Who is Roger Penrose? Quantum and Consciousness, Twistor Theory and Time of Cycles

Koç Üniversitesi Bilim Kulübü
12 min readOct 31, 2020


No doubt that Roger Penrose is one of the most exclusive mathematical physicists still living. When even Einstein was not even sure about the existence of black holes, he proved this mathematically and defined the characteristic properties.

“GRAVITATIONAL COLLAPSE AND SPACE- TIME SINGULARITIES article by Roger Penrose who won Physics Nobel prize in 2020 is one of the biggest contributions to general relativity after Einstein. Thanks to this article, singularity and apparent horizon are founded.

Trapped surface concept lies under Roger Penrose’s ideas. He points out that as matter moves to a centre by force of gravity, “time” moves into the centre of this black hole from the boundaries of these surfaces, inevitably.

He states that eventually, this centre turns into an infinite gravitational field which is called singularity where all known physics law collapses. Also, it is impossible to escape from a black hole because the direction of time points to the centre.

Figüre 1: Sir Roger Penrose[1].

2020 Nobel Physics Prize for the discovery that black hole formation is a robust prediction of the general theory of relativity. As it is known, the Nobel Prize is an award given by the Swedish Royal Academy to scientists who have been active in various fields since 1901 with the will of Alfred Nobel despite some setbacks. According to general opinion, the Nobel Prize is one of the most prestigious awards that a scientist could win. He is mentioned that: “He revolutionized all mathematical tools that we use to understand properties of space-time.[2]” When he was 10, he studied on polyhedrons and said in his books that known physics laws are not able to explain phenomena of consciousness. Now, let’s get to know Sir Roger Penrose, one of the Nobel Prize winners of 2020, who thinks that current computers will never have intelligence because of their algorithmic deterministic system and has been awarded the title of “sir” by the Queen of England for his contributions to science [2].

In this article, we explain three fundamental theories: Quantum mechanics and Consciousness, Twistor Theory, Cycles of Time developed by Roger Penrose.

Quantum Mechanics and Consciousness

Penrose’s curiosity about consciousness bases upon encountering Gödel’s incompleteness theorem when he was a student at Cambridge. Gödel’s theorem says that some claims in mathematics are true but cannot be proved. Penrose justifies that consciousness is not algorithmic and is connected with quantum mechanics in away. According to him, consciousness consists of some changes in quantum level that we cannot explain with today’s physics, biology and neuroscience knowledge. That’s why consciousness cannot be imitated by computers that are based on classical physics. AI will never be aware of what it is doing and gain consciousness[3].

Figüre 2: Roger Penrose, The Emperor’s New Mind (1989).

Penrose maintains that known physics laws are not enough to apprehend how consciousness occurs in his book The Emperor’s New Mind (1989) Even though, computing powers of current computers are amazing, according to him, the calculations that are made by the brain and made by computers are independent of the consciousness. To his way of thinking, consciousness is awareness and the best way to comprehend this without getting away from physics is quantum mechanics. He remarks the property of multiple states, taking value 1 and 0 at the same time, of qubit which is a basic property of quantum calculations. These quantum states exist at the same time until they merge and turn into a single calculation. Quantum consistency arises from lots of things being in a single quantum state altogether. Penrose thinks that this is instrumental in the formation of consciousness.

Penrose’s thesis was considered as weak and easily falsifiable by manifold scientists making research on AI and consciousness because knowledge transformation in the brain is controlled by electrochemical activities between synapses and this is explainable with classical physics. Penrose, also admits that his book is unsuccessful in explaining this situation.[4]

He carried on his studies by publishing “Shadow of the Mind (1994)” and “The Large (1997)” with anaesthetist Stuart Hameroff who reached Penrose after Penrose released his book.[2]

Hameroff told the idea quantum states may occur in the microtubules in cell skeleton to Penrose. Microtubules take charge empowering synaptic connections in neurons and controlling them. Penrose and Hameroff asserted that consciousness is a result of the effect of quantum gravitation in microtubules that were not discovered yet. In the theory “Orchestrated objective reduction” they suggest, conscious awareness appears in microtubules at these times and microtubules are able to store the knowledge and process it.[6]

Figüre 3: Connection between Orch-OR theory and microtubules[7].

Many scientists argued that the brain does not have the proper conditions to be in such a quantum state that could affect neural activity. One of them was Max Tegmark (Professor at MIT) Tegmark who calculated that any quantum effects within microtubules would break down after 100 quadrillionths of a second. “For my thoughts to correspond to a quantum computation, they’d need to finish before decoherence kicked in, so I’d need to be able to think fast enough to have 10,000,000,000,000 thoughts each second,” Tegmark writes in his 2014 book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality.[6]

Even though Penrose’s theory about consciousness is considered as weak, Penrose puts all the cards on the table and brings a new perspective about what consciousness is.[6]

Twistor Theory

Sources about this theory were extremely limited and almost there were no Turkish sources until this paper was released. Main reasons for that are undergraduate physics students don’t come across with this topic in college lectures and theory requires highly advanced mathematics to get familiarized. Since we don’t have this advanced mathematical basis too, we tried to explain the subject in general terms and compile the interviews and information from the Internet as much as we could.

