On the Realization of the Dynamics Relativity
ChiYi Chen${}^{a,b}$
Based on the universal principle of the causality, the realization of the relativity of physics laws is discussed in this paper. First, we propose a kind of new relativity, that is the gravitational interaction survey actually may for the observation of any local region is relative. Moreover, the equivalence of such a relativity with the kinematic quantity further lead to the same mathematical form of gravity theory as Einstein's field equation. Secondly, inertial reference frames can be naturally established resorting to "the minimal-gravity-free observer", which is defined to apply the "law of inertia" locally. Therefore, dynamical equations would be form-invariant only to such inertial reference frames at different levels. After that, the correctness of the application of the dynamical law to any practical case has been guaranteed by use of the method of inertial reference frame. \\ PACS number(s): 98.80.-k, 95.10.-a
astro-ph0502256.tex
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\begin{document}
\title{On the Realization of the Dynamics Relativity}

\author{ChiYi Chen${}^{a,b}$}
\email{chenchiyi@center.shao.ac.cn}

\author{Kang Li${}^{c}$}
\email{kangli@hztc.edu.cn}



\affiliation{$^{a}$Shanghai Astronomical Observatory, Chinese
Academy of Sciences, Shanghai 200030, PR China}
\affiliation{$^{b}$Graduate School of Chinese Academy of Sciences,
Beijing 100039, PR China}
\affiliation{${}^c$Hangzhou Teachers
College, Hangzhou 310036, PR China}


\begin{abstract}
Based on the universal principle of the causality, the realization
of the relativity of physics laws is discussed in this paper.
First, we propose a kind of new relativity, that is the
gravitational interaction survey actually may for the observation
of any local region is relative. Moreover, the equivalence of such
a relativity with the kinematic quantity further lead to the same
mathematical form of gravity theory as Einstein's field equation.
Secondly, inertial reference frames can be naturally established
resorting to "the minimal-gravity-free observer", which is defined
to apply the "law of inertia" locally. Therefore, dynamical
equations would be form-invariant only to
such inertial reference frames at different levels. After that, the correctness
 of the application of the dynamical law to any practical case has been guaranteed by use
 of the method of inertial
 reference frame. \\
 PACS number(s): 98.80.-k, 95.10.-a
\end{abstract}


\maketitle
\section{INTRODUCTION}

No matter what dynamics law is, the principle of the causality is
always its soul and usually carried out by the method of inertial
reference frame. For example, in classical mechanism, the dynamics
equation must be established on the inertial reference frame, so to
provides a guarantee for the consistence of the casualty. In the
same reason, the geometry equivalence of the gravity must also be
established on the background of a inertial reference frame because
this is just the requirement of the principle of the causality.
However, this point is not clarified in Einstein's general
relativity.

In addition, the dynamics law can satisfy the principle of causality
once it was adjusted by making a comparison with the experiment.
Therefore, The most important property in the definition of "
inertial reference frame " would be given by the dynamics
relativity. In this paper we aim at finding a kind of reference
frames, which exist universally and in all of them the causalities
are unified consistently, so has provided the guarantee for the same
form of the dynamics law being applied in such a kind of reference
frames, then in fact this kind of reference frames are qualified to
be defined as the physical "inertial reference frame".

\section{ THE SYMMETRY OF THE RELATIVITY }
In realistic experiences, the observation of a physical phenomenon
is always localized and we must choose the different observers in
different local areas. On the other hand, a most important
property to a physical principle is its universality applicable.
Therefore this has directly caused our physical law should be
invariant for different observer, this is the so-called kinematic
relativity. Therefore, as the actual carrier of any dynamical
principle, the dynamical equations should keep the same
mathematical form in any local area in the universe. In other
words, the dynamical equations have been automatically required
to be universal and its form do not depended on at least one kind
of observers who stay in any local area of the universe.


In theoretically, to realize this point, a natural idea is that
the executed force is also relative to observers and the
equivalence on the relativity of both sides of the dynamical
equations should be maintained, then it is possible for the form
of the dynamical equations do not change with the changes of
observers. In short, to keep the symmetry of relativity is a
nature way which can keep the the mathematical form of the
dynamical equations invariant. Without doubt, the force executed
on any particle is absolute in nature, as well as the motion of
any particle is absolute in nature. But in fact the observation is
always local, and our description of the motion of particles must
be dependent on the observers. So the kinematical quantities of
particles are just relative, this is why dynamical equations have
relativity. Along this way, to realize the relativity of the
dynamical equations on different observers, the counting of the
executed force on the particle must also be capable being treated
as an equally relative quantity to some special kinds of
observers. In fact, we have never actually been able to count the
absolute force for even the most special particle in the universe.


