Technical, Life as it is, Astrophysics, Advanced science

From Newton’s Gravitational Law to Einstein’s Gravitational waves

Visualisation of Newton’s gravitational attraction

Summer 1666, a young Cambridge University physics student by the name Isaac Newton was sitting under an apple tree in his mother’s garden at Woolsthorpe Manor in Lincolnshire, England. An apple fell from the tree on the ground and that triggered him to think: why did the apple come down straight to earth, not go sideways or upwards? That question led him to delve deeper into the mystery of attraction between two bodies and to come up with the law of gravity. He published his research work in “The Principia Mathematica” in 1687, where he described, among other things, this seminal work on the law of universal gravitation.  

This law of gravitation tells us that two bodies attract each other with a force which is proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between them. This simple empirical formula was astonishingly successful in calculating the force of attraction between two bodies on earth. This law was also applied to calculate the attractive force between the earth and the moon and to the orbital motion of the moon round the earth. The law was quite accurate in defining the orbits of many other celestial bodies, although in few cases the law was somewhat inaccurate.

This law was and still is the centre piece of what is now known as the ‘classical physics’ or ‘Newtonian Physics’. We all studied this law, Newton’s laws of motion, properties of matter, electricity and magnetism, heat and thermodynamics, optics etc in our schools and they gave the grounding for advanced physics.

For nearly 300 years this law was supreme and explained how the force of gravity controls the motions of all celestial bodies. However, the law did not say anything about the nature of this force or how the force is propagated through space; it just stated that the force diffuses through space without leaving any trace. As the predictions of the law were right in most of the cases, nobody bothered too much about these minor details or even ignored some minor discrepancies.    

At the turn of the 20th century, a patent clerk by the name Albert Einstein was working on patent submissions of electrical devices in Bern, Switzerland as a ‘Technical Expert, Third Class’ and in his spare time he was working on gravitational problems. The Patent Office work took up 48 hours of his time per week over six days. Einstein described his work load subsequently as, it left him with ‘eight hours for fooling around each day and then there is also Sunday!’.

In 1905 he published a technical paper outlining the Special Theory of Relativity giving revolutionary scientific ideas and concepts. In this paper, he introduced two fundamental concepts: the principle of relativity and the constancy of speed of light. The speed of light was stated to be independent of the speed of the observer. In other words, whether the observer moves in the direction of light or opposite to it, he would see the speed of light always remaining constant (c= 3*108 m/s). (It may be mentioned that in 1905, Albert Einstein produced three more monumental papers of enormous significance: (i) the mass-energy equivalence (E=mc2), (ii) Brownian motion of small particles, and (iii) photoelectric effects. For his work on photoelectric effects showing the particulate nature of light, which laid the foundation for quantum mechanics, he was awarded Nobel prize in 1921. As mentioned above, the year 1905 was extremely productive for Albert Einstein.

Visualisation of Einstein’s spacetime construct

Einstein developed his relativity concept even further and produced the General Theory of Relativity in 1915. In this General Theory of Relativity, he advanced the principle of spacetime, not space and time. He stipulated that the three dimensions of space (such as X, Y and Z dimensions of cartesian coordinates) and one dimension of time are not independent of each other, but intricately linked to form a single four-dimensional spacetime continuum.

This concept of spacetime continuum was revolutionary at that time and even now they make human beings baffled. The relativistic consideration has produced what is now called the time dilation. The passage of time is relative and so it depends on the motion of an observer relative to a stationary observer. Also, the passage of time depends on the location in a gravitational field. For example, a clock attached to an observer in a spaceship will tick slower than that of a clock attached to an observer in a stationary position. Also, a clock in a higher gravitational field, such as at the surface of earth, will tick slower than that of a clock in lower gravitational field such as the top of a mountain.

