Constructor Theory

Published on Apr 4, 2015

An introduction to Constructor Theory presented by David Deutsch and Chiara Marletto, introduced by Simon Benjamin.

Constructor Theory is a new approach to formulating fundamental laws in physics. Instead of describing the world in terms of trajectories, initial conditions and dynamical laws, in constructor theory laws are about which physical transformations are possible and which are impossible, and why. This powerful switch has the potential to bring all sorts of interesting fields, currently regarded as inherently approximative, into fundamental physics. These include the theories of information, knowledge, thermodynamics, and life.

With support from the Templeton World Charity Foundation, Oxford University is conducting research into constructor theory and its implications in a project involving David Deutsch, Chiara Marletto, and Simon Benjamin.

Table of Contents

The Philosophy of Constructor Theory

Authors: David Deutsch

Journal: Synthese, Volume 190, Issue 18

Date: 11 April 2013


Affiliations: Centre for Quantum Computation, University of Oxford



Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations–those that can be caused to happen and those that cannot. This is a departure from the prevailing conception of fundamental physics which is to predict what will happen from initial conditions and laws of motion. Several converging motivations for expecting constructor theory to be a fundamental branch of physics are discussed. Some principles of the theory are suggested and its potential for solving various problems and achieving various unifications is explored. These include providing a theory of information underlying classical and quantum information; generalising the theory of computation to include all physical transformations; unifying formal statements of conservation laws with the stronger operational ones (such as the ruling-out of perpetual motion machines); expressing the principles of testability and of the computability of nature (currently deemed methodological and metaphysical respectively) as laws of physics; allowing exact statements of emergent laws (such as the second law of thermodynamics); and expressing certain apparently anthropocentric attributes such as knowledge in physical terms.

The Constructor Theory of Information

Authors: David Deutsch, Chiara Marletto

Journal: Proceedings of the Royal Society A, Volume 471, Issue 2174

Date: 17 December 2014


Affiliations: Centre for Quantum Computation, University of Oxford (Deutsch) // Materials Department, University of Oxford (Marletto)



We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible – i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are directly about information, independently of the details of particular physical instantiations, it does not regard information as an a priori mathematical or logical concept, but as something whose nature and properties are determined by the laws of physics alone. It does not suffer from the circularity at the foundations of existing information theory (namely that information and distinguishability are each defined in terms of the other). It explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and entanglement (locally inaccessible information).

Published on Oct 13, 2014

Work jointly performed with David Deutsch. From the workshop “Information and Interaction: Eddington, Wheeler, and the Limits of Knowledge,” held 20-23 March 2014, Trinity College, Cambridge.

The Constructor Theory of Life

Authors: Chiara Marletto

Journal: Journal of the Royal Society Interface, Volume 12, Issue 104

Date: 14 January 2015


Affiliations: Department of Materials, University of Oxford



Neo-Darwinian evolutionary theory explains how the appearance of purposive design in the sophisticated adaptations of living organisms can have come about without their intentionally being designed. The explanation relies crucially on the possibility of certain physical processes: mainly, gene replication and natural selection. In this paper I show that for those processes to be possible without the design of biological adaptations being encoded in the laws of physics, those laws must have certain other properties. The theory of what these properties are is not part of evolution theory proper, and has not been developed, yet without it the neo-Darwinian theory does not fully achieve its purpose of explaining the appearance of design. To this end I apply Constructor Theory’s new mode of explanation to provide an exact formulation of the appearance of design, of no-design laws, and of the logic of self-reproduction and natural selection, within fundamental physics. I conclude that self-reproduction, replication and natural selection are possible under no-design laws, the only non-trivial condition being that they allow digital information to be physically instantiated. This has an exact characterisation in the constructor theory of information. I also show that under no-design laws an accurate replicator requires the existence of a “vehicle” constituting, together with the replicator, a self-reproducer.

The Constructor Theory of Probability

Authors: Chiara Marletto

Journal: Proceedings of the Royal Society A, Volume 472, issue 2192

Date: 17 August 2016


Affiliations: Oxford



Unitary quantum theory, having no Born Rule, is non-probabilistic – hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. By generalising and improving upon the so-called ‘decision-theoretic approach’ (Deutsch, 1999; Wallace, 2003, 2007, 2012), I shall recast that problem in the recently proposed constructor theory of information – where quantum theory is represented as one of a class of ‘superinformation theories’, which are non-probabilistic theories conforming to certain constructor-theoretic conditions. I characterise the unpredictability of measurement outcomes exactly in constructor theory, showing that it necessarily arises in superinformation theories because of the impossibility of cloning certain sets of states. Then I explain how the appearance of stochasticity in (finitely many) repeated measurements arises under superinformation theories. Specifically, I establish sufficient conditions for a superinformation theory to inform decisions (made under it) as if it were probabilistic, via a Deutsch-Wallace-type argument. In my version, some of that argument’s assumptions, previously construed as merely decision-theoretic, follow from physical properties expressed by constructor-theoretic principles.

Published on Jun 3, 2015

Audio and static slides from a talk by David Deutsch 1st June 2015.

The Constructor Theory of Thermodynamics

Authors: Chiara Marletto

Journal: Forthcoming

Date: 26 July 2016

DOI: forthcoming

Affiliations: Materials Department, University of Oxford



The laws of thermodynamics, powerful for countless purposes, are not exact: both their phenomenological and their statistical-mechanical versions are valid only at ‘macroscopic scales’, which are never defined. Here I propose a new, exact and scale-independent formulation of the first and second laws of thermodynamics, using the principles and tools of the recently proposed constructor theory. Specifically, I improve upon the axiomatic formulations of thermodynamics (Carathéodory, 1909; Lieb & Yngvason, 1999) by proposing an exact and more general formulation of ‘adiabatic accessibility’. This work provides an exact distinction between work and heat; it reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second); it resolves the clash between the irreversibility of the ‘cycle’-based second law and time-reversal symmetric dynamical laws. It also achieves the long-sought unification of the axiomatic version of the second law with Kelvin’s.



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