\section{THE SYMMETRY OF THE RELATIVITY AND THE GRAVITY THEORY}


It naturally brings a problem, to what kind of observers, then the
kinematical quantities and the observed force in a dynamical
equation can be naturally respectively defined on the
equivalent(observer) relativity? To transformation between
relatively accelerated observers, we have previously pointed out
that if the form-invariant dynamical equations are available to
some special kinds of observers, then it would be required that
the influence brought by the transformation between relatively
accelerated observers must be equivalently erased from the whole
dynamical equation by some kinds of interaction which are executed
on both the particle and the observer. Therefore, the problem that
we are faced with has now turned to finding the qualified
interaction which is equivalent to the  kinematics of the
observer.

 In the requirement of the equivalence of the relativity, if such a kind of interaction
exists, then it must possess the following two properties:

 1, The relativity induced by a relative acceleration of the observer is
 determined by the state of the observer, and is irrespective to
 the selection of the particle in the local region. That is to say,
 the kinematical effect induced by this kind of interaction is
 irrespective to the special properties of the particle. Hence it
 must be a kind of universal interaction at least on the local region.

 2, The selection of the observer is irrespective to the
 distance between the observer and the particle. Hence
 the kinematical effect induced by this kind of interaction must
 be capable being counteracted in the dynamical equation by the relative acceleration
 for observers' change on the large scale of the universe. Therefore, it must further be a kind of long-range interaction
in the universe.

By far, four kinds of interactions discovered in the physical world
are concerned, only the gravitational interaction is qualified as
the candidate. Furthermore, considering that the inertial mass
always exactly equals to the gravitational mass, we are not able to
distinguish between what part of the motion of the particle is
native, and what part of the motion of the particle is induced by
the gravitational interaction from the distant place of the
universe. On one hand, this is just the direct reason for our
investigations on particle dynamics, in reality, are always
localized. On the another hand, it indicates that the gravitational
interaction on the cosmological scale has actually been throughly
geometrized into the global acceleration of the subsystems in the
universe. For these reasons, the equivalence on the respective
relativity of the kinematical quantities and the observed (or
counted) gravity must further lead to the geometrization description
of the gravity. In other words, as long as the equivalence between
the gravitational mass and the inertial mass is presented, the
geometry description must be available for the gravitational
interaction. Further considering the mass-energy relation in Special
Relativity and the deflection of light in gravity field, then it has
been enough for us to recover the mathematical form of Einstein's
gravity theory\cite{kolb,weinberg}:
\begin {eqnarray}
G_{\mu\nu}=-\kappa<T_{\mu\nu}>_{grav}.
\end {eqnarray}
Viewed from the opposite direction, the great success of the
geometrized theory of gravity has given eloquent proof of such an
equivalency between the dynamical property of the gravitational
interaction and the geometric language, and it also provides the
guarantee for the essential equivalence of the discussed two kinds
of relativity in the dynamical equations.

\section{THE SYMMETRY OF THE RELATIVITY AND THE INERTIAL REFERENCE FRAMES}


Now we turn back to the problem of finding the observers who are
able to establish the dynamical equations on the equivalent
relativity. As far as the gravitational interaction is concerned
now, the only feasible way is that, the kinematical effect induced
by "the global gravity" to a whole system must be equivalent to
the global acceleration of the whole system. Then the uncertainty
brought by the relativity of the kinematical quantities is capable
to be erased from the whole dynamical equation. The qualified
observer to above requirements are those that hold both  "the
global gravity" and the global acceleration of the system, we may
name it as "the minimal-gravity-free observer". According to
above discussion on the realization of the dynamical relativity,
then to an arbitrary particle, "the minimal-gravity-free
observer" may be defined to satisfy, at the same time, the
following two conditions:

1, It must be the observer who is executed only by gravitational
interaction and being gravity-free in the universe.

2, the gravitational field around the observer must be completely
contained within the area  around the particle considered.

Besides, the word "minimal" just means, to the whole system
considered, such an observer is the most fundamental gravity-free
one, since in the inner region of the system where may still
exist the gravity-free phenomenon at another level. As an
illustration, once an object as the test particle is specified,
we firstly should chose a local system including this particle
according to the scope of the interaction which should be counted
in. Secondly, we have to find out the observer who are in the
lowest-level gravity-free in this system (which would be rest on
the mass center of the system if the system is in global
gravity-free).