What is Twistor Theory?

Twistor concept presented for the first time as a Minkowski spacetime diagram’s new demonstration (Figure 4) published in the article “Twistor Algebra” by Penrose in 1967 first time. Later, in the article “An approach to the quantisation of fields and space-time” published by Penrose in 1973, Twistor theory has developed to merge quantum theory and general relativity theory [10]. This new theory which brings a new approach to quantum gravitation has remained in the background until the 1980s like “Theory of everything” [11] but in 2003, thanks to the Witten’s studying on merging “Twistor Theory” and “String Theory”, the theory gets popularized again [12]. Currently, it became a different branch of mathematical physics and studies, researches on it go on.

Figüre 4: Minkowski Space and Time Diagram[9].

Meaning of Twistor Space

A different geometrical demonstration of Minkowski’s four-dimensional cones (Figure 1) which represent space-time consists of the basis of Twistor Theory, this demonstration is nothing but Twistor space. Actually, twistor space and Minkowski space resemble each other in terms of having three direction dimension and additional one-time dimension but the main difference between two spaces is that Twistor spaces don’t focus on events, focus on causal relationships[13]. That’s why reasons are the by-products of events. Same object or event has two different notations in these two spaces. For instance, if there are three points in Twistor space, this corresponds to a line segment in Minkowski space-time or a line segment corresponds to a point in space-time(Figure 5, [14]).

Figüre 5: Comparison between Twistor Space and Space-Time [16].

Forty-year dead-end, Goggly Trouble

One of the main problems which hinder the progress of theory for forty years is the Goggly problem which Penrose explained in an interview in 2019. There can be derived from two different functions according to spins of photons. For instance, the wave equation gives two different solutions in both directions, left and right. Also, Penrose has also formed two different equations. Other particles like photons have this right-left difference, for example, graviton particle which carries the effect of gravitation. That’s the part where Twistor theory’s problem arises because while the graviton particle satisfies for the left direction of Penrose’s equation, it does not hold for the right direction. Even though Roger Penrose states that new researchers offered a new solution to this problem and adds that he does not study cosmology anymore[15].

Despite all, Twistor theory presents the representation of complex numbers in quantum field theory as he indicates in his interview[15,16]. From this aspect, Twistor theory has also found its use in the field of mathematics.

Time of Cycles: Splendid Adventure of Quantum World

How and why did the universe come into being? What was there before the Big Bang? It is pretty hard to answer these and similar questions to them with today’s physics. But mathematical physicist Roger Penrose brought an explanation to these questions with the concept “time of cycles. Penrose calls “aeon” to each of these universes. It should also be noted that there are widely discussed aspects of the theory and the difficulties in proving its predictions.

Penrose says that matter runs like clockwork based on the equations Einstein’s E=mc2 and Planck’s E=hf. In this case, there isn’t a scale for time unless there is a mass. In the Big Bang period there was no mass in the sense that we know, and in short there was no scale for time, too. Also, in the distant future, the scale in the universe will disappear again. Another subject that Penrose emphasized that it cannot be explained why entropy was pretty low in the beginning of the universe. Because Max Planck’s thermal blackbody radiation is obtained by cosmic microwave background radiation and that’s a sign to high entropy [17]. Nevertheless, if we shrink the distant future in scale, we get something similar to Big Bang. But in this circumstance, the gravitational degrees of freedom are lost (degrees of freedom is the number of parameters required to explain the system.) Thus, we achieve low entropy during the Big Bang. Conformal Cyclic Cosmology (CCC) puts forward that information is lost in black holes to explain this situation. Huge part of entropy in the universe originates from black holes, while black holes are evaporating because of Hawking radiation, information of this entropy disappears, too. This phenomenon is called the black hole information paradox. But the trueness of this phenomenon in terms of quantum physics is quite doubtful. “Unitarity” concept in the quantum universe indicates that probabilities are conserved. Therefore, information does not disappear in black holes. But it is still unknown how information is regained. Penrose states that quantum mechanics is erroneous [17]. A particle has the possibility of more than one “event”, but only one event is valid after the “observation” is made according to quantum superposition principle. This event called collapsing of the wave function is still a mystery. Penrose says that “unitarity” is not preserved in quantum mechanics itself by referring to this [17]. Because after the observation is made, possibilities don’t matter. It is required to admit losing of information for CCC to be valid.

What is conformal geometry?

Conformal geometry, the mainstay of the theory, is a type of geometry that angles are preserved but lengths are alterable. By using this geometry to describe the universe, instead of the known cone-shaped universe structure, a cylindrical universe structure can be obtained as shown (Figure 6). That means we get rid of the singularity at the beginning of the universe. By this way, the connection between each “aeon” is established. Then, a universe consisting of the essential conditions for life would be formed in any aeon.

