5.4 Space-Time Reference Based on General Relativity
305
transformation, and Maxwell’s equations are covariant for the Lorentz transformation, so two theoretical systems, the electromagnetism and Newtonian mechanics,
have been unified by the special relativity. The discrepancy between the special relativity and Newtonian mechanics is: the time in the Newtonian mechanics is absolute,
and if two events occur simultaneously in an inertial system, then they must also
do at the same time in other inertial systems; in Einstein’s space-time view, the
absoluteness of the simultaneity is discarded.
However, the special relativity did not solve completely the problem of Newton’s
theory of gravitation. For this reason, in 1915 Einstein published a covariant theory
of gravitation, known as the general relativity, which is a basic theoretical system
composed of equivalence principle and general relativity principle. The general relativity generalizes the special relativity and refines Newton’s law of universal gravitation, providing a unified description of gravity as a geometric property of space
and time. In particular, the space-time bending is directly related to the energy and
momentum of whatever matter and radiation are present. This relation is expressed
as the Einstein field equations which represent the dependence of the spatial metric
on the distribution of matter.
Both the Newtonian mechanics and special relativity fail to solve the essential
problem of inertial system and inertial force. Inspired by the equality of the inertial
mass with the gravitational mass, Einstein proposed the first basic principle of general
relativity that a gravitational field is locally indistinguishable from the dynamical
effects of an inertial force. The equivalence of inertial force and gravity obtained
from mechanical experiments is called weak equivalence principle, which has been
proved by more and more precise experiments. Furthermore, it is assumed for any
physical experiments, such as mechanical, electromagnetic and other ones, that the
effects of both inertial force and gravity are indistinguishable in a local region. In other
words, the dynamical effects in the weak equivalence principle are extended to the
deeper assumption for any physical effects, which is known as strong equivalence
principle. It should be pointed out that the strong equivalence principle does not
have sufficient experimental supports and needs to be verified in practice.
From the equivalence principle, it is known that there is no strict inertial system
in the universe, so it is usually inevitable for people to investigate the physical laws
in the non-inertial system. For the equivalence principle, the inertial force in the noninertial system is regarded as the gravitational field, and considering the influence of
the gravitation field on the physical laws, the gravitational effect is merged into spacetime background. Therefore, another basic principle was generalized by Einstein,
which all reference systems are equally weighted. In other words, the real- objective
physical laws should have the same form under any coordinate transformation and
be generally covariant, which is called the general relativity principle.
Obviously, the superiority of the inertial frame has been removed for the equivalence principle and general relativity principle, so that all reference frames are equally
weighted, and the influence of gravitational field must be considered to get a correct
physical law. For the equivalence principle, it is allowed to describe the physical
process by using the non-inertial system and treat the permanent and non-permanent
gravitational fields as the same. The equivalence principle is the basis and premise for
305
transformation, and Maxwell’s equations are covariant for the Lorentz transformation, so two theoretical systems, the electromagnetism and Newtonian mechanics,
have been unified by the special relativity. The discrepancy between the special relativity and Newtonian mechanics is: the time in the Newtonian mechanics is absolute,
and if two events occur simultaneously in an inertial system, then they must also
do at the same time in other inertial systems; in Einstein’s space-time view, the
absoluteness of the simultaneity is discarded.
However, the special relativity did not solve completely the problem of Newton’s
theory of gravitation. For this reason, in 1915 Einstein published a covariant theory
of gravitation, known as the general relativity, which is a basic theoretical system
composed of equivalence principle and general relativity principle. The general relativity generalizes the special relativity and refines Newton’s law of universal gravitation, providing a unified description of gravity as a geometric property of space
and time. In particular, the space-time bending is directly related to the energy and
momentum of whatever matter and radiation are present. This relation is expressed
as the Einstein field equations which represent the dependence of the spatial metric
on the distribution of matter.
Both the Newtonian mechanics and special relativity fail to solve the essential
problem of inertial system and inertial force. Inspired by the equality of the inertial
mass with the gravitational mass, Einstein proposed the first basic principle of general
relativity that a gravitational field is locally indistinguishable from the dynamical
effects of an inertial force. The equivalence of inertial force and gravity obtained
from mechanical experiments is called weak equivalence principle, which has been
proved by more and more precise experiments. Furthermore, it is assumed for any
physical experiments, such as mechanical, electromagnetic and other ones, that the
effects of both inertial force and gravity are indistinguishable in a local region. In other
words, the dynamical effects in the weak equivalence principle are extended to the
deeper assumption for any physical effects, which is known as strong equivalence
principle. It should be pointed out that the strong equivalence principle does not
have sufficient experimental supports and needs to be verified in practice.
From the equivalence principle, it is known that there is no strict inertial system
in the universe, so it is usually inevitable for people to investigate the physical laws
in the non-inertial system. For the equivalence principle, the inertial force in the noninertial system is regarded as the gravitational field, and considering the influence of
the gravitation field on the physical laws, the gravitational effect is merged into spacetime background. Therefore, another basic principle was generalized by Einstein,
which all reference systems are equally weighted. In other words, the real- objective
physical laws should have the same form under any coordinate transformation and
be generally covariant, which is called the general relativity principle.
Obviously, the superiority of the inertial frame has been removed for the equivalence principle and general relativity principle, so that all reference frames are equally
weighted, and the influence of gravitational field must be considered to get a correct
physical law. For the equivalence principle, it is allowed to describe the physical
process by using the non-inertial system and treat the permanent and non-permanent
gravitational fields as the same. The equivalence principle is the basis and premise for