Once we have find "the minimal-gravity-free observer" to the
particle, it would immediately mean that we have established the
frame of inertial reference. Meantime, in the requirement of the
symmetry of the relativity, the external gravity executed on "the
minimal-gravity-free observer" (namely "the global gravity"
)should be equally counteracted in counting the force for any
particle in the system. For example, in the inertial reference
frame of the earth system, where the mass center of the earth is
the coordinate origin where "the minimal-gravity-free observer"
located, the gravitational force we are to count in should not
contain the interaction originated from the cosmic dust, the
galaxy, the sun and even any other planets in the solar system.
That is just the one of most important differences between what
we want to proposed in this Letter with the correlative issue in
the Einstein's special relativity, and it is such a subtlety which
may cannot be emphasized enough for the realization of the
dynamical relativity. Then, the form invariance of the dynamical
equations on different observers can be realized in our method.
Along this way, the statement of the "law of inertia" should be
correspondingly revised as: In any inertial reference frame
$with$ $a$ $minimal$-$gravity$-$free$ $observer$, every particle
preserves its state of rest, or its uniform motion in a straight
line, unless it is acquired a $additional$ forces $relative$ $to$
$the$ $minimal$-$gravity$-$free$ $observer$. After that, "the
relative gravity" can be naturally defined in the inner region of
local systems resorting to the "law of inertia" and which is just
symmetric to "the relative kinematical quantities".

There is one point we should keep in mind that, in applying these
dynamical equations to practical cases, the correspondence between
the scope of the interaction in the counting and the choice of
inertial reference frame should be one to one. For example, to
ascertain the Mars' influence upon the relative motion between the
Moon and the Earth, the center of the Earth is not applicable to
be "the minimal-gravity-free observer" any longer, in this case we
may choose the mass center of the Sun as the origin of a new
inertial reference frame instead. More importantly, at the same
time, the scope of the interaction under the consideration must be
spread to all the possible relative interactions in the inner
region of the sun system (relativity gravity of the sun's
reference). Therefore, in our theory, the inertial reference frame
is no more defined globally. The difference among the different
inertial frames of different levels is the different background
gravity, i.e. the different scale of the inertial space time of
the physics event.

Consequently, the symmetry of the relativity turns out to be a
possible method to achieve a consistent scenario of the dynamical
relativity. In our approach the mathematical form of the dynamical
equations would not only be applicable to arbitrary particle in the
inner region of a uniform gravity-free local system, but also be
unchanged with the transformation between different systems being in
"the global gravity" free. This is just the new principle of the
relativity which is proposed. Namely, it is the principle of
"minimal-gravity-free-observer" relativity. Furthermore, from the
two properties of the relatively observed interaction listed above,
the transformation between different minimal-gravity-free observers
is a $consistent$ $relativity$, it is realizable and actually
sufficient for us describe our physical universe. From the
discussion below, we think that this $consistent$ $relativity$ may
be more physical than the principle of general relativity in
Einstein's theory.

\section{THE DYNAMICAL RELATIVITY UNDER THE INERTIAL FORCE}

On the other hand, we re-investigate the reliability of the basis
of the standard cosmology---General Relativity. Firstly, we may
recur to the successful experiments on the solar scale which had
been made in the early period of the last century. There are two
important concepts have been confirmed from these experiments: the
one is that the gravitational interaction can be completely
geometrized, the another is that the gravity will also lead to the
photon's redshift, which is different to the Doppler redshift in
kinematical meaning.

The another principle of the Einstein's gravity theory is the
general relativity, which is to say that the field equation would
be form-invariant under the  general coordinates transformation.
However this point still has not been confirmed from the existing
experiments of gravity. Einstein's  principle of general
relativity based on two considerations: the one is the dynamical
equivalence between the gravitational force and the inertial
force, Einstein thought that his another consideration is  the
"Mach principle".  Considering its objective base, however, we
still have not drawn out the essential connection between the two
origins of the gravitational force and the inertial force.
Therefore even though we are able to unify the dynamical
principle of the gravity and the inertial force into the same
general covariant formulism, but the contribution from the
inertial force still can not be erased from the mathematical form
of a general covariant gravity theory. Therefore, the complete
formula of a general covariant gravity theory may be written as,
\begin {eqnarray}
G_{\mu\nu}=-\kappa<T_{\mu\nu}>_{grav}+\kappa<T_{\mu\nu}>_{iner}.
\end {eqnarray}
The second term on the right-hand-side of the above equation in
the case of Brans-Dicke gravity theory just corresponds to the
contribution from the gravitational scalar. In other theories
where do not claim that the inertial force originates from the
external gravitational matter, then the existence of this second
term would be more indispensable. In fact we do not assure how to
correctly describe the inertial force in origin, so we still have
to select a special coordinates reference frame in cosmology,
where we do not have to consider the inertial force any more.
Once such a reference frame has been naturally chosen, the
mathematical form of the cosmological field equation would not be
capable to be further performed by the generalized coordinates
transformation. That is to say, if we apply the Einstein's field
equation to the cosmology and deal only  with the gravitational
energy-momentum of the ordinary matter, then the coordinates
reference frame under the consideration must have been
substantively chosen from a special kind of reference frames
\cite{Rosen}.



