# **Information, Matter, and the Universe** ## Abstract The concept of an informational universe, where information is not merely a descriptor but a fundamental constituent of reality, challenges traditional notions of matter and energy. This article explores the interplay of information, matter, and the nature of time, drawing on insights from quantum entanglement, superstrata research, and the arrow of time. We examine the implications of non-linear Planck-constant derivatives and discuss open questions regarding the unification of quantum mechanics and general relativity, the fundamental nature of information, and the role of consciousness in an information-based universe. --- ## **1. Introduction** The concept of an informational universe, eloquently encapsulated by physicist John Wheeler’s “it from bit” proposition, suggests that information is not merely a way to describe physical reality but rather a fundamental constituent of it (Wheeler, 1990). This challenges traditional notions of matter and energy as the primary building blocks of the cosmos, placing information as a crucial player in shaping the fabric of reality. Within this framework, superstrata research, stemming from string theory, offers a unique lens through which to explore the interplay of matter, information, and the nature of time (Mathur & Turton, 2014). This article delves into the intricate relationship between these concepts, examining how matter interacts with information, whether the nature of information itself is subject to change, and the implications for the arrow of time and the non-linearity of Planck-constant derivatives. --- ## **2. Quantum Entanglement and the Speed of Light** ### **Einstein’s Equation and Momentum** Einstein’s equation $E = mc^2$ is often simplified to emphasize the relationship between energy and mass. However, the full relativistic energy-momentum relation is: $E^2 = (mc^2)^2 + (pc)^2$ where $E$ is energy, $m$ is mass, $c$ is the speed of light, and $p$ is momentum. This equation shows that the total energy of a particle is a combination of its rest mass energy and its kinetic energy (which depends on momentum). This extended version is crucial when considering relativistic effects, such as those involving high-speed particles or systems with significant kinetic energy. ### **Entanglement And Faster-than-Light Signaling** Quantum entanglement appears to allow instantaneous correlations between entangled particles, regardless of the distance separating them. This phenomenon seems to bypass the speed of light limitation, which is a cornerstone of special relativity. However, it is crucial to distinguish between **correlation** and **signaling**: - **Correlation**: Entangled particles can instantly correlate their states, but this does not allow for the transmission of information faster than light. - **Signaling**: No information can be transmitted faster than the speed of light, as this would violate causality and the principles of relativity. #### **Why Entanglement Does Not Imply Faster-than-Light Signaling** Despite the instantaneous correlations observed in entanglement, no experiment has demonstrated faster-than-light signaling. The no-signaling theorem in quantum mechanics explicitly states that entanglement cannot be used to transmit information faster than light (Ghirardi et al., 1990). This theorem is supported by numerous experiments, including those by Aspect et al. (1982), Salart et al. (2008), and Yin et al. (2017), which have consistently shown that entangled particles maintain their correlations without violating causality. #### **Implications For the Structure of Spacetime** The instantaneous nature of entanglement raises questions about the nature of spacetime itself. While entanglement appears to bypass the speed of light constraint, it does not imply that information travels faster than light. Instead, it suggests that the structure of spacetime may be more complex than classical theories suggest. Some interpretations propose that spacetime is not a fundamental entity but emerges from more fundamental principles, such as information (Wheeler, 1990). #### **Einstein’s Full Energy-Momentum Relation and Entanglement** The full relativistic energy-momentum relation $E^2 = (mc^2)^2 + (pc)^2$ is essential for understanding the behavior of entangled particles. This equation shows that the total energy of a particle is determined by both its rest mass energy and its kinetic energy. In the context of entanglement, this equation ensures that the energy and momentum of entangled particles are conserved, even though their states are correlated instantaneously. This conservation ensures that no information can be transmitted faster than light, preserving causality. ### **Experimental Evidence** Several experiments have been conducted to test the nature of entanglement and its relationship to the speed of light: **Aspect et al. (1982)**: Alain Aspect and colleagues performed a series of experiments using entangled photons to test Bell’s inequalities. These experiments confirmed that entangled particles exhibit correlations that cannot be explained by classical physics, strongly supporting the quantum mechanical prediction of non-locality (Aspect et al., 1982). **Quasar Experiments**: In 2008, a team led by Daniel Salart used entangled photons and quasars to test the non-locality of quantum mechanics over vast distances. The results showed