Structured list of physical theories

What is a scientific theory

All our perceptions of the world consist in the information (like files in computers, even if the correspondence between natural and digital types of information is fuzzy) that our senses (nerves) give us. They do not directly reveal (at least not in an obvious way) any ontological aspects, i.e. "real nature" of things (or aspects of the world, such as time), that may be causes, or sources, of our perceptions. Without trying to directly discuss any ontology, the work of science is to develop our understanding of the world as follows:

Systematically collect observable information (possibly in hopefully reliable measurement and storage devices - but their reliability can usually be itself verified too),
Express scientific theories : a scientific theory is a description (claim) about structures in the data from some fields of perceptions (thus giving some predictions on future observations in these fields), expressed as deduced from a precise description of some sort of world (of abstract or imaginary objects) with an indication of how our perceptions connect to it (how they are inserted there).
Check how that fits : analyze the structure of observed information, compute deductions and predictions from candidate scientific theories, and check and compare how well do theories fit with observed data. Depending on the types of claims, the notion of "how they fit" may take different meanings : logical claims are accurate, continuous functions are good approximations, probabilistic claims minimize the entropy of observed data.

This structure of observable information, once understood and formulated in the form of theories, even while remaining on a scientific level (giving the practical shape of things, what we can work with in practice without entering any ontological debate) is already a rich, fascinating, and often sufficient understanding of the world.

Theories of physics and their plurality

Among sciences, Physics focuses on fields or aspects of the world that are especially "elementary", which happened to be successfully described by mathematical theories (thus rigorously clear about their consequences, without risk of being relative to anyone's fanciful interpretation). Aspects that way "elementary", include

Microscopic systems (with few particles or atoms),
Rather simple systems (without life nor any other too complex combinations of internal processes : balls and other solids, water, gases),
Good approximations of systems where any contribution of their possibly living content can be neglected (trajectories of planets),
General non-deterministic laws (classical mechanics, thermodynamics, properties of machines and dynamics of bodies...) such as the conservation of energy, that specify only some aspects of behaviors, which can be logically distinguished from the influence of the complex content that we do not try to predict or explain (but just treat as variables in the theory).

To describe these diverse ranges of phenomena, all somehow elementary in different ways, physicists found different theories with their respective fields of application.
It was a big success, as they are

very deep and wonderful mathematical theories, quite elegant and unified in comparison with the range of phenomena they can explain.
excellent approximations in their respective fields, verified as agreeing with observations (and thus faithful descriptions of the structures of the observable universe) with a high accuracy, at least in principle (while the effectively available predictive power of theories can be very limited for some phenomena, even seemingly simple ones such as a chemical reaction between a few atoms, whose computation from the theory would be so complex that it may require powerful supercomputers, or even be inaccessible by them).
partially "united" by being all mathematical theories with strong logical articulations together, which are the "real articulations" between the aspects of the world (the fields of observations) that they describe.

Before enumerating the known (established) theories of physics, let us first explain the principles of their hierarchy. In fact there are two different types of hierarchical relations between them.

The fundamental vs. the approximated (phenomenological) theories

The first kind of hierarchical relation is when a theory A is more fundamental than a theory B, so that A explains B as its approximation that works in some restricted range of phenomena among those described by A.
Namely, here is the transition in most cases:
The law A makes its predictions (for its given class of phenomena) as expressed depending on some parameter (physical constant). These predictions converge to the law B when this parameter approaches some limit value (zero or infinity).
So there is a range of phenomena with a range of requirements on the accuracy of predictions in each case, for which the consequences of B cannot be distinguished from those of A. As long as the considered experiences remain inside this range, the best (simplest, most relevant, best understandable) way to effectively describe (predict) them, is in terms of theory B, while the use of theory A would be uselessly complicated (even if A is a more elegant theory than B so that it theoretically is a better explanation why things go this way, namely, why B is applicable).
We leave this range (of applicability of B inside the range of applicability of A) either when changing the choice of phenomena (conditions of the experiment), letting differences become bigger, or when increasing the precision of measurements to detect the small effects of the difference between laws A and B.

The framework vs. the specific theories

The other hierarchy between theories is the opposition between frameworks and specific theories. Framework theories give some general styles of how things may behave, but they still allow for many possibilities. They give a general common language of physics, in which specific theories (specific laws) may be expressed, and may coexist (interact) with other laws, other phenomena. Frameworks don't give all the information of what are the laws, but only give a range of possibilities of how they may be. They leave a conceptual possibility for some other universes with the same framework, to have different specific laws.
This hierarchy of framework vs specific theories, goes beyond physics. Namely we may consider that mathematics itself is a framework for physics, and physics is itself a framework for the study of many possible kinds of physical systems : each physical system is a specific, contingent situation that provides its own local "laws", more specific than the global set of all physical laws of the universe. For example the "laws of the Solar System" have their own "constants" : the mass of the Sun, the masses of each planet, their current orbital parameters and so on. Other fields of study "more specific than the laws of physics" include for example, biology, engineering, climatology and earth sciences.

