标准量子力学假设，当一个量子系统的波函 数被测量时，它不再遵循线性的 薛定谔方程，而是瞬时坍缩为对应于测量结果的新的波函数。然而，这一波函数坍缩假设无法令人满意，因为它没有解释在测量过程中为什么以及如何发生波函数坍塌。 20 世纪 60 年代，美国物理学家 费曼 猜测，如果波函数坍缩真的发生的话，它很可能与引力现象有关。这一猜想后来被一些研究者进一步发展。其中最有影响的是英国物理学家 彭罗斯 于 1996 年提出的引力导致波函数坍缩的论证。这一论证以量子力学的叠加原理与广义相对论的广义协变原理之间的根本冲突为基础。在最近 一篇文章 中 ，我对彭罗斯的论证进行了分析。文章摘要如下： According to Penrose, the fundamental conflict between the superposition principle of quantum mechanics and the principle of general covariance of general relativity entails the existence of wavefunction collapse, e.g. a quantum superposition of two different space–time geometries will collapse to one of them due to the ill-definedness of the time-translation operator for the superposition. In this paper, we argue that Penrose's conjecture on gravity's role in wavefunction collapse is debatable. First of all, it is still a controversial issue what the exact nature of the conflict is and how to resolve it. Secondly, Penrose's argument by analogy is too weak to establish a necessary connection between wavefunction collapse and the conflict as understood by him. Thirdly, the conflict does not necessarily lead to wavefunction collapse. The reason is that the conflict or the problem of ill-definedness for a superposition of different space–time geometries also needs to be solved before the collapse of the superposition finishes, and once the conflict has been resolved, the wavefunction collapse will lose its physical basis relating to the conflict. In addition, we argue that Penrose's suggestions for the collapse time formula and the preferred basis are also problematic. 详细内容请参见我的 学术网页 上的 文章 原文 。 Comments are welcome!
在彭罗斯看来，我们周围确定的宏观世界的存在正是量子（不确定性）屈服于引力的结果。But why? 这篇文章通俗地介绍了 彭罗斯的引力导致量子坍缩论证 。同时，它对量子理论与广义相对论的不相容性进行了精彩的解释，对量子引力研究非常具有启发意义。 文章的作者 Joy Christian 是著名量子物理学家、科学哲学家西蒙尼(Abner Shimony)的学生。目前在Perimeter Institute for Theoretical Physics做长期访问学者。 Why the Quantum Must Yield to Gravity Quantum mechanics one of our most fundamental and successful theories is infested with a range of deep philosophical difficulties collectively known as the measurement problem (Schrodinger 1935, Shimony 1963, Wheeler and Zurek 1983, Bell 1990). In a nutshell the problem may be stated as follows: If the orthodox formulation of quantum theory which in general allows attributions of only objectively indefinite properties or potentialities (Heisenberg 1958) to physical objects is interpreted in compliance with what is usually referred to as scientific realism, then one is faced with an irreconcilable incompatibility between the nonnegotiable linearity of quantum dynamics which governs evolution of the network of potentialities and the apparent definite or actual properties of the physical objects of our macroscopic world. Moreover, to date no epistemic explanation of these potentialities (e.g., in terms of hidden variables) has been completely successful (Shimony 1989). Thus, on the one hand there is overwhelming experimental evidence in favour of the quantum mechanical potentialities, supporting the view that they comprise a novel (i.e., classically uncharted) metaphysical modality of Nature situated between logical possibility and actuality (Shimony 1978, 1993b, 140-162 and 310-322), and on the other hand there is phenomenologically compelling proliferation of actualities in our everyday world, including even in the microbiological domain. The problem then is that a universally agreeable mechanism for transition between these two ontologically very different modalities i.e., transition from the multiplicity of potentialities to various specific actualities is completely missing. As delineated, this is clearly a very serious physical problem. What is more, as exemplified by Shimony (1993a, 56), the lack of a clear understanding of this apparent transition in the world is also quite a dark cloud for any reasonable program of scientific realism. Not surprisingly, there exists a vast number of proposed solutions to the measurement problem in the literature (Christian 1996), some of which the Copenhagen interpretation (Bohr 1935) for example being almost congenital to quantum mechanics. Among these proposed solutions there exists a somewhat dissident yet respectable tradition of ideas going all the way back to Feynmans pioneering thoughts on the subject as early as in mid-fifties (Feynman 1957) on a possible gravitational resolution of the problem. The basic tenet of these proposals can hardly be better motivated than in Feynmans own words. In his Lectures on Gravitation (Feynman 1995, 12-13) he devotes a whole section to the issue, entitled On the philosophical problems in quantizing macroscopic objects, and contemplates on a possible breakdown of quantum mechanics: ...I would like to suggest that it is possible that quantum mechanics fails at large distances and for large objects. Now, mind you, I do not say that I think that quantum mechanics does fail at large distances, I only say that it is not inconsistent with what we do know. If this failure of quantum mechanics is connected with gravity, we might speculatively expect this to happen for masses such that GM2/hc = 1, of M near 10-5 grams Indeed, if quantum mechanics does fail near the Planck mass, as that is the mass scale Feynman is referring to here, then at last we can put the annoying problem of measurement to its final rest (see Figure 1 for the meanings of the constants G, h, and c). The judiciously employed tool in practice, the infamous postulate often referred to as the reduction of quantum state which in orthodox formulations of the theory is taken as one of the unexplained basic postulates to resolve the tension between the linearity of quantum dynamics and the plethora of physical objects with apparent definite properties may then be understood as an objective physical phenomenon; i.e., one affording an ontological as opposed to epistemological understanding. From the physical viewpoint such a resolution of the measurement problem would be quite satisfactory, since it would render the proliferation of diverse philosophical opinions on the matter to nothing more than a curious episode in the history of physics. For those who are not lured by pseudo-solutions such as the decohering histories approaches (Kent 1997) and/or many worlds approaches (Kent 1990), a resolution of the issue by objective reduction (OR, to use Penroses ingenious pun) comes across as a very attractive option, provided of course that that is indeed the path Nature has chosen to follow. Figure 1: The great dimensional monolith of physics indicating the fundamental role played by the three universal constants G (the Newtons gravitational constant), h (the Plancks constant),1/c (the causality constant, where c is the absolute upper bound on the speed of causal influences) in various basic theories. These theories, appearing at the eight vertices of the cube, are: CTM = Classical Theory of Mechanics, STR = Special Theory of Relativity, GTR = General Theory of Relativity, NCT = Newton-Cartan Theory, NQG = Newton-Cartan Quantum Gravity, GQM = Galilean-relativistic Quantum Mechanics, QTF = Quantum Theory of (relativistic) Fields, and FQG = the elusive Full-blown Quantum Gravity. Note that FQG must reduce to QTF, GTR, and NQG in the respective limits G=0, h=0, and 1/c= 0.
