Constructor Theory
I believe things cannot make themselves impossible - Stephen Hawking

27 June 2015

Reformulate science in terms of possible and impossible tasks.

In past few weeks, I continued my research on Quantum Computing and the role of information in our Universe. I came across a series of papers by David Deuth and Chiara Marletto, in which they present a new theory called Construction Theory. It may be classified among the so-called Theories of Everything. I must say that it is a rather revolutionary approach to explain the physical reality. Everything is very different from the traditional view that describes the transformations in the Universe starting from initial states and the laws of motion. Constructor Theory, indeed, aims to explain what happen in Nature in terms of transformations which are possible and impossible, and why.

This, as we shall see, provides extra-power in dealing with notoriously difficult problems as self-reproduction and self-organization, for which has not yet come to a complete characterization using the Laws of Physics. The authors, in particular, propose a new Theory of Computation, showing how it is possible to relate the concepts of classical and quantum information, and what are the characteristics that need to exist in Nature so the information can be stored. The last aspect that struck me reading the articles, is that the authors repropose an old question about what is the ultimate goal of a scientific theory: describe what really happens in the physical reality even if this is against our intuition (ie. Many-Worlds interpretation, String Theory, Computational Universe or even provide predictions.

###Reformulate science is not an easy job Constructor Theory, from now simply CT, aims to express all fundamentals scientific theories in terms of the dichotomy between possible and impossible physical transformations, i.e. among those that can happen because they are allowed in Nature, and those which are not. This point of view is rather far from the traditional view of physics, where the initial states and laws of motion are fundamental tools to predict changes in the world.

CT is built on the concepts of constructor and task:

  1. a constructor task, or shortly task, is a set of pairs that specifies a legitimate state for input and a legitimate state for output

  2. a constructor is an object that can perform a task. It must be capable of triggering a physical transformation in a system without losing its ability to do it again. A transformation performed by a constructor is called construction.

A constructor is capable of performing a task A if, whenever he is presented with a legitimate input of A, it transform the input to one of the outputs of A associated with the input. A task is said to be possible if the laws of nature do not impose any limitation on how accurately A can be effected.

Examples of constructor are catalysts in chemical reactions. However, constructors often do not appear at all in the laws of physics. In fact, there is no role for them in the prevailing convention of fundamental physics, which speaks roughly like this: any physical element is composed of elementary particles such atoms and molecules, and interact with the other objects into space-time field. There is an initial state for these objects, and the laws of motion determine how the state will evolve over time.

Conversely, a construction is characterized only by its input and its output, and describes the world in terms of transformations involving two types of systems, which play different roles:

  1. a constructor: the object which triggers a transformation, and the characteristics of which remain unchanged after the transformation has taken place, ie retains its ability to genereare again the same transformation.

  2. a substrate, ie, the system that is going to be transformed, which can be constituted by one or more subsystems. A substrate is composed of attributes, which are seen as system properties that can be changed by a physical process.

The proposed theory, however, is not a theory of constructors, but a theory of transformations that may be possible or not, and why.

This is a switch to a new formulation of science in terms of tasks performed by constructors. The possible tasks are those for which the laws of physics allow the existence of a constructor, and this explains why constructors are part of this design.

The laws of Construction Theory are all principles

The specification of a task includes all the necessary inputs and the inevitable output, and any additional things needed (ie sources of energy, waste products). Furthermore, the set of the manufacturer and of its substrate must be a closed system. It is worth emphasizing that by definition, a given constructor C for a task A implies that after that A is performed, it must still be possible reuse C for the same purpose.

The world is described in terms of changes in two basic objects: the transformer and the transformed. The requirement to know both the initial conditions and the laws of motion to explain what happens in Nature, here, disappears. But a new question arises: is possible to reformulate Physics in this way?

Is worth to underline that some of the deepest laws of physics are actually meta-laws; they contain other laws rather than a direct description of behavior of physical objects. The Law of Conservation of Energy does not make any explicit reference to the type of energy, even less the kind of energy. In fact, for any closed system S, it defines a property of S. The laws of CT are, in effect, all principles. The authors conjecture that they are respected by all physical laws, which are called subsidiaries theories. Principles are meta-laws, because they don’t make any direct statements on the outcome of an experiment. However, they are experimentally verifiable (ie a principle P is rejected if any law that violates P survives experiments while all other laws conform to P are reject).

The basic principle of CT sounds like this: all the other laws of physics are completely expressible in terms of predicates about such physical changes are possible and which are not, and why.

