Semiclassical Gravitation

量子理论与引力的统一仍然是一个悬而未决的问题。将标准量子化规则应用于经典广义相对论导致了许多概念和技术问题(如时间问题、寻找Wheeler-DeWitt方程的解等)。因此，人们常常求助于半经典近似。在这种近似下，引力被经典地处理，用时空度规来描述，而物质，比如标量场，被视为弯曲时空中的量子场，采用能量应力张量的量子力学平均。直到现在，这种处理仍然受到臭名昭著的测量问题的困扰：空间分离的波包(薛定谔猫态)的叠加将产生一个引力场，这表明这里和那里都有物质，而根据伯恩规则，物质可能只存在这里或那里。测量问题是由Bohmian力学解决的，因此在半经典情况下应用Bohmian力学是很自然的。我们将研究这种半经典的方法，从更简单的模型开始，并以更好的半经典引力理论结束，其结果比到目前为止所取得的结果更尖锐。对我们更尖锐的结果的实验验证是可行的。这项工作是与Ward Struyve博士(现为罗格斯大学)合作计划的，是Post Doc。

The unification of quantum theory with gravity is still an open problem. The application of standard quantization rules to classical general relativity has led to a number of conceptual and technical problems (like the problem of time, finding solutions to the Wheeler-DeWitt equation, etc.). Therefore one often resorts to a semi-classical approximation. In this approximation, gravity is treated classically, being described by a space-time metric, while matter, say a scalar field, is treated as a quantum field on curved space-time, taking the quantum mechanical average of the energy stress tensor.Still this treatment suffers from the notorious measurement problem: A superposition of spatially separated wave packets (Schrödinger cat states) would generate a gravitational field which suggests that there is matter here and there, while according to Born's rule matter could be only here or there. The measurement problem is solved by Bohmian mechanics and it is therefore natural to apply Bohmian mechanics in semiclassical situations. We shall study this approach to semi classicality starting from simpler models and ending in a better semiclassical theory of gravity with sharper results than the ones achieved until now. Experimental verifications of our sharper results are feasible. The work is planned in collaboration with Dr. Ward Struyve (now Rutgers) as Post Doc.