引力-惯性场的黎曼和Finsler-Lagrange近似双度规理论
Bimetric Theory of Gravitational-Inertial Field in Riemannian and in Finsler-Lagrange Approximation
摘要：
本文通过引入纯惯性场张量$g^{ac}_{ij}$，使$R_{μνλ}^{α}(g^{ac}_{ij})\neq0$成为爱因斯坦世界张量$g_{ij}$的推广，给出了引力-惯性场双度规理论的一个新的命题。惯性场要么是由理想磁流体控制的。在过去十年发表的一系列关于旋转系统中穆斯堡尔实验的论文中，[71]-[75]，实验表明，共振辐射源之间的相对能量偏移ΔE/E（位于旋转系统的中心）和共振吸收器（位于转子边缘上）由关系式$ΔE/E=-ku^2/c^2$描述，其中u是吸收体的切向速度，c是真空中的光速，k是某个系数，与经典预测的等于1/2相反（参见例如[35]），结果大大大于1/2。再怎么强调也不为过的是，等式$k=1/2$已经由广义相对论（GTR）基于由旋转吸收体的切向位移描绘的狭义相对论时间膨胀效应而预测，其中爱因斯坦的“时钟假设”（即，任何时钟的时间速率都不依赖于其加速度[35]）。因此，所揭示的不等式$k>1/2$表明在所发射的和所吸收的共振辐射之间存在一些额外的能量偏移（仅次于仅由切向位移引起的通常的时间膨胀效应）。利用引力-惯性场的双度规理论[76]，我们得到了与实验结果$k=0.69+(-)0.03$ [75]符合得很好的$k=0.75$。
英文摘要：
In present article the original proposition is a generalization of the Einstein's world tensor $g_{ij}$ by the introduction of pure inertial field tensor $g^{ac}_{ij}$ such that $R_{μνλ}^{α}(g^{ac}_{ij})\neq0$.Bimetric theory of gravitational-inertial field is considered for the case when the gravitational-Inertial field is governed by either a perfect magnetic fluid.In a series of papers published during the past decade with respect to Mössbauer experiments in a rotating system [71]-[75],it has been experimentally shown that the relative energy shift ΔE/E between the source of resonant radiation (situated at the center of the rotating system) and the resonant absorber (located on the rotor rim) is described by the relationship $ΔE/E=-ku^2/c^2$, where u is the tangential velocity of the absorber, c the velocity of light in vacuum, and k some coefficient, which -- contrary to what had been classically predicted equal 1/2 (see for example [35]) -- turns out to be substantially larger than 1/2. It cannot be stressed enough that the equality $k=1/2$ had been predicted by general theory of relativity (GTR) on account of the special relativistic time dilation effect delineated by the tangential displacement of the rotating absorber, where the "clock hypothesis" by Einstein (i.e., the non-reliance of the time rate of any clock on its acceleration [35]) was straightly adopted. Hence, the revealed inequality $k>1/2$ indicates the presence of some additional energy shift (next to the usual time dilation effect arising from tangential displacement alone) between the emitted and absorbed resonant radiation. By using Bimetric Theory of Gravitational-Inertial Field [76] we obtain $k=0.75$ in a good agreement with experimental result $k=0.69+(-)0.03$ [75].
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