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Episode 19: Einstein’s Universe
[Note for script writer: This brief has been prepared keeping the average non-specialist
listener in mind. The attempt has been to develop the subject in a logical sequence that could
bring out excitement of the process of making new discoveries and relating them to the
gradual understanding of the nature of the universe. It is designed to be a popular account of
the development of astronomy as a scientific discipline and its impact on our understanding
of the cosmos. Since the treatment is not rigorous, many details are not included. The script
has to be developed along the outline suggested using simple colloquial language as far as
possible. The dialogues and conversations need to be lively without any suggestion of
pedagogy.]
Points to be covered:
- Limitations of Newtonian gravity
- Precession of Mercury’s orbit
- General relativity, space-time continuum
- Force vs field
- Gravitation as distortion in space-time continuum
- Bending of light by gravity
Outline of content:
Despite its many successes, the challenge to Newton’s law came in the form of an anomaly in
the orbit of Mercury, the planet closest to the Sun. Years of observation had shown that
Mercury’s point of nearest approach to the Sun, or perihelion, changed from one orbit to the
next. It moved forward a bit in each orbit. The anomaly could not be explained by
Newton’s law. According to Newton’s law, every planet should follow exactly the same path
forever, except for minor irregularities caused by the gravitational influence of other planets
in the neighbourhood, as in the case of Uranus. But the regular change in Mercury’s orbit
could not be explained on the basis of gravitational influence of the other known planets.
The solution finally came in 1915, in the shape of the work of the German physicist Albert
Einstein. In 1905 Einstein had published a revolutionary paper on “special theory of
relativity” that altered our ideas of space, time, mass energy, motion and gravitation. It
provided a new approach to the study of cosmos. In 1915, Einstein published his “general
theory of relativity” that finally solved the riddle of Mercury’s orbit. When Mercury’s orbit
was calculated using Einstein’s theory, the shift of the planet’s perihelion could be exactly
accounted for. It was one of the first successes of the new theory of gravitation based on
relativity.
The basic problem with Newton’s law of gravitation was its treatment of mass and inertia.
Newton defined mass as a measure of a body’s inertia; that is, its resistance to any change in
motion. Higher the mass, higher is the resistance and higher the inertia. For example, a
railway train has more mass and more inertia than a small car because it takes much more
force to move a stationary train or to stop a moving one than to do the same to a stationary or
running car.
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As every student of science knows, if two bodies of different masses are dropped from the
same height simultaneously in a vacuum, where there is no air resistance, then both will reach
the bottom at the same instant – a phenomenon first postulated by Galileo ion 1604. Galileo
is said to have tested his hypothesis by dropping objects of different sizes from the top of the
famous Leaning Tower of Pisa at the same instant of time.
If objects of different masses fall at the same rate when dropped from a height, it would mean
that the force of gravity produces the same acceleration in bodies irrespective of their mass.
But such a situation would go against Newton’s law of inertia, according to which
acceleration produced by a force should be proportional to mass.
Einstein’s theory of general relativity did not agree with Newton’s theory in two important
aspects. Newton considered the mass of a body to be constant, but Einstein’s theory asserted
that the mass of a moving body is by no means constant; it increases with its velocity relative
to an observer. Einstein’s theory also stated that no material object could ever reach the
speed of light because as it tended to do so its mass would become very large, almost
reaching infinity. Einstein’s theory also rejected the idea of gravitation being a force that can
be exerted instantaneously over great distances, as Newton had assumed in his law of
universal gravitation.
Einstein showed that it was not necessary to think of gravity as a force acting at a distance.
Instead, he described gravity in terms of its local effects on space and time, i.e., as the curved
geometry of space-time, as determined by the distribution of matter and energy. Simply
stated, Einstein’s law of gravitation contains nothing about force. Rather it describes the
behaviour of objects in a gravitational “field”. The planets, for example, move in orbits
around the Sun not because the Sun attracts them but because they follow different paths in a
curved space. According to Einstein’s theory, gravity is a distortion in the fabric of space; as
a result of the presence of matter, space becomes curved. The stars, planets and other celestial
bodies simply follow the lines of least resistance among the curves.
We cannot visualise Einstein’s concept of space-time using any physical analogy because it
can be represented only by mathematical equations. Still, we can have an idea of what
curved space looks like by considering a flat, flexible surface made of rubber stretched over a
large wooden frame. If we drop an iron ball on the stretched rubber, the elastic surface will
sag around the iron ball, making a depression on the surface. We can say the space around
the ball has become curved because of the presence of mass. A similar thing happens in
Einstein’s four-dimensional space-time continuum in the presence of mass. If a glass marble
is now rolled across the deformed surface of the stretched rubber, it will roll round and round
in the depression, just like planet orbiting the Sun. This is, of course, a very crude analogy
with a two-dimensional surface, but it certainly helps in understanding the concept of curved
space in Einstein’s theory.
Einstein’s general theory of relativity thus gave a completely new concept of gravitation. It
not only provided a plausible solution to the riddle of Mercury’s perihelion anomaly but also
predicted two entirely new phenomena that were totally unexpected.
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The verification of Einstein’s second prediction of the bending of light rays by gravitational
field came dramatically in 1919. That year, in photographs taken during a total eclipse of the
Sun, stars were found to indeed shift position. Comparing photographs of the same part of the
sky taken earlier, when the Sun was not in the vicinity, it was found that position of stars
indeed changed as they passed near the Sun. More significantly, the degree of bending was
exactly as predicted by Einstein’s theory.
Einstein’s theory of general relativity revolutionised our ideas of space, time and motion.
And in doing so it solved several cosmic mysteries and provided a new concept of gravity.
Einstein’s equations also anticipated the existence of bizarre cosmic objects such as black
holes – remnants of massive stars with gravitational fields so strong that not even light can
escape from them. His equations also gave us the famous little formula of mass-energy
equivalence (E = mc2) that sums up all actions and creations in the universe.