Earlier, a cosmology with changing physical values for the gravitational constant G was proposed by P.A.M. Dirac in 1937. Field theories applying this principle have been proposed by P. Jordan and D.W. Sciama and in 1961 by C. Brans and R.H. Dicke. According to these theories the value of G is diminishing. Brans and Dicke suggested a change of about 0.00000000002 per year. This theory has not been accepted on the ground that it would have profound effect on the phenomena ranging from the evolution of the Universe to the evolution of the Earth. For instance, stars evolve faster if G is greater. Thus, the stellar evolutionary ages computed with constant G at its present value would be too great. The Earth compressed by gravitation would expand having a profound effect on surface features. The Sun would have been hotter than it is now and the Earth’s orbit would have been smaller. No one bothered to check whether such a scenario existed or is possible. Our studies in this regard show that the above scenario did happen. We have data to prove the above point.
Precise measurements in 1999 gave so divergent values of G from the currently accepted value that the result had to be pushed under the carpet, as otherwise most theories of physics would have tumbled. Presently, physicists are measuring gravity by bouncing atoms up and down off a laser beam (arXiv:0902.0109). The experiments have been modified to perform atom interferometry, whereby quantum interference between atoms can be used to measure tiny accelerations. Those still using the earlier value of G in their calculations, land in trajectories much different from their theoretical calculations. Thus, modern science is based on a value of G that has been proved to be wrong. The Pioneer and Fly-by anomalies and the change of direction of Voyager 2 after it passed the orbit of Saturn have cast a shadow on the authenticity of the theory of gravitation. Till now these have not been satisfactorily explained. We have discussed these problems and explained a different theory of gravitation in later pages.
According to reports published in several scientific journals, precise measurements of the light from distant quasars and the only known natural nuclear reactor, which was active nearly 2 billion years ago at what is now Oklo in Gabon suggest that the value of the fine-structure constant may have changed over the history of the universe (Physical Review D, vol 69, p 121701). If confirmed, the results will be of enormous significance for the foundations of physics. Alpha is an extremely important constant that determines how light interacts with matter – and it shouldn’t be able to change. Its value depends on, among other things, the charge on the electron, the speed of light and Planck’s constant. Could one of these really have changed?
If the fine-structure constant changes over time, it allows postulating that the velocity of light might not be constant. This would explain the flatness, horizon and monopole problems in cosmology. Recent work has shown that the universe appears to be expanding at an ever faster rate, and there may well be a non-zero cosmological constant. There is a class of theories where the speed of light is determined by a scalar field (the force making the cosmos expand, the cosmological constant) that couples to the gravitational effect of pressure. Changes in the speed of light convert the energy density of this field into energy. One off-shoot of this view is that in a young and hot universe during the radiation epoch, this prevents the scalar field dominating the universe. As the universe expands, pressure-less matter dominates and variations in c decreases making α (alpha) fixed and stable. The scalar field begins to dominate, driving a faster expansion of the universe. Whether the variation of the fine-structure constant claimed exists or not, putting bounds on the rate of change puts tight constraints on new theories of physics.
One of the most mysterious objects in the universe is what is known as the black hole – a derivative of the general theory of relativity. It is said to be the ultimate fate of a super-massive star that has exhausted its fuel that sustained it for millions of years. In such a star, gravity overwhelms all other forces and the star collapses under its own gravity to the size of a pinprick. It is called a black hole as nothing – not even light – can escape it. A black hole has two parts. At its core is a singularity, the infinitesimal point into which all the matter of the star gets crushed. Surrounding the singularity is the region of space from which escape is impossible – the perimeter of which is called the event horizon. Once something enters the event horizon, it loses all hope of exiting. It is generally believed that a large star eventually collapses to a black hole. Roger Penrose conjectured that the formation of a singularity during stellar collapse necessarily entails the formation of an event horizon. According to him, Nature forbids us from ever seeing a singularity because a horizon always cloaks it. Penrose’s conjecture is termed the cosmic censorship hypothesis. It is only a conjecture. But some theoretical models suggest that instead of a black hole, a collapsing star might become a naked singularity.
