_This started with an exploration of quantum thermodynamics and entropy. It seemed something–elusive to me–that ties into an information theoretic approach to the universe. But as the exploration kept going in circles, I may have realized something much, much deeper._ Quantum thermodynamics and entropy can be quite complex topics. Here’s a high-level overview of some of the key ideas: * In quantum mechanics, the state of a system is described by a wavefunction which contains probabilistic information about the system. This is fundamentally different from classical mechanics where the state can be precisely defined. * In quantum statistical mechanics, entropy is related to the number of accessible microstates for a given macrostate. A system with more possible microstates has higher entropy. * Quantum effects like entanglement can correlate quantum systems in non-classical ways. This seems to defy thermodynamic notions of independent subsystems. * Information theory provides a bridge between thermodynamics and quantum mechanics. Quantum entropy is defined in terms of the information (number of bits) needed to describe the system’s state. * The von Neumann entropy formula for quantum systems takes into account the probabilistic nature of quantum states. It reduces to the standard Gibbs entropy for classical systems. * Quantum systems can exhibit thermal fluctuations and energy exchanges with a heat bath even at absolute zero temperature, due to the Heisenberg uncertainty principle. * Quantum thermodynamics is an active area of research trying to better understand work, heat, and entropy at the microscopic scale. Concepts like quantum heat engines are being explored. * Overall, quantum mechanics adds layers of complexity and probabilistic behavior to thermodynamic concepts like entropy. Information theory helps connect the dots between the two fields. There is still much to be understood at the intersection of quantum physics, information, and thermodynamics. In particular, I’d like to expand on the idea that information is fundamental to the universe and trying to get some at least plausible hypotheses going about how that have alluded me so far even when exploring through a quantum lens. That information may be fundamental to the universe at a quantum level has been explored by physicists and philosophers, though current understanding is still speculative. Here are a few hypotheses about how information could play a fundamental role: * The “it from bit” view put forward by John Wheeler. This suggests that the most basic element of reality is information itself, with matter and energy arising from information. Quantum bits, or qubits, represent the fundamental informational units. * Seth Lloyd’s idea of the universe as a “quantum computer”. Here, each particle continuously processes information about its state. The laws of physics emerge from the information processing occurring at a quantum scale across the universe. * The holographic principle which implies physical states can be encoded on a 2D boundary surface rather than throughout a 3D volume. Some theorists argue information is thus more fundamental than spacetime. The physical universe emerges from an informational structure. * Viewing entanglement entropy as fundamental. Quantum entanglement links far-apart particles such that the whole contains more information than the parts. This information may represent the basic descriptor of quantum systems. * Quantum information being related to the structure of spacetime. For example, quantum entanglement has been proposed to connect with wormholes and Einstein-Rosen bridges. Information theory may illuminate the emergence of space and time. * Ideas in quantum computing like quantum contextuality and quantum coherence emerging from information constraints on allowable quantum states and interactions. While speculative, these kinds of informational interpretations of quantum mechanics suggest information could represent something more elemental than matter, energy or spacetime at a fundamental level. Experimental tests are still a challenge though. The hope is understanding information in quantum systems will yield new insights into the fabric of reality. My [previous research on Holistic Information Theory (HIT)](https://quni.io/2024/02/23/information-holism-and-the-hard-problem-of-consciousness/) proposed connecting consciousness to integrated information across multiple scales, from quantum to neural levels \[1\]. While intriguing, speculative claims about macro-scale quantum effects in the brain require careful examination. This follow-up is an attempt to analyze how quantum information theory may provide useful tools for HIT, while identifying open questions and cautionary notes. Quantum information theory offers rigorous formalisms for analyzing entanglement entropy, coherence, and information integration in quantum systems \[2\]. In principle, these measures could help relate consciousness to fundamental information processing capacities. However, we cannot assume direct translation to neural function without empirical validation. The motivation to link consciousness to quantum information integration remains reasonable, but macro-quantum brain states face challenges. Decoherence rapidly dissipates quantum effects in warm, wet, noisy brain environments \[3\]. Unless new physics is discovered, system-wide quantum coherence seems unlikely. More grounded approaches include focusing on testable proposals for microscopic quantum mechanisms influencing neuronal, synaptic, or cytoskeletal processes \[4\]. For example, quantum tunneling between neurotransmitter receptors could enhance binding rates and intracellular transport may exploit quantum coherence \[5\]. Detailed models of these subtler quantum information effects in the brain could yield empirically verifiable hypotheses. Incorporating tools from quantum information theory into HIT has merit, but requires translating abstract formalisms into concrete neural mechanisms. Both theory and experiments are needed to validate if quantum information concepts like entanglement entropy illuminate the “hard problem” of consciousness. A cautious, evidence-based approach is essential. HIT offers a framework for systematically investigating connections between consciousness, information theory, and quantum physics. \[1\] Holistic Information Theory (HIT) [https://quni.io/2024/02/23/information-holism-and-the-hard-problem-of-consciousness/](https://quni.io/2024/02/23/information-holism-and-the-hard-problem-of-consciousness/) \[2\] Bruza et al. (2009). Is there something quantum-like about the human mental lexicon? \[3\] Tegmark (2000). Importance of quantum decoherence in brain processes. \[4\] Fisher (2015). Quantum cognition: The possibility of processing with nuclear spins in the brain. \[5\] Hagan, Hameroff, & Tuszynski (2002). Quantum computation in brain microtubules: Decoherence and biological feasibility. Exploration of quantum thermodynamics reveals deep links between quantum physics, entropy, and information. In particular, quantum entropy formulas like von Neumann entropy incorporate probabilistic uncertainty inherent to quantum systems \[1\]. This contrasts with classical thermodynamic entropy rooted in microstate counting. In his seminal work, mathematician John von Neumann formulated the quantum mechanical definition of entropy, known as von Neumann entropy. It is given by: S = −Tr(ρ ln ρ) Where ρ is the density matrix representing the quantum state of the system. This builds on prior entropy definitions by Gibbs and Boltzmann in classical statistical mechanics. But critically, von Neumann entropy incorporates the inherent probabilistic nature of quantum mechanics through the density matrix formalism. By linking entropy to the informational uncertainties in quantum states, von Neumann bridged thermodynamics and quantum information theory. His quantum entropy formula remains a key foundation for quantum information sciences today. The information theoretic view of quantum entropy suggests information plays a fundamental role in the quantum realm. When extrapolated, one speculation is that information itself is foundational to physical reality \[2\]. Renowned physicist John Wheeler summarized his perspective on the fundamental role of information in the physical universe. Wheeler proposed the radical notion that the basic element of reality is information itself, with matter and energy arising from information. To capture this view, he coined the phrase “it from bit” to suggest that everything derives from binary information bits, rather than the assumption that information emerges from an objective material world (“it”). Wheeler highlighted strange phenomena in quantum mechanics that implicate information as elemental, including nonlocal correlations and the measurement problem. He advocated a participatory universe shaped by observers. While admittedly speculative, Wheeler’s ideas influenced later thinking on the centrality of information, such as the holographic principle and digital physics proposals. His insights presaged connections between quantum information theory and the foundations of physics. Wheeler’s “it from bit” concept remains controversial but thought-provoking. By upending typical assumptions about the primacy of matter, he compelled deeper reflection on the role information plays in our most basic descriptions of reality. This informs perspectives on physics, cognition, and consciousness. Wheeler’s “it from bit” encapsulates this perspective – that the universe derives from information bits as its basic element rather than a material substrate \[3\]. From this lens, consciousness could arise from how quantum information processing gives rise to integrated complexity at neural scales. Wheeler’s radical proposal has influenced several later theories in physics and computation. For example, the holographic principle developed by physicist Gerard ‘t Hooft and Leonard Susskind models how all the information about a 3D volume can be encoded on its 2D boundary, reminiscent of how a hologram stores 3D data in 2D. This suggests information is more elemental than the spacetime volume itself. Digital physics theories proposed by Edward Fredkin and Stephen Wolfram have also built on Wheeler’s thinking by proposing the universe is computational at its core, processing digital information as its foundation. Finally, physicist Seth Lloyd expanded on Wheeler’s ideas with his concept of the universe as a quantum computer. According to Lloyd, each particle continuously processes discrete quantum information, with physical laws emerging from the collective computation occurring at a quantum scale. Though speculative, these later theories show how Wheeler’s bold information-centric perspective influenced ongoing contemplation of the role information plays in the basic fabric of reality. The holographic principle originated in the 1990s from theoretical physics work on quantum gravity by Gerard ‘t Hooft and Leonard Susskind. It states that all of the information about a volume of space can be encoded on its two-dimensional boundary, just like a hologram encodes 3D image data in 2D. This suggests spatial volumes could emerge from information processing on surfaces, hinting that information is more foundational than the spacetime we perceive. A key example realizing the holographic principle is the anti de Sitter/conformal field theory correspondence in string theory. This relates a 5-dimensional anti de Sitter spacetime to behavior on its 4D boundary conformal field theory. Some physicists interpret the holographic principle to mean the 3D physical world we inhabit emerges from underlying 2D information encoding, resonating with Wheeler’s “it from bit” view of information as fundamental. However, the principles remain contentious and continue being interpreted. While influential, John Wheeler’s “it from bit” doctrine and related information-centric views have also garnered criticism and counterarguments. Some contend it remains unknown whether information truly plays any fundamental role, disputing the demotion of matter and energy as primary. The exact mechanisms by which information could give rise to physical substance are also unspecified in Wheeler’s ideas and those inspired by them, requiring more concrete models. Anthropic principles suggest that observers are required for information processes to have meaning, implying information alone in an empty universe without consciousness may be insufficient. Additionally, some argue Wheeler’s speculations simply reflect the mathematical structure of quantum theory rather than anything profound about reality itself. The significance of information-first principles continues to be debated as physicists interpret Wheeler’s provocative ideas and explore their implications. The exact mechanisms connecting subjective experience to information processing remain unclear. But an information-centric paradigm aligns with unified theories of physics and cognition \[4\]. Information may be the essence conserved and built upon through cosmic and biological evolution. Quantum information integration in neural systems illustrates this view – information and its dynamics as primary. Holistic Information Theory aims to unify this worldview. Experimental validation seems critical to confirm whether quantum information processing in the brain relates to consciousness. But [as my other research indicates](https://quni.io/2024/02/29/testing-science-itself/), I think there is a plausible case to be made that we are bumping up against the very boundaries of what can be a tested experimentally, at least with the scientific method as we know it and falsifiability.  