\section{REMARKS}
Such new relativity of the dynamical equations which we put forward,
its key lies in such a fact, namely, comparing to all the objects in
a gravity-free system in the universe,  our direct observation of
the gravitational force are always local, in fact it is also
relative. The influence of the gravity originated from the outer
space of the system on their relative motion is almost equally
counteracted by their uniform global acceleration. A direct reason
for this point is just the equality of the inertial mass and the
gravitational mass. Therefore, it turns out that there actually
exists a preferred coordinates system, determined by the large-scale
gravity-free systems in the universe, in which the laws of the
physics have their simplest form. In other words, it is just the
peculiar property of gravitational interaction and its peculiar
status in the universe that make the definition of "inertial
reference frame" available in the practical case.

 This paper is just aimed to make a theoretical exploration along the
realization of the dynamical relativity. Therefore, the first
thing we have proposed is that the counted gravity can be treated
as a relative quantity in any gravity-free system. This point is
comprehended just from the viewpoint of the symmetry, we know
that the observed speed of a particle is relative, the observed
acceleration of the particle is also relative, so it is natural
to require that the counted force should also be relative (namely
the relative gravity) to keep holding the principle of relativity
on the dynamical equations.

The introduction of the relativity of gravity is especially
important for a natural definition of the inertial reference
frames. Therefore, the second thing we have proposed is that "the
minimal-gravity-free observer" can naturally constitute the frames
of inertial reference. After establishing the dynamical equations
on this kind of observers, the symmetry of the relativity to all
objects in the system is realized. Therefore, the principle of the
relativity in our theory is the "minimal-gravity-free-observer"
relativity. As well as the symmetry of the relativity is required
by the causality in the dynamics law, the symmetrical
counteracting of the relativity of dynamical quantities in
different inertial reference frames is further to unify the
causality in their corresponding dynamical equations. In this
sense, for the reference frames with the origin of a minimal
gravity-free observer have been derived out along the symmetry of
the relativity, the unification of the form of the dynamics law is
truly carried out in our theory.

In addition, for the dynamics law concerning the principle of
causation, the geometrized gravity theory should be established on
the basis of the background inertial reference frame. It is to say
that Einstein's mathematical form is here maintained for gravity
theory just because nothing but dynamical effects of the gravity
in the inner region of a system are capable being globally
geometrized on its background inertial reference frame.

The principle of consistent relativity means the establishing of the
geometrized equation of gravity on the basis of the inertial
reference frame, namely the causality. Hence in fact it has
naturally harmonized the special relativity and the geometry theory
of gravity in the level of the method of inertial reference frame.




{\bf{Acknowledgments:}} This work has been supported in part by
National Nature Science Foundation of China under grant No.
10273017. K.Li also recognize the support from the Nature Science
Foundation of Zhejiang Province under the grant number
M103042,102011,102028.







\begin{thebibliography}{nn}
\bibitem{Rosen} N. Rosen, Phys.Rev.D(America)3, 2317(1971).
\bibitem{kolb} Edward W.Kolb and Michael S.Turner "The Early
Universe"  (Addison-Wesley Publishing Company, 1990), Chap. 2.
\bibitem{weinberg} Steven. Weinberg  "Gravitational and Cosmology:
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\end{thebibliography}
\end{document}

astro-ph0502256.extracted_bib
\begin{thebibliography}{nn}
\bibitem{Rosen} N. Rosen, Phys.Rev.D(America)3, 2317(1971).
\bibitem{kolb} Edward W.Kolb and Michael S.Turner "The Early
Universe"  (Addison-Wesley Publishing Company, 1990), Chap. 2.
\bibitem{weinberg} Steven. Weinberg  "Gravitational and Cosmology:
Principles and Applications of the General Theory of
Relativity"(John Wiley {\&} Sons, Inc, New York, 1972), Part 3.
\end{thebibliography}