By Mr. RATAN KUMAR, Bachelor of Engineering in Marine Engineering from Jadavpur University, and had a vast knowledge of Physics. He has 12 years of experience and physics faculty at Rajeev classes.
Nature is stranger than our imaginations and its laws are more mysterious than we can think. Our observable universe is 13.7 billion years old, having a diameter of 93 billion light-years which contains at least 2 trillion galaxies. This is really the grand scale. But the beauty of Physics is that it can explain almost each and every phenomenon of nature on the basis of just four fundamental interactions, namely, Gravitational interaction, Electromagnetic interaction, Strong interaction, and Weak interaction. The scientific journey of mankind encountered with gravitation before than it has even recognized any other fundamental interactions. But, as of now, we can understand all interactions except Gravitation pretty well, yet gravitation still is a mystery and a challenge for the intelligence of physicists.
In ancient India, Aryabhatta, identified gravitation as a force to explain why objects fall down and not thrown upwards. Brahmagupta described gravitation as a force of attraction and he used the term Gurutvakarshan for it. Ancient Greek philosopher Archimedes introduced the concept of the centre of gravity. In modern times, astronomers contributed the most, in the development of mathematical models of Gravitation. Ptolemy had proposed the geocentric model for the solar system, in which the earth is believed to be stationary and at the center of the solar system. This model has survived for centuries. But, this model was challenged in 1543 and replaced by Nicolaus Copernicus by his heliocentric model, in which the sun is believed to be at the center of the solar system. Before Galileo, the laws governing terrestrial objects were believed to be different from the laws governing heavenly objects. But, things started to change with Galileo and by the time of Newton, it has been established that the laws of nature are the same for both terrestrial objects as well as heavenly objects. Newton discovered the first mathematical model for the gravitational interactions and proved that it is the same force that causes an apple to fall from the tree and make planets orbit around the sun. This was probably the first unification of the laws of nature. And we started to believe that someday we would discover a theory of everything that will explain each and every phenomenon of nature.
The laws of gravitation, as proposed by Newton, simply state that the force of gravitation is directly proportional to the product of masses of the two-point objects and inversely proportional to the square of the distance between them. By this, we came to know about a very important constant of nature, namely universal gravitational constant (G). In nature we have two types of constants, one is universal and another is non-universal. A universal constant is believed to have a constant value irrespective of anything. No matter when, where, or how we measure the value of this, we must find the same result. In nature, we really have only four universal constants, namely universal gravitational constant (G), Planck’s constant (h), speed of light/causality in free space (c), and Boltzmann constant (K). Thus, the universal gravitational constant is the first universal constant that we have discovered. The first direct measurement of the value of gravitational constant was performed by Henry Cavendish, in 1798, some 71 years after the death of Newton. He used a torsional beam with two lead balls and he found its value to be 6.744*10^(-11) cubic meters per kilogram per second square, which was around 1% above the modern value, measured more accurately.
Bylaws of gravitation, many new questions have come into existence. And the first among them was the equivalence of inertial mass and gravitational mass. The inertial mass is traditionally defined as the total matter content of a body, which is responsible for the inertia or resistance of that body against any change in its state of motion or velocity. But with Newton’s laws of gravitation, one more aspect of mass came into existence, namely gravitational mass, which is responsible for gravitational pull it experiences or causes. Although, there is no direct link between the property of inertia and gravitation, but surprisingly both the gravitational and inertial mass were found to have the exact same value in all cases. We can conclude that the property which enables a body to maintain its state of motion is also responsible for its gravitational effects.
Another, mystery that surrounds the gravity, was its propagation. Before gravitation, we were aware of only contact forces, like friction, tension, or spring forces that require contact for its application. But gravitation was different. Its effect can be felt even from the farthest corner of the universe. It doesn’t require any contact. The sun and the earth are 14,95,97,870 Km, so much, so that even light takes 500 seconds to cover this distance. Even, then the gravitational pull of the sun makes the earth to orbit around it. So the natural question arises, how the sun and earth, being so much distant from each other can apply gravitational force on each other. Newton has no idea, how gravity actually works over such large distances. And in his book, Principia Mathematica, Newton actually writes, “I have not yet been able to discover the cause of these properties of gravity from phenomena and I feign no hypotheses… It is enough that gravity does really exist and acts according to the laws I have explained and that it abundantly serves to account for all the motions of celestial bodies.”
In his letter to Bentley, in 1692, he says, ” “That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.”
Newton’s laws of gravitation were very accurate in many predictions e.g. The orbit of planets, timing of tides of seas, timing of solar and lunar eclipses. In fact, Newton’s laws of gravity are sufficient to launch a rocket in space with the amount of precision we require.
