Penrose spent the academic year 1956–57 as an assistant lecturer at Bedford College (now
Royal Holloway, University of London) and was then a research fellow at
St John's College, Cambridge. During that three-year post, he married Joan Isabel Wedge, in 1959. Before the fellowship ended Penrose won a
NATO Research Fellowship for 1959–61, first at
Princeton University and then at
Syracuse University. Returning to the
University of London, Penrose spent 1961–1963 as a researcher at
King's College, London, before returning to the United States to spend 1963–64 as a visiting associate professor at the
University of Texas at Austin. He later held visiting positions at
Yeshiva University, Princeton and
Cornell University during 1966–67 and 1969.
Dennis Sciama drew his attention from pure mathematics to astrophysics. Until then, work on the curved geometry of general relativity had been confined to configurations with sufficiently high symmetry for Einstein's equations to be solvable explicitly, and there was doubt about whether such cases were typical. One approach to this issue was by the use of
perturbation theory, as developed under the leadership of
John Archibald Wheeler at Princeton. The other, and more radically innovative, approach initiated by Penrose was to overlook the detailed geometrical structure of spacetime and instead concentrate attention just on the topology of the space, or at most its
conformal structure, since it is the latter – as determined by the lay of the lightcones – that determines the trajectories of lightlike geodesics, and hence their causal relationships. The importance of Penrose's paper "Gravitational Collapse and Space-Time Singularities" (summarised roughly as that if an object such as a dying star implodes beyond a certain point, then nothing can prevent the gravitational field getting so strong as to form some kind of singularity) was not its only result. It also showed a way to obtain similarly general conclusions in other contexts, notably that of the cosmological
Big Bang, which he dealt with in collaboration with Sciama's student
Stephen Hawking. of a
black hole lit by a thin accretion disc It was in the local context of gravitational collapse that the contribution of Penrose was most decisive, starting with his 1969 cosmic censorship conjecture, to the effect that any ensuing singularities would be confined within a well-behaved
event horizon surrounding a hidden space-time region for which Wheeler coined the term
black hole, leaving a visible exterior region with strong but finite curvature, from which some of the gravitational energy may be extractable by what is known as the
Penrose process, while accretion of surrounding matter may release further energy that can account for astrophysical phenomena such as
quasars. Following up his "weak
cosmic censorship hypothesis", Penrose went on, in 1979, to formulate a stronger version called the "strong censorship hypothesis". Together with the
Belinski–Khalatnikov–Lifshitz conjecture and issues of nonlinear stability, settling the censorship conjectures is one of the most important outstanding problems in
general relativity. Also from 1979 dates Penrose's influential
Weyl curvature hypothesis on the initial conditions of the observable part of the universe and the origin of the
second law of thermodynamics. Penrose and James Terrell independently realised that objects travelling near the speed of light will appear to undergo a peculiar skewing or rotation. This effect has come to be called the
Terrell rotation or Penrose–Terrell rotation. |alt= In 1967 Penrose invented the
twistor theory, which maps geometric objects in
Minkowski space into the 4-dimensional complex space with the metric signature (2,2). Penrose is well known for his 1974 discovery of
Penrose tilings, which are formed from two tiles that can only
tile the plane nonperiodically, and are the first tilings to exhibit fivefold rotational symmetry. In 1984 such patterns were observed in the arrangement of atoms in
quasicrystals. Another noteworthy contribution is his 1971 invention of
spin networks, which later came to form the geometry of
spacetime in
loop quantum gravity. He was influential in popularising what are commonly known as
Penrose diagrams (causal diagrams). In 1983, Penrose was invited to teach at
Rice University in Houston, by the then provost Bill Gordon. He worked there from 1983 to 1987. His doctoral students have included, among others,
Andrew Hodges,
Lane Hughston,
Richard Jozsa,
Claude LeBrun,
John McNamara,
Tristan Needham,
Tim Poston,
Asghar Qadir, and
Richard S. Ward. In 2004 Penrose released
The Road to Reality: A Complete Guide to the Laws of the Universe, a 1,099-page comprehensive guide to the
Laws of Physics that includes an explanation of his own theory. The
Penrose Interpretation predicts the relationship between
quantum mechanics and
general relativity, and proposes that a
quantum state remains in
superposition until the difference of
space-time curvature attains a significant level. Penrose is the Francis and Helen Pentz Distinguished Visiting professor of Physics and Mathematics at
Pennsylvania State University.
