying to describe the world rather than merely exploring abstract structures.
Theoretical physicists do not all work the same way, and it is worth separating out the main approaches rather than treating them as a single undifferentiated activity.
Some theorists focus on phenomenology: building mathematical descriptions that reproduce experimental data and point toward further measurement, often without deriving the model from deeper principles. It is a bit like fitting a curve to data points before you understand what the curve means. The Bohr model of the hydrogen atom and the early analyses of spectral lines by Johann Balmer and Johannes Rydberg are good historical examples. They worked, and they were useful, even though the underlying mechanism was not yet understood.
Others construct model-based frameworks built around specific properties, such as internal consistency or compatibility with known symmetries, and then check whether the resulting theory matches observations. The Standard Model of particle physics was built this way during the 1960s and 1970s, combining quantum field theory with insights about the symmetries that govern the fundamental forces.
A related strategy involves effective theories: frameworks that describe the behaviour of a system accurately within a particular range of energy scales or length scales, without necessarily providing a complete account of what is happening at a deeper level. This is widespread in both particle physics and condensed matter physics, and it is a practical response to the fact that fully general theories are often impossible to solve in realistic settings.
Then there is the ambition of unification: finding frameworks that consolidate previously separate theories into a single coherent one. The electroweak unification of electromagnetism and the weak nuclear force, worked out by Sheldon Glashow, Abdus Salam, and Steven Weinberg in the 1960s, is the most recent fully successful example. The effort to incorporate gravity into a quantum framework has been going on for decades and remains, at the time of writing, unfinished.
Finally, theoretical physics sometimes advances simply because someone notices that a piece of mathematics developed for entirely different reasons happens to describe a physical situation perfectly. This happens more often than one might expect, and it is genuinely strange.
Ancient and medieval foundations
The attempt to account for natural phenomena in terms of physical principles, without invoking the supernatural, appears in ancient Greece at least as early as the sixth century BC. What we now call pre-Socratic philosophy was, in important respects, theoretical physics in its earliest form: an effort to identify general principles from which the behaviour of the natural world could be understood. Aristotle later synthesised much of this into a comprehensive account of motion, matter, and the cosmos. He was often wrong, but he was systematic, and his framework remained the dominant reference point in European and Islamic natural philosophy for well over a thousand years.
During the medieval period, the eleventh-century scholar Ibn al-Haytham made advances in optics and articulated, earlier than most accounts acknowledge, the importance of checking theoretical claims against controlled observations. His work on the behaviour of light and the mechanism of vision was influential across Europe for centuries after his death.
Things began to change rapidly in the sixteenth and seventeenth centuries. Nicolaus Copernicus proposed a heliocentric model of the solar system, which cut against centuries of received opinion. Johannes Kepler, working from Tycho Brahe's careful observational records, derived three precise mathematical laws describing planetary orbits. What is striking about Kepler's laws is not just that they fit the data, but that they gave theorists something concrete to explain. That invitation was taken up by Isaac Newton.
Newton's Philosophiae Naturalis Principia Mathematica of 1687 is arguably the founding document of theoretical physics in the modern sense. From a small number of laws of motion and a universal law of gravitation, Newton derived the orbits of the planets, the behaviour of falling bodies, and the shape of the tides. More than that, he established a template: a compact set of mathematical principles from which a vast range of phenomena could be derived and, crucially, quantitatively predicted.
The nineteenth century extended and deepened classical physics along several fronts. Joseph-Louis Lagrange, Leonhard Euler, and William Rowan Hamilton reformulated Newtonian mechanics in increasingly general mathematical terms, producing what are now called Lagrangian mechanics and Hamiltonian mechanics. These frameworks proved essential for the later development of both statistical mechanics and quantum mechanics, so the investment in abstraction paid off very handsomely indeed.