Title: Time dispersion and quantum mechanics Show Chinese title

Title: 时间色散和量子力学

Abstract: In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum effects along the time axis to be of order an attosecond. Such effects are not ruled out by current experiments. But they are large enough to be detected with current technology, if sufficiently specific predictions can be made. To supply such we use path integrals. The only change required is to generalize the usual three dimensional paths to four. We predict a large variety of testable effects. The principal effects are additional dispersion in time and full equivalence of the time/energy uncertainty principle to the space/momentum one. Additional effects include interference, diffraction, and entanglement in time. The usual ultraviolet divergences do not appear: they are suppressed by a combination of dispersion in time and entanglement in time. The approach here has no free parameters; it is therefore falsifiable. As it treats time and space with complete symmetry and does not suffer from the ultraviolet divergences, it may provide a useful starting point for attacks on quantum gravity. Show Chinese abstract

Abstract: 在量子力学中，时间维度被当作一个参数处理，而三个空间维度则被当作可观测量。 这种假设既未经检验，也与相对论不一致。 从量纲分析来看，我们预期沿时间轴的量子效应大约为阿秒量级。 这些效应目前的实验并未排除。 但如果能做出足够具体的预测，它们大到足以用现有技术检测到。 为了提供这样的预测，我们使用路径积分。 所需的唯一改变是将通常的三维路径推广到四维。 我们预测了各种可检验的效应。 主要效应是在时间上的额外色散，以及时间/能量不确定性原理与空间/动量不确定原理的完全等价性。 其他效应包括时间上的干涉、衍射和纠缠。 通常的紫外发散不会出现：它们被时间色散和时间纠缠的组合所抑制。 这里的方法没有自由参数；因此它是可以被证伪的。 由于它对时间和空间的处理具有完全的对称性，并且不受紫外发散的影响，它可能为研究量子引力提供一个有用的起点。