that entangled particles maintained their correlations even when separated by distances that would require faster-than-light signaling if classical causality were to hold (Salart et al., 2008). **Cosmic Bell Tests**: More recent experiments, such as those conducted by Juan Yin and colleagues, have used entangled photons sent from satellites to ground stations to test Bell’s inequalities over even longer distances. These tests have consistently confirmed the non-local correlations predicted by quantum mechanics (Yin et al., 2017). --- ## **3. Falsifying the Assumption of Instantaneous Entanglement** To falsify the assumption that entanglement is instantaneous, one would need to detect a violation of causality or a faster-than-light signal. However, no such violations have been observed in experiments. Despite the instantaneous correlations, no experiment has shown that information can be transmitted faster than light using entanglement. This is consistent with the no-signaling theorem in quantum mechanics, which states that entanglement cannot be used to send information faster than light (Ghirardi et al., 1990). Additionally, experiments testing Lorentz invariance, a fundamental symmetry of special relativity, have not found any violations that would suggest entanglement operates outside the constraints of relativity (Mattingly, 2005). ### **Can We Prove That Quantum Phenomena Like Entanglement Happen Instantaneously?** Quantum entanglement has been experimentally verified in numerous studies, with results consistent across different setups and conditions (Aspect et al., 1982). For example, in experiments involving entangled photons, measurements on one particle instantaneously correlate with the state of the other, regardless of the spatial separation. These correlations have been observed even when the measurements are made faster than light could travel between the two particles, suggesting that entanglement operates outside the constraints of classical spacetime. However, proving “instantaneous” action is challenging due to the limitations of measurement precision. The Planck time ($t_P \approx 5.39 \times 10^{-44}$ seconds), the smallest meaningful unit of time in physics, represents a boundary below which our current understanding of time and causality breaks down (Planck, 1899). If quantum effects occur at or near this scale, it may be impossible to measure them directly using existing technology. ### **Measuring Events at the Planck Scale** The Planck constant (\(\hbar\)) governs quantum phenomena, but measuring events at the Planck scale is currently beyond our technological capabilities. To measure something happening at a Planck interval would require instruments capable of resolving time intervals on the order of $t_P$, which is far smaller than any measurable timescale today. Additionally, a framework that integrates quantum mechanics and general relativity would be necessary, as both theories are needed to describe phenomena at this scale. Since we lack such instruments and a unified theory, we cannot definitively measure or falsify whether quantum effects occur instantaneously or are subject to some unknown constraints. ### **Are Quantum Effects Subject to $E = mc^2$ and Related Principles?** The equation $E = mc^2$ is often simplified for clarity, but its full form includes additional terms that account for momentum and potential energy: $E^2 = (mc^2)^2 + (pc)^2$ In the context of quantum mechanics, entangled particles do not violate conservation laws, including energy and momentum. The correlations observed in entanglement experiments are consistent with the principles of relativity, even if they appear non-local. The instantaneous nature of entanglement suggests that information transfer (if it occurs) might bypass the constraints imposed by the speed of light, leading to the hypothesis that information transcends or can somehow overcome these limitations (Einstein, Podolsky, & Rosen, 1935). If quantum effects are subject to $E = mc^2$ and related principles, then the energy associated with entangled states must still obey relativistic constraints. Any hidden mechanisms governing entanglement (e.g., superdeterminism or pilot-wave theories) would need to reconcile quantum non-locality with the structure of spacetime (Bohm, 1952). ### **What We Know:** Experiments confirm that entangled particles exhibit correlations that cannot be explained by classical physics (Aspect et al., 1982). Despite the instantaneous correlations, no information can be transmitted faster than light using entanglement. This is consistent with the no-signaling theorem in quantum mechanics, which states that entanglement cannot be used to send information faster than light (Ghirardi et al., 1990). Additionally, no violations of Lorentz invariance have been observed, suggesting that the speed of light remains a fundamental limit (Mattingly, 2005). ### **What We Assume:** Entanglement involves non-local correlations, but these do not violate causality or the speed of light constraint. Current interpretations of quantum mechanics (e.g., Copenhagen, Many-Worlds, or Bohmian mechanics) accurately describe reality, despite their philosophical differences. The assumption that spacetime is continuous and smooth down to the Planck scale, though this is untested and potentially flawed (Hawking, 1988). ### **Potential Falsifications:** If future experiments detect information