It is discussed the role of mathematics in forming concepts of quantum theory, its effectiveness in comprehending the nature beyond the immediately sensual experiment.
It has become ever more clear over the past 70 years that reality is best described by a theory that no one fully understands and which cannot be applied to most everyday phenomena. Quantum theory has been subjected to many stringent tests and all of its predictions, however strange, have always been borne out. Originally developed to account for why atoms do not collapse and why they radiate and absorb energy in discrete amounts (quanta), it has now gone far beyond these rather simple beginnings. It is essentially a mathematical theory, so trying to describe it in words is analogous to transforming a picture into a poem. Inaccuracies, distortions and over-simplifications inevitably creep in. Nevertheless, one can convey the essence of the picture, and that is what is attempted here. Some grasp of what the material world is really like, and of the unfamiliar ways in which it can behave, is probably necessary to reaching an understanding of awareness and is certainly needed to comprehend the experimental evidence set out in Chapter 5.
The relationship between physical notions and the structures expressing them is an issue of primary importance the history and philosophy of pre-modern natural philosophy and of modern science. Historical evidence suggests that, when investigating the relationship between physics and mathematics, one should pay attention to the material, sensually perceivable forms mediating it: spoken or written words, drawings, artefacts, descriptions of experimental set-ups or, as the case discussed the present paper, symbolic notation. The reason for this is that, historically, physical notions and their expressions have very often been developed as one, and only distinguished from each other at a later stage. This was for example the case with what we today regard as mathematical and classical mechanics, which were developed the course of the eighteenth century as the discipline of the analysis of motion. When considered from a later point of view, both the physical notions and the concepts involved historical developments appear as being in flux, vague, and, as far as the side is concerned, non-rigorous. In such cases, verbal description, mechanical artefacts or symbols do not simply mediate between physical notions and structures, as might be the case at a later stage, but represent both of them one, allowing the historical actors to construct and manipulate physical-mathematical meaning by following, at times, their physical reasoning and, at times, their criteria of rigour. The history of quantum mechanics offers many examples of how new physics and new mathematics can emerge as one, with symbolic notation playing a central role shaping both. Among the many creators of quantum theory, Paul Dirac was particularly sensitive to questions of notation:
Abstract Quantum theory has presented scientists and philosophers of science with a series of perplexing questions. It seems to many that any attempt to comprehend a world described by quantum theory will require revision in our understanding of the nature of things far more radical than the revision in our understanding of the nature of space and time demanded by the theories of relativity. It has been claimed that to comprehend quantum theory we must revise our very understanding of such matters as the objective nature of reality and its independence from our perception of it, the nature of a complex system and its relation to its components, and the nature of causal and other kinds of determination in the world.
Abstract In this contribution, the role of epistemology in understanding quantum chemistry is discussed. Quantum chemistry is the study of the behavior of atoms and molecules using the principles of quantum mechanics. Epistemology helps us evaluate claims to knowledge, distinguish between justified and unjustified beliefs, and assess the reliability of scientific methods. In quantum chemistry, the epistemology of knowledge is heavily influenced by the mathematical nature of quantum mechanics, and models can be tested, proven, and validated through experimentation. This paper also discusses key concepts used in quantum chemistry, such as the wave-particle duality of matter and the uncertainty principle. This work utilizes Kant’s philosophy of science to frame debates and discussions in quantum chemistry, particularly with regard to the interplay between empirical observation and theory. Additionally, the text explores how Kant’s ideas about the role of the mind in constructing our understanding of the world can help us comprehend the counterintuitive phenomena of quantum mechanics and its applications in quantum chemistry theory.
В общем контексте проблемы недооценки социально-гуманитарной мысли профессионалами различных областей науки и техники обсуждается пример интерпретации квантовой механики. Аргументирована перспектива формирования этой интерпретации с учетом квантовой концепции целостности как особенного воплощения рационального холизма.