Vacuum Brans-Dicke (BD) theory continues to receive widespread attention since it is consistent with solar and cosmological experiments. The theory can be self-consistently described in two frames, the Jordan frame (JF) and the conformally rescaled Einstein frame (EF), the transformations providing an easy passage from one frame to the other at the level of actions and solutions. While coordinate transformations do not change curvature properties, conformal transformations do change them leading to corresponding changes in the numerical values of observables. A previous article by Bhadra et al.[Formula: see text] did exemplify this change between JF and EF using the diagnostic of second-order light deflection. This important work leaves room for further improvements on two points, which we do here. First, the measurement of second-order effect faced technically unsurmountable difficulties even around the Sun, hence actually abandoned. Second, the comparison of quantitative values between JF and EF should be based on a common value of [Formula: see text] connecting the two frames. Keeping these in mind, we investigate a technically easier diagnostic, viz., the weak field lensing (WFL) and compare the quantitative changes at common [Formula: see text] to show that the two frames can indeed be distinguished by lensing experiments. Specifically, the predictions of light deflection, image position, total magnification and magnification factor are computed in the EF and compared with those recently obtained (by Gao et al.[Formula: see text]) directly in the JF BD class I solution. The use of the value of BD coupling constant [Formula: see text], suggested by the Cassini spacecraft solar experiment, reveals that an exceptionally high degree of accuracy is needed to experimentally rule out one or the other frame by means of WFL measurements.

中文翻译：

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Jordan 和 Einstein 框架中的真空 Brans-Dicke 理论：可以通过透镜区分它们吗？

真空布兰斯-迪克 (BD) 理论继续受到广泛关注，因为它与太阳和宇宙学实验相一致。该理论可以在两个框架中自洽地描述，Jordan 框架 (JF) 和共形重新缩放的爱因斯坦框架 (EF)，这些转换在动作和解决方案的层面上提供了从一个框架到另一个框架的简单通道。虽然坐标变换不会改变曲率属性，但保形变换确实会改变它们，从而导致可观测值的数值发生相应的变化。Bhadra 等人之前的一篇文章 [公式：见正文] 确实使用二阶光偏转的诊断来举例说明 JF 和 EF 之间的这种变化。这项重要的工作在两点上留下了进一步改进的空间，我们在这里做。第一的，二次效应的测量即使在太阳周围也面临技术上无法克服的困难，因此实际上被放弃了。其次，JF和EF的定量值比较，应该基于连接两个框架的[公式：见正文]的共同值。牢记这些，我们研究了一种技术上更简单的诊断方法，即弱场透镜 (WFL)，并比较了常见 [公式：见文本] 处的定量变化，以表明这两个框架确实可以通过透镜实验来区分。具体来说，在 EF 中计算了光偏转、图像位置、总放大率和放大系数的预测，并与最近在 JF BD I 类解决方案中直接获得的（由 Gao 等人[公式：见文本]）进行比较。BD耦合常数值的使用[公式：见正文]，