However inside physics we already have this kind of hierarchy between several theories.
More precisely there are 2 framework theories that may roughly be considered (studied) independently of each other, and that are both involved as necessary frameworks to describe any physical process (the different particles and interactions in nature). These frameworks are

Space-time
The principle of mechanics

The space-time framework

Space-time is of course a framework for all physical processes, as any phenomenon necessarily happens at some place and some time.
There is already a diversity of theories describing the space-time of our universe. These theories of space-time form a hierarchy from the most fundamental to the most approximated version. This hierarchy forms a linear order here listed from top to bottom, except for two separate intermediate versions that don't compare to each other:

Curved spacetime (Lorentzian manifold with signature (3, 1))
Minkowski spacetime (Special Relativity)	Classical spacetime (absolute time) with Equivalence principle of General Relativity
Galilean spacetime (relative speed)
Aristotelian spacetime absolute speeds: some things stay fixed (on the ground), others move
Euclidean (3-dimensional) space (no movement)

though the transition between Galilean and Aristotelian space-times is not a matter of fundamental vs approximation, but a change of viewpoint (description formalism).

This framework may be considered to be itself a specification out of a list of similarly conceivable spaces with different dimensions. In other words, even some other laws of physics remain compatible with the case of a space with dimension other than 3 (but only consequences differ, such as that there cannot be any stable orbiting behavior with gravitation, nor any stable atom built from the same laws).
Pedagogically, the simplest is to start from the Euclidean 3-dimensional space, that we are already familiar with; and (through possible studies of affine geometry and vector spaces) use it as a model to understand the Minkowski spacetime (thanks to the analogies between both geometries).

The principle of mechanics

This is the general framework expressing the behavior of physical systems. In fact, there are many versions of this framework that apply to different kinds of situations, and the connections (hierarchy) between these theories (frameworks) are often more complex than the general standard kind of hierarchy (from the fundamental to the approximated) that we stated above. We often need to enter some details of these theories to specify in which way they relate to each other. Let us first give the list of the most important ones in bulk:

Abstract Quantum Theory
Markov chains (discrete classical probabilities) and information theory
Theory of Quantum States and Measurements, and its resulting concept of entropy
Least Action Principle (fundamental expression of classical mechanics, reversible phenomena)
Conservation Laws (macroscopic approach of classical mechanics)
Symplectic Chaos Theory (continuous probabilities in reversible phenomena. Examples: study of stability of planetary orbits; asteroid belts and globular clusters - even if some kinds of irreversible processes are present there too)
Dissipative Chaos Theory (example : climatology)
Statistical equilibrium (Boltzmann distribution, microscopic description at a fixed temperature)
Classical Thermodynamics (macroscopic description; either static or dynamic behaviors, using the macroscopic effects of the thermodynamic equilibrium of every small zone of matter at their respective temperatures)

The two fundamental ones from which all others are approximations, are the Abstract Quantum Theory and the Theory of Quantum States and Measurements. We cannot really define an order between them. The Abstract Quantum Theory generally consists in operating with Hilbert spaces (though this definition is linked to the role of time; this theory may be expressed in other ways depending on its articulation with space-time). Its laws are time-reversible (where reversing time goes with taking conjugation of complex numbers). But it is a mere abstract mathematical theory that does deal with any effective realities.
The Theory of Quantum States and Measurements, works with positive Hermitian forms on these Hilbert spaces. Thus its mathematical content is simply built over the objects of Abstract Quantum Theory, but in a time dissymmetric way, and with its special, metaphysical rather than strictly mathematical concepts of "what is real" (states of physical systems, and what is the form of produce experimental predictions).

The only proper frameworks where to express fundamental specific laws (the different types of elementary particles and fields), are the Abstract Quantum Theory and the Least Action Principle (while the specific laws in others frameworks are consequences or phenomenological versions of these fundamental specific laws). We may roughly consider the Least Action Principle as an approximation of the Abstract Quantum Theory, however most of the specific fundamental laws can in a first step be defined in the framework of the Least Action Principle, after which a more or less standard mathematical tool called quantization, converts them into a specific fundamental law in the framework of Abstract Quantum Theory.

Conservation Laws are exact consequences of the Least Action Principle (thus not approximations, but still less fundamental). They remain valid from a macroscopic viewpoint, where the quantum undeterminations of their object vanishes, but while we lose trace of the fundamental (microscopic) processes underlying the considered processes. For example the phenomenon of friction satisfies the conservation laws but cannot be analyzed in terms of the least action principle.