Let’s take an example. There were three men in the UK, all of them exactly of the same age, say, 25 years. They decided to offer themselves as guinea pigs for a research on gravity. One was asked to stay in Lincolnshire, England (not too far from Newton’s famous apple tree), the other was told to go and live high up in the Himalayan mountains and the third, most adventurer of the lot, got the opportunity to have a space travel in a superfast spaceship. The spaceship travelled fast and so his clock was ticking slowly. Let’s say his spaceship was so fast that one year in the spaceship clock was equal to five earth years and the mountain man clocked 10 minutes more than the Lincolnshire man in five years. When after five years they met on earth, they found that the mountain man was 10 minutes older than 30 years, Lincolnshire man was 30 years of earth age and the spaceship man was whopping four years younger than 30 years! To the spaceship man, it would look like he had come back four years in the future!     

Einstein stipulated that the gravitational field creates space and the bodies with masses bend and warp space; more like massive bodies create curvature in a trampoline. All less massive bodies fall into the curvature in the trampoline created by the massive bodies. When there are a large number of bodies warping the space, the space becomes jagged and celestial bodies move around in tortuous paths. There is no force of gravity pulling objects towards each other; just the bodies move around the jagged curved space along the path of least resistance.

Space, like any other force field, is discreet, quantised and granular. The quantum of space is dubbed as graviton, similar to the term photon in electromagnetic field, and it is so small that we cannot feel its discreteness, as we cannot feel the discreteness of photons of light or discreteness of atoms in a solid body.

Exactly hundred years after Einstein’s General Theory of Relativity, experimental evidence of gravitational field and gravitational wave have been produced by the LIGO (Laser Interferometer Gravitational-wave Observatory) experiment and shown that space is modulated by the gravitational field. A monochromatic laser beam of light was split and sent at right angles to each other along two arms, each of 4 km long. These beams were reflected back along the same path and allowed to interfere back at source. If there is no distortion or modulation of the path lengths, the two beams would interfere in anti-phases and there would be no interference patterns.

When two super massive black holes some 1.3 billion light years away merged and produced a gigantic massive black hole, an enormous amount of energy, equal to three solar masses, was produced and sent out as gravitational energy. It rippled through the whole universe in the form of gravitational wave at the speed of light and deformed the spacetime fabric. That deformation in spacetime was detected by the LIGO experiment in the form of interference pattern and that proves that gravitational waves modulates the space. 

The implication of Einstein’s spacetime is that at the very beginning when even the ‘Big Bang’ did not take place, there was no spacetime. Spacetime came into existence following that ‘Big Bang’, when gravity came into play along with other forces such as electrical force, strong nuclear force and weak nuclear force. If at the end, as Physics predicts, the whole universe starts to collapse, there would be what is called the ‘Big Crunch’ and the spacetime would collapse too and disappear. There will be nothing, no material, no space and no time. These are the predictions of scientific theories as exist today.

In 1930 when Einstein came to London as the guest of honour at a fundraising dinner to help the East European Jews, George Bernard Shaw, the chief guest, said humourously, “Ptolemy made a universe which lasted for 1400 years. Newton made a universe which lasted for 300 years. Einstein has made a universe, and I can’t tell you how long that will last.” The audience laughed loudly, but none louder than Einstein.

  • Dr A Rahman is an author and a columnist


Advanced science, Astrophysics, International, Technical

Stephen Hawking: The supernova of cosmology

In 1974, by predicting the apparently paradoxical concept of radiation emanating from black holes, Hawking reminded us that mass and energy are two sides of the same coin.

Stephen-Hawking5

We humans are a recent phenomenon in the Universe that is very old, mostly imperceptible and beyond our comprehension. Had it not been for great scientists like Isaac Newton, Albert Einstein, Edwin Hubble, Karl Schwarzschild, Subrahmanyan Chandrasekhar, Stephen Hawking and many more who unlocked the enduring mysteries of the boundless Universe, it would have been a struggle for lesser mortals like us getting our bearings straightened about our place in the cosmos. Their ground-breaking work, forever, changed our view of the “heavens.”

Postulated in 1687, Newton’s law of gravity was a beautiful synthesis between terrestrial and celestial phenomenon, reaching across the vast expanse of the Universe. It allows us to study the waltzing motion of the planets, moons, stars and other objects in the sky with clockwork precision.