Most physicists operate under the assumption that a horizon must indeed form around a black hole. What exactly happens at a singularity – what becomes of the matter after it is infinitely crushed into oblivion – is not known. By hiding the singularity, the event horizon isolates this gap in our knowledge. General relativity does not account for the quantum effects that become important for microscopic objects, and those effects presumably intervene to prevent the strength of gravity from becoming truly infinite. Whatever happens in a black hole stays in a black hole. Yet Researchers have found a wide variety of stellar collapse scenarios in which an event horizon does not form, so that the singularity remains exposed to our view. Physicists call it a naked singularity. In such a case, Matter and radiation can both fall in and come out, whereas matter falling into the singularity inside a black hole would land in a one-way trip.
In principle, we can come as close as we like to a naked singularity and return back. Naked singularities might account for unexplained high-energy phenomena that astronomers have seen, and they might offer a laboratory to explore the fabric of the so-called space-time on its finest scales. The results of simulations by different scientists show that most naked singularities are stable to small variations of the initial setup. Thus, these situations appear to be generic and not contrived. These counterexamples to Penrose’s conjecture suggest that cosmic censorship is not a general rule.
The discovery of naked singularities would transform the search for a unified theory of physics, not the least by providing direct observational tests of such a theory. It has taken so long for physicists to accept the possibility of naked singularities because they raise a number of conceptual puzzles. A commonly cited concern is that such singularities would make nature inherently unpredictable. Unpredictability is actually common in general relativity and not always directly related to cosmic censorship violation described above. The theory permits time travel, which could produce causal loops with unforeseeable outcomes, and even ordinary black holes can become unpredictable. For example, if we drop an electric charge into an uncharged black hole, the shape of space-time around the hole radically changes and is no longer predictable. A similar situation holds when the black hole is rotating.
Specifically, what happens is that space-time no longer neatly separates into space and time, so that physicists cannot consider how the black hole evolves from some initial time into the future. Only the purest of pure black holes, with no charge or rotation at all, is fully predictable. The loss of predictability and other problems with black holes actually stem from the occurrence of singularities; it does not matter whether they are hidden or not. Cosmologists dread the singularity because at this point gravity becomes infinite, along with the temperature and density of the universe. As its equations cannot cope with such infinities, general relativity fails to describe what happens at the big bang.
In the mid 1980s, Abhay Ashtekar rewrote the equations of general relativity in a quantum-mechanical framework to show that the fabric of space-time is woven from loops of gravitational field lines. The theory is called the loop quantum gravity. If we zoom out far enough, the space appears smooth and unbroken, but a closer look reveals that space comes in indivisible chunks, or quanta, 10-35 square meters in size. In 2000, some scientists used loop quantum gravity to create a simple model of the universe. This is known as the LQC. Unlike general relativity, the physics of LQC did not break down at the big bang. Some others developed computer simulations of the universe according to LQC. Early versions of the theory described the evolution of the universe in terms of quanta of area, but a closer look revealed a subtle error. After this mistake was corrected it was found that the calculations now involved tiny volumes of space. It made a crucial difference. Now the universe according to LQC agreed brilliantly with general relativity when expansion was well advanced, while still eliminating the singularity at the big bang. When they ran time backwards, instead of becoming infinitely dense at the big bang, the universe stopped collapsing and reversed direction. The big bang singularity had disappeared (Physical Review Letters, vol.96, p-141301). The era of the Big Bounce has arrived. But the scientists are far from explaining all the conundrums.