being transmitted faster than light during entanglement measurements, it would challenge the assumption that entanglement is purely correlational. Discovering deviations from quantum predictions at extremely small scales (e.g., near the Planck length) could indicate new physics beyond the Standard Model (Smolin, 2001). Finding evidence of hidden variables or alternative frameworks (e.g., superdeterminism) could overturn the probabilistic nature of quantum mechanics (Bell, 1964). --- ## **4. The Nature of Information and the Big Bang** ### **Information And the Big Bang** The idea that information played a fundamental role in the creation of the universe is a fascinating hypothesis. Some theoretical frameworks suggest that the universe emerged from a state of pure information. In these frameworks, the Big Bang could be seen as a point where information was encoded in a non-physical form, which then gave rise to the physical universe. ### **Quantum Information and the Big Bang** Theories like the holographic principle and the information-theoretic approach to quantum gravity propose that the universe can be described in terms of information. The holographic principle posits that all the information contained within a volume of space can be represented as a theory on the boundary of that space. In the context of the Big Bang, this suggests that the entire universe could have originated from a highly compressed state of information, akin to a hologram (Bousso, 2002). The information-theoretic approach to quantum gravity suggests that spacetime itself may emerge from the entanglement of quantum degrees of freedom, with the geometry of spacetime being determined by the amount of information encoded in these entanglements (Susskind, 1995). This perspective aligns with the idea that the universe is fundamentally informational, with physical laws and structures emerging from a primordial state of pure information. ## **Non-Physical Information** The concept of non-physical information that transcends the constraints of space and time is speculative but intriguing. It suggests that the fundamental laws of physics, including the speed of light, might emerge from more fundamental principles of information (Wheeler, 1990). In this view, information exists independently of physical reality, potentially preceding the Big Bang. The universe as we know it emerges from a primordial state of pure information, which then gives rise to the physical laws and structures we observe. --- ## **5. Hypotheses and Open Questions** ### **Non-Local Hidden Variables** Some interpretations of quantum mechanics propose the existence of non-local hidden variables that could explain entanglement without violating relativity. The de Broglie-Bohm theory, also known as the pilot-wave theory, is one such interpretation. According to this theory, particles are guided by a “pilot wave” that determines their motion. This wave ensures that entangled particles remain correlated even when separated by large distances, providing a deterministic explanation for entanglement (Bohm, 1952). The de Broglie-Bohm theory avoids the need for faster-than-light signaling by positing that the correlations observed in entanglement experiments are not the result of instantaneous communication but rather the result of the pre-existing wave function that guides the particles. This approach resolves the apparent conflict between quantum non-locality and the principles of relativity by introducing a hidden variable that accounts for the observed correlations. ### **Superdeterminism** Superdeterminism is another hypothesis that avoids the need for faster-than-light signaling. This hypothesis suggests that the outcomes of entanglement experiments are predetermined by the initial conditions of the universe. In this framework, the choice of measurement settings in entanglement experiments is not random but predetermined by the initial conditions of the universe (Hossenfelder, 2014). This would explain the observed correlations without requiring faster-than-light communication. Superdeterminism challenges the assumption of free will in experimental design, suggesting that the choices made by experimenters are not truly independent but are instead influenced by the initial conditions of the universe. While this hypothesis is controversial, it provides a way to avoid the apparent violation of causality implied by entanglement without resorting to faster-than-light signaling. ### **Informational Universe Hypothesis (IUH)** The **Informational Universe Hypothesis (IUH)** posits that the universe can be fundamentally described in terms of information, with physical laws emerging from underlying informational principles. In this framework, gravity is not just a force but a manifestation of information density. The IUH suggests that the curvature of spacetime, as described by general relativity, arises from the distribution of information within the universe. This perspective aligns with the holographic principle, which posits that all the information contained within a volume of space can be represented as a theory on the boundary of that space (Bousso, 2002). The IUH proposes that the gravitational force is a consequence of the way information is distributed and processed within the universe. In this view, the strength of gravity is proportional to the density of information, and the geometry of spacetime emerges from the