In quantum mechanics we have a consistent mathematical structure, but no interpretation in terms of physical images in the classical sense. I question the universal applicability of such images, by arguing that they are products of a classical language. This point of view is in accordance with the Sapir‐Whorf Hypothesis, which states that intuition is a product of language, rather that language being an expression of a pre‐linguistic intuition. The resulting position is denoted linguistic empiricism. This tenet, with the additional assumption that mathematics is a language in physics, is applied to both classical and quantum physics. Some applications of this theory are outlined, mainly in the quantum theory of molecules, and the concept of space.
In quantum mechanics we have a consistent mathematical structure, but no interpretation in terms of physical images in the classical sense. I question the universal applicability of such images, by arguing that they are products of a classical language. This point of view is in accordance with the Sapir‐Whorf Hypothesis, which states that intuition is a product of language, rather that language being an expression of a pre‐linguistic intuition. The resulting position is denoted linguistic empiricism. This tenet, with the additional assumption that mathematics is a language in physics, is applied to both classical and quantum physics. Some applications of this theory are outlined, mainly in the quantum theory of molecules, and the concept of space.
According to traditional empiricist philosophy of science, concepts and meaning grow out of sense experience, and the mathematical structure of a physical theory is nothing but a formalisation of a given meaning‐content. This view seems to work well in classical mechanics. But it breaks down in quantum physics, where we have a self‐supported mathematical structure which resists any conceptual or pictorial interpretation in the traditional sense. Thus, traditional empiricism is flawed. Quantum physics teaches us that mathematics is a language in itself which extends beyond ordinary language. To understand the meaning of this extended language, we have to explore how new concepts and intuitions grow out of mathematics, not the other way around. The symbolic structure is prior to its meaning. This point of view is called linguistic empiricism, to stress that the connection with experience is still crucial. As cases, I compare the concept of stiffness in classical mechanics and the concept of electron density in quantum mechanics. The last case demonstrates that the wave function has a richer interpretation than the probabilistic one concerning measurement of position.
A philosophy of physics called “linguistic empiricism” is presented and applied to the interpretation problem of quantum mechanics. This philosophical position is based on the works of Jacques Derrida. The main propositions are (i) that meaning, included the meaning attached to observations, are language‐dependent and (ii) that mathematics in physics should be considered as a proper language, not necessary translatable to a more basic language of intuition and immediate experience. This has fundamental implications for quantum mechanics, which is a mathematically coherent and consistent theory; its interpretation problem is associated with its lack of physical images expressible in ordinary language.
About twenty years ago, we proposed the mathematical formulation of Heisenberg's uncertainty principle, and further, we concluded that Heisenberg's uncertainty principle and EPR-paradox are not contradictory. This is true, however we now think that we should have argued about it under a certain firm interpretation of quantum mechanics. Recently we proposed the linguistic quantum interpretation (called quantum and classical measurement theory), which was characterized as a kind of metaphysical and linguistic turn of the Copenhagen interpretation. This turn from physics to language does not only extend quantum theory to classical systems but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics, in other words, quantum philosophy). In fact, we can consider that traditional philosophies have progressed toward quantum philosophy. In this paper, we first review the linguistic quantum interpretation, and further, clarify the relation between EPR-paradox and Heisenberg's uncertainty principle. That is, the linguistic interpretation says that EPR-paradox is closely related to the fact that syllogism does not generally hold in quantum physics. This fact should be compared to the non-locality of Bell's inequality.
The argument of this article is threefold. First, the article argues that from its rise in the sixteenth century to our own time, the advancement of modern physics as mathematical-experimental science has been defined by the invention of new mathematical structures. Second, the article argues that quantum theory, especially following quantum mechanics, gives this thesis a radically new meaning by virtue of the following two features: on the one hand, quantum phenomena are defined as essentially different from those found in all previous physics by purely physical features; and on the other, quantum mechanics and quantum field theory are defined by purely mathematical postulates, which connect them to quantum phenomena strictly in terms of probabilities, without, as in all previous physics, representing or otherwise relating to how these phenomena physically come about. While these two features may appear discordant, if not inconsistent, I argue that they are in accord with each other, at least in certain interpretations (including the one adopted here), designated as “reality without realism”, RWR, interpretations. This argument also allows this article to offer a new perspective on a thorny problem of the relationships between continuity and discontinuity in quantum physics. In particular, rather than being concerned only with the discreteness and continuity of quantum objects or phenomena, quantum mechanics and quantum field theory relate their continuous mathematics to the irreducibly discrete quantum phenomena in terms of probabilistic predictions while, at least in RWR interpretations, precluding a representation or even conception of how these phenomena come about. This subject is rarely, if ever, discussed apart from previous work by the present author. It is, however, given a new dimension in this article which introduces, as one of its main contributions, a new principle: the mathematical complexity principle.
Recently we proposed the linguistic Copenhagen interpretation (or, quantum language), which has a great power to describe both classical and quantum systems.Thus we think that quantum language can be viewed as the language of science.Therefore, it makes sense to study, from the quantum linguistic point of view, Wittgenstein's picture theory, since he must have wanted to create a language of science.In this paper, we show that the proposition that Wittgenstein studied in his book "Tractatus Logico-Philosophicus" can be regarded as a binary projective measurement in classical quantum language.And thus, we conclude that Wittgenstein's language (i.e., the language that he supposed in his book) is realized by classical quantum language.Hence, now we can fully understand Wittgenstein's picture theory since the reason his book is incomprehensible is that he did not define his language.
Recently, we proposed quantum language (in short, QL) as a mathematical realization of the quantum mechanical worldview. QL has the form of “axioms (measurement and causality)” + “linguistic Copenhagen interpretation”. And the quantum language can cover both quantum and classical systems. In this way, QL is one of the most powerful scientific theories beyond statistics, and I believe QL is the only dualism that has been scientifically successful. If so, the history of Western philosophy (mostly dualistic idealism) can be discussed from the quantum linguistic point of view. In this paper, we discuss the similarities between quantum language and Cartesian and Kantian epistemology. We conclude that “Axioms (measurement and causality)” can be characterized as a study belonging to Continental rationalism that sought to advance Descartes’s mind-body dualism. On the other hand, “linguistic Copenhagen interpretation” belongs to British empiricism (Locke, Berkeley, Hume, Kant), which can be characterized as the epistemological application of Descartes’s mind-body dualism. The conventional theory is that continental rationalism and British empiricism were synthesized by Kant. Therefore, I think it is necessary to weigh the usual conventional theory with our claims.