Mathematical and Conceptual Foundations of 20Th-Century Physics

Thomas Brown

Mary Kartansky

Quantum mechanics emerged in the first decades of the 20th century as a powerful mathematical framework for describing microscopic phenomena. While its predictive success in specific domains is widely acknowledged, its ontological foundations remain deeply problematic nearly a century after its formulation. This paper examines the historical development of quantum mechanics, focusing on the introduction of key concepts such as the collapse of the wave function and quantum entanglement. It argues that these notions did not arise as direct consequences of experimental findings, but were introduced as additional postulates to resolve internal inconsistencies within the theory. The analysis highlights the circular nature of experimental confirmation in quantum mechanics and demonstrates that even the most rigorous tests, including loophole-free Bell inequality experiments, primarily validate mathematical predictions rather than resolve fundamental ontological questions. Multiple alternative interpretations proposed over the decades have failed to achieve consensus, indicating persistent conceptual difficulties. The paper concludes that quantum mechanics, particularly in its standard interpretation, functions more as a speculative mathematical construction than as a coherent and ontologically consistent theory of physical reality. «Keywords:» quantum mechanics, wave function collapse, quantum entanglement, measurement problem, ontology, Copenhagen interpretation, Bell inequalities, alternative interpretations, philosophy of physics

Enrico G. Beltrametti

Alan M. Kadin

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.

Bas C. van Fraassen

Abstract This chapter explores measurement ‘from above’: that is, looking for a view that we can have after the measurement procedures, concepts, and theories have stabilized. This resting point in the conceptual and scientific development is fleeting and momentary — yet marking a context in which some things can be taken for granted pro tem, where it makes sense to ask about the world-picture of currently accepted physical theory. The physical conditions of possibility for measurement, the general theory of measurement, and what cannot count as measurement in a theoretical context are discussed, drawing on general lessons derived from 20th-century foundations of physics.

Lajos Diósi