In the 20th century, physics became dominated by abstract mathematics, with a fundamental role for uncertainty. In contrast, computing was built on a foundation of mathematical certainty. John von Neumann was a primary source for both these foundations. I argue that both are misleading, and should be revised to reflect microscopic determinism with varying degrees of macroscopic uncertainty. I predict a future neoclassical physics without quantum entanglement, but no “theory of everything”. Future computing will involve neural networks that can embody consciousness, but no quantum computing. Formal mathematical proofs of undecidability or uncomputability will have little practical impact on either computing or physics, but absolute knowledge will remain unattainable. All future predictions should be regarded with skepticism.
In the 20th century, physics became dominated by abstract mathematics, with a fundamental role for uncertainty. In contrast, computing was built on a foundation of mathematical certainty. John von Neumann was a primary source for both these foundations. I argue that both are misleading, and should be revised to reflect microscopic determinism with varying degrees of macroscopic uncertainty. I predict a future neoclassical physics without quantum entanglement, but no “theory of everything”. Future computing will involve neural networks that can embody consciousness, but no quantum computing. Formal mathematical proofs of undecidability or uncomputability will have little practical impact on either computing or physics, but absolute knowledge will remain unattainable. All future predictions should be regarded with skepticism.
Extraordinary mathematicality of physics is also shown by dimensionlessness of Planck spacetime and mass. At the same time the Planck granularity of spacetime also shows that physics can be simulated by a binary computer. So physics is informational. But mathematics is not everything in physics, consciousness cannot be solely explained by mathematics. The reason that quantum gravity (QG) does not yet exist is the lack of knowledge about spacetime as background. Quantum mechanics is not complete, because foundational principle is not yet known, and because consciousness and QG are not yet explained. The free will and quantum randomness are similar unexplained phenomena. Even philosophy is important in physics, because what mathematics cannot describe in physics is ontology. And, intuition affects what is mainstream physics. Simplicity and clearness of physics and mathematics of physics are important not only for beginners, but also for the development of the fundamental physics. Uncertainty principle is so simple that maybe it could be derived without the use of wave functions. On the simplicity and clearness of fundamental physics it can be done a lot.
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.
Quantum mechanics was developed in the early 20th century as a computational algorithm to organize and predict the strange results of a wide variety of experiments involving the microscopic world (molecules, atoms, elementary particles), which appeared random but had a predictable probabilistic distribution. Despite its overwhelming success, the conceptual foundations of this algorithm remain unclear and extremely controversial. How can we connect the microscopic world described by quantum mechanics with the macroscopic world of our daily experience? What is the role of observers in this connection? Why don't strange quantum phenomena occur on macroscopic scales? How can we explain the nonlocal nature of quantum phenomena? In this article I will present some attempts to answer these and other basic questions, which constitute different theories with completely different worldviews, commenting on their strengths and weaknesses. We will conclude that quantum theory is still under construction, as there is no consensual formulation. Its development is a fundamental problem in contemporary physics, and in thought in general.
Classical physics is traditionally characterized as deterministic and founded on the real number continuum, while quantum mechanics is distinguished by its indeterminism and fundamental uncertainty relations. This apparent dichotomy, however, obscures a deeper continuity. We argue that both frameworks embody a common ontological principle: the physical prohibition of absolute precision. In classical physics, this prohibition is implicit, manifesting in information-theoretic bounds, the non-physicality of infinite-precision initial conditions (chaos theory), and the breakdown of determinism in singular configurations (Norton's dome). These phenomena reveal that the classical reliance on mathematical real numbers with infinite information content is an unphysical idealization. Quantum mechanics, by contrast, does not merely reflect this prohibition; it provides its precise quantitative expression. The Heisenberg uncertainty principle σxσp≥ℏ/2 and the non-commutative structure of observables are the exact mathematical formulation of the fact that physical information is fundamentally finite. The Planck constant ℏ is the universal scale that quantifies the minimal phase space volume—the “atom” of information—below which no further refinement is possible. Thus, quantum mechanics is not a separate theory but the completion of classical physics: it supplies the missing quantification of the principle that nature admits no infinite information density, and consequently, no absolutely precise physical quantities.
Abstract: Quantum computing and quantum information science constitute a rapidly evolving discipline at the intersection of physics, computer science, and information theory. This paper presents a systematic analysis of the conceptual foundations, theoretical frameworks, and technological challenges shaping the field. The discussion begins with the quantum-mechanical principles underpinning computation and information, followed by a rigorous framework analysis of key models such as qubits, entanglement, and quantum channels. The central problem addressed is the fragility of quantum states under noise and the corresponding need for reliable methods of computation, communication, and security. Methodologically, the paper integrates formal analysis of entropy and channel capacities with the study of error-correcting codes, fault-tolerant architectures, and emerging hardware platforms. The results synthesize advances in quantum algorithms, quantum error correction, quantum cryptography, and hybrid quantum–classical systems, highlighting both their theoretical limits and engineering realizations. The impact is evaluated through implications for secure communication, computational complexity, and future architectures, alongside ethical and societal reflections. By bridging foundational theory with practical challenges, the book offers a comprehensive resource that informs both academic inquiry and technological development. Its neutral, integrative perspective emphasizes not only the purpose of advancing reliable quantum technologies but also their broader implications for science, security, and society. Keywords Quantum computing, quantum information theory, quantum algorithms, quantum error correction, fault-tolerant quantum computation, quantum cryptography, quantum key distribution, post-quantum cryptography, entanglement, quantum channels, von Neumann entropy, quantum capacity, hybrid quantum–classical systems, quantum machine learning, quantum networks, emerging quantum architectures
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by position vectors as functions of time, x(t), while waves are modeled by tensor fields in space-time, Φ(t,x). These functions are embedded in, and evolve within space-time. All information about the physical system are coded in these mathematical functions, upon which the classical technologies are developed. In contrast, quantum theory models the physical system using a quantum state ∣α,t⟩, situated in an evolving within Hilbert space, portraying the system's reality with inherent uncertainty. Despite the probabilistic nature of reality observation, the quantum state ∣α,t⟩ can be precisely determined due to the unitary principle, provided we know the initial state. Therefore, it can serve as a foundation for developing quantum technologies, which we call quantum state-tronics similar to electronics. This discussion focuses on quantum computation, given its expansive scope. One of the paramount challenges in quantum computing is the scarcity of individuals equipped with the requisite knowledge of quantum field theory and the training necessary for this field. This article aims to elucidate the fundamental concepts of quantum field theory and their interconnections with quantum computing, striving to simplify them for those engaged in quantum computing.