Agreed. In a stationary metric m(r) does not depend on time by definition, and the metric defines the basic geometry in which the dynamics take place. In the classical Galilean metric diag (1, 1, 1) for example, the Newton equations take place in a Galilean covariant theory and the unit vectors i, j, and k do not depend on time. In a non stationary metric the m function depends on time. Orbits worked out in a non stationary metric should be different from those worked out in a stationary metric. In UFT95 the Coulomb and Ampere Maxwell Laws were worked out in the obsolete Big Bang metric, the FLRW metric, which illustrates a metric that was supposed to produce an expanding universe. Steve Crothers showed that there is a geometrical error in the FLRW metric. Steve’s own metric, the Crothers metric, also developed in the UFT papers, represents the most general spherical spacetime. In UFT301 (CEFE) you developed many metrics, some of these are non stationary. So orbits can be worked out in non stationary metrics using your powerful integrator routine. This is a test of Big Bang, an orbit in an expandig universe ought to be different from an orbit worked out with a stationary metric. As far as I know there is no experimental evidence at all for an orbit being different in an expanding universe from an orbit worked out with a stationary metric. This again shows that the Einsteinian general relativity is totally wrong due to neglect of torsion. By now it is well known that Big Bang has been refuted in nearly a hundred different ways in the UFT papers alone, and it has also been refuted experimentally and by other theoreticians. Vigier replaced Big Bang by photon mass theory many years ago. Big Bang is still taught to school children, making a mess out of education.
m theory function
ok, thanks. m(r) is a property of space while orbits appearing in Hamiltonian and Lagrangian depend on time. I supposed something like this.
Horst
Am 25.09.2018 um 07:09 schrieb Myron Evans:
m theory function
Many thanks for going through these notes. This is a good point. The reason why m does not have a time dependence is given in chapter seven of Carroll’s online notes for "Spacetime and Geometry: an Introduction to General Relativity" which is cited often in the UFT series as you know. The reason is that all spherically symmetric vacuum metrics produce a time like Killing vector and are stationary metrics. As in previous UFT papers the most general spherically symmetric vector is :
ds squared = – exp (2 alpha(r)) dt squared + exp (beta(r)) dr squared + c squared d cap omega squared
where r is defined not to depend on t in the metric. In the Minkowski metric, which is spherically symmetric, alpha(r) = beta(r) = 0. In the m theory metric:
exp(2 alpha(r)) := m(r), exp( beta(r)) := 1 / m(r)
In the orbit, on the other hand, r is a function of t for the following reason. In the spherically symmetric Minkowski space the Cartesian metric is diag (1,-1, -1, -1) and does not depend on t, but the hamiltonian and lagrangian defined in this metric depend on t. In the spherically symmetric m space the metric, similarly, does not depend on t but the hamiltonian and lagrangian depend on t. In both cases the hamiltonian and lagrangian are dynamic quantities defined in a stationary metric. So I followed this received wisdom in setting up the m theory.