Often it is said that the language of physics is mathematics. In a famous essay, Wigner wrote about the “unreasonable effectiveness of mathematics”. Most physicists resonate with the perplexity expressed by Wigner and Einstein’s dictum that “the most incomprehensible thing about the universe is that it is comprehensible”. They marvel at the fact that the universe is not anarchic – that atoms obey the same laws in distant galaxies as in the lab. Yet, Gödel’s Theorem implies that we can never be certain that mathematics is consistent: it leaves open the possibility that a proof exists demonstrating that 0=1. The quantum theory tells that, on the atomic scale, nature is intrinsically fuzzy. Nonetheless, atoms behave in precise mathematical ways when they emit and absorb light, or link together to make molecules. Yet, is Nature mathematical?
Language is a means of communication. Mathematics cannot communicate in the same manner like a language. Mathematics on its own does not lead to a sensible universe. The mathematical formula has to be interpreted in communicable language to acquire some meaning. Thus, mathematics is only a tool for describing some and not all ideas. For example, “observer” has an important place in quantum physics. Everett addressed the measurement problem by making the observer an integral part of the system observed: introducing a universal wave function that links observers and objects as parts of a single quantum system. But there is no equation for the “observer”.
We have not come across any precise and scientific definition of mathematics. Concise Oxford Dictionary defines mathematics as: “the abstract science of numbers, quantity, and space studied in its own right”, or “as applied to other disciplines such as physics, engineering, etc”. This is not a scientific description as the definition of number itself leads to circular reasoning. Even the mathematicians do not have a common opinion on the content of mathematics. There are at least four views among mathematicians on what mathematics is. John D Barrow calls these views as:
Platonism: It is the view that concepts like groups, sets, points, infinities, etc., are “out there” independent of us – “the pie is in the sky”. Mathematicians discover them and use them to explain Nature in mathematical terms. There is an offshoot of this view called “neo-Platonism”, which likens mathematics to the composition of a cosmic symphony by independent contributors, each moving it towards some grand final synthesis. Proof: completely independent mathematical discoveries by different mathematicians working in different cultures so often turn out to be identical.
Conceptualism: It is the anti-thesis of Platonism. According to this view, scientists create an array of mathematical structures, symmetries and patterns and force the world into this mould, as they find it so compelling. The so-called constants of Nature, which arise as theoretically undetermined constants of proportionality in the mathematical equations, are solely artifacts of the peculiar mathematical representation they have chosen to use for different purposes.
Formalism: This was developed during the last century, when a number of embarrassing logical paradoxes were discovered. There was proof which established the existence of particular objects, but offered no way of constructing them explicitly in a finite number of steps. Hilbert’s formalism belongs to this category, which defines mathematics as nothing more than the manipulation of symbols according to specified rules (not natural, but sometimes un-physical man-made rules). The resultant paper edifice has no special meaning at all. If the manipulations are done correctly, it should result in a vast collection of tautological statements: an embroidery of logical connections.
Intuitionism: Prior to Cantor’s work on infinite sets, mathematicians had not made use of actual infinities, but only exploited the existence of quantities that could be made arbitrarily large or small – the concept of limit. To avoid founding whole areas of mathematics upon the assumption that infinite sets share the “obvious” properties possessed by finite one’s, it was proposed that only quantities that can be constructed from the natural numbers 1,2,3,…, in a finite number of logical steps, should be regarded as proven true.
None of the above views is complete because it neither is a description derived from fundamental principles nor conforms to a proper definition of mathematics, whose foundation is built upon logical consistency. The Platonic view arose from the fact that mathematical quantities transcend human minds and manifests the intrinsic character of reality. A number, say three or five codes some information differently in various languages, but conveys the same concept in all civilizations. They are abstract entities and mathematical truth means correspondence between the properties of these abstract objects and our system of symbols. We associate the transitory physical objects such as three worlds or five sense organs to these immutable abstract quantities as a secondary realization. These ideas are somewhat misplaced. Numbers are a property of all objects by which we distinguish between similars. If there is nothing similar to an object, it is one. If there are similars, the number is decided by the number of times we perceive such similars (we may call it a set). Since perception is universal, the concept of numbers is also universal.