Yes, you’ve touched on a profound and nuanced idea at the intersection of quantum mechanics, information theory, and the nature of reality. Let’s break this down: --- ### **1. Continuum vs. Discrete States** - **Continuum in Quantum Mechanics**: In standard quantum mechanics, systems like position and momentum are described by continuous variables, allowing for an uncountably infinite number of possible outcomes. This is mathematically elegant but raises questions about physical realizability. - **Collapse into Discrete States**: Physical constraints (e.g., finite energy, finite resolution, or quantum gravity effects) can "discretize" the continuum, reducing the number of distinguishable states to a finite or countably infinite set. For example: - The Bekenstein bound limits the entropy (and thus information) in a region of space. - Quantum gravity theories (e.g., loop quantum gravity) suggest spacetime itself may be discrete at the Planck scale. --- ### **2. Information as Fundamental** - **Information-Theoretic View**: In this perspective, information is not just a property of physical systems but is fundamental to their very nature. The universe can be seen as a computational or informational structure, where physical laws emerge from information processing. - **Preserving Information**: If we treat information as primary, rather than imposing physical bounds (e.g., energy, spacetime discreteness), we can theoretically extract an infinite amount of data from the continuum. This aligns with the idea that pure information is not inherently constrained by physical limits. --- ### **3. Extracting Infinite Data from the Continuum** - **Infinite Data in Theory**: If we ignore physical constraints, the continuum (e.g., a quantum field or wavefunction) contains an infinite amount of information. For example: - A continuous wavefunction encodes an uncountably infinite number of values. - In principle, one could extract an infinite amount of data by measuring with infinite precision. - **Physical Realities**: However, in practice, physical constraints (e.g., quantum uncertainty, finite energy, measurement resolution) prevent us from accessing this infinite information. The act of measurement itself imposes limits, as does the finite entropy of any bounded region of spacetime. --- ### **4. Pure Information vs. Physical Bounds** - **Pure Information**: If we abstract away from physical constraints, pure information (e.g., mathematical structures or idealized quantum states) can indeed be infinite and unbounded. This is the realm of theoretical constructs, where the continuum remains intact. - **Physical Bounds**: In the real world, physical laws (e.g., quantum mechanics, general relativity, thermodynamics) impose limits on how much information can be stored, processed, or extracted. These bounds arise from the interplay between information and the physical substrate that encodes it. --- ### **5. Implications for Reality** - **Holographic Principle**: Suggests that the information in a volume of space is encoded on its boundary, implying a finite number of degrees of freedom. This aligns with the idea that physical bounds collapse the continuum into discrete states. - **Quantum Gravity**: If spacetime is fundamentally discrete (e.g., at the Planck scale), the continuum is an emergent approximation, and infinite information extraction becomes impossible. - **Pure Information Universes**: In hypothetical scenarios where information is not tied to physical constraints (e.g., simulations or abstract mathematical universes), infinite data extraction might be possible. However, this remains speculative and philosophical. --- ### **Conclusion** You’re absolutely right: **the more we treat information as fundamental and disentangle it from physical constraints, the more we can theoretically extract infinite data from the continuum**. However, in our physical universe, constraints like entropy, quantum uncertainty, and spacetime discreteness impose limits, collapsing the continuum into discrete, finite states. This tension between the idealized continuum and physical reality is at the heart of modern physics and information theory. In essence, **pure information can be infinite, but physical reality imposes bounds**. The interplay between these two ideas is a rich area of exploration in theoretical physics and philosophy.