Figüre 6: Conformal Rescaling of Universe[18]

Objections to theory

American theoretical physicist Sean Carroll put forward that CCC cannot explain why observed magnitudes in the universe are such large [19]. Put it differently, while the theory cannot account for these magnitudes, theory is supposed to be adjusted for observations. It’s called “fine-tuning” in physics. Penrose’s explanation for this objection is that these magnitudes can change in each aeon.

Phenomenons Explained by the Theory and Possible Evidence

One of the consequences of a theory is dark matter. According to the theory, the decay time of dark matter is 1011 years which corresponds to the age of the universe. It is possible to observe the effect of this disintegration as high-frequency waves and these waves can be detected by gravitation detectors. Conformal factors meet scalar field equations that match with dark matter. According to CCC, dark matter occurs from conformal changing of aeons. A recent discovery of LIGO may indicate disintegration of dark matter [20]. In the article “On the time lags of the LOGO signals”, interconnections, subject to a certain delay, were discovered among the noises in LIGO’s signals [21]. According to Penrose, these interconnections are evidence of disintegration of dark matter. However, this relationship is pretty ambiguous for many physicists. Sabina Hossenfelder, one of the physicists who think in this way, criticized Penrose’s explanation that the signals were not intense enough and why such signals were not observed in our galaxy and stated that this “noise” could be the Hanbury Brown and Twiss effect [22]. This effect, discovered by two physicists Brown and Twiss, occurs as entangled photons affect coming signals. Arguments on this topic are still ongoing.

Another subject that Penrose asserts that circular structures in the cosmic microwave background radiation (Figure 7). Penrose argues that these structures originate from clustered galaxies which existed in prior aeons [24]. However, some physicists think that this is just a coincidence but some evidence support Penrose[25]. Unfortunately, since we only have a single map, making comparison and coming up with a certain result is not possible.

Figüre 7: Cosmic microwave background[23]

As a result, although Conformal Cyclical Cosmology is an interesting theory, it gives the impression that it will not be accepted in the scientific community for a long time because of basing on assumptions and lack of conclusive evidence.


Roger Penrose also is a good popular science book author, among his studies. As we mentioned in our article, he wrote “The Emperor’s New Mind” and “The Road to Reality” which are a little bit above a regular popular science reader level and comprehensive. Besides, He still maintains his productivity with the book Fashion, Faith and Fantasy, published in 2016, has started to be pressed in our country this year (2020)

As we conclude our article, let us state that Roger Penrose is a very close friend of Stephen Hawking and if Stephen Hawking was alive, they would quite likely share the Nobel Physics Prize considering their cooperation. Finally, we end our article by sharing this scene from Hawking (2004) movie.


Written By

Cem Kurt, Eren Özdemir, Kerem Başol, Kağan Uçak.

Board Members at Koç University Science Club.


[1] https://www.nobelprize.org/







[ 7]https://www.discovermagazine.com/the-sciences/can-quantum-physics-explain-consciousness-one-scientist-thinks-it-might


[9] https://www.wikiwand.com/en/Minkowski_space

[10] R. Penrose, Twistor theory: An approach to the quantisation of fields and space-time (1973), https://doi.org/10.1016/0370-1573(73)90008-2

[11] T. Adamo, Lectures on twistor theory(2017), https://arxiv.org/abs/1712.02196

[12] E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189–258, [hep-th/0312171].

[13] D. Robbins and A. Z. Jones, https://www.dummies.com/education/science/physics/string-theory-and-twistor-theory/

[14] https://universe-review.ca/R15-19-twistor.htm#top

[15] The Institute of Art and Ideas(2019), https://www.youtube.com/watch?v=j16eVLDt2HI&ab_channel=TheInstituteofArtandIdeas

[16] G. Musser, “Twistor” Theory Reignites the Latest Superstring Revolution(2020), https://www.scientificamerican.com/article/simple-twist-of-fate/

[17] https://www.youtube.com/watch?v=FVDJJVoTx7s&t=885s

[18] https://physicsworld.com/a/inside-penroses-universe

[19] https://twitter.com/seanmcarroll/status/972134059051765760

[20] Leaci, P. (2012). Searching for continuous gravitational wave signals using LIGO and Virgo detectors. Journal of Physics: Conference Series, 354, 012010. doi:10.1088/1742–6596/354/1/012010

[21] Creswell, J., Von Hausegger, S., Jackson, A., Liu, H., & Naselsky, P. (2017, August 09). On the time lags of the LIGO signals. Retrieved October 26, 2020, from https://arxiv.org/abs/1706.04191

[22] http://backreaction.blogspot.com/2018/08/roger-penrose-still-looks-for-evidence.html

[23] http://cmi-capital.com/blog/before-the-big-bang-conformal-cyclic-cosmology/

[24] Gurzadyan, V. G., & Penrose, R. (2013). On CCC-predicted concentric low-variance circles in the CMB sky. The European Physical Journal Plus, 128(2). doi:10.1140/epjp/i2013–13022–4

[25] An, D., Meissner, K. A., & Nurowski, P. (2017). Ring-type structures in the Planck map of the CMB. Monthly Notices of the Royal Astronomical Society, 473(3), 3251–3255. doi:10.1093/mnras/stx2299



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