### Thoughts on Sir Roger Penrose’s Conformal Cyclical Cosmology (CCC)

I finally collected all my notes, and in this article, I am writing down my thoughts around CCC, comparing Capra and Penrose’s worldview and parallels with Eastern mysticism and creation stories. This is the first part. In the second part, I will briefly explain scientific works to reconcile CCC with modern quantum information theory and gravitational entropy.

Abstract

While CCC offers a thought-provoking alternative to the standard cosmological model and attempts to resolve some outstanding issues in quantum information theory, it is not as widely accepted as the standard model. The standard model of cosmology, based on the Big Bang theory and inflationary cosmology, remains the most well-supported and extensively tested framework for understanding the universe’s evolution. CCC faces challenges in terms of both theoretical consistency and observational evidence, and more research is needed to determine its viability as a cosmological model.

Background

Reading Sir Roger Penrose’s “The Emperor’s New Mind” during my twelfth grade was a transformative experience that significantly broadened my worldview. At a time when my interests were blossoming beyond the confines of the standard high school curriculum, Penrose’s exploration of the intersections between mathematics, physics, and consciousness presented a compelling narrative that challenged my understanding of reality. The book’s ambitious goal to reconcile the mechanistic view of the mind with quantum physics and mathematical theory intrigued me deeply. It was Penrose’s audacious questioning of artificial intelligence’s capacity to replicate human consciousness that especially resonated with me, sparking a lifelong fascination with the philosophical questions surrounding mind, matter, and the cosmos.

Following “The Emperor’s New Mind,” I eagerly delved into Penrose’s subsequent works, such as “Shadows of the Mind” and “Cycles of Time.” In “Shadows of the Mind,” Penrose further develops his argument against the possibility of strong AI, proposing instead that human consciousness arises from quantum effects within the brain. This radical hypothesis, though controversial, pushed me to appreciate the complexity of scientific inquiry and the value of interdisciplinary research. Many years later, “Cycles of Time” introduced me to Penrose’s Conformal Cyclic Cosmology, a groundbreaking theory suggesting that the universe undergoes an infinite sequence of cycles, from the Big Bang to ultimate expansion and back again. Penrose’s ability to weave together cutting-edge physics with profound philosophical implications has continually inspired me to look beyond surface explanations and appreciate the elegance and interconnectedness of the universe.

Penrose’s work has profoundly influenced my intellectual journey, instilling in me a deep appreciation for the intricate dance between science and philosophy. His bold hypotheses and the eloquent way he navigates complex ideas have encouraged me to adopt a more inquisitive, critical approach to knowledge. The way Penrose challenges conventional wisdom and explores the mysteries of the human mind and the universe has not only expanded my understanding but has also taught me the value of creativity and persistence in the pursuit of truth. His legacy, embodied in his revolutionary ideas and contributions to mathematical physics, continues to guide those who seek to unravel the mysteries of our existence.

I read “The Tao of Physics” by Fritjof Capra, around 1986. I was in 10th grade and leaning towards Buddhism as a personal choice.

Many years later, a decade and more, I found similarities between “The Tao of Physics” and Roger Penrose’s concept of Conformal Cyclic Cosmology (CCC). Both represent intriguing attempts to bridge the gap between modern physics and ancient philosophical or religious ideas, though they approach this task from different angles. Capra’s work focuses on drawing parallels between modern physics — especially quantum mechanics — and Eastern mysticism, including Hinduism, Buddhism, and Taoism. He explores how these spiritual traditions anticipate many of the counterintuitive aspects of modern physics, suggesting a fundamental unity in the understanding of the cosmos.

On the other hand, Penrose’s CCC is a scientific proposal within the field of cosmology. It posits that the universe undergoes an infinite sequence of cycles, each beginning with a Big Bang and ending in an infinitely expanded future that becomes the Big Bang of the next cycle. This theory is rooted in mathematics and physics, particularly in the concepts of entropy and the conformal geometry of the universe.

The similarities between “The Tao of Physics” and CCC, particularly in relation to Hindu creation stories, can be found in their shared themes of cyclicity and eternal return. Hindu cosmology, especially as described in texts like the Bhagavata Purana, presents the universe as undergoing endless cycles of creation, preservation, and destruction, known as “kalpas.” Each cycle is overseen by Brahma, the god of creation, who himself has a lifespan that spans millions of years of human reckoning, at the end of which the universe is dissolved and then recreated.

