Dear Dr. Azzam K AlMosallami,
I have read your essay, where you discuss interrelation between the real
physical processes and observation of these processes in different
coordinate systems. It is a very old problem. This problem was considered by
A. Einstein and H.Lorentz. They have different viewpoints on the special
relativity theory.
Einstein assumes that all inertial coordinate systems are equal, and
physical processes are equal in all inertial coordinate systems. Dynamic
equations in different coordinate systems are connected by means of the
Lorentz transformation.
Lorentz assumes that there is one liberated coordinate system where all
physical processes are described truly. Observation of these physical
processes from other coordinate systems is transformed, because of
transformation of time and of distance according to the Lorentz
transformations.
Both approaches are true. They describe truly all physical processes. There
is only difference in interpretation, which is not a conceptual difference.
In your essay you use consideration based on the nonrelativistic approach,
when space and time are considered as different essence (but not as
attributes of the space-time, as it is used in the special relativity). Of
course, such an approach is admissible, but a use of a space-time scheme is
more effective in the consideration of physical processes.
The best way of the physical processes description is a use of a such a
description, which does not refer to the way of description (coordinateless
description). Such a description removes many problems, connected with a use
of a coordinate system. Unfortunately, a coordinateless description is not
used practically, because one is not able to describe the space-time
geometry without a use of coordinates, although such a description is
possible, and it is very effective.
According to slogan of this contest: "Questioning the Foundations,Which of
Our Basic Physical Assumptions Are Wrong?" the main goal of my essay is a
formulation of the relativity principles in the coordinateless form.
The relativity principle looks as follows: THE SPACE-TIME IS
DESCRIBED BY THE ONLY SPACE-TIME STRUCTURE - WORLD FUNCTION
\sigma.
In the nonrelativistic case the space-time is described by two
space-time structures: by the space structure S and by the time
structure T. Any structure \sigma, S and T are functions of two
points P,Q\in \Omega of the space-time. Here \Omega is the set of
points of the space-time (the event space). The set \Omega
equipped by one space-time structure forms a physical geometry.
The physical geometry equipped by additional structure forms a
fortified geometry. The additional structure may be spatial
structure S, or a coordinate system. Any additional structure
transforms the physical geometry into fortified geometry.
The relativity principle states that the space-time is a physical
geometry (described by a physical geometry, but by a fortified
geometry). In other words, in the space-time there is only one
space-time structure \sigma and there are no other space-time
structures (neither structure S, nor a coordinate system
considered as a really existing structure). Space-time structures
are connected by the relation
\sigma =T-S (1)
Thus, additional structure S determines together with \sigma the
structure T. In the nonrelativistic approximation one uses usually
the space-time structures S and T. The world function \sigma
appears as a derivative structure. In the nonrelativistic
approximation according to such an approach the event space is not
considered as described by a geometry. One considers the geometry
on the 3-dimensional space and the time separately. This is
incompatible with the relativity principle which states that
there is ONLY ONE space-time structure in the event space.