量子平衡的松弛与Nelson随机动力学中的Born规则

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY Foundations of Physics Pub Date : 2023-11-06 DOI:10.1007/s10701-023-00730-w
Vincent Hardel, Paul-Antoine Hervieux, Giovanni Manfredi
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引用次数: 1

摘要

Nelson的随机量子力学提供了一个理想的领域来测试Born规则是如何从与波函数的平方模不相同的初始概率分布中建立的。在这里,我们对三种相关情况下的这个问题进行了数值研究:双缝干涉装置、谐振子和均匀引力场中的量子粒子。对于所有情况,Nelson的随机轨迹最初都定位在一个确定的位置,从而违反了Born规则。对于双缝谐振子,在玻恩规则建立之后,通常会出现典型的量子现象,如干涉。相反,对于量子粒子在地球重力场中自由下落的情况,在量子弛豫完成之前观察到干涉模式。这一发现可能为能够区分标准量子力学和纳尔逊理论的实验铺平道路,在纳尔逊理论中,Born规则总是得到满足,在完全量子弛豫发生之前,可能存在早期的亚量子动力学。尽管迄今为止,量子粒子可能违反Born规则的机制仍然未知,但我们推测,这可能发生在基本过程中,如β衰变或粒子反粒子对的产生。
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Relaxation to Quantum Equilibrium and the Born Rule in Nelson’s Stochastic Dynamics

Nelson’s stochastic quantum mechanics provides an ideal arena to test how the Born rule is established from an initial probability distribution that is not identical to the square modulus of the wavefunction. Here, we investigate numerically this problem for three relevant cases: a double-slit interference setup, a harmonic oscillator, and a quantum particle in a uniform gravitational field. For all cases, Nelson’s stochastic trajectories are initially localized at a definite position, thereby violating the Born rule. For the double slit and harmonic oscillator, typical quantum phenomena, such as interferences, always occur well after the establishment of the Born rule. In contrast, for the case of quantum particles free-falling in the gravity field of the Earth, an interference pattern is observed before the completion of the quantum relaxation. This finding may pave the way to experiments able to discriminate standard quantum mechanics, where the Born rule is always satisfied, from Nelson’s theory, for which an early subquantum dynamics may be present before full quantum relaxation has occurred. Although the mechanism through which a quantum particle might violate the Born rule remains unknown to date, we speculate that this may occur during fundamental processes, such as beta decay or particle-antiparticle pair production.

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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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