ture of Li 7 is treated as a single P$_{3}$$_{/}$$_{2}$ proton in a central nuclear potential, the variation Δ m of mass with direc- tion, if it exists, was found to satisfy Δ m m ≤ 10 − $^{20}$. This proves that there is no anisotropy of mass which is due to the effects of mass in our galaxy. If the curvature of Riemannian space is associated with gravitational inter- action then it would indicate an universal feature equally suitable for action on all the matter fields at once. Then another objection is that this is rather applicable only for gravity but not for inertia since the inertia depends solely on the state of motion of individual test particle or coordinate frame of interest. So, the curvature arisen due to acceleration of coordinate frame of interest relates to this coordinate system itself and does not acts at once on all the other systems or matter fields. Such inter- esting aspects which deserve further investigations, un- fortunately, have attracted little attention in subsequent developments. This state of affairs has not much changed up to present, as well as the RLI still remain unknown. The present paper aims to fill this gap. Furnishing justi- fication for introduction of the Principle of Equivalence, in addition to those of available experimental verifica- tions [3, 4], we must also assign a high importance to the prove on the theoretical basis. 

Another purpose of present article is to explore the re- arrangement of vacuum state in gravity at huge energies, which will be of vital interest for the physics of super- dense matter in very compact astrophysical sources [8– 11] and references therein. Note that the Riemannian space interacting quantum field theory cannot be a sat- isfactory ground for addressing this question. The ge- ometrical interpretation of gravitation arisen from the dual character of the metrical tensor in its metrical and gravitational aspects, is a noteworthy result of GR. Al- though this interpretation has advantage in solving the problems of cosmology, nevertheless such a distinction of gravitational field among the fields yields the difficulties in the unified theories of all interactions of elementary particles, and in quantization of gravitation. Therefore, the GR as a geometrized theory of gravitation clashes from the very outset with basic principles of field theory. This rather stems from the fact that Riemannian geome- try, in general, does not admit a group of isometries, i.e., Poincar´ e transformations no longer act as isometries and, for example, it is impossible to define energy-momentum as Noether local currents related to exact symmetries. This posed severe problems in Riemannian space inter- acting quantum field theory. The major unsolved prob- lem is the non-uniqueness of the physical vacuum and associated Fock space. Actually, a peculiar shortcoming of the interacting quantum field theory in curved space- time is the following two key questions to be addressed yet: a) an absence of the definitive concept of space- like separated points, particularly, in canonical approach, and the ’light-cone’ structure at each spacetime point; b) the separation of positive- and negative-frequencies for completeness of the Hilbert-space description. Due to it, a definition of positive frequency modes cannot, in gen- 

eral, be unambiguously fixed in the past and future which leads to | in > ̸ = | out >, because the state | in > is unsta- ble against decay into many particle | out > states due to interaction processes allowed by lack of Poincar´ e in- variance. Non-trivial Bogolubov transformation between past and future positive frequency modes implies that particles are created from the vacuum and this is one of the reasons for | in > ̸ = | out > . Note that a remarkable surge of activity of investigations towards an extension of GR has arisen recently. They are expressible geometri- cally in the language of fundamental structure known as a fiber bundle. This provides an unified picture of gravity modified models based on several Lie groups, see e.g. [12– 29]. All these approaches have their own advantages, but in the same time they are subject to many uncertainties. Currently no single theory has been uniquely accepted as the convincing gauge theory of gravitation, which will be able successfully to address the aforementioned problems. 

To innovate the solution to the problems involved, in this paper we develop on the general gauge principle (GGP), an early version of which is given in [11, 30, 31]. The GGP accounts for gravitation gauge group G$_{R}$ gen- erated by hidden local internal symmetries implemented on the flat space M$_{6}$ . Involving the auxiliary flat space M$_{6}$ , with the whole set of well-defined Killing’s vectors, just has a single aim as a guiding tool in dealing with an intricate ’jungle’ of curved geometry. In this paper much more will be done (Sect.2) to make clear and rigorous these early results and formulations. The following part of the present paper will be the original contribution, whereas we relate the group G$_{R}$ to the Lie group G$_{D}$ of distortion of local internal properties of flat space M$_{6}$ . It can be achieved by nonlinear realization of the group G$_{D}$ in the framework of method of phenomenological La- grangians. This approach was originally introduced by Coleman, Wess and Zumino [32–34] in the context of in- ternal symmetry groups. It was later extended to the case of spacetime symmetries by Isham, Salam, and Strathdee [35, 36] considering the nonlinear action of GL (4, R ) mod the Lorentz subgroup, see [15] and references therein for a comprehensive review. We study geometrical structure of the space of parameters in terms of Cartan’s calculus of exterior forms and derive the Maurer-Cartan’s struc- ture equations. We derive key relation which uniquely determines, for given distortion field, the six angles of distortion rotations around each axes of the M$_{6}$ . We treat distortion fields as Goldstone fields to which the metric and connection are related. We infer group in- variants and calculate conserved currents. The metric is no more a fundamental dynamical field. The funda- mental field is distortion gauge field and, thus, both the actions and the equations of motion depend on the con- cept of gauge potential. The metric and connection may be derived from this gauge field. To test the proposed 

## A. Rational 

