34
R. N. Mohapatra
how massive the objects are. It has infinite range and goes down as the square
of the distance between two objects. Now, we know that the gravitational force
does not distinguish between matter and anti-matter. In Newton’s time, people
did not know about the existence of anti-matter. The discovery of Newton gave
a complete understanding of planetary motions observed by Johannes Kepler,
and proved once and for all that the Earth was not the center of the universe.
It could explain tides in the ocean and trajectory of comets. It also led to the
discovery of Neptune. Neptune was not discovered via telescopic observation
as many other planets were, previous to that. Applying Newton’s laws of gravity
and using mathematics, Johann Gottfried Galle, Urbain Jean Joseph Le Verrier,
and John Couch Adams, who all worked independently, helped discover this
planet in 1846, more than a century and half after Newton gave his laws of
gravity. The way this came about was that astronomers observed discrepancies
in Uranus’s observed position, in contrast to its predicted position according to
the laws of Newton by the above mathematicians. For a while, people thought
that Newton’s laws did not apply to objects at such a large distance. The
discrepancy in Uranus’s position could however be explained if a planet—
Neptune— was orbiting beyond Uranus. Thus Neptune may have resolved
a crisis for Newton’s laws.
Einstein proposed the general theory of relativity in 1915, combining the
theory of relativity with Newton’s law of gravity. In his theory, known as the
general theory of relativity, gravitational force is described in terms of geometry
i.e. the gravitational force is equivalent to a curvature of space around the
object which is creating the force. It is a very profound and novel concept and
the beauty is that it works. He introduced the concept of the metric of a spacetime which describes its geometry as a way to describe the gravitational force
in a subtle way. No extra force need be postulated to understand motion under
gravity. The metric itself is enough.
Imagine a plain page of paper and draw a triangle on it. All three angles of
the triangle add up to 180
◦ —this is what we learn in high school. If instead,
the triangle was drawn on the surface of a spherical vessel, the sum of the
three angles would be more than 180
◦ . The geometry of the surface of a
spherical vessel is different from that of a plain paper. If there was a big
source of gravitational force, the space around it would look more like the
surface of a spherical vessel, rather than a piece of plain paper. The stronger
the gravitational force, the more curved the space around it is. The stronger
the gravitational force in a region (for example, due to a large massive object),
the more curved the space would be. In other words, gravity changes geometry.
If we have a particle that is experiencing the gravitational force from an
object, creating the spherical vessel like space around it, the particle will move
R. N. Mohapatra
how massive the objects are. It has infinite range and goes down as the square
of the distance between two objects. Now, we know that the gravitational force
does not distinguish between matter and anti-matter. In Newton’s time, people
did not know about the existence of anti-matter. The discovery of Newton gave
a complete understanding of planetary motions observed by Johannes Kepler,
and proved once and for all that the Earth was not the center of the universe.
It could explain tides in the ocean and trajectory of comets. It also led to the
discovery of Neptune. Neptune was not discovered via telescopic observation
as many other planets were, previous to that. Applying Newton’s laws of gravity
and using mathematics, Johann Gottfried Galle, Urbain Jean Joseph Le Verrier,
and John Couch Adams, who all worked independently, helped discover this
planet in 1846, more than a century and half after Newton gave his laws of
gravity. The way this came about was that astronomers observed discrepancies
in Uranus’s observed position, in contrast to its predicted position according to
the laws of Newton by the above mathematicians. For a while, people thought
that Newton’s laws did not apply to objects at such a large distance. The
discrepancy in Uranus’s position could however be explained if a planet—
Neptune— was orbiting beyond Uranus. Thus Neptune may have resolved
a crisis for Newton’s laws.
Einstein proposed the general theory of relativity in 1915, combining the
theory of relativity with Newton’s law of gravity. In his theory, known as the
general theory of relativity, gravitational force is described in terms of geometry
i.e. the gravitational force is equivalent to a curvature of space around the
object which is creating the force. It is a very profound and novel concept and
the beauty is that it works. He introduced the concept of the metric of a spacetime which describes its geometry as a way to describe the gravitational force
in a subtle way. No extra force need be postulated to understand motion under
gravity. The metric itself is enough.
Imagine a plain page of paper and draw a triangle on it. All three angles of
the triangle add up to 180
◦ —this is what we learn in high school. If instead,
the triangle was drawn on the surface of a spherical vessel, the sum of the
three angles would be more than 180
◦ . The geometry of the surface of a
spherical vessel is different from that of a plain paper. If there was a big
source of gravitational force, the space around it would look more like the
surface of a spherical vessel, rather than a piece of plain paper. The stronger
the gravitational force, the more curved the space around it is. The stronger
the gravitational force in a region (for example, due to a large massive object),
the more curved the space would be. In other words, gravity changes geometry.
If we have a particle that is experiencing the gravitational force from an
object, creating the spherical vessel like space around it, the particle will move