entanglement of quantum degrees of freedom. This hypothesis is supported by recent research in quantum gravity and the holographic principle, which suggest that the universe may be fundamentally informational (Susskind, 1995; Van Raamsdonk, 2010). #### **Foundational Research Supporting IUH** **Holographic Principle**: The holographic principle, a cornerstone of modern theoretical physics, supports the idea that the maximum amount of information in a region of space is proportional to the area of its boundary, rather than its volume (Bousso, 2002). This principle implies that the universe can be described as a two-dimensional information surface projected onto a three-dimensional space, suggesting that information density is a fundamental property of the universe. **Black Hole Thermodynamics**: Black hole thermodynamics provides further evidence for the informational nature of spacetime. The entropy of a black hole, which is proportional to the area of its event horizon, can be interpreted as a measure of the information contained within the black hole (Hawking, 1975). This connection between entropy, information, and spacetime geometry underscores the importance of information density in understanding quantum gravity. **Entanglement Equals Geometry**: Recent work in quantum gravity suggests that entanglement entropy, a measure of the quantum correlations between subsystems, could give rise to the geometry of spacetime (Van Raamsdonk, 2010). This “entanglement equals geometry” paradigm aligns with the IUH, where information density determines the structure of spacetime. ### **Open Questions** #### **Unification Of Quantum Mechanics and General Relativity** The lack of a unified theory of quantum gravity leaves open the possibility that our understanding of both quantum mechanics and relativity is incomplete. The quest for a unified theory of quantum gravity aims to reconcile the principles of quantum mechanics with those of general relativity. This could provide a deeper understanding of the role of information in the structure of spacetime (Smolin, 2001). Current approaches to quantum gravity, such as string theory and loop quantum gravity, offer different perspectives on how quantum mechanics and general relativity might be reconciled. String theory, for example, proposes that fundamental particles are one-dimensional strings vibrating at different frequencies, while loop quantum gravity suggests that spacetime itself is quantized at the Planck scale. Both approaches aim to provide a consistent framework for describing the universe at both the quantum and cosmic scales. #### **Fundamental Nature of Information** The idea that information is a fundamental aspect of reality, possibly preceding the physical universe, is a topic of ongoing research. Theories like the “it from bit” concept, proposed by John Wheeler, suggest that all physical entities, from particles to spacetime, arise from the fundamental bits of information (Wheeler, 1990). This idea challenges traditional notions of matter and energy as the primary building blocks of the cosmos, placing information at the center of reality. The “it from bit” hypothesis suggests that the universe is fundamentally informational, with physical laws and structures emerging from a primordial state of pure information. This perspective raises profound questions about the nature of reality and the role of information in shaping the universe. While this hypothesis is speculative, it provides a compelling framework for exploring the deep connections between information, matter, and the structure of spacetime. #### **Role Of Consciousness in the Informational Universe** The informational universe framework may offer valuable insights into the nature of consciousness and its connection to information processing. Studies suggest a deep intertwining of consciousness and information, proposing that the universe is not merely an expanse of inert matter and energy but a dynamic, conscious entity (Penrose, 1989). This perspective challenges traditional views of consciousness as an emergent property of complex biological systems, suggesting instead that it might be a fundamental aspect of reality, interwoven with the fabric of information that constitutes the universe. The role of consciousness in the informational universe raises important questions about the nature of reality and the relationship between mind and matter. Some researchers propose that consciousness is not merely an epiphenomenon of brain activity but a fundamental aspect of the universe, potentially influencing the flow of information and the structure of spacetime. This idea challenges the traditional materialist view of the universe and opens up new avenues for exploring the deep connections between consciousness, information, and the nature of reality. #### **Informational Universe Hypothesis (IUH) and Gravity** The IUH asserts that gravity represents information density, with the curvature of spacetime arising from the distribution of information within the universe (Quni, 2025). This hypothesis is supported by recent research in quantum gravity and the holographic principle, which suggest that the universe may be fundamentally informational. While this is a speculative idea, it aligns with the growing body of evidence that suggests information plays a central role in the structure of the universe. --- ## **6. The Nature of Information: Static or Dynamic?