The Theory of General Relativity (GR) is a theory of the space-time arena in which all physical processes taking place. Since its explanatory structure, it follows that it is a basis of all other scientific theories known and unknown, as it requires them to be expressible in terms of tensors in spacetime. This means that any new theory that postulates the existence of a particle that is not affected by gravity (ie the space-time curvature), would be contrary to the GR.

Another theory which claims to underline all other theories is Quantum Mechanics (QM). It requires that all observable quantities must be expressed in terms of quantum mechanical operators. It follows that no new theory can claim to be able to observe simultaneously a physical variable and its derivatives over time with infinite precision. A theory like this, in fact, can never be in agreement with QM.

CT aims to underline of GR and QM. It puts you at a deeper level of physics and the laws of physics, and the prevailing view of the initial conditions and laws of motion.

Note: what is the true initial state? At the moment there is not a proved therory about which was the initial state. Thermodynamics suggests that it was a state with zero entropy, while cosmologists suggest it was a state isotropic and homogeneous, Anyway, if galaxies are evolved from quantum fluctuations, this is still a matter of debate.

there is a set of scientific questions that can not be answered with predictions: self-reproduction, information in nature, the meaning of the concept of probability in physics

In CT, the important thing is that known the initial state is not essential. Sometimes, the idea of ​​an initial state corresponds essentially to an old idea of ​​divine creation origin of time.

The fundamental distinction in CT between impossible and possible task, indicates the difference between tasks that are allowed by the laws of nature and those that are not valid, even in theory. CT is therefore incompatible with the ​​long-standing idea that the laws of physics are nothing but a mere summary of what happens in nature. According to the authors (and my humble opinion too), scientific theories are not pure predictions. They are explanations of what really happen in the physical world and how our Universe behaves.

###Information is qualitatively different CT has the effect of replacing a narrow view of Physics, where a theory is valid only if it makes predictions. From this point of view, both QM and Darwin’s Evolution Theory are still under debate. For many scientists it is not obvious to confirm that both are scientific theories. Here, the key point is that there is a set of scientific questions that can not be answered with predictions: self-reproduction, information in nature, the meaning of the concept of probability in physics.

These problems are very interesting because they deal with the features of living beings (ie self-reproduction), and have not yet found a clear and definite description in the current laws of physics. For example, consider the information. It pervades us. But this implies an underlying idea which is often implicitly assumed: information is physical, ie. is reproducible, copyable, reconstructible. But what we do not yet know, it is what are the regularities in Nature that enable the creation of information. We are not capable of expressing precisely if a physical object contains information. One of the most interesting things explained in the papers, is how the authors have applied the CT to address problems that are on the border between biology and physics: a fundamental theory of information and a fundamental theory of life.

what we do not yet know, it is what are the regularities in Nature that enable the creation of information

As human beings, we physically react to the information. The question that physicists arise is: the information is physical or exists only in the observer’s mind? The trend that complex systems have to produce patterns of organized matter that are physically copied and passed on to other physical entities and as a last bodies and a fairly clear evidence that natural systems produce and process information all the time.

The physical information is also central to the life of the universe, and this is one example of how CT can solve certain problems that are so-called resilient for a long time. When you consider the simplest example of life, a bacterium, it shows two impressive properties:

  1. the ability to perform tasks with a high degree of accuracy while maintaining the property of being able to redo it
  2. build a new instance of itself, a property that has a lot to do with life.

It is questionable whether these fundamental biological elements are compatible with the laws of physics as we actually know them or if they require something more. The most famous and fundamental theories, the Theory of General Relativity (GR) and Quantum Mechanics (QM), the former deals with enormous masses as stars and galaxies, the latter refers to elementary sub-particles such as electrons and atoms, but do not deal with self-reproduction or self-organization.

In some respects, the information is an entity qualitatively different from any others in terms of which science describes the world. It is not a tensor in spacetime (like the GR requires to be for all physical quantities), nor will an observable quantum-mechanical state. But in other ways, information is similar to many other entities that appear in the laws of physics: the Theory of Computation and Statistical Mechanics, seem to refer to it directly without considering the specific physical medium in which it is instantiated.

Information is independent from the substrate, and it is interoperable, as it can be transferred from one medium to another. If information is physical, that there should be physical laws to govern it. But it is well known that one can not say that an object in a particular state physical carries information unless it can not be in a different physical state.

The way a bacterium reproduces itself (actually laws of physics do not include the concept of self-reproduction), is similar to a car factory. In both cases there is a recipe, a bit of information that has the ability to trigger and steer a process of construction. In case of bacteria, we’re talking about DNA. In CT, this information works as a constructor because it has the ability to perform a task and maintains the capacity to do so still. These elements, knowledge and information, have not a direct expression in laws of physics but instead found clear expression in CT.

