Posting #36:- "The Lorentz Transformation for Velocity"
(See also our sister site reticsessays.com)
"Great spirits have always encountered violent oppositions from
mediocre minds." - A. Einstein
It is recognized that Special Relativity provides the Lorentz
Transformations for Length and Time and Mass between reference frames having a
relative velocity. What is too often not recognized that, in so doing, it
provides the transformations for all other physical quantities! These remaining
transformations may be determined by applying the conventional Lorentz
Transformations to accepted physical equations.
Since a velocity is equal to a length divided by the time
required to traverse that length, the Lorentz Transformation for Velocity must
equal the Lorentz Transformation for Length [1/(1-V^2/C^2)^0.5] divided by the
Lorentz Transformation for Time [(1-V^2/C^2)^0.5]. The Lorentz Transformation
for Velocity is therefore equal to 1/(1-V^2/C^2). (As incredible as it may seem,
the writer has received a communication from an individual who asserts that a
Lorentz Transformation for Velocity cannot be determined by dividing the Lorentz
Transformation for Length divided by the Lorentz Transformation for Time even
though velocity is defined as length divided by time! I suspect that this
individual is a PhD who has a vested interest in maintaining the intellectual
status quo. If he is a physicist he is in the wrong line of work, I understand
that Walmart is hiring.)
This transformation yields a conclusion which is in conflict
with the current understanding of Special Relativity. Present dogma asserts that
the velocity of light is the same in all velocity reference frames. If one
considers two reference frames, A and B, moving at a relativity velocity V with
respect to each other, one finds that an observer in A measures the velocity of
light in his own reference frame as its conventional value of C and the velocity
of light in B as having been reduced by the Lorentz Transformation for Velocity.
Similarly, an observer in B measures the velocity of light in his own reference
frame as C and the velocity of light in A as having been reduced by the Lorentz
Transformation for velocity. While superficially this may seem to be a
contradiction, the difficulty vanishes when one factors in the effects of the
limit on the velocity of information transfer imposed by the velocity of light.
We are forced to accept the conclusion, however, that the
velocity of light changes as a result of a change in velocity and that this
change in velocity is concealed by a change in the size of the units of
measurement for velocity (length/time) making it appear that the velocity of
light is the same in both reference frames. In terms of unchanging units of
measurement, the velocity of light does differ between reference frames which
differ in velocity, it only appears to be unchanged when it is measured within
each reference frame. It may be stated, therefore, that Special Relativity
requires that the velocity of light be a "constant" but cannot be constant
between reference frames having a relative velocity. This conclusion is
consistent with the Lorentz Transformation Aether Theory which asserts that our
velocity with respect to the Aether is indeterminate.
However, one may derive more information from Special
Relativity. Consider two velocity reference frames, for example Earth and Mars. (See the figure below).
A rocket is located on Earth and three identical clocks are in use. One clock is
located on Earth, one is located in the rocket, and the third clock is located on
Mars. The observer on Earth and the observer in the rocket report that their
clocks run at the same speed and that the clock on Mars runs slower due to the
relative velocity between the two locations. The observer on Mars reports that
the clocks on the Earth and on the rocket run slower than his clock.
After the readings have been taken, the rocket takes off and
travels to Mars and stops there. The observer on Earth notes that the speed of
the clock on the rocket has slowed to the speed of the clock on Mars while the
observer on Mars notes that the speed of the clock on the rocket has increased
to match the speed of his own clock which is faster than the speed of the clock
on the Earth. The observer on the rocket does not notice a change in the speed
of his clock, but since he is familiar with Special Relativity knows that the
speed of his clock has changed as a result of his observed change in velocity
but that he cannot observe that change in the speed of his clock. He observes
that the change in velocity of his rocket has occurred and that the speed of the
clock on the Earth has appeared to slow and the speed of the clock on Mars has
appeared to increase. This observation does not bother him or the other
observers since all are familiar with Special Relativity.
Consider what this thought experiment has shown. It has shown
that not only is it impossible to measure our velocity with respect to the
Aether and hence it is impossible to assert that the Aether does not exist, It
has also shown that Special Relativity requires that there be an absolute
velocity reference frame (i.e.- the Aether). In the Rocket Experiment all three
observers report that the speed of the clock has changed as a result of the
change in the rockets velocity. The observer on Earth asserts that the speed of
the clock on the rocket has slowed, the observer on Mars asserts that the speed
of the clock on the rocket has increased, and the observer on the rocket asserts
that the speed of his clock has changed but that he cannot observe that change.
There is one item of information that all three observers agree on. The speed of
the clock on the rocket changed as a result of the change in the rocket's
velocity.
One event, the change in speed of the rocket, has caused the
speed of the clock on the rocket to change. Since there was only one causal
event, there can only be one result, the speed of the clock must actually
increase or decrease, it cannot do both! In order for that conclusion to be
true, there must be an absolute reference frame for velocity. The classical
Aether, which cannot be proven not to exist, must exist!
Two objections have been raised to this argument. The first is
that it involves acceleration and Special relativity does not include the effect
of acceleration. This argument is meaningless since no acceleration occurred
when observations were being made. The second argument involves the speed of
communication between the Earth and Mars. This is a foolish argument since the
observations were all made prior to the start and after the finish of the
experiment. The observers could have communicated by pony express without
affecting the conclusions. NOT ONLY DID SPECIAL RELATIVITY NOT ELIMINATE THE CLASSICAL AETHER, IT REQUIRES THAT THE CLASSICAL AETHER EXIST!
The source material for this posting may be found in "The Einstein Hoax" (1997) ; "Gravity" (1987) ; and "Corrections to Special Relativity" (1997). EVERYTHING WHICH WE ACCEPT AS TRUE MUST BE CONSISTENT WITH EVERYTHING ELSE WE HAVE ACCEPTED AS TRUE, IT MUST BE CONSISTENT WITH ALL OBSERVATIONS, AND IT MUST BE MATHEMATICALLY VIABLE. PRESENT TEACHINGS DO NOT ALWAYS MEET THIS REQUIREMENT. THE WORLD IS ENTITLED TO A HIGHER STANDARD OF WORKMANSHIP FROM THOSE IT HAS GRANTED WORLD CLASS STATUS.
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