We argue that it is logically possible to have a sort of both reality and locality in quantum mechanics. To demonstrate this, we construct a new quantitative model of hidden variables (HV's), dubbed solipsistic HV's, that interpolates between the orthodox no-HV interpretation and nonlocal Bohmian interpretation. In this model, the deterministic point-particle trajectories are associated only with the essential degrees of freedom of the observer, and not with the observed objects. In contrast with Bohmian HV's, nonlocality in solipsistic HV's can be substantially reduced down to microscopic distances inside the observer. Even if such HV's may look philosophically unappealing to many, the mere fact that they are logically possible deserves attention.
We argue that it is logically possible to have a sort of both reality and locality in quantum mechanics. To demonstrate this, we construct a new quantitative model of hidden variables (HV's), dubbed solipsistic HV's, that interpolates between the orthodox no-HV interpretation and nonlocal Bohmian interpretation. In this model, the deterministic point-particle trajectories are associated only with the essential degrees of freedom of the observer, and not with the observed objects. In contrast with Bohmian HV's, nonlocality in solipsistic HV's can be substantially reduced down to microscopic distances inside the observer. Even if such HV's may look philosophically unappealing to many, the mere fact that they are logically possible deserves attention.
What does quantum physics tell us about the nature of reality, specifically the parts of reality we do not directly perceive called hidden variables? One may think it could tell us a lot because of our enhanced technological sensing abilities that delve into the realms that quantum physics covers so well. Surprisingly, it seems to surround us in a deeper mystery rather than reveal more of nature's secrets. It seems that we cannot escape from philosophical consideration when dealing with what is hidden in quantum physics. In Part I we will look at how Epistemology and Ontology bear upon Hidden Variables. In Part II we will consider Hidden Variables in the light of Contextuality, and Non-Classicality. Inevitably questions of subjectivity and objectivity arise in dealing with states of observation. How should we think about these states? Perhaps it is a question of the meaning associated with our knowledge of a state-that is, a question of ontology or epistemology. The issue of ontic and epistemic states is particularly important when considering hidden variables in quantum physics because, as one may argue, the interpretation of quantum states as either ontic or epistemic will naturally lead to different assumptions about how reality is constructed; if it is constructed or not. It also raises the question of what attributes we are able to observe simultaneously and that brings contextuality into the discussion. If it turns out that reality is constructed contextually what does that imply about ontological realism? If on the other hand reality is constructed non-contextually what does that imply about ontological realism? Many implications can arise when considering these questions from a quantum physical point of view. In this paper I shall discuss how quantum physics provides some answers to these questions by considering quantum physical states and their measurements.
An interpretation of Quantum Mechanics published at the International Journal of Quantum Foundations. Abstract: A new interpretation of quantum mechanics is presented in which there is one hidden variable. This could be described as “partial realism” where sometimes quantum variables have real values before we measure and sometimes they don’t. While one hidden variable is insufficient to explain Bell nonlocality, it is allowed by Bell’s inequality. This can help solve the measurement problem and may, in principle, be testable. In addition, a theory of nonlocality emerges directly from this assumption. From the perspective of an outside observer, not correlated with an observed system, we treat all interactions within the system as unitary. However, from the perspective of an “observer” inside the system, we treat all new entanglements as “micromeasurements”, as a projection onto some basis of measurement. One particle can act as a measurement device on another and give the other particle a defined value on one possible measurement axis from an inside perspective. This means that the wave function, from the outside view, will at times describe an objective, fundamentally stochastic uncertainty, at other times a subjective uncertainty that reflects only our lack of knowledge, and at yet other times a combination of both. The standard wave function describes the total uncertainty, the minimal uncertainty that is present for any observer outside of the system, whereas for an “observer” inside the system, only the objective, fundamentally stochastic part of the uncertainty remains, and this can be described by an inner wave function. The hidden variable is invisible to the outside observer.
A new interpretation of quantum mechanics is presented in which there is one hidden variable. This could be described as “partial realism” where sometimes quantum variables have real values before we measure and sometimes they don’t. While one hidden variable is insufficient to explain Bell nonlocality, it is allowed by Bell’s inequality. This can help solve the measurement problem and is in principle testable. In addition, a theory of nonlocality emerges directly from this assumption. From the perspective of an outside observer, not correlated with an observed system, we treat all interactions within the system as unitary. However, from the perspective of an “observer” inside the system, we treat all new entanglements as “micromeasurements”, as a projection onto some basis of measurement. One particle can act as a measurement device on another and give the other particle a defined value on one possible measurement axis from an inside perspective. This means that the wave function, from the outside view, will at times describe an objective, fundamentally stochastic uncertainty, at other times a subjective uncertainty that reflects only our lack of knowledge, and at yet other times a combination of both. The standard wave function describes the total uncertainty, the minimal uncertainty that is present for any observer outside of the system, whereas for an “observer” inside the system, only the objective, fundamentally stochastic part of the uncertainty remains, and this can be described by an inner wave function. The hidden variable is invisible to the outside observer.
Motivated by Popescu's example of hidden nonlocality [Phys. Rev. Lett. 74, 2619 (1995)], we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden-variables model. We exhibit quantum states which either (i) are nontrivial counterexamples to this conjecture or (ii) possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we propose a nonlocality complexity classification scheme suggested by the latter possibility. Furthermore, we show that Werner's [Phys. Rev. A 40, 4277 (1989)] (and similar) hidden-variables models can be extended to an important class of generalized observables. Finally, a result of Fine [Phys. Rev. Lett. 48, 291 (1982)] on the equivalence of stochastic and deterministic hidden variables is generalized to causal models.
An interpretation of quantum mechanics is presented in which there is one hidden variable. While this number of hidden variables is insufficient to explain Bell nonlocality, it can help solve the measurement problem. It also provides an explanation of the delayed choice quantum eraser experiment that is more intuitive than current explanations. In addition, a theory of nonlocality emerges directly from its assumptions. The key idea is that from the perspective of an outside observer, not correlated with an observed system, we treat all interactions within the system as unitary. However, from the perspective of an “observer” inside the system, we treat all new entanglements as “micro-observations” and as a projection onto some basis of measurement. One particle can “observe” another. Thus, particles will have a defined value on one measurement basis from an inside perspective. This means that the wave function, from the outside view, will at times describe an objective uncertainty, at other times a subjective uncertainty and at yet other times a combination of both. The standard wave function describes the total uncertainty, the minimal uncertainty that is present for any observer outside of the system, while for an observer inside the system, only the objective part of the uncertainty remains, and this can be described by an inner wave function. The hidden variable is invisible to the outside observer.
An interpretation of quantum mechanics is presented in which there is one hidden variable. While this number of hidden variables is insufficient to explain Bell nonlocality, it can help solve the measurement problem. It also provides an explanation of the delayed choice quantum eraser experiment that is more intuitive than current explanations. In addition, a theory of nonlocality emerges directly from its assumptions. The key idea is that from the perspective of an outside observer, not correlated with an observed system, we treat all interactions within the system as unitary. However, from the perspective of an “observer” inside the system, we treat all new entanglements as “micro-observations” and as a projection onto some basis of measurement. One particle can “observe” another. Thus, particles will have a defined value on one measurement basis from an inside perspective. This means that the wave function, from the outside view, will at times describe an objective uncertainty, at other times a subjective uncertainty and at yet other times a combination of both. The standard wave function describes the total uncertainty, the minimal uncertainty that is present for any observer outside of the system, while for an observer inside the system, only the objective part of the uncertainty remains, and this can be described by an inner wave function. The hidden variable is invisible to the outside observer.