An earlier universe image of the (extremely tiny) anisotropies in the
cosmic background radiation In 2010 Penrose reported possible evidence, based on concentric circles found in
Wilkinson Microwave Anisotropy Probe data of the
cosmic microwave background sky, of an earlier universe existing before the
Big Bang of the present universe. He mentions this evidence in the epilogue of his 2010 book
Cycles of Time, a book in which he presents his reasons, to do with
Einstein's field equations, the
Weyl curvature C, and the
Weyl curvature hypothesis (WCH), that the transition at the Big Bang could have been smooth enough for a previous universe to survive it. He made several conjectures about C and the WCH, some of which were subsequently proved by others, and he also popularized his
conformal cyclic cosmology (CCC) theory. In this theory, Penrose postulates that at the end of the universe all matter is eventually contained within black holes, which subsequently evaporate via
Hawking radiation. At this point, everything contained within the universe consists of
photons, which "experience" neither time nor space. There is essentially no difference between an infinitely large universe consisting only of photons and an infinitely small universe consisting only of photons. Therefore, a singularity for a Big Bang and an infinitely expanded universe are equivalent. In simple terms, Penrose believes that the singularity in
Einstein's field equation at the Big Bang is only an apparent singularity, similar to the well-known apparent singularity at the
event horizon of a
black hole. One implication of this is that the major events at the Big Bang can be understood without unifying general relativity and quantum mechanics, and therefore we are not necessarily constrained by the
Wheeler–DeWitt equation, which disrupts time. Alternatively, one can use the Einstein–Maxwell–Dirac equations.
Consciousness Penrose has written books on the connection between fundamental physics and human (or animal) consciousness. In ''
The Emperor's New Mind (1989), he argues that known laws of physics are inadequate to explain the phenomenon of consciousness. Penrose proposes the characteristics this new physics may have and specifies the requirements for a bridge between classical and quantum mechanics (what he calls correct quantum gravity''). Penrose uses a variant of
Turing's halting theorem to demonstrate that a system can be
deterministic without being
algorithmic. (For example, imagine a system with only two states, ON and OFF. If the system's state is ON when a given
Turing machine halts and OFF when the Turing machine does not halt, then the system's state is completely determined by the machine; nevertheless, there is no algorithmic way to determine whether the Turing machine stops.) Penrose believes that such deterministic yet non-algorithmic processes may come into play in the quantum mechanical
wave function reduction, and may be harnessed by the brain. He argues that computers today are unable to have intelligence because they are algorithmically deterministic systems. He argues against the viewpoint that the rational processes of the mind are completely algorithmic and can thus be duplicated by a sufficiently complex computer. This contrasts with supporters of
strong artificial intelligence, who contend that thought can be simulated algorithmically. He bases this on claims that consciousness transcends
formal logic because factors such as the insolubility of the
halting problem and
Gödel's incompleteness theorem prevent an algorithmically based system of logic from reproducing such traits of human intelligence as mathematical insight. The
Penrose–Lucas argument about the implications of Gödel's incompleteness theorem for computational theories of human intelligence has been criticised by mathematicians, computer scientists and philosophers. Many experts in these fields assert that Penrose's argument fails, though different authors choose different aspects of the argument to attack.
