Leinweber Institute for Theoretical Physics, University of California, Berkeley（加州大学伯克利分校莱因韦伯理论物理研究所）；Theoretical Physics Group, Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室理论物理组）
相对性原理被扩展以适应具有量子性质的有限质量观测者，通过引入两个操作性要求：(i) 转移振幅层面的观测者等价性，以及 (ii) 观测者无法访问自身运动的量子状态。这导致了完全相对的量子力学 formulation，具有观测者依赖的希尔伯特空间、相对量化规则和新的不确定性关系，同时澄清了当前量子力学 formulation 中存在的一些解释问题，并给出了可实验检验的特征。
英文摘要：
The principle of relativity is extended to accommodate finite-mass observers with quantum properties by introducing two operational requirements: (i) equivalence of observers at the level of transition amplitudes, and (ii) the impossibility for an observer to access its own quantum state of motion. This results in a fully relative formulation of quantum mechanics with observer-dependent Hilbert spaces, relative quantization rules, and novel uncertainty relations, while also elucidating some interpretational issues present in the current formulation of quantum mechanics and giving experimentally testable signatures.
The problem of the observer in quantum mechanics is getting new human content. The paradox of Wigner's friend and its extended versions have observers who not only observe quantum phenomena, but communicate, have memories and even super-observer powers. Observers are represented by particle paths and state memories and advanced AI has been suggested to act as an observer. There is a new call for a solid theory of the observer in quantum mechanics. Two different branches of observer theories have emerged. The purely physical one is Heisenbergian, e.g. relational quantum mechanics where the obse…
Non-Inertial Frames in Minkowski Space-Time, Accelerated either Mathematical or Dynamical Observers and Comments on Non-Inertial Relativistic Quantum Mechanics
Bohmian mechanics, also known as pilot-wave theory or de Broglie-Bohm theory, is a formulation of quantum mechanics whose fundamental axioms are not about what observers will see if they perform an experiment but about what happens in reality. It is therefore called a "quantum theory without observers," alongside with collapse theories and many-worlds theories and in contrast to orthodox quantum mechanics. It follows from these axioms that in a universe governed by Bohmian mechanics, observers will see outcomes with exactly the probabilities specified by the usual rules of quantum mechanics fo…
Relational quantum mechanics (RQM) is an interpretation of quantum mechanics based on the idea that quantum states describe not an absolute property of a system but rather a relationship between systems. In this article, we observe that there is a tension between RQM's naturalistic emphasis on the physicality of information and the inaccessibility of certain sorts of information in current formulations of RQM. Therefore we propose a new postulate for RQM which requires that all of the information possessed by a certain observer is stored in physical variables of that observer and thus accessib…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the relational probability amplitude matrix is transformed and how mutual information is exchanged during measurement, we derive the formulation that is mathematically equivalent to the traditional quantum measurement theory. More importantly, the formulation results in significant conceptual consequences. We show that for a given quantum system, it is possible t…
A modified version of relational quantum mechanics is developed based on the three following ideas. An observer can develop an internally consistent description of the universe but it will, of necessity, differ in particulars from the description developed by any other observer. The state vector is epistomological and relative to a given quantum system as in the original relational quantum mechanics. If two quantum systems are entangled, they will observe themselves to be in just one of the many states in the Schmidt biorthonormal decomposition and not in a linear combination of many.
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory. This article proposes an alternative formulation of the Standard Quantum Mechanics, in which the Projection Postulate is replaced with a version in which measurements and observations are not assumed as fundamental. More precisely, the Wigner functions representing the quantum states on the phase space are required to be tightly constrained to regions of the…
We develop an extension of special relativity in $1+3$ dimensional spacetime to account for superluminal inertial observers and show that such an extension rules out the conventional dynamics of mechanical point-like particles and forces one to use a field-theoretic framework. Therefore we show that field theory can be viewed as a direct consequence of extended special relativity.
We show that rejection of local realism in quantum mechanics can be tested by Bell-type inequalities for two observers and low-order moments of continuous and unbounded observables. We prove that one requires three observables for each observer for a maximally entangled state and two observables for a non-maximally entangled state and write down appropriate inequalities and show violation by quantum examples. Finding an example for quadratures or position and momentum is left as an open problem.