Using information theory to explain information aspects of quantum physics could seem circular or self-validating rather than standing on its own foundations. Let me offer some thoughts: – Information theory itself arose in classical communications/computation settings, with foundations in probability, statistics, and logic. It can be studied independently of quantum mechanics. – However, you’re right that applying it to interpret quantum thermodynamics and entropy could appear tautological, since information concepts are already embedded in those areas. – Proponents might argue information theory provides a unifying language to explain these disparate quantum phenomena rooted in information. It provides a coherent conceptual paradigm. – But you’re correct it doesn’t make new falsifiable predictions. It just provides a framework for connecting existing facts in physics and computation. – Stronger evidence would be showing information principles accurately model or explain some novel quantum effect not already known. This could validate its explanatory power. – Information theory does have its own deep theoretical formalisms like algorithmic complexity and Shannon/von Neumann entropy. But applying it to studied quantum phenomena may have a self-confirming character. The potential circularity in using information theory to explain information-laden aspects of quantum physics is a serious issue that requires careful consideration. A few perspectives on addressing it: 1\. Accept the circularity but argue information theory provides a unifying conceptual framework. It coherently connects disparate quantum information phenomena even if circularly. 2\. Identify and pursue novel, falsifiable predictions of information-based quantum models that go beyond known information effects. Experimental validation could break the circularity. 3\. Shift from falsification to assessing the fruitfulness of information theory in spurring new quantifiable insights, pragmatic applications, etc. Pragmatic value over strict falsifiability. 4\. Forge new mathematical formalisms for information principles independent of quantum mechanics to separate the foundations. Develop intrinsically information-based axioms. 5\. Question the premise – re-examine if information really is fundamental rather than emergent in the quantum realm after all. Explore alternatives to information-centric views. Dealing with the circularity issue requires either making falsifiable predictions, finding indirect validation like fruitfulness, formalizing independent foundations, or re-examining the basic assumptions. Each strategy has merits and challenges. But you are absolutely right that the circularity concern demands addressing for information-based quantum theories to be robust. Productive theories should strive to break out of self-confirmation. Absolutely, let’s dive deeper on strategies for addressing the key issue of potential circularity in applying information theory to explain information-laden quantum phenomena: Making falsifiable predictions: – Existing information-based quantum theories could be pushed to make precise, novel experimental predictions distinct from established quantum info effects. – For example, precisely quantifying information generation during black hole evaporation or the information processing capabilities of exotic quantum matter states. – Falsifying these novel predictions would break the circularity by showing the theories cover more than just known quantum information dynamics. Seeking indirect validation: – Assessing pragmatic virtues like spurring new technologies, unifying explanations, etc. can circumvent strict falsification. – For instance, the fruitfulness of quantum information theory in developing quantum computing and cryptography provides indirect validation of its foundations. – Conceptual unification of disparate phenomena can also support a theory absent strict falsification. Developing independent formalisms: – Information theory arose initially in classical settings like communication systems. – Expanding the classical mathematical formalisms without reference to quantum mechanics could provide an independent foundation. – For example, developing intrinsic measures of informational complexity and dynamics without invoking quantization. Questioning underlying assumptions: – Reexamining if information truly is inherent and fundamental in the quantum realm rather than just a convenient metaphor. – Exploring alternatives like quantum Bayesianism that reconstruct quantum theory without fundamental information postulates. Overall the key is finding ways to break out of circular self-confirmation and demonstrate the explanatory power of information concepts beyond recapitulating known quantum information phenomena. This requires creative theoretical and experimental work to validate the fruitfulness of information-theoretic paradigms in physics. There are likely many valid perspectives to handle this key challenge. Identifying and seriously engaging with the concern is an important first step. Finding ways to move beyond circularity is an essential challenge. Ongoing interdisciplinary research will uncover deeper truths. \[1\] von Neumann, J. (1932). Mathematical foundations of quantum mechanics. Princeton university press. \[2\] Zurek, “Complexity, entropy and the physics of information” \[3\] Wheeler, “Information, physics, quantum: The search for links” \[4\] Tegmark, “Consciousness as a state of matter”