Einstein’s special relativity, published in 1905, tells us that time is not only elastic, it is also the fourth component of the spacetime fabric of the Universe. Ten years later, his general relativity redefined gravity as matter’s response to the curving of spacetime caused by surrounding massive objects.

In 1916, Schwarzschild found that the solution of Einstein’s general relativity equations characterized something that confounds common sense ‒ an unfathomable hole drilled in the superstructure of the Universe. Today, we call this voracious gravitational sinkhole a black hole, a single point of zero volume and infinite density.

Much to Einstein’s consternation, in 1929, Hubble discovered that the Universe is expanding in size. His “constant” enabled us to estimate the age of the Universe. In 1930, Chandrasekhar’s calculations indicated that when a massive star runs out of fuel, it would blow itself apart in a spectacular but violent explosion and then collapse into a black hole.

Black holes were discovered in 1971, when astronomers detected a hint of radio wave emissions coming from an object in the constellation Cygnus. The emissions were later interpreted as the fingerprint of the black hole Cygnus X-1. Since then, numerous black holes, including supermassive ones, have been detected in our own Galaxy ‒ The Milky Way, and elsewhere in the Universe. According to NASA, supermassive black holes are growing faster than the rate at which stars are being formed in their galaxies.

Cloaked behind the event horizon, which is not a physical barrier but just an information barrier, it must seem that there is no way of getting mass from the black hole back out into outer space. No way, that is, not until the British physicist Stephen Hawking, arguably one of the greatest minds in scientific history, joined the Big League of Cosmology in the mid-twentieth century. With his seminal contributions to the fields of astrophysics, general relativity, quantum gravity and black holes, he raised the field of cosmology from a niche topic to a well-developed subject in the forefront of science.

In 1974, by predicting the apparently paradoxical concept of radiation emanating from black holes, Hawking reminded us that mass and energy are two sides of the same coin. He was able to show that a black hole, like any other body whose temperature is not absolute zero, emits energy in the form of radiation, energy now known as Hawking Radiation.

The continual emission of radiation causes the black hole to shrink in mass. In other words, black holes “evaporate,” although the time it takes for a solar-mass black hole to evaporate completely is immensely long ‒ vastly larger than the age of the Universe, which is 13.7 billion years. The implications are nonetheless important ‒ even black holes evolve and die.

One of the Gordian knots of cosmology is the missing mass of the Universe. There is irrefutable evidence that visible matter accounts for only four percent of the Universe’s mass. The remaining 96 percent is invisible of which 73 percent is attributed to a pervasive “dark energy,” believed to be manifestation of an extremely powerful repulsive force that is causing the expansion of the Universe to accelerate. The additional 23 percent is thought to be dark matter whose origin obviously is the many black holes spread throughout the cosmos. However, their total mass does not add up to account for all the dark matter.

To address this issue, in 1971, Hawking advanced the idea that in the intergalactic space, there may be “mini” black holes with very small masses ‒ much smaller than the mass of the Earth ‒ yet numerous enough to account for most of the unaccounted dark matter. He hypothesized that they may have been formed during the first instants of chaos following the Big Bang when matter existed in a hot, soupy plasma. Since mini black holes have not been detected so far, Hawking lamented: “This is a pity, because if they had, I would have got a Nobel Prize.”

During the 1980s, Hawking devoted much of his time contributing to the theory of cosmic inflation ‒ the expansion of the Universe at an exponential pace before settling down to expand at a slower pace. In particular, he demonstrated how minuscule variations in the distribution of matter during this period of expansion, known as the Planck era, helped shape the spread of galaxies in the Universe.

As noted above, the core remnant of a high-mass star would eventually collapse all the way to a point ‒ a so-called singularity. Having said that, singularities are places where laws of physics break down. Consequently, some very strange things may occur near them. As suggested by Hawking, these strange things could be, for instance, gateway to other universes, or time travel, but none has been proved, and certainly none has been observed. These suggestions cause serious problems for many of our cherished laws of physics, including causality ‒ the idea that cause should precede the effect, which runs into immediate problem if time travel is possible ‒ and energy conservation, which is violated if matter can hop from one universe to another through a black hole.

