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Measurement of intervals of time.
[chrono- + G. metron, measure]
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where [sup.*][[nabla].sub.i][Q.sub.l] = [sup.*][partial derivative][Q.sub.l]/[partial derivative][x.sub.i] - [[DELTA].sup.j.sub.ji][Q.sub.l] is the chronometrically invariant derivative of the vector ([sup.*][[nabla].sub.i][Q.sup.l] = [sup.*][partial derivative][Q.sub.l]/[partial derivative][x.sub.i] + [[DELTA].sup.j.sub.ji][Q.sub.l] respectively).
We also use the aforemonetioned assumptions on small values and high order terms that reduce the chronometrically invariant differential operators to the regular differential operators: [sup.*][partial derivative]/[partial derivative]t = [partial derivative]/[partial derivative]t, [sup.*][partial derivative]/[partial derivative][x.sup.i] = [partial derivative]/[partial derivative][x.sup.i].
The first (scalar) equation of the system of the conservation equations (39) means actually that the chronometrically invariant derivative of the vector [J.sup.i] is zero
Geometric space characteristics of (2) are chronometrically invariant Christoffel symbols [[DELTA].sup.k.sub.ij] of the second kind:
In general, Zelmanov defines a pseudo-vector of an angular velocity [[OMEGA].sup.i] = 1 / 2 [[epsilon].sup.imn] [], where [[epsilon.sup.imn] is a completely antisymmetric chronometrically invariant unit tensor.
It is also contained in the chronometrically invariant Christoffel symbols (6).
A chronometrically invariant criterion for gravitational inertial waves, formulated according to Zelmanov's idea, is:
where [A.sup.ij.sub.(1)], [A.sup.ijk.sub.(2)], [A.sup.iklj.sub.(3)] are chronometrically invariant and spatially invariant tensors, which have no more than first order derivatives of the wave functions [X.sup.ij], [Y.sup.ijk], [Z.sup.iklj].
As it easy to see, the Synge equation in its chronometrically invariant form (10) under the entanglement condition d[tao] = 0 becomes nonsense.