Does Locality Imply Reality of the Wave Function? Hardy’s Theorem Revisited

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY
Shan Gao
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Abstract

Hardy’s \(\psi\)-ontology theorem proves the reality of the wave function under the assumption of restricted ontic indifference. It has been conjectured that restricted ontic indifference, which is a very strong assumption from the \(\psi\)-epistemic view, can be derived from two weaker sub-assumptions: an ontic state assumption and a locality assumption. However, Leifer argued that this derivation cannot go through when considering the existence of the vacuum state in the second-quantized description of quantum states. In this paper, I present a new analysis of Hardy’s theorem. First, I argue that the ontic state assumption is valid in the second-quantized description of quantum states. Second, I argue that the locality assumption is a locality assumption for product states and it is weaker than the preparation independence assumption of the PBR theorem. Third, I argue that Leifer’s objection to the derivation of restricted ontic indifference is invalid. Finally, I argue that although the vacuum state is irrelevant, the existence of the tails of the wave function will block the derivation of restricted ontic indifference from the ontic state assumption and the locality assumption.

Abstract Image

位置性意味着波函数的现实性吗?哈代定理再探讨
哈代的本体论定理证明了在受限本体冷漠假设下波函数的现实性。有人猜想,从(\psi\)-本体论的观点来看,受限本体无所谓是一个非常强的假设,它可以从两个较弱的子假设中推导出来:本体状态假设和局域性假设。然而,Leifer 认为,当考虑到量子态二量子化描述中真空态的存在时,这一推导无法通过。在本文中,我对哈代定理进行了新的分析。首先,我认为本征态假设在量子态的二次量化描述中是有效的。其次,我论证了局部性假设是积状态的局部性假设,它比 PBR 定理的准备独立性假设更弱。第三,我论证了莱弗对受限本体无关性推导的反对是无效的。最后,我认为尽管真空态无关紧要,但波函数尾部的存在会阻碍从本体态假设和局域性假设推导出受限本体无差别。
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来源期刊
Foundations of Physics
Foundations of Physics 物理-物理:综合
CiteScore
2.70
自引率
6.70%
发文量
104
审稿时长
6-12 weeks
期刊介绍: The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.
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