It is shown that, with some reasonable assumptions, the theory of generalrelativity can be made compatible with quantum mechanics by using the fieldequations of general relativity to construct a Robertson-Walker metric for aquantum particle so that the line element of the particle can be transformedentirely to that of the Minkowski spacetime, which is assumed by a quantumobserver, and the spacetime dynamics of the particle described by a Minkowskiobserver takes the form of quantum mechanics. Spacetime structure of a quantumparticle may have either positive or negative curvature. However, in order tobe describable using the familiar framework of quantum mechanics, the spacetimestructure of a quantum particle must be "quantised" by an introduction of theimaginary number $i$. If a particle has a positive curvature then thequantisation is equivalent to turning the pseudo-Riemannian spacetime of theparticle into a Riemannian spacetime. This means that it is assumed theparticle is capable of measuring its temporal distance like its spatialdistances. On the other hand, when a particle has a negative curvature and anegative energy density then quantising the spacetime structure of the particleis equivalent to viewing the particle as if it had a positive curvature and apositive energy density.
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机译：结果表明，在一些合理的假设下，可以通过使用广义相对论的场方程来构造量子粒子的Robertson-Walker度量，从而使广义相对论与量子力学兼容，从而可以将粒子的线元完全转化为Minkowski时空（由量子观测器假设）的时间，Minkowskiobserver描述的粒子的时空动力学采用量子力学的形式。量子粒子的时空结构可以具有正曲率或负曲率。但是，为了使用熟悉的量子力学框架进行描述，必须通过引入虚数$ i $来“量化”量子粒子的时空结构。如果粒子具有正曲率，则量化等效于将粒子的伪黎曼时空转换为黎曼时空。这意味着假定粒子能够像空间距离一样测量其时间距离。另一方面，当粒子具有负曲率和负能量密度时，则对粒子的时空结构进行量化等效于将粒子视为具有正曲率和正能量密度。
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