Constructor theory expresses physical laws in terms of the physical transformations or changes which the laws make possible. By allowing the existence of counterfactuals, statements about transformations which may prove false, it is also able to describe information in terms of known physical laws.
The foundational element in the theory is the constructor, an entity which can cause some change while retaining the ability to cause it again. Examples of constructors include a heat engine (a thermodynamic constructor), a catalyst (a chemical constructor) or a computer program controlling an automated factory (an information constructor).
The theory was developed by physicists David Deutsch and Chiara Marletto. It draws together ideas from diverse areas including thermodynamics, statistical mechanics, information theory and quantum computation.
Quantum mechanics and all other physical theories are claimed to be subsidiary theories and quantum information a special case of superinformation.
Chiara Marletto's Constructor theory of life build on constructor theory to "show that self-reproduction [i.e. evolution] is compatible with no-design laws of physics, in particular with quantum theory"
Current theories of physics based on quantum mechanics 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 shows that the reverse transformation, of the dye clumping back together, is not possible. 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. It 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 in a thermodynamic system is so strong that they are sometimes identified. For example the area of a black hole's event horizon is a measure both of the hole's entropy and of the information it contains. Constructor theory is an attempt to bridge this gap, providing a physical model which can express counterfactuals, thus allowing the laws of information and computation to be seen as laws of physics.
In constructor theory, a transformation or change is described as a task. A constructor is a physical entity which 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, 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.
- Deutsch D.; Marletto C. (14 July 2014). "Constructor Theory of Information". arXiv:1405.5563v2.
- "CONSTRUCTOR THEORY: A Conversation with David Deutsch". Edge. 22 October 2012. Retrieved 20 July 2014.
- Marletto C. (1 July 2014). "Constructor Theory of Life". Royal Society Interface 12 (104). arXiv:1407.0681v1. doi:10.1098/rsif.2014.1226.
- Heaven, D. (6 November 2012). "Theory of everything says universe is a transformer". New Scientist. Retrieved 20 July 2014.
- Deutsch, D. "Constructor Theory", revised 17 January 2013, arxiv.org (retrieved 23 May 2014)
- Deutsch, D. and Marletto, C.; "Why we need to reconstruct the universe", New Scientist, 24 May 2014, pages 30-31.
- Constructor theory of information David Deutsch, Chiara Marletto Proc. R. Soc. A:2015471 20140540;DOI: 10.1098/rspa.2014.0540.Published 17 December 2014. (retrieved 12 Jan 2015)
- Videos: Constructor Theory - David Deutsch, Oxford Martin School
- Merali, Z.; A Meta-Law to Rule Them All: Physicists Devise a “Theory of Everything”: “Constructor theory” unites in one framework how information is processed in the classical and quantum realms Scientific American, 26 May 2014
- Deeper Than Quantum Mechanics—David Deutsch’s New Theory of Reality 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