Semiclassical Gravitation

量子理论与引力的统一仍然是一个悬而未决的问题。标准量子化规则在经典广义相对论中的应用导致了许多概念和技术问题（如时间问题，寻找惠勒-德威特方程的解等）。因此，人们常常诉诸于半经典近似。在这种近似中，引力被经典地处理，用时空度规来描述，而物质，比如说标量场，则被当作弯曲时空上的量子场，取能量应力张量的量子力学平均值。空间分离波包的叠加（薛定谔猫态）会产生一个引力场，表明这里和那里都有物质，而根据玻恩规则，物质只能在这里或那里。测量问题由玻姆力学解决，因此在半经典情况下应用玻姆力学是很自然的。我们将从较简单的模型开始研究这种半经典性的方法，并以一种更好的半经典引力理论结束，其结果比迄今为止所取得的结果更尖锐。实验验证我们的尖锐的结果是可行的。这项工作计划与沃德·斯特鲁夫博士（现在的罗格斯大学）合作，作为博士后。

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.