has to exist, where the values *t*
can depend only on *g* and their derivatives” [18, p. 321]. It is understandable that from (49) there
follows the condition (43) by which Einstein substituted the conservation law (44). But
firstly, such substitution is not so much obvious even from the view of conception he
developed, as “however,
generally covariant systems of equations like (49) do not exist” [18, p. 323]. Well, if so, what is the sense to substitute
this, which, by Einstein’s opinion, is invalid in general case by that which does not
exist? Secondly, as we revealed before, in general case the energy-pulse tensor determines
not only gravity but also electromagnetic interaction. With it, if we follow Einstein, in
gravitation field the conservation law has to be recorded as (49), as the gravity field
changes the energy of studied body. At the same time, with the electric interaction which
is an indivisible part of electromagnetic interaction, we may use the conservation laws as
(46). But if an electric interaction also was able to change the body’s energy, the
initial Einstein’s admission “assume for a while that in
an improved so electrodynamics, the scalar of energy tensor also turns into zero!” is
wrong and we have, both in general case and in case of EM interaction, to write the
conservation law as (43), with all consequences for SR. And for GR too, as equations like
(43) do not exist in limits of general covariance. “Deeper
study shows that such systems are covariant only in relation to linear transformations.
Consequently, requiring to formulate the equations of gravity field so that to provide the
conservation laws to be true, we limit our choice of the reference frames so that only
linear transformations can transfer one allowed frame into another” [18, p.
323]. Namely this condition caused Schwarzschild to confine his problem to the sought of
just linear element - and we showed in our work that he factually has not fulfilled this
task. At the same time, we clearly see a dual, insincere Einstein’s attitude in
formulation of both SR and GR. From the full amount of physical properties, he selected
some amount of revelations that were convenient for him, which, dependently on his own
convenience, can be revealed either absent. Thereupon, the condition (39) appears to be
the atavism of SR in GR which Einstein intentionally retained to provide the invariance of
4-metric in passing to GR. With it, Einstein himself did not care that such condition puts
both mathematical formalism and phenomenology of GR onto two diverging ice floes. It was
more important for him that out of this condition, GR basically could not be formulated.
From this view, there become quite sensible multiple notices by Einstein like this: “if we, doing not knowing the generally covariant equations of
gravity field, specialise the reference frame and compose the equations of gravity field
only for this specialised frame, the theory cannot rise any objections except the only,
namely - that the composed equations, possibly, have a lack of physical meaning. But in
the considered case, no one will support this objection seriously” [18, p.
322].
Is it worthy after that to be surprised that writing the
element of volume in spherical coordinates (38), Schwarzschild accounted what was
convenient for him, omitting the coefficients *G* and *H*. But if we consider
this passing in rigorous accordance with mathematical formalism, we will see that
Schwarzschild, with help of his artificial trick, has not provided the Jacobian equal to
unity in passing from the initial rectangular coordinates to the artificial *x*-coordinates,
since, as we pointed in our paper, he did not account *G* and *H*. And by the
way, Einstein’s (39), with account of his own determinant (20), is invalid in static
gravity field. But if we consider (39) from the view of keeping the local invariant of the
light speed, then with accuracy to the coefficient which tends to unity with the motion
away from the field source (of course, if tends with it to the unity, which is quite doubtful), not
equal to unity in passing from one coordinate system to another, the logic of this
condition remains in limits of GR. The Jacobian with it, as Einstein defined, has to
determine the passing between the systems of spatial coordinates. So the claim of
colleagues who tried to find our mistake, as if we did not account in our Jacobian in (21)
of our work, page 6, the time coefficient *F*, is groundless. Because, as we already
said, after the above Einstein’s opinion, the symmetry of metric has to be conserved
only with respect to the spatial coordinates. Just so Schwarzschild also considered the
Jacobian in 3 D form. |