Symplectic Chaos and Dissipative Chaos are but probabilistic studies of the consequences of classical physics. The symplectic case comes from Least Action Principle, while the dissipative case comes from the mere conservations laws completed by classical thermodynamics and other phenomenological specific laws roughly determining behaviors in short time intervals.

Putting all together

The double choice of a type of space-time and a principle of mechanics, first constitutes itself a theoretical framework that can be given its own name. Then, it can allow for (include) for several types of particles or fields (but particles and fields are the same thing for quantum field theory) described by their respective specific laws. So let us put them all in a big table. Columns represent principles of mechanics ; lines represent types of space-time.
Each cell first contains the name of the framework defined by this double choice, then specific laws for particles and fields that can interestingly fit there. Let us just keep here both principles of mechanics where fundamental specific laws are expressed:

	Abstract Quantum Theory	Least Action Principle
Curved spacetime	Quantum gravity (more tricky than a curved spacetime because of quantum indeterminations) TOE (theory of everything, yet to be discovered)	General Relativity Electromagnetism in general relativity. As simple particular cases we have cosmology, black holes, gravitational waves...
Minkowski space-time	Quantum Field Theory Inside it : specification of the Standard Model, including: QCD = Quantum Chromodynamics (nuclear force); Electroweak interaction, that approximates into QED (quantum electrodynamics = the quantized version of electromagnetism)	Relativistic Mechanics Electromagnetism Nuclear reactions
Classical with Equivalence principle		Classical gravitation and cosmology (allows for a universe with a density of matter that does not decrease for large distances)
Galilean space-time	Schrodinger equation for a system of particles	Classical mechanics; usual expression of Newton's law of gravitation (not requiring the equivalence principle but requiring vanishing of density at large distances); electricity (dynamics of electric charges, neglecting magnetic induction); magnets and electricity with magnetic induction (neglecting capacitors)
Aristotelian space-time	Chemistry	Mechanics of matter, acoustics, electromagnetism in matter (that may be well explained in that article, though I did not read it in details)
Euclidean space		Equilibrium (stable or unstable cases - the role of action is played by potential energy) : Electrostatics, magnetostatics, geometric optics.

The different possible ways by which the known laws may not suffice to understand or predict effects:

The real (fundamental) unpredictability (randomness): the quantum randomness, the butterfly effect, or both (as the latter increases the effects of the former to the macroscopic level)
The extreme complexity of calculations that would be necessary to effectively derive predictions from the theory (may be resolved by new mathematical methods of approximations and tricks, and/or by the use of supercomputers)
The lack of knowledge of the initial conditions of the given systems

The unification problem

Thanks to the hard work accomplished by physicists, we have now enough theories to form a clear pack of complementary description and prediction tools addressing (well predicting) seemingly all accessible physical processes without conflict (not contradicting each other nor disturbing each other in non-understood ways in any practically accessible field of observation). Namely, almost every specific accessible physical phenomenon can be either properly described by some physical theory (i.e. is in the range of its good approximate validity, without visible margin of errors), or split into several phases of process that can each be described by some theory, so that a succession or combination of computations for each phase of process from its relevant theory, can produce good effective predictions for the global phenomenon.

But despite this success, we might still feel not fully satisfied as we have not one theory but different theories for different ranges of observable phenomena (or phases of computations of phenomena), and we do not currently know how to unify them (or rather, the most fundamental among known ones, from which others come as approximations) into a single fully coherent theory, that would make exactly well-defined predictions (thus, predictions on any observation "possible in principle"), and thus would more deeply explain everything as deduced from a clear common foundation.

The connections between quantum field theory and gravity by other theories (namely, relativistic mechanics and the Least Action Principle), provide hints in the search for possible theories unifying them (while the issue of quantum measurement and thermodynamics is usually ignored by necessity, by lack of reasonable possibilities to dig into it), but anyway this search is extremely hard, involving very high mathematical works where it is far from clear on what conceptual basis might things be coherently defined (anyway, even if found, a unification theory will probably remain very hard to understand, quite harder than current theories).

