Stephen Hawking is an English theoretical physicist, cosmologist, and an author, and his work with the University of Cambridge includes singularity theorems. In 2002, Hawking was ranked no 25 in BBC’s poll of the 100 Greatest Britons.
He was the Lucasian professor of mathematics at Cambridge University from 1979 to 2009. His book, A Brief History of Time, appeared on the British Sunday Times bestseller list for a record breaking 237 weeks. Hawking has a rare slow progressing form of amyotrophic lateral sclerosis that has gradually paralysed him over the decades and he now communicates using a single cheek muscle attached to a speech generating device.
Hawking has, very recently, allowed his 1966 doctoral thesis to be available online, thereby providing a glimpse into his mind as a 24-year-old student. His thesis titled, Properties of Expanding Universes, has been made accessible through Cambridge’s open access repository, Apollo. Previously a paper copy of his thesis was available for purchase, at Cambridge, for a fee of $85.
Hawking in this generous gesture welcomes the world with his words, “Anyone, anywhere in the world, should have free unhindered access not just to my research but to the research of every great and enquiring mind across the spectrum of human understanding.” His 119-page thesis has two parts with an Introduction to the Properties of Expanding Universes, followed by four chapters of the main presentation, including one chapter, “Singularities” where he has quoted Professor A Raychoudhuri, who is a theoretical particle physicist at Calcutta University. Hawking enlightens one through his Introduction, which elaborates on how the four chapters are linked by the Hoyle-Narlikar theory of gravitation, perturbation, gravitational radiation in an expanding universe and singularities.
The thesis includes several pages that feature complicated mathematical equations, hand written by Hawking. A few aspects have been briefly described, in this narrative, from Hawking’s Introduction to his famous thesis. The implications and consequences of the expansion of the universe are examined. Hawking explains that this expansion creates grave difficulties for the HoyleNarlikar theory of gravitation.
He elaborates on perturbation (a disturbance) of an expanding, homogeneous and isotropic universe (Isotropic is a physical property having the same value when measured in different directions.) Hawking concludes that galaxies cannot be formed as the result of the growth of perturbations, because initially they were small. The propagation and absorption of gravitational radiation is also investigated. Gravitational radiation in the expanding universe is examined by a method of symptotic expansions, or constituting a symptom, like the “peeling off” behaviour.
The occurrence of singularities in cosmological models is also defined. It is explained that a singularity is inevitable provided that certain general conditions are satisfied. The initial singularity was the gravitational singularity of infinite density thought to have contained all the mass and space-time of the universe. This was prior to the Big Bang and subsequent inflation, creating the present day universe. He affirms that the idea of the universe expanding is of recent origin.
All the early cosmologies were essentially stationary and even Einstein whose theory of relativity is the basis for almost all solar developments in cosmology, found it natural to suggest a static model of the universe. But Hawking saw a grave difficulty associated with a static model, such as Einstein’s. The stars had been radiating energy at their present rates for an infinite time and would have needed an infinite supply of energy.
If the stars had only a limited supply of energy then the entire universe would have reached thermal equilibrium, which is not the case. Olbers, a German scientist, known as the “Dark night sky paradox,” emphasised that the night sky conflicts with the assumption of an infinite and eternal static universe. Hawking adds that the recent expansion of the universe may have occurred by a contraction, which in turn may have been preceded by another expansion, the “bouncing” or “oscillating” model.
But this suffers from the same problem as the static model. It is thought that one of the weaknesses of Einstein’s theory of relativity is that although it furnishes field equations it does not provide boundary conditions for them. As a result it does not give a unique model for the universe but instead allows a whole series of models. Clearly, a theory providing boundary conditions and thus restricting possible solutions would be very attractive. Hawking suggests that science can postulate on some form of continual creation of matter in order to prevent the expansion from reducing the density. This leads to yet another model —the “steady state”.
He states that from the time of Copernicus, we have been demoted to a medium sized star somewhere near the edge of a fairly average galaxy; we are so humble that we would not claim to occupy any special position. This thesis helped launch Hawking and formed the bedrock of his reputation as one of the world’s most famous scientists.
He has, by circulating this valuable document, reflected his thoughts, “Look up at the stars and not down at your feet. Try to make sense of what you see and wonder about what makes the universe exist. Be curious.”