Constructor Theory in Fundamental Physics

• Constructor Theory is a framework that reformulates fundamental physics in terms of possible and impossible tasks executed by physical systems called constructors.
• It unifies diverse fields such as information theory, computation, and thermodynamics under a scale-independent, counterfactual approach to physical laws.
• Practical insights include novel formulations of conservation laws, the emergence of irreversibility, and implications for both classical and quantum phenomena.

Constructor Theory is a unifying framework for fundamental physics in which the central objects of study are possible and impossible physical transformations—termed "tasks"—and the definite physical systems ("constructors") that can cause those tasks to occur repeatedly without degradation. Rather than expressing fundamental laws in terms of dynamical trajectories, differential equations, or probabilities, Constructor Theory reformulates physics in terms of explicit counterfactual claims about what can and cannot be brought about in the physical world. Its scope encompasses information theory, computation, thermodynamics (at all scales), conservation laws, life, and even the emergence of knowledge, offering a scale-independent, substrate-independent foundation for diverse physical phenomena (Deutsch, 2012, Marletto, 2016, Deutsch et al., 2014, Marletto et al., 5 Jun 2026).

1. Core Constructs: Tasks, Constructors, and Principles

Tasks are defined as finite sets of ordered input-output attribute pairs on some substrate system; for example,

$$\mathcal{A} = \{ x_i \rightarrow y_i \mid i = 1, \dotsc, n \}$$

with each $x_i, y_i$ being sets of physical states (attributes) of a substrate $S$ (Deutsch, 2012, Deutsch et al., 2014). The transpose task $\mathcal{A}^\sim$ exchanges inputs and outputs: $\{ y_i \rightarrow x_i \}$.

A constructor $C$ for task $\mathcal{A}$ is a physical system that, when presented with a substrate in any $x_i$, reliably produces $y_i$ and remains able to do so for subsequent instances. A task is possible (written $\mathcal{A}^\checkmark$) if arbitrarily accurate, cyclic constructors exist for it, and impossible ($x_i, y_i$0) if no such constructor can in principle exist (Deutsch, 2012, Marletto et al., 2020).

The core principles of Constructor Theory include:

• Composition: Regular networks (serial, parallel) of possible tasks are themselves possible.
• Locality: Tasks on composite substrates $x_i, y_i$1 act on disjoint state pairs $x_i, y_i$2 and do not cross-influence.
• Interoperability: Information media of equal capacity compose to yield media of their Cartesian product variables; all permutations become possible.
• Testability: Any physical law's falsification is itself a possible task.
• Computability: Universal constructors, programmable to implement any possible task, are themselves possible (Deutsch, 2012, Marletto et al., 5 Jun 2026).

2. Formal Structure: Algebra of Tasks, Universal Constructors

Tasks admit a rich algebra: union, parallel composition $x_i, y_i$3, serial composition $x_i, y_i$4, and transposition. Crucially, the composition principle ensures closure of the set of possible tasks under these operations.

A universal constructor is a programmable device capable (if given an appropriate program and resources) of implementing every task that is not impossible. The existence of such a universal constructor is conjectured to follow from the basic meta-laws of the theory (Deutsch, 2012, Marletto et al., 5 Jun 2026). Determining the scope of the universal constructor's repertoire for a subsidiary physical theory amounts to specifying the physically possible transformations under that theory.

3. Embedding of Information, Computation, and Superinformation

Within Constructor Theory, information media are substrates supporting variables on which all permutations and cloning (copy tasks) are possible. Classical information is characterized by pairwise and collective distinguishability, arbitrary permutations, and cloning (Deutsch et al., 2014).

A superinformation medium possesses at least two information observables whose union is not itself jointly observable or clonable; this captures the non-classical (quantum) features such as no-cloning, measurement disturbance, and entanglement. Quantum theory and, more broadly, any theory with superinformation media (local, non-probabilistic theories with variables obeying these constraints) are naturally encompassed (Deutsch et al., 2014, Marletto, 2015, Franco, 2019). Constructor Theory of Probability formalizes stochasticity as arising from the impossibility of predictors and the structure of superinformation media, not from fundamental probabilistic laws (Marletto, 2015).

4. Thermodynamics and Conservation Laws: Scale-Independent Reformulation

Constructor Theory recasts thermodynamics and conservation laws as statements about the (im)possibility of certain tasks.