In fact this problem of currently having a mere "pack of prediction tools" with a limited but satisfying accuracy (enough well defined for what our limited tools of observation could check in practice) rather than a mathematically well-defined and coherent theory, is not specific to the problem of uniting several existing theories, but is already an intrinsic defect of one of these known fundamental "theories", namely the Standard Model. Indeed, this "theory" is full of hard mathematical concepts but only forming a sort of approximate expression of a theory, not a fully well-defined mathematical theory, despite the huge play of internal reformulations that were applied. Some extreme physical phenomena (very hard to detect: first fractions of second of the big bang, high-energy collisions, details of dark matter...), still escape predictability from the Standard model, and would require to find either a more coherent expression of it, or some more fundamental theory (may it be or not the ultimate one).
But these "extreme phenomena" still do not explicitly touch the problem of quantum gravity. If considered just for itself, the problem of finding a "ultimate theory" unifying gravity with quantum theory (and more precisely with the Standard Model), would be practically pointless (not effectively qualifiable as a "scientific question"), as it would only concern much too "extreme phenomena" (too far from any reasonable hope of ever touching mankind's field of possible observations, even after millenia).

Pedagogical issues

About intuitive understanding of theories, and the risk of wrong intuitions

A usual mistake of many people (especially beginners) about physics, is to fail making the full proper distinction between these 3 things:

The way things feel to our senses in our daily experience
The most efficient ways to use our imagination to express and understand some theories (mathematical structures) or aspects of fundamental physics.
Any idea of "what is physical", any ontology ("deep nature") of things.

To most efficiently learn theoretical physics, we need to study it in the form of mathematical theories. While our available understanding abilities (structures of imagination) are the way they are coming from our human nature, the optimal ways to use them to understand the known concepts of theoretical physics (structures of the world), are a matter of being convenient (optimal) to the clear expression of the mathematical theories, which may require to break the specific connections (dependence) of our imagination with the world, usually given by our daily direct perceptions (at least for things we happen to perceive at all), or that may come from any ontological ideas we may have. Such mathematically optimal ways to imagine things (the practical level of knowledge which suffices in most cases), while in principle closer to these things, may still remain as empty of significance to any possible "true nature" (ontology) of these things, as any other discussion. Example : discussions about time in relativity theory.

More about the ontological implications I see from theoretical physics

The pedagogical order

It is possible to tell a lot of things about fundamental physics with very little mathematical background, namely with the mere dimensional analysis - even if this is just a sort of popularization without genuine understanding of the theories.

More fundamental physics, especially special relativity and quantum physics, can be done just based on the understanding of affine geometry and vector spaces.

The mathematical formalism of tensors is necessary for a clean general expression of most theories of fundamental physics, including classical mechanics.
It is reputed "difficult", but in fact not only because it is really difficult (somehow it is but not necessarily so much), but also because the common way of introducing this formalism is not as clear as it could and would deserve to be.

Thus ideally, a scientific curriculum that aims to teach physics up to some good level, should give some priority to the development of the algebraic concepts needed for the clean introduction of tensors. It would not be quite hard for students if it was well done (as compared to the current first year mathematics curriculum); it just requires some changes, some new concepts and ways to define things.
In parallel and before the achievement of that goal, some theoretical physics can already be introduced. But for the general optimization of the curriculum, it would be better to focus this teaching specifically on those concepts that really don't need tensors - so as to not pitifully waste efforts making up odd, obscure mathematical tools just to express without any explicit use of tensors, some concepts that would in fact need them. Already the following concepts are example of such things made made odd (obscure) by the try to express them without their natural framework of tensors:

Maxwell's equations of electromagnetism (that simplify into 2 equations in 4-dimensional tensorial expression)
The full expression of conservations laws in classical or relativistic mechanics (screw theory), somehow already starting with the expression of angular momenta in 3 dimensions

Also, quantum theory may be first introduced without tensors in the simplest cases (as done in the pages linked above), but require tensors as soon as we want to consider more complex cases.
It is well-known that general relativity is normally expressed with tensors, but there is still some way to simply express it without tensors (but only in principle, in a way that does not appear like "a formula" but as concepts to be carefully applied, and only usable in practice for the simplest, most symmetric types of applications such as cosmology and the Schwarzchild black hole)

Now, what are the theories and other useful mathematical concepts for physics, that can be cleanly introduced before tensors, and in which order ?
Here are they, and a possible order in which to put them.

Euclidean geometry
Articulations between different geometric theories (that can use the concept of Galois connection, relating transformations with invariant structures): vector spaces and duality. Affine and projective geometries
Classification of quadratic forms; particular case of the Minkowski space-time
Concepts of fields, conservation of quantities; case of the conservation of electric charges and current;
Least action principle and some of the resulting conservation laws: energy and momentum (in introductory ways, not up to its full expression that requires tensors). In two dimensions only : angular momentum
Newton's law of gravitation
Electrostatic potentials and forces.
Classical thermodynamics (introduced at any time after the concept of conservation laws, to express that entropy may be conserved of created but not reduced).
Equations of gases; acoustics, wave propagation
Introduction to quantum physics (as linked above)

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