According to the orthodox interpretation of quantum mechanics (Bohr being its leading voice), the attributes of a physical object (position, momentum, spin, etc.) can be assigned only when they have been measured. Einstein advocated the local realist viewpoint that an object had definite attributes whether they had been measured or not. The Copenhagen school view that measurement actually produces an object’s property would imply that the measurement of one part of an entangled quantum state can instantaneously fix the value of another part, no matter how far the two parts have been separated. Einstein, Podolsky, and Rosen devised a thought experiment to shine a light on this “spooky action-at-a-distance” feature; its discussion and debate have illuminated the meaning of quantum mechanics (QM). It led later to Bell’s theorem showing that these seemingly philosophical questions can lead to observable results. The experimental vindication of the orthodox theory has sharpened our appreciation of the nonlocal features of quantum mechanics. Nevertheless, the counter-intuitive QM picture of objective reality still troubles many, leaving one to wonder whether quantum mechanics is ultimately a complete theory.
According to the orthodox interpretation of quantum mechanics (Bohr being its leading voice), the attributes of a physical object (position, momentum, spin, etc.) can be assigned only when they have been measured. Einstein advocated the local realist viewpoint that an object had definite attributes whether they had been measured or not. The Copenhagen school view that measurement actually produces an object’s property would imply that the measurement of one part of an entangled quantum state can instantaneously fix the value of another part, no matter how far the two parts have been separated. Einstein, Podolsky, and Rosen devised a thought experiment to shine a light on this “spooky action-at-a-distance” feature; its discussion and debate have illuminated the meaning of quantum mechanics (QM). It led later to Bell’s theorem showing that these seemingly philosophical questions can lead to observable results. The experimental vindication of the orthodox theory has sharpened our appreciation of the nonlocal features of quantum mechanics. Nevertheless, the counter-intuitive QM picture of objective reality still troubles many, leaving one to wonder whether quantum mechanics is ultimately a complete theory.
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.
In the Einstein-Bohr debate, Einstein considered quantum mechanics incomplete and disagreed with Born's probabilistic interpretation of wave-functions, which collapse abruptly once measurements are performed on the corresponding microscopic objects. Inspired by Einstein, Bell and his followers intended to complete quantum mechanics within the framework of local realism. Regrettably, the deterministic correlation between distant components of a separable system in Einstein's local-realist description of the world is mistaken for the so-called non-locality or "nonlocal-interaction" in the world described by Bell's theorem, which leads to the questionable interpretation of the experimental results obtained by testing Bell inequalities. This article introduces a new principle, the general principle of measurements, which is proved as a mathematical theorem and allows quantum mechanics to be completed within the framework of local realism while keeping the formal axiomatic definition of a general Hilbert space essentially unchanged. Using disjunction ("or") as the logical relation between orthonormal vectors spanning a given Hilbert space, the completed quantum theory precludes inexplicable collapses of wave-functions and is intuitively comprehensible, thus alleviating much difficulty in understanding quantum mechanics. Among various world views, Einstein's local-realist world view is correct.
In the interpretation of Quantum Mechanics, there were four major mistakes done at different levels: (1)A misinterpretation of Bell’s theorem in which the original intent did not include non-locality, but as a test to see whether or not a particle has a certain property that can be measured. (2)A misinterpretation of the disagreement between Einstein and Bohr. Einstein’s objection to the collapse of the wave function implied a spooky action at a distance, while Bohr insisted on the instantaneous collapse of the wave function which he mistook to be a real wave. (3)A misinterpretation that the wave function represents a real wave when in actuality it represents the possible states of a quantum system before a measurement. (4)When Bell’s theorem was violated by a quantum system, those violations were misinterpreted as evidence of an instantaneous collapse of the wave function and non-locality. We will argue: there is no collapse of the wave function. Bell’s theorem is not about non-locality. There is no spooky action at a distance. And Quantum Mechanics is about measuring quantities at the microscopic scales and in doing so, these quantities are altered. So what we get is partial knowledge. But in spite of that obstacle, we still get a theory of reality with considerable success.
As we all know, Einstein disagreed with Born's probabilistic interpretation of wave-functions, which collapse abruptly once measurements are performed on the corresponding systems. In the Einstein-Bohr debate, Einstein considered quantum mechanics incomplete. Inspired by Einstein, Bell and his followers intended to complete quantum mechanics within the framework of local realism. Regrettably, deterministic correlations in Einstein's local-realist description of the world are mistaken for "nonlocal-interactions" (non-locality) in the world described by Bell's theorem, which leads to the questionable interpretation of the experimental results obtained by testing Bell inequalities. This article introduces a new principle, the general principle of measurements, which is proved as a mathematical theorem and allows quantum mechanics to be completed within the framework of local realism while keeping the axiomatic definition of a general Hilbert space essentially unchanged. Using disjunction ("or") as the logical relation between orthonormal vectors spanning a given Hilbert space, the completed quantum theory precludes inexplicable collapses of wave-functions and is intuitively comprehensible, thus alleviating much difficulty in understanding quantum mechanics. Among various world views, Einstein's local-realist world view is correct.
As we all know, Einstein disagreed with Born's probabilistic interpretation of wave-functions, which collapse abruptly once measurements are performed on the corresponding systems. In the Einstein-Bohr debate, Einstein considered quantum mechanics incomplete. Inspired by Einstein, Bell and his followers intended to complete quantum mechanics within the framework of local realism. Regrettably, deterministic correlations in Einstein's local-realist description of the world are mistaken for "nonlocal-interactions" (non-locality) in the world described by Bell's theorem, which leads to the questionable interpretation of the experimental results obtained by testing Bell inequalities. This article introduces a new principle, the general principle of measurements, which is proved as a mathematical theorem and allows quantum mechanics to be completed within the framework of local realism while keeping the axiomatic definition of a general Hilbert space essentially unchanged. Using disjunction ("or") as the logical relation between orthonormal vectors spanning a given Hilbert space, the completed quantum theory precludes inexplicable collapses of wave-functions and is intuitively comprehensible, thus alleviating much difficulty in understanding quantum mechanics. Among various world views, Einstein's local-realist world view is correct.
Lying at the heart of quantum mechanics, the notion of quantum superposition causes enormous difficulty in understanding the problem of quantum measurement, which concerns the Einstein-Bohr debate on the conceptual foundations of the quantum theory. According to Bell’s theorem, Einstein’s viewpoint in his debate with Bohr seems to be wrong. In the present paper, a new principle (referred to as the general principle of measurements) is introduced and proved as a mathematical theorem. Based on this principle, various forms of quantum superposition (including quantum entanglement) and the corresponding experiments are scrutinized. The main findings are as follows. (a) Einstein’s viewpoint is correct and Bell’s theorem is problematic. (b) Measurement outcomes of any actual experiment with individual microscopic objects described in a form of quantum superposition, in particular, the experimental results of testing Bell inequalities, are all erroneously explained. (c) Bell inequalities failed to capture the essence of the Einstein-Bohr debate, i.e., whether quantum superposition is legitimate for describing individual microscopic objects. (d) All kinds of quantum superposition violate the general principle of measurements and hence are illegitimate. (e) Quantum mechanics can be completed by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space for describing a single microscopic object, and the mathematical setting will remain essentially unchanged; hidden-variable theories are irrelevant to the real world. (f) After completing quantum mechanics as above, the difficulty in understanding the problem of quantum measurement disappears naturally. Implications of the findings are also discussed.