OT: Einsstein's BooBoos - A^2
- From: "eleaticus" <eleaticus@xxxxxxxxxxxxx>
- Date: Fri, 31 Jul 2009 23:11:26 -0700
The theme of the A^n series is time.
[[ Any A^m, m=n+1 is one addon to the A^n post, the new material placed
after a === line. Corrections or "minor" changes in the n<m material is in
all-caps.]]
In his seminal 1905 paper - title "On the Electrodynamics of Moving
Bodies" (in English translation of the original German) - the second major
thing Albert did was to derive his basic Special Relativity transformation
equations.
I call these the BEER (Basic Equations of Einstein's Relativity).
The third major thing Albert did was to use the time coordinate equation
of the BEER to argue that a (relatively) moving clock slows (dilates)
relative to the base, "stationary" system clocks.
That equation is:
t' = ( t - vx/c^2 ) / sqrt( 1 - v^2/c^2 ), where
The x is a location coordinate in the stationary system, and t is that
system's universal (everywhere synchronized) clock time, given that at t =
t' =0 the two system's coordinate origins were aligned/adjacent.
With x and t being the independent variables the equation shows what the
stationary system observer "sees" that the moving clock "says' at some
particular values of x and t.
In effect Albert asked "what does this equation tell us about what the
ever-changing stationary system x-location observer adjacent to the moving
origin sees for the clock with that moving origin?".
The equation for that ever-changing stationary location is:
x = vt.
Albert gets his answer by substituting vt for x in the time transformation
and algebraicly reducing the result:
t' = ( t - vx/c^2 ) / sqrt( 1 - v^2/c^2 ).
t' = ( t - v^2t/c^2 ) / sqrt( 1 - v^2/c^2 ).
t' = t( 1 - v^2/c^2 ) / sqrt( 1 - v^2/c^2 ).
t' = t*sqrt( 1 - v^2/c^2 ).
Because v is in Relativity theory always less than c for anything that has
mass, sqrt( 1 - v^2/c^2 ) is always less than 1 (one) when v <> 0 and
only as small as zero when v is impossibly great, equal to c.
Therefore, Albert takes this result as indicating time dilation (slowing)
because it says the moving clock shows less time than does the stationary
clock.
That is, t' < t.
Note that Albert's technique in this demonstration is to reduce the time
transform by using a "particular" value of x.
But, asking about an ever-changing stationary SYSTEM location is perhaps a
little bizarre. "CHANGING" AND "STATIONARY"?
A more thematic question about an equation for what a stationary system
observer sees is what a stationary observer sees, to belabor the obvious.
Using Albert's technique let's ask: what does a stationary observer see en
re the moving clocks as they pass it?
That is, use x = 0 in the time transform equation:
t' = ( t - vx/c^2 ) / sqrt( 1 - v^2/c^2 ).
t' = ( t - v0/c^2 ) / sqrt( 1 - v^2/c^2 ).
t' = t / sqrt( 1 - v^2/c^2 ).
Because sqrt( 1 - v^2/c^2 ) is always less than 1 (one) for any non-zero
v, that means we have shown - using Albert's basic technique - that:
t' > t.
That would be time contraction (speeding up) of moving clocks in analogy
to the supposed spatial/object contraction the BEER actually do support.
If Albert's technique is valid - and it is if one disregards the BEER's
derivation - so is my usage of the technique and we have proved by
reduction to the absurd (reduction ad absurdum) that Albert's time
transform equation is nonsense.
That is, t' < t (dilation) contradicts t' > t (contraction). (If you wish
to consider v=0 just add an = to each inequality.)
It's worse than just that one contradiction. Try x = -1 for example.
t' = ( t - vx/c^2 ) / sqrt( 1 - v^2/c^2 ).
t' = ( t + v/c^2 ) / sqrt( 1 - v^2/c^2 ).
That's even more CONTRACTION than for x = 0 if v > 0, and less CONTRACTION
if v < 0.