** The question of whether the fundamental nature of information is subject to change is a crucial aspect of the informational universe paradigm. Some researchers argue that the way information is represented and transmitted influences its nature, while others contend that certain fundamental aspects of human information-related behavior and information organization remain invariant despite technological advancements. This section explores these perspectives and evaluates the evidence supporting each viewpoint. ### **Dynamic Perspective** Some researchers argue that the Internet, as a medium of information transmission, has fundamentally altered the nature of knowledge itself (Floridi, 2010). This perspective suggests that the way information is represented and transmitted influences our understanding and interpretation of it. For example: - **Representation and Transmission**: The digital age has transformed how information is stored, accessed, and shared. Social media platforms, search engines, and other digital tools have changed the way people interact with information, leading to new forms of knowledge and understanding. - **Technological Evolution**: Technological advancements, such as artificial intelligence and machine learning, have introduced new ways of processing and generating information, potentially altering the very nature of what constitutes “information.” ### **Static Perspective** Others contend that despite technological advancements, certain fundamental aspects of human information-related behavior and information organization remain invariant. This implies that while the way we access and process information may evolve, the underlying principles governing information itself remain constant (Kuhn, 1962). For example: - **Consistency in Information Processing**: Human cognition and information processing have remained relatively stable over time, suggesting that the fundamental nature of information may be more static than dynamic. - **Scientific Durability**: Scientific knowledge, while subject to change and refinement, is generally durable. New discoveries and theories often build upon existing knowledge rather than completely rejecting it, indicating a certain degree of stability in the fundamental nature of information. ### **Physical Nature of Information** From a scientific perspective, there is a presumption that the universe operates in consistent patterns that are comprehensible through careful, systematic study. This suggests that the fundamental nature of information, as a reflection of these patterns, may be more static than dynamic. Furthermore, the **Shannon-Hartley theorem** demonstrates a strict mathematical relationship between information and energy. This finding supports the idea that information is not merely an abstract concept but a fundamental entity subject to physical laws, including the speed of light limitation. This constraint ensures that information cannot travel faster than light, maintaining causality in the universe (Shannon, 1948). ### **Bremermann’s Limit** The concept of **Bremermann’s limit**, which posits an upper bound on the rate at which information can be processed by matter, adds another layer to this intricate relationship. This limit suggests a fundamental constraint on the processing capacity of physical systems, potentially influencing the flow and transformation of information within the universe (Bremermann, 1962). ### **Summary Of Perspectives** | **Perspective** | **Key Arguments** | |-----------------|-------------------| | **Dynamic** | The way information is represented and transmitted influences its nature. The digital age has transformed how information is stored, accessed, and shared, leading to new forms of knowledge and understanding. | | **Static** | Certain fundamental aspects of human information-related behavior and information organization remain invariant despite technological changes. Scientific knowledge is generally durable, with new discoveries often building upon existing knowledge. | | **Physical** | Information is a fundamental entity subject to physical laws, including the speed of light limitation. The Shannon-Hartley theorem demonstrates a strict mathematical relationship between information and energy. | | **Durable** | Scientific knowledge, while subject to change, is durable, with modifications and refinements building upon existing knowledge. | --- ## **7. Implications for the Arrow of Time** ### **Introduction** The concept of the arrow of time, the unidirectional flow of time from past to future, is closely intertwined with the informational universe and superstrata research. The second law of thermodynamics, which states that entropy (disorder) tends to increase over time, provides a thermodynamic arrow of time. This principle aligns with our everyday experience of irreversible processes, such as an egg breaking or milk dispersing in coffee (Carroll, 2010). However, the fundamental laws of physics, at the microscopic level, are time-symmetric. This apparent contradiction raises questions about how a directed arrow of time can emerge from time-symmetric laws. One possible explanation lies in the cosmological context, with the universe’s initial low-entropy state as a crucial factor. This initial condition, combined with the universe’s tendency towards increased entropy and information processing, could give rise to the observed arrow of time (Hawking, 1988). ### **The Thermodynamic Arrow of Time** The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. This law provides a clear thermodynamic arrow of time, which aligns with our everyday experience of irreversible processes. For example, when you drop an egg, it shatters into pieces, and the entropy of the system increases. This increase in entropy is a hallmark of the thermodynamic arrow of time. However, the fundamental laws of physics, such as Newton’s laws of motion and Schrödinger’s equation in quantum mechanics, are time-symmetric. This means that the equations governing these laws do not distinguish between past and future. The apparent time-asymmetry in the thermodynamic arrow of time arises from the initial conditions of the universe. The universe began in a state of very low entropy, and as it evolved, entropy increased, giving rise to the observed arrow of time (Hawking, 1988). ### **The Cosmological Arrow of Time** The cosmological arrow of time is closely tied to the expansion of the universe and the initial low-entropy state of the Big Bang. The universe started in a highly ordered, low-entropy state, and as it expanded, entropy increased. This expansion process is driven by the positive energy density of matter and radiation, which leads to the observed expansion of the universe. The cosmological arrow of time is thus linked to the overall expansion and cooling of the universe. The cosmological arrow of time is also influenced by the distribution of matter and energy in the universe. The formation of stars, galaxies, and larger structures contributes to the increase in entropy, as these processes involve the conversion of potential energy into heat, which increases disorder. This increase in entropy aligns with the thermodynamic arrow of time, reinforcing the idea that the universe’s initial low-entropy state is a key factor in the emergence of the arrow of time (Hawking, 1988). ### **The Psychological Arrow of Time** In addition to the thermodynamic and cosmological arrows of time, there is also a psychological and perceptual aspect to consider. Our perception of time, including memory and volition, contributes to the psychological arrow of time. We remember the past but not the future, and we feel we can influence the future but not the past. This subjective experience of time’s flow further reinforces the concept of a unidirectional arrow of time (Eagleman, 2009). Recent research suggests the possibility of two arrows of time emerging from certain quantum systems. This challenges our conventional understanding of time as a single, unidirectional flow and opens up new avenues for exploring the nature of time in the quantum realm. For example, in some quantum systems, there may be two distinct directions of time, each corresponding to a different set of quantum states (Zurek et al., 2021). ### **Entropy And Life Processes** Entropy also plays a crucial role in enabling life processes, such as the flow of energy from the sun to the Earth. This connection between entropy and life further emphasizes the significance of the arrow of time in the context of the informational universe (Schrödinger, 1944). Life relies on the continuous input of energy from external sources, such as sunlight, to maintain order and counteract the increase in entropy. This flow of energy drives biological processes, from photosynthesis to cellular respiration, and is essential for the maintenance of life. ### **Information And the Arrow of Time** The informational universe framework suggests that information processing plays a crucial role in the emergence of the arrow of time. As information is fixed in records and structures, it creates a form of irreversibility, aligning with the direction of increasing entropy. This perspective ties together the thermodynamic, cosmological, and psychological arrows of time, providing a unified view of time’s directionality in the context of the informational universe. In this view, the accumulation of information within the universe contributes to the arrow of time. As information is stored and processed, it becomes more structured and less reversible, creating a sense of directionality in time. This perspective challenges traditional views of time as a purely thermodynamic or cosmological phenomenon, suggesting instead that information processing is a fundamental aspect of time’s directionality (Zurek et al., 2021). ### **Decoherence And the Arrow of Time** Decoherence is a process that explains how quantum systems lose their quantum properties and transition to classical behavior due to interactions with their environment. Recent research has explored the phenomenon of decoherence in the context of the arrow of time, specifically investigating the early stages of **einselection**, a process where a quantum system evolves into a stable classical state. This research has identified a new phenomenon called the “copycat process,” which occurs early during decoherence and contributes to the emergence of classical behavior from quantum systems (Zurek et al., 2021). To clarify, **einselection** refers to the process by which certain quantum states become “selected” or stabilized through interactions with the environment, leading to the emergence of classical behavior. The **copycat process** describes how quantum systems mimic the behavior of their environment during decoherence, effectively transitioning from quantum