• Work media are defined via their counterfactual ability to implement "swap" operations between energy eigenstates, making them effective carriers of mechanical side-effects and information variables.
• Heat media are characterized by the asymmetry of adiabatic accessibility (certain transitions are possible in one direction but impossible in the other) and indistinguishability of thermodynamic attributes.

Adiabatic accessibility ($x_i, y_i$5) is defined without reference to probabilistic ensembles or macroscopic limits: a transition $x_i, y_i$6 on $x_i, y_i$7 is adiabatically possible if it can be performed with a side-effect on a work medium via a parallel task. The division between work and heat emerges naturally from these scale-independent definitions. Conservation laws are formalized as equivalence relations (the "is-like" relation) on tasks, partitioning them by additive quantities such as energy or entropy, and forbidding tasks (and their transposes) that would violate these quantities (Marletto, 2016).

The Second Law becomes the existence of adiabatically one-way tasks in heat media mirroring every adjacent step in work media. Entropy arises as the unique additive label of "adiabatic is-like" equivalence classes. Kelvin's statement that "no perfect conversion of heat to work in a cycle" is possible is derived as a corollary (Marletto, 2016).

Moreover, a deep relation is established between information theory and thermodynamics: any work medium is an information medium, and the universality and interoperability of information media provide the foundation for the First Law (all work transfers of a given energy increment are equivalent) (Deutsch et al., 2014, Marletto, 2016).

5. Dynamics and the Constructor Theory of Time

Laws within Constructor Theory are timeless: they specify what transformations can/cannot be effected, without reference to a time parameter. Time and dynamics emerge by considering joint tasks involving "timers" (null constructors cycling through distinguishable attributes) and substrates. The notion of duration is associated with the equivalence class of timers of a given cycle length, and differential equations of motion (classical or quantum) arise as effective descriptions in the infinitesimal limit of such tasks (e.g., systems synchronized with timers of vanishing duration) (Deutsch et al., 13 May 2025). This approach resolves the "problem of time" in quantum gravity and unifies timeless and relational approaches as special cases.

6. Irreversibility, Quantum Phenomena, and Experiment

Constructor-based irreversibility is encapsulated in the fact that some tasks are possible while their inverses are not, even if microscopic laws (e.g., unitary quantum mechanics) are time-reversal symmetric. A key demonstration involves universal quantum homogenizers: for specific transformations (e.g., pure $x_i, y_i$8 mixed states), arbitrarily accurate cyclic implementation is possible, while the inverse (mixed $x_i, y_i$9 pure) is impossible, a result confirmed both theoretically and experimentally using high-quality single-photon qubits (Marletto et al., 2020).

Such definitions sidestep the reliance on statistical ensembles and trajectory-based reasoning in thermodynamics, embedding macroscopic irreversibility within a general task-theoretic, information-based paradigm (Marletto et al., 5 Jun 2026, Marletto et al., 2020).

7. Broader Implications: Cognition, Life, Knowledge, and Unification

Constructor Theory generalizes computation to arbitrary physical tasks, equates testability with possible transformations, and expresses classical and quantum information as subsidiary theories set within the broader class of superinformation theories (Deutsch et al., 2014, Marletto et al., 5 Jun 2026).

The theory rigorously treats the emergence of life and knowledge. Accurate self-reproduction and evolution via natural selection are possible under "no-design" laws only if digital information media (allowing for replication and programmable vehicles) exist, formalizing the replicator–vehicle logic within fundamental physics (Marletto, 2014). Abstract constructors (knowledge) are patterns of information that, once instantiated, tend to cause their own preservation and propagation.

Cognition processes have also been modeled using constructor-theoretic tools. Violations of classical rationality, such as the conjunction fallacy, empirically show the necessity of modeling human reasoning as operating over superinformation media—suggesting a unified substrate-independent approach to both physical and cognitive phenomena (Franco, 2019).

Constructor Theory's program aspires to unify thermodynamics, information, computation, and even biology within a common meta-theoretic framework governed by counterfactual principles (possible/impossible tasks), potentially guiding the selection and synthesis of future physical theories—such as quantum gravity—by identifying the structural constraints that must hold for any successor to current laws (Deutsch, 2012, Marletto et al., 5 Jun 2026).