Research programm of the laboratory-chair
The aim of this study is to construct the particles as emergent structures.
Spacetime continuum is a description of the properties of the macroscopic devices. This model is not valid on the microscopic scale. Quantum theory is not an adequate description of quantum objects. This is a description of measurements of quantum objects by classical devices. A self-consistent description of quantum objects cannot use spacetime continuum.
The first hypothesis of this study is that causality take place on the microscopic scale. In relativity theory the causal structure of the world is described by a partial order of events. In the instant of time there is a hypersurface of disconnected events. These events are connected only by intersections of the past light cones. Thus the structures of the physical world are not physical objects but physical processes.
The second hypothesis is a finite divisibility of any structures. Consequently, the central hypothesis of this study is that a physical process is a finite network of finite elementary processes. A stable object is a stable process. This means a cyclic process. A scale hierarchy of the matter is a hierarchy of embedded cyclic processes.
The primitive entities of the physical world have not an internal structure. This is primordial indivisible objects. Consequently, they itself have not any internal properties except one. They exist. The property “existence” can adopt two values: “the primitive entity exists”, and “the primitive entity does not exist”. The primitive entity is called a material point. The primitive process can be thought of as act of creation. The value of the property “existence” of the material point varies from “the material point does not exist” to “the material point exists” by this process. Its dual represents the act of destruction. Every physical process is a finite combination of finite elementary processes, monads. An ordered pair of creation and annihilation is the propagation of a primitive entity, or a chronon.
Suppose a self-action is impossible. The material point can be destroyed only by interaction with another material point. The interaction of this second material point means the change of its state. Only one kind of change is possible. This is the annihilation of the second material point. Suppose the number of the material points does not change. This is a fundamental conservation law. There is one kind of interactions: two material points are destroyed and two material points are created. This process is called an x-structure. Any process consists of x-structures.
In the considered model any process can be described as some graph. But such description is not useful. By definition, a graph is a set of vertexes and a binary relation (edges) over this set. We cannot describe external lines as in Feynman diagrams. For example, an x-structure is not a graph. We can define a set of edges, and vertexes as a relation over this set. But in this case, if we divide a structure into substructures we must duplicate the edges which connect these substructures. This is not useful either. It is convenient to break the edge into two halves, monads, of which the edge is regarded as composed. Let call this structure a dynamical graph or a d-graph.
Consider the following concept of a d-graph dynamics. The past and the future exist, are determined, and are changeless. This concept is opposite to the concept of an emergent future. It is possible, we can interpret the considered dynamics in the concept of emergent future but we do not discuss this problem. In the discrete mechanics this means that the d-graph of the universe exists. It is meaningless to talk about the exact structure of the d-graph if we cannot determine its structure. The structure of the d-graph of the universe implies the infinite amount of information. But we can only actually know a finite number of facts. Therefore any observer can consider only finite fragments and take into account the rest of the d-graph of the universe in an approximate way.
Suppose we have the information about the structure of some d-graph. This is the description of some part of some physical process. The task is to predict the future stages of this process or to reconstruct the past stages. This mean to determine the structure of the d-subgraph that is connected with the given d-graph. In general case, we cannot determine this structure unambiguously. We can only calculate probabilities of different variants. We can reconstruct the structure of the d-graph step by step. This procedure is called the sequential growth dynamics. The growth of the connected d-graph is a sequence of some elementary processes. We sequentially add new parts to the d-graph. The minimal part is an x-structure. The growth is the addition of new x-structures one after another. The addition of one x-structure is called an elementary extension. This is not an appearance of new parts of the d-graph of the universe. This is an appearance of new information about the existing d-graph of the universe. A set of results of sequential measurements is a classical stochastic sequence. Thus the sequence of the elementary extensions is a classical stochastic sequence.
If we can calculate the probabilities of all elementary extensions of any d-graph, we can calculate the probabilities of all new parts of any d-graph as the probabilities of random sequences of elementary extensions. Now the general dynamics and several examples are given. A simple dynamics generates a hierarchy of cyclic processes. An algebraic representation of this dynamics is given.