In 1915 Albert Einstein presented a new theory of gravity, to the Prussian Academy of Sciences, which changed our perception of physical reality. 100 years later, the theory has retained its success despite many tests, and is yet mysterious in many ways. Bizarre objects such as black holes, wormholes seed galaxies and promise reality of time travel, yet we are searching for direct evidence of `gravity waves’ ripples of space-time carrying gravitational energy. These waves should be detected as they are same as light waves, the carriers of electromagnetic energy.

On December 10th, 2015, the department of physics and astronomy at University of Lethbridge celebrated the 100th anniversary of the discovery of this theory as an outreach activity. The event was well attended by members of the public, and of the university community. The entire event was very enjoyable and fielded curiosity about futuristic science as seen in popular movies like Interstellar. There were many question about time travel, e.g. could we travel to the past? Where did the wormhole get its name and so forth. The day ended with a joke that your neighbour could be a visitor from the future, as time travel exists theoretically and is inevitable.

The discovery of General Theory of relativity has always puzzled historians of science, as there was no experimental compulsion or evidences from nature for a new theory of gravity. In 1905, Einstein, then a Swiss patent clerk, had published four seminal papers, one of which was about the constancy of the speed of light. This theory, known as special theory of relativity (STR), required that time dilated and length contracted in fast moving systems, e.g. rockets. STR has now been verified, and indeed astronaut’s clocks click slower than those on earth by a few milli-seconds. However, STR leads to many paradoxes, one of which was that of the rotating disk.

In a rotating disk, the velocity of rotation increases with distance from the center, and thus for a fast rotating disk, the circumference would contract in length according to STR. The radius, being perpendicular to the direction of velocity would remain unchanged. The Euclidean theorem of the circumference to radius ratio of 2π, would no longer be true. How does one explain this conflict with Euclidean geometry? Einstein realized that a rotating disc is an accelerating system, the centripetal acceleration directed towards the center of the rotation makes this a non-inertial system, outside the scope of STR. Einstein began a solo journey to find the General Theory of Relativity, the theory of non-inertial accelerating systems, which would imply non-Euclidean geometry.

In addition to this, Einstein was inspired by Machian ideas of relativity. In physics measurements are defined with respect to observers and frames are as important as the physical event. Using Gedanken or thought experiments, Einstein formulated his `weak’ and `strong’ equivalence principles. According to this, gravitational fields can be replaced by accelerating frames. This is easy to see, the zero-gravity planes, now popular with tourists, simply take everyone to a sufficiently high level, and then `free-fall’ in earth’s gravity, at `g’ the acceleration due to gravity. The result is that everyone in the plane gets few minutes of `floatation’ or zero gravity as in a space-ship.

However, till 1911 Einstein had not made much progress. At that time, he started discussing with Marcel Grossmann, a mathematician and a classmate from ETH Zurich, who initiated him into principles of differential geometry, and the work of Bernhard Riemann, a French mathematician. General Relativity, slowly took shape, and it was formulated by equating energy momentum of matter with curvature and geometry of space-time. This was `gravity’ and the new physics was covariant in accelerated frames. The curved path taken by planets around the sun, the motion of galaxies is the easiest path or shortest path taken by these in the curved geometry created by massive objects.

General Relativity’s advent as a new theory was soon made credible as it predicted the yet unaccounted for 43 arc seconds (about 0.0119 of a degree) per century perihelion precession of Mercury. The bending of light due to Sun was also calculated correctly by the theory and confirmed by observations in 1919. The latter made Einstein particularly popular as newspapers headlined `Revolution in Science-New Theory of the Universe-Newtonian Ideas Overthrown.’

The presentation of the results in 1915 was soon followed by publication of an exact solution to the Einstein equation, found by K. Schwarzschild, in 1916. This solution, characterized by an event horizon, and a central singularity was named the `black hole’ by J. Wheeler in 1967. Anything which falls inside the black hole event horizon is lost to the outside world, and is destroyed at the central singularity. These bizarre gravitating objects were soon astrophysical realities. In 1930 S. Chandrasekhar had defined his `Chandrasekhar limit’ for gravitational collapse: all stars heavier than 1.39 times the mass of our sun collapse under their own gravity when they use up their fuel and form black holes. Today there are thousands of black hole candidates in the sky, including one at the center of our Milky way, the Sagittarius A* which might have seeded the formation of the galaxy.

The concept of the `big-bang’ and the Universe starting from nothing was a concept developed from the initial work of Lemaitre, Einstein and Friedman from 1917-1930. The current expanding universe solution is due to Robertson-Walker (1935). However, we are still investigating the exact curvature of the spatial Universe. Data from WMAP experiments, Planck satellites suggests that we have a slight positive curvature. In the 1990’s new observations showed that the Universe was not expanding at a uniform rate as predicted, but rather accelerating. This mystery baffled scientists and the current explanation is that there is dark matter and dark energy apart from visible matter which drive the cosmology and cause the acceleration.

Gravitational lensing is also one of the most beautiful astrophysical observations we owe to General Relativity. Light/Electromagnetic wave get bent due to massive compact objects and form multiple images of stars which are behind these compact objects. Einstein’s ring is like a `necklace formation’, one of the first of these was due to a radio source MG1131+0456 discovered in 1988 by Hewitt.

However, the biggest mystery of the theory is the elusiveness of the Gravity waves. Contrary to perceptions, gravitation is one of the weakest forces in nature, 10-35 times weaker than electromagnetic interactions. Theoretically Einstein had discussed ripples in space-time, the waves as in a sea of space-time which will carry away energy from gravitational processes such as galactic mergers, black hole collisions. Indirect evidence exists for these waves, but despite building of ground based interferometers for decades, we have not detected even one direct signal to date. The hope for observing these is now on the shoulders of European Space Agency which is involved in building e-LISA. This space-based antenna will be launched in 2034, with interferometer arms millions of Kms long. Ground based LIGO interferometer has also started functioning with increased sensitivity in September 2014. The hope remains that gravity waves will be detected soon.

As Einstein said in 1919 when General Relativity’s prediction of the bending of light due to Sun was confirmed by observations, for if it had not been “Then I would feel sorry for the dear lord. The theory is correct anyway.’’

At the University of Lethbridge the Theoretical Physics group is also involved in quantizing gravity, finding the `quanta’ of gravity such as the graviton. We ask questions like is space-time coarse grained or discretized at quantum length scales? As General Theory of Relativity is so much different from other theories of nature, maybe we need an Einstein brain to solve for quantum gravity.

Resources:

Einstein-Online http://www.einstein-online.info/

Wikipedia-Online Encyclopedia: https://en.wikipedia.org/wiki/Albert_Einstein

ESA: http://www.esa.int/ESA

LIGO: https://ligo.caltech.edu/

Arundhati Dasgupta, Talk at 100 years of General Relativity, University of Lethbridge, 2015

TALK SLIDES: 100GRf