We discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics (QM) might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the semantic level, has severe difficulties when considering the syntactic level of the theory.
We discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics (QM) might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the semantic level, has severe difficulties when considering the syntactic level of the theory.
In this paper we discuss the relation of quantum theory to the problem of metaphysics.Based on metaphysical and anti-metaphysical stances, we put forward an 'interpretational map' of quantum mechanics in general and of the modal interpretation in particular.Thus, within the modal interpretation, we distinguish between: Modal Interpretations (which start from) the Mathematical Formalism (MIMF) and Modal Interpretations (which start from) Metaphysical Principles (MIMP).Finally, we argue for a middle path in between metaphysical principles and the formal conditions imposed on quantum mechanics.
The measurement problem is one of the major philosophical problems in the Philosophy of Quantum Mechanics. Modal Interpretations of Quantum Mechanics aim to overcome the measurement problem, however, not always without a hitch: other problems arise. That is, some Modal Interpretations claim that a property Q, considered in a subsystem , is a di erent property while considered in the composite physical system , this while both situations are empirically indistinguishable: a non-empirical mismatch ensues. The mismatch, that seems to manifest at the metaphysical level, implies that empirically equivalent propositions like \\the left-hand side of the table is green" (subsystem) and \\the table is green at the left-hand side" (composite system) are metaphysically di erent. Although such a conclusion is clearly at odds with our everyday idea of properties, in my thesis, I question why metaphysical equivalence should (directly) ensue from empirical equivalence. The goal is to provide an explanation why the mismatch can been seen as a correct representation. Furthermore, I question what is exactly ment by metaphysical. As it turns out, under certain circumstances, by using an injective non-surjective function f that sends ordered pairs of operators to quantitative properties, in all possible worlds, the mismatch appears to be a correct representation. Nevertheless, since there are good reasons to renounce the mismatch, I question the level of activity and I invoke a more ne-grained version of metaphysics, i.e hyperintensional metaphysics. A relation between two entities is considered as hyperintensional from the very moment the relation is more ne-grained than necessary equivalence: beyond necessary equivalence. Finally, I claim that the mismatch must be understood in terms of beyond necessary equivalence and should be seen as a correct representation of the relation between language and reality in all hyperintensional worlds.
In this paper we derive a theorem which proves that the physical interpretation implied by the first postulate of quantum mechanics (QM) is inconsistent with the orthodox formalism. In order to expose this inconsistency we will analyze how the concept of ‘physical system’ is built within classical theories through the notion of invariance and explain in what sense a vector in Hilbert space is not capable of fulfilling these same mathematical conditions. Through an analysis of the mathematical formalism we derive a No Dynamical Invariance (NDI) theorem which proves that, contrary to what is claimed in the first postulate, a vector in Hilbert space cannot be interpreted coherently as the state of a physical (quantum) system. We conclude the paper by analyzing the consequences of the NDI theorem with respect to several ongoing debates in QM.
What is the proper metaphysics of quantum mechanics? In this dissertation, I approach the question from three different but related angles. First, I suggest that the quantum state can be understood intrinsically as relations holding among regions in ordinary space-time, from which we can recover the wave function uniquely up to an equivalence class (by representation and uniqueness theorems). The intrinsic account eliminates certain conventional elements (e.g. overall phase) in the representation of the quantum state. It also dispenses with first-order quantification over mathematical objects, which goes some way towards making the quantum world safe for a nominalistic metaphysics suggested in Field (1980, 2016). Second, I argue that the fundamental space of the quantum world is the low-dimensional physical space and not the high-dimensional space isomorphic to the ``configuration space.'' My arguments are based on considerations about dynamics, empirical adequacy, and symmetries of the quantum mechanics. Third, I show that, when we consider quantum mechanics in a time-asymmetric universe (with a large entropy gradient), we obtain new theoretical and conceptual possibilities. In such a model, we can use the low-entropy boundary condition known as the Past Hypothesis (Albert, 2000) to pin down a natural initial quantum state of the universe. However, the universal quantum state is not a pure state but a mixed state, represented by a density matrix that is the normalized projection onto the Past Hypothesis subspace. This particular choice has interesting consequences for Humean supervenience, statistical mechanical probabilities, and theoretical unity.
Quantum Mechanics (QM) has faced deep controversies and debates since its origin when Werner Heisenberg proposed the first mathematical formalism capable to operationally account for what had been recently discovered as the new field of quantum phenomena. Today, even though we have reached a standardized version of QM which is taught in Universities all around the world, there is still no consensus regarding the conceptual reference of the theory and, if or if not, it can refer to something beyond measurement outcomes. In this work we will argue that the reason behind the impossibility to reach a meaningful answer to this question is strictly related to the 20th Century Bohrian-positivist re-foundation of physics which is responsible for having introduced within the theory of quanta a harmful combination of metaphysical dogmatism and naive empiricism. We will also argue that the possibility of understanding QM is at plain sight, given we return to the original framework of physics in which the meaning of understanding has always been clear.
In classical physics, probabilistic or statistical knowledge has been always related to ignorance or inaccurate subjective knowledge about an actual state of affairs. This idea has been extended to quantum mechanics through a completely incoherent interpretation of the Fermi-Dirac and Bose-Einstein statistics in terms of strange quantum particles. This interpretation, naturalized through a widespread way of speaking in the physics community, contradicts Born's physical account of Ψ as a wave which provides statistical information about outcomes that, in fact, cannot be interpreted in terms of 'ignorance about an actual state of affairs'. In the present paper we discuss how the metaphysics of actuality has played an essential role in limiting the possibilities of understating things differently. We propose instead a metaphysical scheme in terms of powers with definite potentia which allows us to consider quantum probability in a new light, namely, as providing objective knowledge about a potential state of affairs.