But, orbits of two planets seemed to defy Newton’s laws and those were Uranus and Mercury. The issue with Uranus was settled by the discovery of Neptune whose gravitational effects were responsible for the discrepancies observed in Uranus’s orbit as observed initially. But Newton’s law of gravity predicted a planet to explain the observed orbit of Uranus, and when Neptune was found at that exact location, then Newton’s law of gravity became a grand success. People used to think that one more such planet would be found between Mercury and the sun to explain the discrepancies in the observed orbit of Mercury. But this never happened. Newton’s laws for gravitation was not able to fully explain the precession of Mercury orbit. There is a 43 arc second per century discrepancy in the Newtonian calculation and the modern observed value. This discrepancy demanded a new genius, Einstein, to solve this mystery and to tell how exactly the force of gravity operates as an action at a distance force.
But before Einstein, Physicists were in love with the second fundamental force of nature, i.e. electromagnetism. Although historically, Electricity and Magnetism developed as two different branches of physics. But with efforts of Orsted and Faraday and the equations of Maxwell, Physicists were able to unify these two seemingly different aspects of nature. This was the second unification that physicists discovered in nature, as the first was done by Newton’s laws of gravitation and unified the laws for terrestrial and celestial objects. Faraday was not from the formal educational background, so he could think in a much different manner and can see things differently. As a result, he developed the concept of field. And applied the concepts of electric and magnetic field lines to describe the action at a distance phenomenon related to these forces. And Maxwell provided a solid mathematical and experimental basis for these fields. The concept of the field was very useful and convincing in explaining the phenomenon of forces without contact.
Einstein, motivated by the work of Maxwell, took the concept of field one notch up and proposed the laws of gravity in a new Avatar. In 1915, Einstein proposed his theory of general relativity. It was the continuation of his work on special relativity that he proposed 10 years before in 1905. Special relativity was applicable for inertial frames of references that move unaccelerated but with a high speed comparable to light. But with the introduction of general relativity, the law can be applied for accelerated frames of reference also. With this generalization of relativity Einstein gave us the unified picture of gravity as a geometric property of space and time or simply space-time. Although, general relativity is a set of nonlinear partial differential field equations that works in Riemannian geometry and extremely difficult to solve, so much so that even Einstein used method of approximation to make predictions initially. But John Wheeler put this law in the simplest manner and says, “Spacetime tells matter how to move and matter tells spacetime how to curve.”
In 1907 Einstein tried to adapt the Newtonian law of gravitation (i.e. Poisson’s field equations) to the special theory of relativity. He also wanted to generalize the special relativity principle to accelerated motion. He then recognized that the key to the solution of his problem lies in Galileo’s law of free fall, namely the fact that all bodies fall with the same acceleration. Einstein formulated the equivalence principle: An observer free-falling with the acceleration due to gravity (of the earth) is equivalent to an observer in a locally flat region of spacetime with no gravity. The geometry used to describe motion in a local free-falling reference frame is the flat Minkowski spacetime geometry of special relativity.
In 1912 Einstein imagined a rotating disk, already in motion. Consider two reference frames, an inertial frame, and a disk frame. The disk is in a uniform rotation with respect to an observer in the inertial frame. An observer on the disk measures the disk’s circumference with small measuring rods. As viewed by the inertial observer, the measuring rods are contracted due to length contraction from special relativity, and more rods are needed to cover the circumference of the disk. Hence, the ratio between the circumference and the diameter would be larger than π. Einstein recognized that in his new gravitational theory he would not be able to use Euclidean geometry anymore; because as judged from the inertial frame, or what is the same thing, an observer at the origin of coordinates of the rotating disk (which does not rotate), the rods which cover the circumference undergo a Lorentz contraction.
In 1907 and 1911 he also found that light propagating through a gravitational field does not follow a straight line but curves in the direction of the field. Einstein suggested that we call the paths of photons of light the straightest lines or the shortest distance between points — called geodesic lines or geodesics. Spacetime is curved or is not flat anymore and particles move along geodesic lines.
Hence, locally we always and everywhere speak about Lorentz reference frames. No evidence of gravitation whatsoever is to be seen by following the motion of a single particle in a free-falling reference frame. An observer has to observe the relative acceleration of two particles slightly separated from each other to have any proper measure of gravitational effect and of the deviation from flat spacetime
The general relativity equation motion is the geodesic equation: when no other forces act on particles in curved spacetime, they would just follow the straightest possible line in curved spacetime, a geodesic. Locally a free-falling observer follows a geodesic which is a straight line in flat spacetime. Einstein described a curved spacetime by the metric tensor.
The equations of motion, i.e. the geodesic equation are: “curved spacetime tells matter how to move”. Earth moves on an elliptic trajectory around the sun because the spacetime around the sun is curved and it tells the earth how to move. However. the mass of the sun curves spacetime and this curved spacetime tells earth how to move.
The field equations of general relativity tell us how the source of mass-energy (or momentum-energy) causes curved spacetime, i.e. “mass tells spacetime how to curve”.