Both Capra’s discussions in “The Tao of Physics” and Penrose’s CCC resonate with this cyclic view of the universe. Capra sees parallels in the way that Eastern mysticism and modern physics conceive of the cosmos as dynamic, with its patterns of change reflecting a deeper, unchanging reality. Similarly, CCC’s concept of the universe undergoing infinite cycles without a definitive beginning or end mirrors the Hindu belief in an eternal cosmic rhythm.

While Capra’s work is more directly focused on drawing parallels between physics and Eastern mysticism, including Hindu creation stories, CCC shares a thematic similarity in its view of the universe as eternally cyclical. Both approaches, in their own ways, challenge linear conceptions of time and the universe, instead proposing a cosmos that is far more dynamic and interconnected, echoing ancient philosophies that see the world in terms of cycles and renewal.

Let’s not digress. back to Sir Penrose. This is my attempt to summarize his three most popular science books. The first two directly relate to my present field of research and professional work.

The Emperor’s New Mind (1989):

In this book, Penrose argues that human consciousness and understanding cannot be fully explained by computational processes or algorithms. He posits that there must be some non-computational elements at work in the human mind, possibly at the quantum level. Penrose suggests that this non-computational nature of consciousness means that true artificial intelligence is impossible, and that the human brain is not simply a computer made of meat.

Shadows of the Mind (1994):

This book is a follow-up to The Emperor’s New Mind, in which Penrose further develops his arguments about the nature of human consciousness. He introduces the concept of “quantum coherence” in the brain’s microtubules as a possible explanation for the non-computational aspects of the mind. Penrose also discusses Gödel’s incompleteness theorems and their implications for the limits of formal systems and artificial intelligence.

Cycles of Time (2010):

In Cycles of Time, Penrose presents his theory of “conformal cyclic cosmology” (CCC), which proposes that the universe goes through infinite cycles of creation and destruction. According to this theory, the Big Bang that started our current universe was actually the end of a previous universe that had expanded to a state of low density and high entropy. Penrose suggests that the transition between universes is marked by a transformation of scale, allowing the next universe to begin anew. The book explores the mathematical and physical implications of this cyclical model of the universe.

## Conformal Cyclic Cosmology (CCC)

In CCC or the Conformal Cyclic Cosmology model, Sir Roger Penrose challenges some aspects of the standard model of cosmology and quantum information theory. He broadly categorized his arguments around five key points.

*Infinite cycles:* CCC proposes that the universe undergoes infinite cycles of expansion and contraction, with each cycle ending in a “conformal rescaling” that sets the stage for a new cycle. This contrasts with the standard model, which posits a single, continuous expansion of the universe from the Big Bang.*Black hole evaporation: *In CCC, black holes are crucial for the transition between cycles. As black holes evaporate via Hawking radiation, they are thought to leave behind a type of low-entropy radiation that seeds the next cycle. This challenges the standard interpretation of black hole evaporation and its implications for quantum information.*Information loss paradox:* CCC attempts to resolve the black hole information loss paradox by proposing that information is not lost but is instead carried forward into the next cycle of the universe. This is a departure from the standard quantum information theory, which struggles to reconcile the apparent loss of information in black holes with the unitarity of quantum mechanics.*Second law of thermodynamics: *CCC suggests that the second law of thermodynamics, which states that entropy always increases, may not hold across the infinite cycles of the universe. Instead, entropy is reset at the beginning of each new cycle, allowing for the emergence of new structure and complexity.*Observational evidence:* CCC makes predictions that could potentially be tested through observations, such as the presence of specific patterns in the cosmic microwave background (CMB) radiation. *These predictions are still debated, and the standard model of cosmology currently remains the most widely accepted framework.*

It’s important to note that while CCC offers an intriguing alternative perspective, it is not as widely accepted as the standard model of cosmology and faces challenges in terms of both theoretical consistency and observational evidence. The standard model, based on the Big Bang theory and inflationary cosmology, remains the most well-supported and extensively tested framework for understanding the universe’s evolution.

Over the years, while following various works on the original CCC posits, it became clearer that the differences between the standard cosmological model and quantum information are stark, and CCC is not reconciling with the standard models.

Here’s a brief overview of how CCC differs from these standard theories:

## Cosmological evolution

Standard model: The universe began with the Big Bang and has been expanding ever since, with no prior cycles.*CCC:* The universe undergoes infinite cycles of expansion and contraction, with each cycle ending in a “conformal rescaling” that sets the stage for a new Big Bang.