While scientists know Hawking for his work on cosmology, millions of others know him because of his book “A Brief History of Time.” His lucid explanation of the mechanism leading to the creation of the Universe, our place in it, how we got there, where did space and time come from, and where we might be going made the notoriously difficult subject of cosmology more understandable to the layperson.
In a follow-up book titled “The Grand Design,” Hawking outlines his consuming quest for the long-dreamed-of “Theory of Everything,” the quantum theory of gravity. Such a theory would unify the two pillars of twentieth century physics, general relativity and quantum theory.

Known as the M-Theory (M stands for Mother-of-All), it would enable us to understand all phenomena in space-time, especially the first split second of cosmic creation, when everything was unimaginably small and densely packed.

Hawking was about as pure an atheist as one can be. He dismissed the existence of an omnipotent by noting that “regularities in the motion of astronomical bodies such as the sun, the moon, and the planets suggested that they were governed by fixed laws rather than being subjected to the arbitrary whims of gods and demons.” Nevertheless, in December 2016, he had a surprising but cordial encounter with Pope Francis at a convention on Big Bang in Rome.

Besides being a genius, Hawking’s celebrity status derives from his spunk in the face of physical adversity. Born on 8 January 1942 in Oxford, England, Hawking was diagnosed with a debilitating, incurable neuromuscular disorder, commonly known as motor neurone disease (MND), when he was just 21 years old. Although doctors predicted that he has only two more years to live, he lived another 55 years and died on 14 March, 2018. There are some interesting anecdotal coincidences. Hawking was born on the 300th anniversary of Galileo’s death and died on the 139th anniversary of Einstein’s birth. Following his cremation, his ashes will be interred on 15th June 2018 in Westminster Abbey’s nave, next to the grave of Isaac Newton and close to Charles Darwin.

Instead of ruing about his mortality, Hawking considered his illness as a blessing, allowing him, in his own words, “to focus more resolutely on what he could do with his life.” Indeed, with a crumpled, voiceless body ensconced in a wheelchair, he soared and established an exalted scientific reputation as the most recognizable scientist of the modern era. The name of this supernova of cosmology will be engraved in the sands of time as long as humanity lives.

The writer, Quamrul Haider, is a Professor of Physics at Fordham University, New York

 

International, Life as it is, Technical

Gravitational Waves

Gravitational waves, space-time deformation, quantum gravity etc are now the buzz words in the scientific as well as non-scientific parlance. People tend to show off their academic pedigree by frequently and quite often inappropriately using these terms and baffling their audience, but now they can have some inkling of the implications of these terms. These terms ushered in a new frontier of scientific discipline in the general area of cosmology. A new scientific toolkit has been invented for the cosmologists and astrophysicists to use.

If the early part of the 20th century could be categorised as the age of theory of relativity (produced by Einstein in 1905 and in 1916) and then the age of quantum mechanics (produced by Max Planck, Niels Bohr, Heisenberg, Schrodinger and others), then this part of the 21st century can surely be ascribed as the age of gravitational waves.

But the invention of gravitational wave now is not a fortuitous event. Back in 1916, when Einstein produced the general theory of relativity, he stipulated space-time continuum. But nobody, except a few elites in theoretical physics, had the faintest idea what it really means.

According to general relativity, gravity is a manifestation of the curvature of space-time. Space-time becomes curved and time slows down in the presence of material body. The more the mass, the greater is the curvature and slower is the time. When a massive body moves, the curvature moves with it to a new position stretching the space in one direction and compressing it in another direction. This deformation in space-time produces ripples, called gravitational waves, which travel outward from the gravitational source at the speed of light. But there is no light involved, only gravitational energy travels at the speed of light.

In a more mundane way one can say that when a body is attracted and moves towards another body, it follows the curved space-time fabric. When there are a number of bodies, the space-time curvature becomes quite jagged and a body travelling in that space follows a tortuous path.

