Solipsistic hidden variables

📝 Abstract

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.

💡 Analysis

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.

📄 Content

arXiv:1112.2034v2 [quant-ph] 7 Jan 2013 Solipsistic hidden variables Hrvoje Nikoli´c Theoretical Physics Division, Rudjer Boˇskovi´c Institute, P.O.B. 180, HR-10002 Zagreb, Croatia e-mail: hrvoje@thphys.irb.hr September 10, 2018 Abstract 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. Keywords: hidden variable; locality; particle trajectory; observer 1 Introduction The no-local-hidden-variable theorems [1, 2, 3] for quantum mechanics (QM) have pro- found, but not unambiguous [4], implications on the nature of objective physical reality – reality supposed to exist even without observations. Two typical but mutually confronting views inferred from these theorems are (i) that nature is local but objective reality does not exist [5, 6, 7], or (ii) that objective reality exists but is not local [1, 8, 9]. Moreover, many seem to agree that an intermediate option, which would retain both objective reality and locality, is not possible. With a motivation to reduce the confrontation between these two views, as well as to demonstrate that an intermediate option is at least not impossible, in this paper we propose a new “hybrid” approach. In this approach, some elements of each of the two options are combined into a new interpretation that, to a certain extent, retains both objective reality and locality. But of course, saving both objective reality and locality cannot be without a price. It turns out that our intermediate approach naturally leads 1 to a so-called solipsistic1 reality, the meaning of which will become clear through the rest of the paper. To understand the basic idea, consider first a variant of the approach without objective reality. This approach asserts that there is no reality except the observed reality. Presum- ably, any observation ultimately happens in some part of a (conscious) brain, which is an object well localized in space. In this sense, observations are local events. In particular, when an experimentalist (say, Alice) studies nonlocal EPR correlations, then all what she really observes are signals conveyed to her brain, even if some of these signals originated from a distant apparatus that measured spin of a distant member of the EPR pair. In this way Alice can insist that, from her point of view, entangled particles and the distant apparatus do not really exist. From her point of view, all what exists are her observations, which are local. For her this is the only reality. But since this is her reality, it is not objective reality. In this way locality is saved with a price of loosing objective reality. Now our approach can be understood as a relatively small modification of the above. What if the Alice’s subjective observations are actually a result of some objective physical processes in her brain? That would promote her subjective reality into an objective one. And what if it is still true that other objects (such as entangled particles and spatially separated measuring apparatuses supposed to measure spins of these particles) are not real? That would retain locality. So in this way, it would be possible to have both objective reality and locality. In this paper we construct an explicit quantitative model of objective reality inspired by the qualitative idea above. Our model can be thought of as a variation of the Bohmian hidden variable (HV) theory [10, 11, 12], with a difference that objective existence and deterministic trajectories are ascribed only to those particles which describe the degrees of freedom ultimately observed by the observer. We show in detail how such a model is compatible with all measurable statistical predictions of QM. Before starting with a quantitative analysis, there is one additional important problem to be addressed at a qualitative level. What if there is more than one observer, say Alice and Bob? Alice could be egocentric by believing that only she really exists, but Bob, who may be conscious of his own observations, would strongly disagree. (Likewise, the author of this paper could believe that only he exists, but the reader of it would not buy it.) So, to avoid such an egocentric view of reality, it is necessary to associate objective reality (in our model, particle trajectories) with each conscious observer. Then each of them is local as an individual,

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