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# 3.1.1. Frame

V. I. Melnikov

The concept of “frame” (F) in the narrow sense of its definition is usually applied for considering the mechanical motion. In dynamics the frame concept is referred to inertial frames. On the other hand, in kinematics any system can be taken as a frame, with the apparent condition of a simple and elementary solution to the problem and, accordingly, with elementary notations.

In the most general sense frame is one of the means to describe quantitatively the object of investigation, in particular, its measurements. The results of investigations and the correctness of solutions depend on model accuracy.

It is possible to obtain any desirable results by arbitrary changing (fitting) of F, but in this case, at first face, the sense of measurements as a source of obtaining the objective information vanishes. This arbitrariness is eliminated by inverse counting, while measurements acquire the objective nature which is confirmed experimentally. However, the arbitrariness of F distorts and complicates both the process of solution and the system of quantities and their relations involved to solve the problem.

At present, there is no general criterion of the best frame choice for arbitrary problems. At the same time, there is a set of practically developed frames with the corresponding units of measurements. Their availability and utility are of primary importance, and their accuracy and optimality are of secondary significance.

TCS allows one to schedule the ways for establishing the frame optimal for the solution of any problems. The criteria applied for this purpose are the solution accuracy and simplicity as well as the simplest notation form.

The problem quantities and solutions can be compared in the simplest way in the case of the minimum number of governing factors. So, it is possible to draw the conclusion that the optimal frame choice depends on the solution which is necessary and sufficient. As is shown in Sec. 4.1, this condition is satisfied in the framework of one CS corresponding to the current process of interaction.

The requirement of notation simplicity of representing the laws of nature in inertial systems shows that they should be СS (from the viewpoint of the processes of mechanical motion). In its turn, the condition of notation simplicity is directly connected with the known statement that the mechanical and electromagnetic laws are the same in inertial systems. Hence, all the laws should be of the same notation in these systems. So, it is possible to state that the inertial system is the СS for the processes indicated and that this CS is the optimum frame (see Sec. 3.4).

Essentially new governing factors, i.e. inertial forces appear in noninertial systems. This indicates that the inertial system becomes open, and a new process appears. The TGR takes into account this fact by means of frame changing [19, 113]. Thus, the frame is endowed with active functions unusual to it or, in other words, a СS attains the capability of external action on processes going on in it. This contradicts the СS definition.

Thus, for the description of processes in noninertial systems it is necessary to search for new governing factors. The mechanism of appearance of inertial forces is described in more detail in Sec. 3.3 in the context of the ТСS. The new process which causes the appearance of inertial forces is the unbalanced "mass" interaction, or, in other words, spatially unbalanced interaction of mass with the surrounding physical vacuum.

The frame concept and the criterion of its optimality can be extended apart from mechanical motion to other kinds and forms of changes. Physical processes are described, as is known, with the help of the system of units of physical quantities. As the units of these quantities are assumed to be constant, each of them represents some СS model for its physical process. Accordingly, science and practice have developed other units and frames for other forms and kinds of changes (chemical, biological, financial, medical, etc.).

However, in all the cases the optimum frame is the corresponding CS, as the measurement standard of constancy and independency, and it should satisfy the following conditions:

• F is the tool of comparison of the state parameters of different objects (some kind of "intermediary");
• process of measurement is an information process (it does not produce real changes);
• independence (and invariance) of F from measured quantities and the processes going on between them;
• CCS is the optimum F, АCS is the absolute F;
• availability and convenience of application.

Contemporary frames and measurement systems are not linked to specific individual CSs for the purpose of simplicity and convenience. They are classified into large groups of one-type processes: mechanical, electric, optical, etc. The concepts of energy and time as well as the units of their measurements refer to all physical processes and to many other forms of changes, including chemical, biological, geologic, climatic, and other ones. In this case, however, energy parameters are less significant than other parameters peculiar to the given kind of change. The optimum frame changes as well. Organism, medium, and population are basic structural concepts for biological systems; matter, molecules, ions, and valence for chemical systems; money, production rate, credit, currency rates, and stock for finances; bits, bytes, etc. for information science. Each of these groups is characterized by its own frame corresponding to characteristic CS, e.g. the "organism – medium" system, financial balance, chemical equation, etc.

Thus, the most general form of F (which is mandatory for any kind of measurements with accuracy criterion) is a CCS, and the unified and general frame for all kinds of changes is an ACS.

There is no such a unified optimum solution which can satisfy the complex criterion of accuracy, objectivity, and the reasonability of practical use. For example, this criterion suggests that for the person–medium system the temperature of a healthy man should be taken as the zero temperature. Deviation in any side is an indication of the system disequilibrium, i.e. illness. In practice, however, the Celsius scale is taken as a frame unified for a variety of kinds and forms of changes (technical, physical, climatic, etc.). In other words, the CCS is artificially extended and generalized at the expense of accuracy. At the same time, the Kelvin scale (some kind of "temperature АCS") is absolute with respect to temperature for systems of any nature.

Unified frames are similarly selected with respect to other parameters such as atmospheric and absolute pressure, absolute and relative humidity, time (Greenwich and local), etc. At the same time, the local frame (in the framework of the given CS) allows the processes and laws in the given CS to be described in the simplest way.

Thus, the adopted frames should allow for a number of conditions, but the main point is the use of the CS specific for each form of changes, or the ACS as the unified frame for all forms of changes in the absolute limit.

Based on the above-stated concepts, it is possible to formulate the following general definition of ideal (absolute) frame: frame is the outer boundary of the CS in which the given process is going on or the given object is located and in which, which particular parameters of these processes and objects can be compared (defined).

Such a frame is independent of the given CS and other CSs, and it secures constancy and objectivity of the description. The optimal choice is the absolutely closed system (АCS). Approximate results are obtained when a conditionally closed system (CCS) is used as a frame. The practical criterion for the CS definition is the absence of interaction of this system with any external objects, including measured ones.