It may, however, be mentioned here that there is no scientific reason why bodies should always attract each other, as they do in our observable universe. In another parallel universe, it may be that bodies repel each other or some bodies repel each other, while others attract each other. When these attracting and repelling bodies are scattered randomly in the vast space, they may stabilise and create a stable universe – all attracting bodies may not collapse and all repelling bodies may not push each other into infinity.

How does this gravitational attraction get propagated between the bodies? Drawing analogy between the electromagnetic energy and gravitational energy, physicists coined the term ‘graviton’ for gravitational energy, as ‘photon’ for electromagnetic energy. The photon is the smallest packet of energy (the quantum of energy) that came into the jargon of physics following Einstein’s theory of photoelectric effect in 1905. It may be mentioned that Einstein received Nobel prize for his theory of photoelectric effect, not for the theory of relativity; although both of these theories are of immense importance and monumental in physical sciences.

Whereas photon had been detected experimentally, graviton had never been detected. How come, despite all the predictions of the general theory of relativity being found to be meticulously accurate, the central plank of this theory involving gravitational waves had been left undetected? Now that gap has been filled. This recent discovery of gravitational waves may eventually lead to the identification of graviton. But whether graviton comes into the scientific arena or not, gravitational wave is now a reality.

When the LIGO (Laser Interferometer Gravitational-wave Observatory) collaborative experiments in Baton Rouge, Louisiana and in Hanford, Washington State first detected the gravitational wave, they hesitated to make it public. It was so earth shattering that the researchers had to make it absolutely certain that the results are genuine, not spurious. After all, no scientist wants egg on his face! On September 14, 2015 they disclosed the detection of gravitational waves.

When two super massive black holes some 1.3 billion light years away, one 36 times and the other 29 times of the mass of the Sun, spiralled around each another and eventually merged, a gigantic massive black hole was created. And in the final half a second or so in this cataclysmic event, a massive amount of energy was produced. It had been estimated that the final black hole, instead of having 65 times the mass of Sun was 62 times and the remaining three solar masses had been converted to gravitational energy. This energy was so massive that it rippled through the entire universe at the speed of light and deformed the space-time fabric in the form of gravitational waves. It may be noted that there was no emission of light at all from the collapse of those spiralling black holes – the energy was all gravitational energy. The generated energy from the conversion of three solar masses (each having a mass of 2×1030kg) was absolutely staggering (~ 5×1047 J).

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At the LIGO facility, a monochromatic laser beam was produced and then split in two directions at the point of origin. The facility comprises two arms at right angles to each other and each arm is 4 km long through which the laser beams travel. At the edge of these arms, precisely positioned reflecting mirrors are placed. The reflected beams are allowed to interfere back at the source. If there is no space distortion due to ripples in the space time, the reflected beams combining in anti-phases will cancel each other and there will be no interference pattern. On the other hand, if the arms of the facility are deformed due to stretching and compression by the incoming gravitational wave, there would be interference. This physical deformation is extremely small – trillion times smaller than the width of a human hair (~ 10-18 m) – and even with the emission of astounding amount of energy (~ 5×1047 J, an extreme precision in detection by laser interferometer was needed.

Since that discovery in 2015, more black hole mergers of smaller sizes had been detected. That shows that the technique is becoming more refined and sensitive. Even smaller masses than black holes can create ripples in gravitational waves and they may be detected by this technique. In September 2017 LIGO had been closed for about a year for upgrade. But before shutdown, on August 17, 2017, LIGO detected gravitational waves produced by the collision of two neutron stars in the galaxy Hydra, 130 million light years away. This is the first time that collision between stars had been detected. In August, a new facility in Italy, called the Virgo interferometer, had joined in. India also is going to build a facility in Maharashtra, which is similar to LIGO facility in Washington State and plan to start its operation in 2024.

This gravitational wave may be a cosmic messenger, which may lead human beings to probe right into the origin of the universe. This is the exciting time not only for cosmologists and astrophysicists but also for humanity as a whole; no longer we will have to rely on myths and mysteries passed down from generations to generations of the creation of universe.

 

  • Dr A Rahman is an author and a columnist.