## Black hole evaporation and information loss:

*Standard quantum information theory: *Suggests that information is lost when matter falls into a black hole, violating the unitarity principle of quantum mechanics.*CCC:* Proposes that information is preserved across cosmological cycles, with black hole evaporation playing a crucial role in the transfer of information from one cycle to the next.

## Second law of thermodynamics:

*Standard model:* Entropy always increases over time, as stated by the second law of thermodynamics.*CCC:* Suggests that entropy is reset at the beginning of each new cosmological cycle, allowing for the emergence of new structure and complexity.

## Observational evidence:

*Standard model:* Supported by extensive observational evidence, including the cosmic microwave background (CMB) radiation and the expansion of the universe.*CCC: *Makes predictions that could potentially be tested through observations, such as specific patterns in the CMB, but these predictions are still debated and not yet widely accepted.

Very recently, I came across this paper, which tried to reconcile CCC with observational evidence.

The paper presents an examination of Roger Penrose’s Conformal Cyclic Cosmology (CCC) in the context of modern quantum information. The authors argue that the presumed loss of degrees of freedom in black holes within the CCC framework is inconsistent with the quantum concept of entropy. They propose a unitary version of CCC, in which quantum information is globally conserved throughout the universe’s entire evolution and across the crossover surface to the subsequent aeon. This unitary model seeks to address the compatibility issue between the CCC and quantum information theory.

The analysis put forward in the paper suggests that the entanglement with specific quantum gravitational degrees of freedom may underlie the second law of thermodynamics and the quantum-to-classical transition at mesoscopic scales. The authors highlight the potential connection between quantum entanglement and the emergence of classical behavior, shedding light on the fundamental mechanisms driving the macroscopic world from a quantum perspective.

The paper offers a critical assessment of CCC through the lens of modern quantum information theory and proposes an alternative unitary version to address the apparent conflict with quantum entropy. The implications of the proposed model extend to the fundamental understanding of the second law of thermodynamics and the quantum-to-classical transition, emphasizing the role of entanglement with quantum gravitational degrees of freedom in shaping the dynamics of the universe.

The introduction of the research paper discusses the universe’s model within general relativity, which is characterized by a spacetime manifold with a Lorentzian metric solving the Einstein field equations. The observational data supports the standard model of cosmology with cold dark matter, a positive cosmological constant, and ordinary baryonic matter. The existence of a global time function in the universe requires it to be stably causal. The paper highlights an evolutionary viewpoint of the universe, starting with the Big Bang and expanding into a “dark era” dominated by the cosmological constant.

The paper identifies several problems with the cold dark matter model, including the unknown nature of dark matter and dark energy, the high-degree homogeneity of the cosmic microwave background, and the flatness problem related to the present matter-energy density in the universe. On the mathematical side, the Big Bang is portrayed as a naked singularity, and the well-posedness of the Cauchy problem under suitable assumptions about isotropy is discussed.

The paper introduces Roger Penrose’s Conformal Cyclic Cosmology (CCC) as a proposal to resolve cosmic riddles and discusses its confrontation with modern understanding of quantum information. The paper presents a unitary variant of CCC, based on two independent hypotheses: gravitational clumping inducing the activation of quantum gravitational degrees of freedom and the restoration of quantum information in the correlations between modes of Hawking radiation. The implications of these hypotheses are explored, including the entanglement of matter with gravitational degrees of freedom and the issues related to quantum gravitational degrees of freedom and causal loops. The paper points towards the challenges for unitary Conformal Cyclic Cosmology.

## Thermodynamic entropy and information in CCC

The research paper discussed the Conformal Cyclic Cosmology (CCC) and its implications for thermodynamic entropy and information. It emphasized the structure of the universe within CCC, consisting of a sequence of aeons separated by crossover hypersurfaces, with each aeon equipped with a Lorentzian metric. The CCC proposal involved identifying the future conformal infinity of one aeon with the Big Bang of the subsequent aeon, achieved through conformal rescaling of the metric. Within CCC, the aeons are causally connected, allowing information carried by massless particles to flow through crossover hypersurfaces.

The paper delved into the Second Law of thermodynamics, highlighting its universal nature and dependence on the physical context and entropy definition. The application of the Second Law to the universe led to the conclusion that the Big Bang must have had low entropy, which seemingly contradicted empirical data from the cosmic microwave background (CMB). To resolve this, Penrose incorporated gravitational degrees of freedom and associated entropy with the Weyl tensor, proposing that the growth of entropy is associated with gravitational clumping.

