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This paper is concerned with the signal method of clock synchronization. A new relation for the proper time is deduced. New transformations of coordinates in two-dimensional space-time are obtained. Space-time has the structure of a flat anisotropic Finsler space with a general nonstandard clock synchronization. Different cases of clock synchronization between inertial systems are considered.

This paper derives a general definition of distance within the context of general clock synchronization with the signal method. The unified context includes both isotropic and anisotropic descriptions of physical processes in inertial reference systems. Taking anisotropy of a metric space into account, new transformations of space and time are derived. Different cases of anisotropy are considered. Galilei transformations in anisotropic space have an invariant value of the speed of light over the closed path.

A hundred years ago, Poincar? pointed out that relativistic mechanics can be described within different geometries of space-time. This paper assumes the signal method of clock synchronization in pseudo-Euclidean, Euclidean and Galilean geometries, and obtains transformations of coordinates and time for these geometries under general nonstandard clock synchronization.

This paper is concerned with clock synchronization by the method of slow transport of clocks. A new derivation of transformations of space and time with general nonstandard synchronization of clocks is given. Different cases of clock synchronization between the systems are considered. A new physical condition for the conservation of clock synchronization in the case of slow transport is obtained.

This paper is concerned with the signal method of clock synchronization. A general definition of the simultaneity of the distant events is derived. In the unified context, both isotropic and anisotropic descriptions of physical processes in inertial reference systems are considered. A new relation for the proper time is deduced. New transformations of coordinates in two-dimensional space-time are obtained. In special cases the transformations describe Euclidean, pseudo-Euclidean, Galilean and other kinematics. All such cases have validity equal to relativistic mechanics for the description of physical processes