Initially proposed by Hugh Everett III as the “theory of the universal wave function,” the many worlds interpretation has since been developed and refined into one of the most influential ways of giving meaning to quantum mechanics. This volume explores the idea that if one adopts the many worlds interpretation, then one can avoid what Einstein called “spooky action at a distance,” the non-locality that is supposed to be a consequence of quantum entanglement according to other approaches. The essays in this volume articulate a clear and defensible formulation of the argument from locality for preferring the many worlds interpretation of quantum mechanics over its rivals and evaluate it. They question in what sense those in quantum foundations should care about locality, in particular, whether and how an interpretation of quantum mechanics must avoid action at a distance in order to maintain consistency with special relativity. Finally, these essays assess whether the many worlds theory needs a particular metaphysical or mathematical interpretation in order to achieve the aim of providing a local interpretation of quantum mechanics.
In a complete quantum theory, one would construct it based on what we can observe in a system and operationally define in our universe. This philosophy goes back to some of the original ideals of quantum theory defined by W. Heisenberg, N. Bohr, and others as part of the Copenhagen school of thought. We argue in this letter that that if one wishes to construct a complete quantum field theory, that it is most natural to construct it based on a nonlocal theory of observable principles. If this interpretation is valid, then the one-particle nonrelativistic limit that recovers quantum mechanics would as well be dynamically nonlocal. In this interpretation we derive the nonlocal Schr\"odinger equation. We will as well demonstrate that the canonical position--momentum commutator and the Heisenberg uncertainty principle emerge from translation covariance.
We present a historical-epistemological analysis of the foundations of quantum mechanics, highlighting the relationships between quantum mechanics and scientific realism, as well as the influence of the neo-positivist philosophy of the first decades of the 20th century. The great significance of the measurement process in the context of quantum mechanics is underlined as an essential element in providing a coherent description of reality, moving from micro to macrocosm, as well as the role that the measurement apparatus and the consciousness of the observer assume during the act of measurement, the related ontological problems, the question of the objectification of the wave function, and that of the definition of discernibility. We consider also an overview of the most important alternative proposals to the standard interpretation of quantum mechanics (Copenhagen interpretation), with particular reference to hidden variable theories and other alternatives to standard quantum mechanics philosophical approach, that are modifying the vision of reality, such as the Everett’s many-worlds theory, the QBism and unified holistic approaches, such as the Primordial Dynamic Space.
This doctoral dissertation on the foundations of quantum theory isolates and then formalizes a physically relevant concept that I have called"Epistemic Constraint."Here, epistemic constraints are the definite, intersubjectively agreeable, ordinary-language conditions under which experiments are described. The usual formulation of the quantum measurement problem, which I call the Schrodingerian measurement problem, has the structure of an anomaly: if we take quantum theory at face value, we expect no definite values, and yet we see definite values in experiments. The responses to this problem have been either to solve it or to dissolve it. These responses, which have taken the form of interpretation, modification, or reconstruction of quantum mechanics, seek either to derive (conceptually or mathematically) epistemic constraints from within quantum mechanics or suitable modifications of it, as is the case with certain interpretations and modifications, or to posit the epistemic constraint, or parts of it, as a primitive assumption with the goal of deriving quantum mechanics, as is the case in some reconstruction programs. In contrast to the Schrodingerian measurement problem, which had the structure of an anomaly, this dissertation develops the Bohrian Program, which (for lack of a better comparison) has a structure similar to the problem historically associated with Euclid's fifth postulate. It seeks to keep epistemic constraints as primitive in an onto-epistemic sense. It then seeks new physical conclusions from the joint consideration of quantum mechanics and epistemic constraints, without seeking to derive one from the other. Among other results, this leads to a notion of the probability of instantiability of the Born Rule that specifies when to apply the Born Rule and when to apply a unitary transformation to a quantum state.
From the fact that many people are dedicated to the quantization of gravity, it can be seen that people crave the integration of quantum theory and macroscopic theory. Let's first combine quantum mechanics with classical mechanics to gain insightful experiences. The citation introduces the Schrödinger-Tu equation, which has gravitational potential energy and can describe macroscopic objects. Several successful computational examples related to atoms and molecules using the combination of quantum and classical methods for use were listed. The wave mechanics representation method of classical mechanics laws has been derived. This indicates that quantum mechanics and classical mechanics can be compatible and coexist. There is still much evidence to suggest that the Schrödinger equation (SE) cannot exclude classical mechanical laws: The mass m in the SE can be large enough to bring the described object into the macroscopic range; Steady state SE is the Tψ+Vψ=Eψ, a combination of the wave function ψ and the expression T+V=E in classical mechanics; The potential energy function in the SE can originate from macroscopic force fields; F=ma and the SE can be converted to each other; Completed electron diffraction experiments that exhibit both wave and particle characteristics simultaneously. Important conceptual changes can drive the renewal of physics. The shift from quantum and classical incompatibility to compatibility is an important conceptual change that can lead to the birth of general wave mechanics.
Runsheng Tu· Brazilian Journal of Science· 0 citations
The physical content of a theory is not intrinsically tied to any single mathematical formalism. Both classical and quantum mechanics admit equivalent representations, notably in phase space and in Hilbert space, related by the Wigner-Weyl correspondence. While this correspondence has long been studied in mathematical physics, its foundational and operational implications are often left implicit. Here we give a systematic account of what changes, and what does not, when classical and quantum theories are expressed in each other's native language. This representational viewpoint separates artifacts (such as the appearance of non-positivity or negativity under certain maps) from robust structural distinctions that persist across representations, in particular noncommutativity and its $\hbar$-dependent $\star$-deformation of the classical algebra. We develop the comparison at the level of states, kinematics, and dynamics, and extend it to measurement by formulating both outcome statistics and state-update rules within the same framework.
S. Schlegel, Borivoje Daki'c, Flavio Del Santo· 0 citations
Rational Quantum Mechanics (RaQM) is a theory consistent with Gerard ’tHooft’s proposals about the locally causal nature of quantum physics. Based on a specific discretisation of the Riemann Sphere, the quantum state only is only defined in bases where squared amplitudes and complex phases (divided by 𝜋) are rational numbers. These ‘rational bases’ correspond to ’tHooft’s ontological bases in which the quantum state has a beable representation. Bell’s inequality is violated without breaking realism, locality or free choice. Instead, for each run in a Bell experiment, a number-theoretic property of the cosine function ensures that the squared amplitude of the singlet state is an irrational number in at least one of the two counterfactual pairs of bases needed to derive Bell’s inequality. Hence, the Measurement Independence assumption is violated - not for the nominal settings under the experimenters’ free control, but for the exact settings which were never under their control anyway. None of the grotesque conspiracies that plague conventional superdeterministic explanations of Bell’s Theorem exist. Bell’s Theorem implies RaQM is a holistic theory. As such, implications for models of cosmology are discussed. An experimental test of RaQM, achievable in about 5 years, is described.
T. Palmer· International Journal of Mod...· 0 citations
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