The paper discussed the conflict between the global growth of entropy and the low entropy requirement at the beginning of each new aeon in CCC and proposed the irreversible loss of information during black hole evaporation as a resolution. Penrose postulated that quantum information is routinely lost in the quantum measurement process, intertwining time-reversible unitary evolution with random irreversible projections due to the spontaneous collapse of spacetime metrics. It was acknowledged that Penrose’s CCC required a departure from standard quantum theory and was deemed incompatible with the quantum notion of entropy based on entanglement.

## Quantum information and entropy

The section of the research paper discusses quantum information and entropy in the context of quantum mechanics. It begins by defining isolated systems in terms of pure states, with the Hilbert space representing the maximal knowledge about the system. For a system that is not perfectly isolated, a density operator is used to describe it in terms of a mixed state when the full knowledge about the system is not available. The concept of purification is introduced to extend the Hilbert space, and the von Neumann entropy is presented as a measure of subjective uncertainty in a given quantum state.

The paper delves into the connection between quantum entropy and thermodynamics, emphasizing the role of entanglement and correlations in determining the entropy of a system. It discusses the subadditivity of entropy and explores scenarios where the total entropy of a system can be smaller than the individual entropies of its subsystems, which is a unique feature in the quantum setting. It explains the relationship between unitary evolution, entropy, and the reversible nature of quantum systems.

The section also addresses the implications of information loss in quantum systems, particularly in the context of black hole evaporation. It delves into the evolution of the universe in a global pure state and the potential increase in von Neumann entropy due to information loss and the transition from a pure state to a statistical mixture. The paper discusses the implications of information loss on the global Second Law of thermodynamics and contrasts conflicting viewpoints regarding the effective decrease of global entropy due to information loss.

This section of the paper provides a comprehensive exploration of quantum information and entropy, emphasizing its connections to thermodynamics, unitary evolution, information loss, and the fundamental principles of quantum mechanics.

## Gravity and quantum information

The section on Gravity and Quantum Information in the research paper proposes a modified unitary-scenario of Conformal cyclic cosmology (CCC) to solve the issue of compatibility between the ‘renormalization of entropy’ required by CCC and the implications of quantum information loss. The proposal is based on two hypotheses: gravitational clumping induces the activation of quantum gravitational degrees of freedom, and during black hole evaporation, all quantum information associated with the black hole region is eventually transferred to the Hawking radiation.

The paper describes the universe in terms of a pure state in an appropriate Hilbert space, dividing it into four sectors involving matter, quantum gravitational degrees of freedom, Hawking radiation, and information carriers outside of black holes. The authors discuss the global unitary evolution of quantum information, entanglement, and the flow of quantum information between different sectors during the cosmic evolution. They propose a global unitary evolution of the universe’s state, quantifying the flow of quantum information by computing the von Neumann entropy associated with the gravitational sector. This leads to the conclusion that the quantum information in the universe is globally preserved, flowing between the matter and gravitational sectors during the cosmic evolution. They also discuss the activation of quantum gravitational degrees of freedom during gravitational collapse and its association with gravitational entropy, providing insight into the quantum-to-classical transition.

In the context of unitary evaporation of black holes, the paper discusses the violation of local quantum mechanics principles and the implications of nonlocality in the gravitational sector. The authors propose that the violation of the local operations and classical communication principle does not necessarily imply the operational violation of relativistic causality and discuss the implications of a new information-theoretic framework. The proposed modified unitary scenario aims to avoid paradoxes and provide a coherent explanation for the preservation and flow of quantum information during cosmic evolution, particularly within the context of black hole evaporation.

The research paper discusses Conformal Cyclic Cosmology (CCC) proposed by Roger Penrose as an alternative to inflationary models. CCC is based on mathematical results regarding the conformal extensions of spacetime manifolds and makes testable predictions. It assumes that quantum gravity effects are insignificant in the early universe but important in black hole descriptions, connecting gravitational degrees of freedom to Weyl curvature.

The central concept in CCC is gravitational entropy, which extends Bekenstein-Hawking black hole entropy and is associated with information loss in black hole evaporation. Penrose’s classical entropy concept does not consider the quantum nature of phenomena, which would lead to an increase in entropy at the quantum level.

The paper also discusses Penrose’s proposal for an objective wave function collapse of massive quantum systems, which requires new notions of information and entropy.

*I am hopeful that with more advanced research and observation, we will be able to reconcile CCC with observed data. The Standard Cosmological Model may be revised, and CCC could play a central role.*

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