最近我的研究又转向波函数坍缩（wavefunction collapse）问题，尤其是波函数坍缩的物理起源问题。这几天在读 彭罗斯 （R.Penrose）1996年的经典论文 On Gravity's Role in Quantum State Reduction 。在这篇文章中，彭罗斯提出了那个引力导致波函数坍缩的著名论证。 1999年当我刚开始研究波函数坍缩问题时就认真看过这篇论文，但每一遍都会有新的理解。前段时间我刚刚写了一篇对彭罗斯论证的批评性文章，发表在《国际理论物理杂志》上。这几天的思考让我进一步相信，他的引力导致波函数坍缩的论证很可能不成立。如果真的是这样的话，我必须去其他地方寻找波函数坍缩的物理起源。时空分立性可能提供了一个极限限制，而非连续运动本身的特性（聚集性）或许是导致波函数坍缩的更普遍的物理原因。我在《量子》(2003)一书逻辑之旅的第三章3.7节中已经提出了这些想法。现在看来它们仍有意义，这几天我将对此进行更深入的研究。 最后，强烈建议对量子引力和量子力学基础研究感兴趣的朋友读一读彭罗斯的文章。从中我们或许可以找到弦论作为万物之理为何没有未来的原因：量子力学还不完备，并且量子与引力的结合还将涉及波函数坍缩。这也是我目前的看法。 It is not sufficient to take a completely formal attitude to such matters, as is common in discussions of quantum gravity. According to the sorts of procedure that are often adopted in quantum gravity, the superposition of different space-times is indeed treated in a very formal way, in terms of complex functions on the space of 3-geometries (or 4-geometries), for example, where there is no pretence at a pointwise identification of the different geometries under superposition. A difficulty with such formal procedures arises, however, if we attempt to discuss the physics that takes place within such a formal superposition of spaces. ---R. Penrose, On Gravity's Role in Quantum State Reduction, p.589 附1：My IJTP paper: On Disi-Penrose Criterion of Gravity-Induced Quantum Collapse PDF下载 Abstract It is shown that the Disi-Penrose criterion of gravity-induced quantum collapse may be inconsistent with the discreteness of spacetime, which is generally considered as an indispensable element in a complete theory of quantum gravity. Moreover, the analysis also suggests that the discreteness of spacetime may result in rapider collapse of the superposition of energy eigenstates than required by the Disi-Penrose criterion. 附2：引力导致量子坍缩猜想简介 如果有什么根本原因导致波函数坍缩的话，那么这个原因很可能是引力。理由在于，在所有物理相互作用中引力是唯一普遍存在的力，而且引力随物体尺度的增加而增强，而量子叠加恰好对于宏观大尺度物体失效。引力导致波函数坍缩的猜想可以追溯至美国物理学家费曼。他在20世纪60年代初写的《引力学讲义》中，考察了量子化宏观物体的问题，并认为量子理论对宏观物体失效是有可能的。他说，我想建议量子力学在大尺度上以及对于大物体失效是可能的... 这并不与我们目前所知道的事实相矛盾。如果量子力学的失效与引力有关，我们或许可以期望这对于10-5克大小的质量会发生。几年后，也许是受到费曼思想的启发，匈牙利物理学家卡洛里哈基（F. Krolyhzy）更具体地探讨了引力导致薛定谔方程失效的可能性，并提出了模糊时空的概念。 20世纪90年代，英国物理学家彭罗斯进一步加强了引力导致波函数坍缩的论证。他认为，由于广义相对论的广义协变原理与量子力学的叠加原理之间存在根本的不相容性，不同时空的量子叠加在物理上是不适当的，而它的演化也无法一致地定义。这要求对应于宏观上不同能量分布的两个时空几何的叠加应当在很短的时间内坍缩。彭罗斯进一步认为，能量分布差异越大，坍缩得越快，其坍缩时间公式类似于海森伯的不确定性关系。彭罗斯相信，人们看待量子力学的方式不得不经历一次主要的革命。目前，牛津大学量子光学组的研究人员正在设计一个叠加镜实验来检验这个有趣的想法，也许在不久的将来就会有实验结果。
标签: 彭罗斯
