Elements of Modern Physics
392
Our discussion so far has been about modern ideas in the domain of high velocity
(special theory of relativity), and small distances (quantum theory and its
applications). There have been important developments in our understanding
of large-distance, large-body phenomena as well. These refer primarily to the
general theory of relativity as applied to large stars, galaxies and cosmology,
i.e. the science of the universe as a whole.
In cosmology, the events taking place in distant objects such as galaxies,
which not only may be moving with high velocity with respect to us but may
also be accelerating, have to be interpreted. It is to be expected that observation
and interpretation are simpler in the galaxy where the events are taking place.
Therefore, a relativistic theory, which can relate observations in frames which
are in arbitrary motion with respect to each other is needed. Einstein’s theory of
general relativity provides the frame-work for relating observations of spacetime events in arbitrary frames. Indeed, the theory accomplishes more than
that. It incorporates gravitational effects as well. This is based on the observation
that the motion of a particle in a gravitational field, with a given initial position
and velocity, is independent of its mass. This implies, as will be discussed later,
that the effect of gravity can be locally simulated by an accelerating frame but
without gravity, so that gravitational effects can be described by the theory of
general relativity. Furthermore, in the discussion of cosmological dynamics, it
is mainly the long-range gravitational forces which are important. Therefore
general relativity is also an appropriate theory for the analysis of the development
of the universe.
Here, an elementary and brief consideration of the main ideas of the theory
of general relativity is presented and the ideas are applied to discuss some
predictions of the dynamical properties of the universe. It is quite appropriate
to end with the description of general relativity, a theory which is grand in its
concepts and structure and awe-inspiring in its predictions. An exposition of
modern ideas in physics cannot be said to be complete without a discussion of
general relativity, and any thing to follow would only be an anticlimax.
11.1 FRAMES OF REFERENCE
An event is a space-time occurrence. To specify an event, we need a frame of
reference, which consists of three spatial coordinate axes and a time coordinate.
It is known that the equations of motion in special relativity or Newton’s theory
take the simplest form in inertial frames. In an inertial frame, a particle on
which no external forces act moves with constant velocity. A description of
motion in frames which accelerate with respect to inertial frames is complicated
by the need to introduce additional forces known as inertial (or pseudo) forces.
For example, an observer in an accelerating or decelerating train experiences
forces in addition to the gravitational or electromagnetic forces. Thus, with
392
Our discussion so far has been about modern ideas in the domain of high velocity
(special theory of relativity), and small distances (quantum theory and its
applications). There have been important developments in our understanding
of large-distance, large-body phenomena as well. These refer primarily to the
general theory of relativity as applied to large stars, galaxies and cosmology,
i.e. the science of the universe as a whole.
In cosmology, the events taking place in distant objects such as galaxies,
which not only may be moving with high velocity with respect to us but may
also be accelerating, have to be interpreted. It is to be expected that observation
and interpretation are simpler in the galaxy where the events are taking place.
Therefore, a relativistic theory, which can relate observations in frames which
are in arbitrary motion with respect to each other is needed. Einstein’s theory of
general relativity provides the frame-work for relating observations of spacetime events in arbitrary frames. Indeed, the theory accomplishes more than
that. It incorporates gravitational effects as well. This is based on the observation
that the motion of a particle in a gravitational field, with a given initial position
and velocity, is independent of its mass. This implies, as will be discussed later,
that the effect of gravity can be locally simulated by an accelerating frame but
without gravity, so that gravitational effects can be described by the theory of
general relativity. Furthermore, in the discussion of cosmological dynamics, it
is mainly the long-range gravitational forces which are important. Therefore
general relativity is also an appropriate theory for the analysis of the development
of the universe.
Here, an elementary and brief consideration of the main ideas of the theory
of general relativity is presented and the ideas are applied to discuss some
predictions of the dynamical properties of the universe. It is quite appropriate
to end with the description of general relativity, a theory which is grand in its
concepts and structure and awe-inspiring in its predictions. An exposition of
modern ideas in physics cannot be said to be complete without a discussion of
general relativity, and any thing to follow would only be an anticlimax.
11.1 FRAMES OF REFERENCE
An event is a space-time occurrence. To specify an event, we need a frame of
reference, which consists of three spatial coordinate axes and a time coordinate.
It is known that the equations of motion in special relativity or Newton’s theory
take the simplest form in inertial frames. In an inertial frame, a particle on
which no external forces act moves with constant velocity. A description of
motion in frames which accelerate with respect to inertial frames is complicated
by the need to introduce additional forces known as inertial (or pseudo) forces.
For example, an observer in an accelerating or decelerating train experiences
forces in addition to the gravitational or electromagnetic forces. Thus, with