A succinct statement and justification of all the principles necessary to understand and evaluate interpretations of quantum mechanics is given. These principles provide strong constraints on interpretations. They imply the particle-like properties of mass, energy, momentum, spin, charge, and locality are actually properties of the wave function, and this in turn implies there is no evidence for the existence of particles. In addition, there is currently no experimental evidence for collapse, and a theory of collapse encounters significant hurdles. Further, the probability law is found to rule out the many-worlds interpretation, so all three major interpretations encounter serious to fatal problems. An interpretation which conforms to all the principles is given.
A succinct statement and justification of all the principles necessary to understand and evaluate interpretations of quantum mechanics is given. These principles provide strong constraints on interpretations. They imply the particle-like properties of mass, energy, momentum, spin, charge, and locality are actually properties of the wave function, and this in turn implies there is no evidence for the existence of particles. In addition, there is currently no experimental evidence for collapse, and a theory of collapse encounters significant hurdles. Further, the probability law is found to rule out the many-worlds interpretation, so all three major interpretations encounter serious to fatal problems. An interpretation which conforms to all the principles is given.
The three major theoretical principles of quantum mechanics relevant to its interpretation are: (T1), linearity; (T2), invariance under certain groups; and (T3) the orthogonality and isolation of the different branches of the state vector. These three imply the particle-like properties of mass, energy, momentum, spin, charge, and locality are actually properties of the state vector; and this in turn implies there is no evidence for the existence of particles. Experimentally there is no evidence for collapse (E1) and theoretically linearity prohibits collapse. One also has the experimentally verified probability law (E2), which is found to rule out the many-worlds interpretation. The failure of these three major interpretation, particles, collapse, and many-worlds, apparently implies an acceptable interpretation must be based on perception. Rather than being a separate principle, probability follows in this interpretation from a weak assumption on perception plus the combinatorics when an experiment is run many times. This suggests a relatively simple experimental test of the perception interpretation.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.
All the concepts and principles necessary to understand quantum mechanics on an initial level are given in a form suitable for the non-expert. The concepts explained include visualizing the wave function, wave-particle duality, the implications of Schrodinger's cat, probability, the uncertainty principle, collapse of the wave function, and others. However, because of the peculiar, non-intuitive nature of quantum mechanics, one must understand the potential interpretations of its mathematics before one can properly understand these concepts. Thus the paper is organized aorund interpretations, conceptual pictures that explain the peculiar properties of the theory. The only interpretation that currently satisfies all the constraints imposed by experiments and the theory itself makes use of a perceiving Mind which is outside the laws of quantum mechanics.
Quantum mechanics gives many versions of reality but we perceive only one. One potential explanation for this, the one considered here, is that the wave function collapses down to just one version. The experimental situation is briefly reviewed, with no evidence found for collapse. The theoretical position is also reviewed and found wanting. Collapse-by-observation schemes are logically untenable. A mathematical theory of collapse must be nonlinear, a significant departure from current quantum theory. In addition, the primary candidate theory, the GRW-Pearle model, requires instantaneous, non-local transmission of information. It also requires transmission of information across versions of reality, which is forbidden in current quantum mechanics. And there is no apparent physical quantity, such as particle number, that can provide the mechanism for collapse in all cases. Further, these aspects, which are in disagreement with current theory, seem to be necessary for any mathematical theory of collapse. The conclusion is that the outlook for mathematical collapse schemes is not encouraging.
Quantum mechanics, a cornerstone of modern physics, elucidates the behavior of particles at the most fundamental level. This paper delves into the foundational aspects and diverse interpretations of quantum mechanics, shedding light on its enigmatic principles and implications. Beginning with a comprehensive overview of the mathematical framework underlying quantum mechanics, including wave functions, operators, and probabilistic interpretations, the study explores key foundational principles such as superposition, uncertainty, and entanglement. Moreover, it critically examines various interpretations of quantum mechanics, including the Copenhagen interpretation, many-worlds interpretation, and pilot-wave theory, elucidating their philosophical underpinnings and empirical consequences. Through a synthesis of theoretical analysis and empirical evidence, this paper navigates the intricate landscape of quantum mechanics, offering insights into its profound implications for our understanding of reality.
We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of a state, its dynamical evolution rule and another rather trivial postulate proposed here (Read-Off Postulate). The wave function collapse and the probability rule are replaced with intrinsic properties of the theory, i.e. decoherence and relative frequency, respectively. Interpretation of the wave function as a faithful representation of the reality naturally emerges, although quantum reality has a peculiar feature which distinguishes it from classical reality.