What is the source of mass-energy? it means that the field equations are non-linear because the gravitational field produced by some source contains energy and hence, by special relativity, mass; and this mass, in turn, is itself a source of the gravitational field. Therefore, the gravitational field is coupled to itself.
The mathematical formalism based on the Riemann curvature tensor and the Ricci tensor written in terms of the metric tensor (that represents curved spacetime) and the stress-energy tensor (which represents the source of mass-energy) was crucial to Einstein for constructing his field equations. The metric field (tensor) which represents curved spacetime, i.e. the inertia-gravitational field, is entirely determined by its sources – that is, by the stress-energy tensor.
With Einstein works on relativity, many things changed in Physics and the first among them was how should we interpret space and time. In the Newtonian classical world, spacetime is just a static stage on which events happen and the stage of spacetime remains unaffected. But in Einsteinian world spacetime is a dynamic actor which participates in the cosmic drama. Here space-time can curve, lengths can contract, time can pass at different rates. With his newly developed theory, Einstein was able to solve the mystery of the precession of Mercury orbit. Not only that Einstein predicted that light should bend near the massive stars. Einstein became the first to measure the correct value of light bending by sun i.e. 1.75 arc second. When Arthur Eddington performed the experiment to verify this value in a total solar eclipse on May 29, 1919, Einstein became a celebrity Physicist.
The first non-trivial solution of Einstein field equations was found out by Karl Schwarzschild in 1916 and famously known as Schwarzschild Metric and it became the basis of the concept of a black hole.
The success list of Einstein general relativity is never-ending. This model predicted the expansion of the universe, but influenced by his contemporary thinkers, Einstein introduced a cosmological constant in his field Equation so that it can result in a static and nonexpanding universe. But when in 1929, Edwin Hubble discovered that the universe is expanding, then Einstein regretted by saying the introduction of cosmological constant was the biggest blunder of his life. But save this blunder, as we will talk about it one more time, after all, it is not an ordinary blender, it is the blunder of the most genius person on the earth.
Ironically these successes of the Einstein model of gravity were not able to understand the gravity completely. Many questions remained unanswered, many mysteries are left to be resolved.
Two of them are dark matter and dark energy. Dark matter is those matter that don’t interact with electromagnetic fields and that’s why light can’t be reflected or absorbed by them. It comes into the picture to explain the motion, existence, and formation of several galaxies. Galaxies would fly apart, or they would not have formed or would not move as they do if they don’t contain a large amount of unseen matter or dark matter. As per current calculation dark matter accounts for 27% of the total matter in the universe having density 2.241*10^(-27) kilogram per cubic meter. While ordinary matter accounts for just 5% of the total matter content of the universe.
Dark energy is yet stranger. It is the unknown form of energy that affects the universe at the largest scale. Its evidence comes from supernovae measurement which shows that the rate of expansion of the universe is neither decreasing nor a constant, rather it is increasing. This accelerated expansion of the universe can’t be explained by ordinary matter or dark matter, both of which are attractive in nature. So we need a new type of energy that permeates the universe and causes the universe to expand at a higher rate by each passing moment.
Einstein general relativity fails to give an account for either dark matter or dark energy. But Einstein biggest blunder, the cosmological constant, is one of the two probable explanations for dark energy. The other one is the zero-point energy or vacuum energy.
The other unsolved mysteries of gravitation are why it is not compatible with quantum field theory. Currently, Physicists have two models for the universe. One is the quantum field model which successfully unifies electromagnetism, weak interactions, and strong interactions. The other model is Einstein general relativity which explains gravitational interactions. But when we try to find a quantum model for gravity by fusion of quantum field theory and general relativity, we fail. A lot has been done to achieve this model since the time of Einstein only. String theory, Loop quantum gravity all efforts have been made. But they all bring some absurd results with them. We need a quantum gravity model to explain the initial moments of the big bang and black hole. But still, we don’t have a working model for quantum gravity.
Another mystery with gravitation is that it is the weakest interaction of all. It is 10^38 times weaker than the strong interactions, 10^36 times weaker than Electromagnetic interaction, and 10^29 times weaker than weak interactions. So, a natural question arises, why gravity is so weak that we can generally ignore it’s effect while working with the other three interactions. But the effect of gravity and all other three interactions come together when the large mass is concentrated in a quantum system like a black hole or a big bang scenario. Here we fail miserably.
The most bizarre part of gravity is that it demands more than four known dimensions to be completely expressed. The string theory demands for 10 or 11 dimensions. And these higher Dimensions can solve the mystery of the strange weakness of gravity.
Finally, the work started by ancient philosophers, Physicists and astronomers have unsolved many mysteries and presented many new mysteries. So, the mystery of gravitation continues, the more we know it, the more mysterious it becomes.