If information is physical, that there should be physical laws to govern it

Computation Theory, as well as formulated by Alan Turing and so how it is used and interpreted by mathematicians and computer scientists, consider information as an abstract thing. What seems difficult to accept is the fact that we have more evidences that information is physical. There is not an abstract computer. Only a physical object can compute. Although physicists have long accepted the idea that information is physical and is independent of the physical objects in which it resides. Information is indipendent by physical means, ie the substrate, is more fundamental then laws of motion.

Note: Physics and its fundamental theories often overlaps with Philosophy. Rolf Laundeuer was a lone voice in the ‘60 said that the information is physical. He realized that the concept of a computer purely abstract did not make sense, and the theory of computation had to have a theory of what physical objects can do with the information.

Computation Theory was originally intended only as a mathematical theory for proofing theorems and truths (in logical sense), not as a branch of physics (indeed Turing’s theory not match with physical reality).

The theory makes a qualitative distinction between computable and non-computable, but has an additional branch called Complexity Theory, which is related to the amount of resources needed to perform computations. Its usefulness is limited by the fact that it cannot treat physical resources (such as mass and time), but only delegates (memory and numbers of computational steps), the size of the input is considered asymptotically and only up to polynomial functions. It is curious to note that the theory of quantum information, in spite of its name does not specify what is the quantum information nor do the relations with the classical information. It is not in fact a new theory, but only a collection of quantum phenomena that violate the laws classical information.

Some believe that Quantum Computing is equivalent to the entire Physics. Curiously, the CT is born from Quantum Theory of Computation and, in particular, by an attempt to associate a quantum program for an universal quantum computer to physical reality. The new fact of CT is that its laws do not affect initial states and laws of motion, but just says what transformations are possible and what impossible, and why. In analogy to the Theory of Computation, CT does not say how things can do something, but instead says what things can do. This is a pretty strong analogy with the Theory of Computation, that does not deal with transistor or CPU, but explains only what are the possible information transformations and what are not. And every possible information transofrmation corresponds to a program for the universal computer. In analogy with Computation Theory, authors’ research is oriented in defining a Universal Constructor.

A well known concept in the classical physical universe but impossible in quantum systems: the ability to make a copy

As mentioned in the introduction, Deutsh and Marletto have succeeded in the remarkable goal of unify classical and quantum information through a system of meta-laws that regulate the world. Starting from the idea that information is not an abstract concept but, on the contrary, is an expression of the presence of certain regularities in the laws that govern our universe, Deutsch and Marletto have established constraints that a given theory must satisfy to allow the existence of information in physical systems. In particular, introducing a well known concept in the classical physical universe but impossible in quantum systems: the ability to make a copy. In the subatomic world, it is not possible to make an identical copy of a quantum state, because it is undefined. According to the authors, thia is the limit to overcome to reach a unification of the classical world and the quantum one. This new theory of computation, provides the ability to play all of the data, in turn governed by a kind of “superinformation” that establishes, as it were, the rules of the game. Including the one for which the quantum world copy of a state is an impossible task because not permitted by the laws of nature: it will thus regained the deal with what is happening in reality.

###Conclusions CT was initially developed as a generalization of the Theory of Quantum Computation, but has been soon extended to cover not only computing but all Laws of Physics. We have seen that at the heart of the CT there is a different vision of Nature. In the predominant conception, the fundamentals objects are the initial conditions of the Universe and the laws of motion. In CT, on the other hand, fundamentals objects are just the transformations that are possible and impossible, and why they can be or not. It follows that from the point of view of CT, mankind, as constructors of knowledge and information, play a key role. The CT is a theory of principles, it is much more powerful fundamental dela GR and QM; is not a scientific theory in the classical sense, that is in charge of providing predictions. The way it is possible to test this theory is the same one that will test principles. One of the most remarkable result that came out is a reformulation of the *Computation Theory, a framework within which the concept of information encompasses both the classical concept of information that quantum.

###Further Information

The Philosophy of Constructor Theory, by David Deutsch, Springer Netherlands

The Constructor Theory of Information by David Deutsch, Chiara Marletto

The Constructor Theory of Life, by Chiara Marletto, Royal Society Interface, Volume: 12, Issue: 104, March 2015

Scientific America A Meta-Law to Rule Them All: Physicists Devise a “Theory of Everything”, By Zeeya Merali

Formulating Science in Terms of Possible and Impossible Tasks, by Chiara Marletto,, by David Deutsch

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