uncertainty to classical predictability. --- ## **8. Non-Linearity of Planck-Constant Derivatives** The Planck constant (\(\hbar\)) is a fundamental physical constant that governs the scale of quantum phenomena. Its non-linearity, particularly in the context of derivatives, has implications for the nature of information and physical reality. In quantum mechanics, the Planck constant appears in the commutation relation between position and momentum operators, which implies an inherent uncertainty in their simultaneous measurement. This uncertainty principle is a cornerstone of quantum theory and highlights the non-linear relationship between these fundamental quantities (Heisenberg, 1927). Moreover, the Planck constant plays a crucial role in the path integral formulation of quantum mechanics, where the evolution of a system is determined by summing over all possible paths, weighted by the exponential of the action divided by \(\hbar\) (Feynman, 1948). This formulation emphasizes the importance of the Planck constant in determining the quantum behavior of systems. The Planck constant is not only crucial for understanding quantum phenomena but also has practical applications in metrology. It is used to define the kilogram, the SI unit of mass. This highlights the fundamental importance of the Planck constant in both theoretical and experimental physics (BIPM, 2019). Furthermore, the Planck constant is intimately connected to the concept of action in physics. Action is a physical quantity that describes the dynamics of a system over time. The Planck constant can be considered the “quantum of action,” meaning it represents the smallest possible unit of action. This connection further emphasizes the significance of the Planck constant in understanding the fundamental laws of physics. The non-linearity of Planck-constant derivatives underscores the unique and counterintuitive nature of quantum mechanics and its departure from classical physics. It highlights the inherent uncertainty and non-deterministic nature of the quantum world, where particles can exist in multiple states simultaneously, and measurements can fundamentally alter the system being observed. ### **Falsifying Assumptions About Quantum Phenomena** The non-linearity of Planck-constant derivatives and the implications for quantum phenomena like entanglement raise important questions about the assumptions we make in physics. For instance, while Einstein’s equation $E = mc^2$ is often interpreted as implying that nothing can travel faster than the speed of light, this interpretation requires nuance. The full form of the equation, which includes momentum, is: $E^2 = (mc^2)^2 + (pc)^2$ This extended version is crucial when considering relativistic effects, such as those involving high-speed particles or systems with significant kinetic energy. In the context of quantum mechanics, entangled particles exhibit correlations that appear to bypass the constraints imposed by the speed of light, suggesting that information might transcend classical spacetime (Zurek et al., 2021). ### **Can We Prove That Quantum Phenomena Like Entanglement Happen Instantaneously?** Quantum entanglement has been experimentally verified in numerous studies, with results consistent across different setups and conditions (Aspect et al., 1982). For example: - In experiments involving entangled photons, measurements on one particle instantaneously correlate with the state of the other, regardless of the spatial separation. - These correlations have been observed even when the measurements are made faster than light could travel between the two particles, suggesting that entanglement operates outside the constraints of classical spacetime. However, proving “instantaneous” action is challenging due to the limitations of measurement precision. The Planck time ($t_P \approx 5.39 \times 10^{-44}$ seconds), the smallest meaningful unit of time in physics, represents a boundary below which our current understanding of time and causality breaks down (Planck, 1899). If quantum effects occur at or near this scale, it may be impossible to measure them directly using existing technology. ### **Measuring Events at the Planck Scale** The Planck constant (\(\hbar\)) governs quantum phenomena, but measuring events at the Planck scale is currently beyond our technological capabilities. To measure something happening at a Planck interval would require: - Instruments capable of resolving time intervals on the order of $t_P$, which is far smaller than any measurable timescale today. - A framework that integrates quantum mechanics and general relativity, as both theories are needed to describe phenomena at this scale. Since we lack such instruments and a unified theory, we cannot definitively measure or falsify whether quantum effects occur instantaneously or are subject to some unknown constraints. ### **Are Quantum Effects Subject to $E = mc^2$ and Related Principles?