What about x = 1?
t' = ( t - vx/c^2 ) / sqrt( 1 - v^2/c^2 )
t' = ( t - v/c^2 ) / sqrt( 1 - v^2/c^2).
That's less CONTRACTION than for x = 0 if v > 0, and more contraction if v
< 0.
And the greater the absolute value of x, the greater the contradictions.
Every single-value examination of the time transformation equation demands
time contraction, not Albert's dilation.
This result would also reduce to absurdity a second basic belief of the
Special Relativity cult, namely that their space-time is isotropic with
respect to direction of velocity. THESE RESULTS FOR x <> 0 ALL DEPEND ON
THE DIRECTION OF RELATIVE MOVEMENT OF THE COORDINATE AXES, AND THAT IS A
HUGE NO-NO IN RELATIVITY DOGMA. (AND IN FACT BY ALL EVIDENCE KNOWN TO
SCIENCE?).
However, it reduces to the absurd only the time transformation equation
which, being absurd, cannot prove anything except its own absurdity.
======================================
If the BEER were correct and Albert's method of determining dilation a
valid algebraic technique (it isn't when viewed from the basis of the
various derivations; another series) then Time Travel is a certainty!
Let's re-examine the BEER's time transformation equation:
t' = ( t - vx/c^2 ) / sqrt( 1 - v^2/c^2 ).
For convenience here we use the conventional units of measurement where c
= 1 (one), one hundred percent of the speed of light, and v will thus be
some fraction of c, it being always less than c if it has mass. [In
theory, anyway.]
Thus, we can divide through by c^2 in t - vx/c^2 and focus on
t - vx,
knowing that the units of measurement are correct.
The denominator's sqrt term is not material to the immediate analysis
because it is always a positive number and has no effect on our target
conclusion: can t' be negative?
Certainly, if the BEER is correct. Just pick an arbitrary x with slightly
greater absolute value than |1/v|. Let the x have the same sign as v.
See?
The moving system clock adjacent to that stationary system location -
certainly showing a correct time if the BEER are valid - shows a negative
time.
Thus, an object only needs to be far enough away from the coordinate axis
origin to reverse in time. LOL.
It is disgusting to have to point out all these ridiculous consequences of
Albert's BEER, his time transformation equation, but there really is a
Relativity cult for whom anything about Einstein and Relativity has an
impenetrable aura. "Don't bother me with the logic, I a member of the
world's most admirable elite!"
[BTW, what with the setup in which t' = t = 0 when the origins are
adjacent, the clocks are actually stop watches in effect.]
A question that may come to mind is whether there is or can be a
v-velocity clock at that location. Why yes in principle. The first major
thing Albert did in his paper was to establish that principle.
In reality, of course, this obvious logic does not demonstrate the
possibility of time travel.It just presents one more demonstration of the
time transform equation's absurdity.
There's a further, related demonstration of the equation's absurdity.
It is completely arbitrary as to when any such two theoretical systems
could declare time zero on their stopwatches.
One could just signal the other: "3 of your seconds after you receive this
will be when we both reset our clocks to zero and we both will place our
origins at the location you then flag as being yours".
As for any stopwatch use, the time is arbitrary except for having to be
zero at the arbitrary starting time. Any delay or hurry up is immaterial
if you start the stopwatch properly.
Just so, the location of the x-coordinate origin. The basic question a
coordinate answers is "where". not "how much".
Hence, the minimum x-values that yield a negative t' are completely
arbitrary. If we had placed the coordinate axis elsewhere either the t'
value would have been non-negative, or the value would have been even more
negative.
The idea that a real "thing" - such as time is in physics - has a
measurement value dependent of the arbitrary location of something that
doesn't actually exist is of course nonsense.
And the coordinate axes of theoretical physics don't actually exist. How
could you construct one to reach from Sol even to the nearest star? Or
even from Chicago to the moon?
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