[9, p. 31].
Yielded expressions (50) are the commonly known equations
that determine the speed summing in relativistic mechanics. From the derivation we first
of all see, in distinct from Einsteinian formula (36), the time increment takes its part
in transformation of infinitesimal sections (49). It would seem, if the transformation of
finite sections of the metric (36) comes to the result discrepant from the view of
Relativity, while the theorem of speeds summing gives the ‘proper’ result, the
first variant is erroneous and we have to use the second, i.e. the theorem of speed
summing, and not in the part of problems but in all studies. Though from another side, it
is strange of course, why the observer in the dotted frame cannot compare independently
his measure of length with the stationary observer, then to compare the rate of clock,
then to measure the speed of light, allowing the stationary observer to count the result
on the basis of compared transformations.
Relativists used to conclude unambiguously: “At the first glance this question seems to be hopelessly confused.
There exist the opponents of relativity principle, simple minds (?! - Authors) who, having got to know this complicacy in determining the ruler length,
with a noble indignation (! - Authors) exclaim: ‘Of
course, one can derive whatever, if one uses wrong clock (? - Authors). This is an example, to which extent of absurdity can lead us a blind
belief in the magic power of mathematical formulas’, - and crush the theory of
relativity in one blow. Our Reader, hopefully, has already guessed, that formulas are not
a least the main circumstance, as we deal with the relationships of mere principle, which
one can successfully grasp without certain applying to mathematics” [2, p.
240].
Born is right, of course: the discrepancy is in the very
phenomenology of Relativity. Mathematical formulas only reflect the presence of
discrepancies. But when he says that the opponents of Einsteinian Relativity are against
the principle of relativity on the whole, not against the relativistic
interpretation of this principle, and that the opponents of Relativity see
‘mistakes’ exceptionally in the wrong clock, - this is an usual trick of
relativists, - we see the substitution of the issue by convenient interpretaions. To show
it, let us follow Born, how he phenomenologically removes the time parameter from Lorentz
transform.
In the relativistic view given by Born, the statement of
problem of sections measurement sounds as follows: “Let the
ruler of an unit length be located in the origin of reference frame S along the
axis x. Let us set ourselves to the question, which is its length in the frame S '. It is immediately clear,
this length will differ from the unit length. The observers who move with S 'will,
of course, measure the locations of ruler ends simultaneously in the frame S '.
But this does not mean ‘simultaneously’ in the frame S. Thus, even if the
location of one end of ruler was determined simultaneously by the observers of frames S
and S ', the S- and S '-observers will be unable to make the
reading of its another end, being simultaneous after S-clock. At the moment when
they do it, the S '-frame has been already shifted ahead and the result yielded
by the observer in the frame S ' reflects the shifted location of the second end of ruler” [2,
p. 240].
It unambiguously follows from this point that the record
of intervals in the speeds summing theorem is true; then in the integral form for finite
sections we would have to use not Einsteinian formula (36) but the expression that follows from (49), |