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Constructor theory is a proposal for a new mode of explanation in fundamental
physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
in the language of
ergodic theory Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behav ...
, developed by physicists
David Deutsch David Elieser Deutsch ( ; ; born 18 May 1953) is a British physicist at the University of Oxford, often described as the "father of quantum computing". He is a visiting professor in the Department of Atomic and Laser Physics at the Centre for ...
and Chiara Marletto, at the
University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...
, since 2012. Constructor theory expresses physical laws exclusively in terms of which physical transformations, or ''tasks'', are possible versus which are impossible, and why. By allowing such counterfactual statements into fundamental physics, it allows new physical laws to be expressed, such as the constructor theory of information.


Overview

The fundamental elements of the theory are tasks: the abstract specifications of transformations as input–output pairs of attributes. A task is ''impossible'' if there is a law of physics that forbids its being performed with arbitrarily high accuracy, and ''possible'' otherwise. When it is possible, a ''constructor'' for it can be built, again with arbitrary accuracy and reliability. A constructor is an entity that can cause the task to occur while retaining the ability to cause it again. Examples of constructors include a
heat engine A heat engine is a system that transfers thermal energy to do mechanical or electrical work. While originally conceived in the context of mechanical energy, the concept of the heat engine has been applied to various other kinds of energy, pa ...
(a thermodynamic constructor), a
catalyst Catalysis () is the increase in rate of a chemical reaction due to an added substance known as a catalyst (). Catalysts are not consumed by the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycles quick ...
(a chemical constructor) or a
computer program A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. It is one component of software, which also includes software documentation, documentation and other intangibl ...
controlling an automated factory (an example of a programmable constructor). The theory was developed by physicists
David Deutsch David Elieser Deutsch ( ; ; born 18 May 1953) is a British physicist at the University of Oxford, often described as the "father of quantum computing". He is a visiting professor in the Department of Atomic and Laser Physics at the Centre for ...
and Chiara Marletto. It draws together ideas from diverse areas, including
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
,
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
,
information theory Information theory is the mathematical study of the quantification (science), quantification, Data storage, storage, and telecommunications, communication of information. The field was established and formalized by Claude Shannon in the 1940s, ...
, and
quantum computation A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. C ...
. Quantum mechanics and all other physical theories are claimed to be ''subsidiary'' theories, and quantum information becomes a special case of superinformation. Chiara Marletto's ''constructor theory of life'' builds on constructor theory.


Motivations

According to Deutsch, current theories of physics, based on
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
, do not adequately explain why some transformations between states of being are possible and some are not. For example, a drop of dye can dissolve in water, but
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
shows that the reverse transformation, of the dye clumping back together, is effectively impossible. We do not know at a quantum level why this should be so. Constructor theory provides an explanatory framework built on the transformations themselves, rather than the components. Information has the property that a given statement might have said something else, and one of these alternatives would not be true. The untrue alternative is said to be " counterfactual". Conventional physical theories do not model such counterfactuals. However, the link between information and such physical ideas as the
entropy Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...
in a
thermodynamic system A thermodynamic system is a body of matter and/or radiation separate from its surroundings that can be studied using the laws of thermodynamics. Thermodynamic systems can be passive and active according to internal processes. According to inter ...
is so strong that they are sometimes identified. For example, the area of a
black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
's
event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an outside observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive c ...
is a measure both of the hole's entropy and of the information that it contains, as per the Bekenstein bound. Constructor theory is an attempt to bridge this gap, providing a physical model that can express counterfactuals, thus allowing the laws of information and computation to be viewed as laws of physics.


Outline

In constructor theory, a transformation or change is described as a ''task''. A ''constructor'' is a physical entity that is able to carry out a given task repeatedly. A task is only possible if a constructor capable of carrying it out exists, otherwise it is impossible. To work with constructor theory, everything is expressed in terms of tasks. The properties of information are then expressed as relationships between possible and impossible tasks. Counterfactuals are thus fundamental statements, and the properties of information may be described by physical laws. If a system has a set of attributes, then the set of permutations of these attributes is seen as a set of tasks. A ''computation medium'' is a system whose attributes permute to always produce a possible task. The set of permutations, and hence of tasks, is a ''computation set''. If it is possible to copy the attributes in the computation set, the computation medium is also an ''information medium''. Information, or a given task, does not rely on a specific constructor. Any suitable constructor will serve. This ability of information to be carried on different physical systems or media is described as ''interoperability'' and arises as the principle that the combination of two information media is also an information medium. Media capable of carrying out quantum computations are called ''superinformation media'' and are characterised by specific properties. Broadly, certain copying tasks on their states are impossible tasks. This is claimed to give rise to all the known differences between quantum and classical information.


See also

* '' Calculating Space'' *
Computability theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since ex ...
*
Undecidable problem In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an ...
*
Quantum circuit In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly o ...
* Generalized probabilistic theory


References


Bibliography

* * Marletto, Chiara (2021). The Science of Can and Can't. Penguin. ISBN 9780525521921.


External links

* *
Deeper Than Quantum Mechanics—David Deutsch’s New Theory of Reality
Mediums.com'
''The Physics arXiv Blog''
28 May 2014. * Kehoe, J.;
To What Extent Do We See with Mathematics?
. ''Scientific American'' Guest blog. 2013. *
Formulating Science in Terms of Possible and Impossible Tasks
. ''edge.org''. 12 June 2014. * {{Cite news , date=21 May 2014 , title=Reconstructing physics: The universe is information , work=NewScientist.com , type=Two leading quantum physicists say information is key to understanding the universe. Their constructor theory puts it centre stage , url=https://www.newscientist.com//article/mg22229700.200-reconstructing-physics-the-universe-is-information Fringe physics