Marvin Minsky, a leading proponent of artificial intelligence, was particularly critical, writing that Penrose "tries to show, in chapter after chapter, that human thought cannot be based on any known scientific principle." Minsky's position is exactly the opposite – he believed that humans are, in fact, machines, whose functioning, although complex, is fully explainable by current physics. Minsky maintained that "one can carry that quest [for scientific explanation] too far by only seeking new basic principles instead of attacking the real detail. This is what I see in Penrose's quest for a new basic principle of physics that will account for consciousness." Penrose responded to criticism of ''The Emperor's New Mind
with his follow-up 1994 book Shadows of the Mind, and in 1997 with The Large, the Small and the Human Mind''. In those works, he also combined his observations with those of anesthesiologist
Stuart Hameroff. Penrose and Hameroff have argued that consciousness is the result of quantum gravity effects in
microtubules, which they dubbed
Orch-OR (orchestrated objective reduction).
Max Tegmark, in a paper in
Physical Review E, calculated that the time scale of neuron firing and excitations in microtubules is slower than the
decoherence time by a factor of at least 10 billion. The paper's reception is summed up by this statement in Tegmark's support: "Physicists outside the fray, such as IBM's
John A. Smolin, say the calculations confirm what they had suspected all along. 'We're not working with a brain that's near absolute zero. It's reasonably unlikely that the brain evolved quantum behavior'". Tegmark's paper has been widely cited by critics of the Penrose–Hameroff position. Phillip Tetlow, although himself supportive of Penrose's views, acknowledges that Penrose's ideas about the human thought process are a minority view in scientific circles, citing Minsky's criticisms and quoting the science journalist
Charles Seife's description of Penrose as "one of a handful of scientists" who believe that the nature of consciousness suggests a quantum process. supports the hypothesis of
Orch-OR theory. A reviewed and updated version of the theory was published along with critical commentary and debate in the March 2014 issue of
Physics of Life Reviews. He appeared on
In Our Time discussing consciousness with
Ted Honderich.
Publications Italian edition signed by Penrose, 2005 His popular publications include: • ''
The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics'' (1989) •
Shadows of the Mind: A Search for the Missing Science of Consciousness (1994) •
The Road to Reality: A Complete Guide to the Laws of the Universe (2004) •
Cycles of Time: An Extraordinary New View of the Universe (2010) •
Fashion, Faith, and Fantasy in the New Physics of the Universe (2016) His co-authored publications include: •
The Nature of Space and Time (with
Stephen Hawking) (1996) •
The Large, the Small and the Human Mind (with
Abner Shimony,
Nancy Cartwright, and Stephen Hawking) (1997) •
White Mars: The Mind Set Free (with
Brian Aldiss) (1999) His academic books include: •
Techniques of Differential Topology in Relativity (1972, ) •
Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (with
Wolfgang Rindler, 1987) (paperback) •
Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (with Wolfgang Rindler, 1988) (reprint), (paperback) His forewords to other books include: • Foreword to "The Map and the Territory: Exploring the foundations of science, thought and reality" by Shyam Wuppuluri and Francisco Antonio Doria. Published by Springer in "The Frontiers Collection", 2018. • Foreword to
Beating the Odds: The Life and Times of E. A. Milne, written by Meg Weston Smith. Published by World Scientific Publishing Co in June 2013. • Foreword to "A Computable Universe" by Hector Zenil. Published by World Scientific Publishing Co in December 2012. • Foreword to
Quantum Aspects of Life by Derek Abbott, Paul C. W. Davies, and Arun K. Pati. Published by Imperial College Press in 2008. • Foreword to
Fearful Symmetry by
Anthony Zee. Published by Princeton University Press in 2007.
