Abstract (MT)
We will
show exactly where and how the Special Theory makes a mistake as regards the time
(directly in the original article). Also we
are going to present a scientifically consistent approach to finding the
required relations t'/t,
based on the solution
to the end of the Lorentz transformations
between the inertial systems K and K' (we
accept that the source of light K'
is moving in relation to K with velocity v
on the axes X'ºX
and replacing b=(1-v2/c2)1/2). Here is the solution itself: The appearance of the transformations t'=1/b(t-v.x/c2)
suggests that the mathematical
operation in brackets is not bringed
to the end. The values v.x/c2=∆t are manifestly corrections
to the time t, caused by transposition
of the systems and the top speed
of light. As
a result (t-∆t)=tcor is the corrected time t, which leads to the conclusion t'=tcor/b,
i.e. t'=t/b
and t=t'.b
– with the increasing velocity, second
К' is shortened and time К' accelerates. With top speed с,
mathematical properly dt' (second prim) tends to zero.
INTRODUCTION
One of the erroneous conclusions of
the Theory is the one regarding time. In
order to show how this conclusion is drawn, first we have to pay
attention to the complete formulation that the Lorentz transformations
are derived from, namely:
Inertial system K'(x', t') is moving to the right towards a stationary system K(x, t) with velocity v along the axes X'ºX. At the time of concurrence
of the origins O'ºO, from this common center a light
signal is
radiated to the right along X'ºX. After a time t in K, respectively t'
in K', the front of the signal will have a
coordinate х, respectively x' in K'. The ratios x'/x и t'/t are wanted (we replace b=(1-v2/c2)1/2).
EXPOSITION
We emphasize
heavily that this is the only condition that leads to the dependencies:
x'=1/b(x-vt)
; t'=1/b(t-v.x/c2) – viewpoint К' (1Т)
Let us explain: As seen from the scheme, for the juxtaposition (1T) are
needed two clocks, in K and К', and the "light signal" event whose parameters x, x' and t, t' are registered (the other possibility is with three clocks – results from the first one, the
signal is in implicit form).
As a second responsible moment, in order to no room for speculations, verbatim
we will quote the
text about the time from the original article (A.
Einstein – On the Electrodynamics of Moving Bodies, 1905, part I, §4, http://www.fourmilab.ch/etexts/einstein/specrel/www/), where for convenience we will use the above designation of the systems only and we will also add some notes in italic. And here are the author’s reasonings:
"Further, we
imagine one of the clocks which are qualified to mark the time t
when at rest relatively to the stationary system K, and the time t' when at
rest relatively to the moving system, to be located at the origin of the
co-ordinates of K', and so adjusted that it
marks the time t' (this design eliminates the light signal). What is the rate of this clock, when viewed from the stationary
system (no way to establish with two clocks only)?
Between the quantities x, t, t',
which refer to the position
of the clock, we have, evidently,
t'=1/b(t-v.x/c2) (the formula is 1T – here x is the abscissa in K
of the light signal)
and x=vt (here x is the
abscissa in K of the origin O')
Therefore, t'=t.b whence it
follows that the time marked by the clock (viewed in the stationary system) is
slow…"
In a word, Einstein arrives
at the conclusion t'=t.b, putting x=vt at the place of x in relation (1Т). However, it is obvious that the two abscissas are not equivalent. Before us is
a wrongful manipulation of formula (1Т). According to the initial
treatment
it compares the light signal’s parameters x, t, t'. While in the scenario of the quoted text this event is discarded. But with his
falling off, drop out and the top speed с, coordinate x'
and time t'. Then, the times t' and
t of which event does the author
compare...and how does he compare them once formulas (1Т) do not make sense anymore?
In order to show even more clearly
the whole untenability of
his reasonings
at this point we will adapt the problematic treatment to the initial one by replacing the light signal with a conditional one*
whose velocity is v. I.e.,
in system K' the front of the signal does not leave
the origin O' and therefore it has a
coordinate x'=0 and time t'=0. And in system K, after
the time t, it will have a coordinate x. So
the situation is adjusted to transformations (1Т), with a
result:
0=x-vt , respectively x=vt
; 0=t-x/v , respectively
t=x/v (1Т*)
Therefore, the author’s idea of x=vt will be in force only when x'=0,
t'=0, which makes the conception
a classical one – the
ongoing event in K is the movement of K', ergo,
the conditional signal with its front in O'. Nothing more! In
this case, one cannot draw a conclusion about the relation t'/t…besides in the way of incorrect physical and mathematical operations (the light signal is the
heart of the Theory).
While here, we
are going to present a scientifically consistent approach to finding the
required relations, based on strict adherence to the initial formulation, with
solution to the end of the transformations derived from it (http://alniko.log.bg/article.php?article_id=78196):
In short, because of displacement of
the systems К and К', reports x', t' in
K' are mono-dimensional (x'=x'mon, t'=t'mon), while reports x, t in K are formed as summary (x=xsum, t=tsum). I.e., the exact description of transformations (1T) is:
x'mon=1/b(xsum-vtsum)
; t'mon=1/b(tsum-v.xsum/c2) – viewpoint К' (1Т)
Now we
must to solve the expressions in brackets. The
coordinate xsum consists of mono-dimensional coordinate xmon
(corresponding to x'mon) and the additional
distance v.tsum=OO',
i.e. xsum=xmon+v.tsum. The
time tsum consists of mono-dimensional time tmon
(corresponding to t'mon)
and a time supplement
v.xsum/c2 for distance OO', i.e. tsum=tmon+v.xsum/c2. The substitution
of the summary quantities leads to the correct direct
comparison:
x'mon=xmon/b ; t'mon=tmon/b (as a generalization x'=x/b ; t'=t/b ) – viewpoint К' (1Т)
xmon=x'mon.b ; tmon=t'mon.b (as
a generalization x=x'.b ; t=t'.b ) – viewpoint К (2)
(the effect of the movement
is reported without displacement of the systems (O'=O))
CONCLUSION
The conclusion is: With the increasing
velocity, second К' is
shortened and time К' accelerates. With
top speed с, mathematical
properly dt' (second prim) tends
to zero. In the opposite direction the amount of movement
decreases, gravitation grows, time
slowed – evolution to a state of
a border peace (maximum gravitation), wherever the second becomes
infinitely long, the time ceases to run...a
moment
of stasis,
marginal density, and collapse...
follows a jump into the extremely contrary condition ("the big explosion").
________________________________________________________________________________
Alexandar Nikolov ©
2010-2013
All rights reserved (COPYRIGHT © 2010-2013)
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