** The equation $E = mc^2$ is often simplified for clarity, but its full form includes additional terms that account for momentum and potential energy: $E^2 = (mc^2)^2 + (pc)^2$ In the context of quantum mechanics: - **Entangled Particles**: Entangled particles do not violate conservation laws, including energy and momentum. The correlations observed in entanglement experiments are consistent with the principles of relativity, even if they appear non-local. - **Instantaneous Correlations**: The instantaneous nature of entanglement suggests that information transfer (if it occurs) might bypass the constraints imposed by the speed of light, leading to the hypothesis that information transcends or can somehow overcome these limitations (Einstein, Podolsky, & Rosen, 1935). If quantum effects are subject to $E = mc^2$ and related principles, then: - The energy associated with entangled states must still obey relativistic constraints. - Any hidden mechanisms governing entanglement (e.g., superdeterminism or pilot-wave theories) would need to reconcile quantum non-locality with the structure of spacetime (Bohm, 1952). ## **9. Recap: Knowns, Assumptions, and Open Questions** ### **What We Know:** **Quantum Entanglement**: Experiments confirm that entangled particles exhibit correlations that cannot be explained by classical physics (Aspect et al., 1982). **No Faster-than-Light Signaling**: Despite the instantaneous correlations, no information can be transmitted faster than light using entanglement. This is consistent with the no-signaling theorem in quantum mechanics, which states that entanglement cannot be used to send information faster than light (Ghirardi et al., 1990). **Relativistic Constraints**: No violations of Lorentz invariance have been observed, suggesting that the speed of light remains a fundamental limit (Mattingly, 2005). ### **What We Assume:** **Entanglement Involves No Faster-than-Light Communication**: Entanglement involves non-local correlations, but these do not violate causality or the speed of light constraint. **Emergence of Physical Laws**: The idea that physical laws, including the speed of light, might emerge from more fundamental principles of information is a speculative but intriguing hypothesis. ### **Potential Falsifications:** **Detection of Faster-than-Light Signaling**: If future experiments detect information being transmitted faster than light during entanglement, it would challenge the current understanding of both quantum mechanics and relativity. **Deviations from Quantum Predictions**: Discovering deviations from quantum predictions at extremely small scales (e.g., near the Planck length) could indicate new physics beyond the Standard Model (Smolin, 2001). **Hidden Variables or Alternative Frameworks**: Finding evidence of hidden variables or alternative frameworks (e.g., superdeterminism) could overturn the probabilistic nature of quantum mechanics (Bell, 1964). ## **10. Discussion** The informational universe paradigm presents a profound shift in our understanding of reality, suggesting that information is not merely a tool for describing the universe but rather a fundamental building block of it. This perspective raises profound questions about the nature of reality, the relationship between information and matter, and the role of consciousness in the universe. While many of these questions remain open, the exploration of the informational universe paradigm has the potential to lead to groundbreaking discoveries and a deeper understanding of our place in the cosmos. One of the key implications of the informational universe paradigm is the possibility that physical laws, including the speed of light, might emerge from more fundamental principles of information. This challenges traditional notions of physics and suggests that information could play a more fundamental role in shaping the universe than previously thought. The exploration of this possibility could lead to a revolution in our understanding of physics and the fundamental laws governing the universe. Another important aspect of the informational universe paradigm is the question of whether the nature of information itself is subject to change. While some argue that the way information is represented and transmitted influences its nature, others contend that certain fundamental aspects of information remain invariant despite technological advancements. The investigation of this question has implications for our understanding of knowledge, technology, and the evolution of information in the universe. The informational universe paradigm also has implications for the arrow of time, suggesting that information processing plays a crucial role in the emergence of time’s directionality. As information is fixed in records and structures, it creates a form of irreversibility, aligning with the direction of increasing entropy. This perspective offers a unified view of time’s directionality, tying together the thermodynamic, cosmological, and psychological arrows of time. The exploration of the informational universe paradigm is still in its early stages, and many open questions remain. However, the pursuit of these questions has the potential to lead to profound insights into the nature of reality and our place in the universe. The informational universe paradigm offers a new lens through which to view the cosmos, and its exploration promises to be a fascinating and fruitful endeavor for years to come. --- ## **References** Aspect, A., Dalibard, J., & Roger, G. (1982). Experimental test of Bell’s inequalities using time-varying analyzers. *Physical Review Letters*, 49(25), 1804–1807. Bousso, R. (2002). The holographic principle. *Reviews of Modern Physics*, 74(3), 825–874. Bremermann, H. J. (1962). Optimization through evolution and recombination. *Self-Organizing Systems*, 93–106. Carroll, S. 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