Awards and honours Penrose has been awarded many prizes for his contributions to science. In 1971 he was awarded the
Dannie Heineman Prize for Astrophysics by the
American Astronomical Society and
American Institute of Physics. He was elected a
Fellow of the Royal Society (FRS) in 1972. In 1975 Hawking and Penrose were jointly awarded the
Eddington Medal of the
Royal Astronomical Society. In 1985 he was awarded the
Royal Society Royal Medal. Along with Hawking, he was awarded the prestigious
Wolf Prize in Physics by the
Wolf Foundation (Israel) in 1988. In 1989 Penrose was awarded the
Dirac Medal and Prize of the British
Institute of Physics. He was also made an
Honorary Fellow of the Institute of Physics (HonFInstP). In 1990 Penrose was awarded the
Albert Einstein Medal for outstanding work related to the work of
Albert Einstein by the
Albert Einstein Society (Switzerland). In 1991, he was awarded the
Naylor Prize of the
London Mathematical Society. Penrose was awarded an honorary
Doctor of Science degree (DSc) from the
University of New Brunswick (Canada) in 1992, and an honorary degree from the
University of Surrey in 1993. From 1992 to 1995 he served as President of the International Society on General Relativity and Gravitation. In 1994 Penrose was
knighted for services to science. In the same year, he was also awarded an honorary degree of
Doctor of Science (DSc) by the
University of Bath, and became a member of
Polish Academy of Sciences. Penrose was awarded honorary degrees from the
University of London in 1995, the
University of Glasgow (
Doctor of Science, DSc) and
University of Essex, both in 1996, from the
University of St Andrews in 1997, both in 1998. In 1998 he was elected Foreign Associate of the
United States National Academy of Sciences. In 2000 he was appointed a
Member of the Order of Merit (OM). He was awarded an honorary doctorate from the
University of Southampton in 2002. In 2004 Penrose was awarded an honorary
Doctor of Science (DSc) degree from the
University of Waterloo (
Ontario, Canada) and was awarded the
De Morgan Medal by the
London Mathematical Society for his wide and original contributions to mathematical physics. To quote the citation from the society: In 2005 Penrose received a
Doctorate Honoris Causa (Dr.h.c.) from each the
Warsaw University (Poland) and the
Katholieke Universiteit Leuven (Belgium), and an honorary Doctor of Philosophy (PhD) degree from the
Athens University of Economics and Business (Greece). In 2005 he was also awarded the
Manchester Literary and Philosophical Society Dalton Medal. In 2006 he was conferred the honorary degree of
Doctor of the University (DUniv) by the
University of York and also won the
Dirac Medal given by the
University of New South Wales (Australia). In 2008 Penrose was awarded the
Copley Medal of the Royal Society. He is also a Distinguished Supporter of
Humanists UK and one of the patrons of the
Oxford University Scientific Society. He was elected to the
American Philosophical Society in 2011. The same year, he was also awarded the
Fonseca Prize by the
University of Santiago de Compostela (Spain). In 2012 Penrose was awarded the Richard R. Ernst Medal by
ETH Zürich (Switzerland) for his contributions to science and strengthening the connection between science and society. In that year he was also awarded the honorary degree of
Doctor of Science (DSc) by the
Trinity College Dublin (Ireland) as well an honorary doctorate degree by the
Igor Sikorsky Kyiv Polytechnic Institute (Ukraine). In 2015 Penrose was awarded a
Doctorate Honoris Causa (Dr.h.c.) by
CINVESTAV (Mexico). In 2017 he was awarded the Commandino Medal at the
Urbino University (Italy) for his contributions to the history of science. In that year as well, he was awarded an
honorary Doctor of Science degree (DSc) by the
University of Edinburgh. In 2018 Penrose received an honorary degree from
King's College London. In 2020 Penrose was awarded one half of the
Nobel Prize in Physics by the
Royal Swedish Academy of Sciences for the discovery that black hole formation is a robust prediction of the general theory of relativity, a half-share also going to
Reinhard Genzel and
Andrea Ghez for the discovery of a
supermassive compact object at the
centre of our galaxy. In 2025 Penrose received the Golden Plate Award of the
American Academy of Achievement. == Personal life ==