Natural Science Forum / Physics / Relativity / April 2006

I am rerunning this article because the TWIN PARADOX tables (which are
crucial) were all screwed up. When the reader comes to them now, he can
see them by following the link placed there.
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TIME DILATION

Vertner Vergon

We examine time dilation as set forth in Einstein's paper and find it
has an inconsistency and a reductio ad absurdum. We ascertain a correct
time variation and illustrate its viability.

There is always an open question as to the accuracy of Scientific
articles. So the question arises, how can we judge the accuracy of an
article that involves a theory?

Firstly, the article (theory) must be consistent both internally and
with empiricism. If it isn't it is flawed.

Secondly, it must not violate any known physics laws. Nor, obviously,
can it lead to a reductio ad absurdum.

Theories necessarily contain speculation - else they are not theories
but simply logical constructs. Such constructs must also meet the above
requirements.

Articles generally contain both theory and reference to facts (such as
experiments). These must be verified.

If an article ( or theory) meets these requirements it cannot be
rejected. If it is, it is done so out of sheer obstinancy and/or
stupidity.

Let us examine the concept of Time Dilation as contained in the Special
Theory of Relativity.
We start our examination of the time dilation concept by going to its
source -- Einstein's paper, On the Electrodynamics of Moving Bodies. We
refer to his gedanken experiment of moving clocks. One of two
synchronized identical clocks remains at rest while the other moves
away and returns. When Einstein perceived the difference of the clock
readings in his calculations, he stated the moving clock "was slow by
...". The immediate perception by the public was that he meant if a
clock was "slow by" - it had to have run slower. He also said the
moving clock was "behind" the inertial clock by ... . These two
statements do not mean the same thing. If one clock is running slower,
then it is running slower, and that has only one meaning.
On the other hand to say one clock is behind the other is open to
alternative explanations, e.g., the moving clock could have traveled a
shorter world line -- or may have traveled faster than observed. In
either case the clock would maintain its normal (proper) rate but for a
shorter duration than the inertial clock and thus be behind. At any
rate the accepted version is that the clock ran slower and thus was
born the concept of time dilation.
This concept is usually presented by an illustration that says if one
were to observe a clock on a fast moving spaceship, they would observe
it to run slowly. It must be emphasized that this running slowly occurs
regardless of the direction or vector of the ship. That is to say it
matters not whether the spaceship is receding or approaching, time runs
slower. Also to be emphasized is that this slowness of time is not just
a matter of observation but actually takes place -- for when the clock
returns it is actually 'behind" the stationary (or Earth) clock.
Since this is the declared case, we are inevitably drawn to only one
conclusion, the moving clock has to be running slowly in its own
coordinate system. Here we are faced with an unforgiving contradiction
for basic relativity states that all clocks keep proper time in their
respective coordinate systems. It is inconsistent that a clock can
actually run slowly in its own coordinate system - and also, the
while, keep proper time; in short the clock would have to keep two
different rates simultaneously, a reductio ad absurdum. This
contradiction requires that the time dilation concept, i.e., t' = t (1
- v2/c2) 1/2 be discarded.
The question arises, is there something to take its place? The answer
is yes.
To lay the foundation for this replacement we note that any known
constant frequency is a clock. The scientific community has chosen the
excited cesium atom as the standard atomic clock. This is an arbitrary
choice. Next, we note that the cesium clock (or any other constant
frequency atom) will never vary in its rate. So they will always keep
proper time. However, observations of these clocks will show a
variation due to the Doppler effect. We declare this variation in
frequency is a variation in observed time. Since the frequency is a
clock, an observed variation in the frequency is an observed variation
in time. Call it Doppler or what one will, that is merely a description
of the mechanics. In the final analysis it is a variation in observed
time.
THINGS ARE NOT ALWAYS WHAT THEY SEEM.
Next, we examine a counter argument which states that the relativistic
Doppler rate is the result of the following: If one takes the
non-relativistic Doppler rate and modifies it by the time dilation
they, come up with the relativistic Doppler rate. This, supposedly,
confirms time dilation. Upon further examination, we perceive that even
if we were to accept that explanation, what we have is the situation
whereby an approaching clock is observed to run fast -- not as fast as
non-relativistic mechanics would have -- but fast. This is contrary to
time dilation which requires an approaching clock to run slowly. That a
reversal in direction results in a reversal of time rate is to be
expected since time variation is the result of velocity vectors - and
vectors are directional.
If a theory conflicts with empiricism, it has to be discarded.
Using the Doppler rate as the time rate will yield the time dilation
effect. And that is the proper way to refer to it -- "time dilation
effect". The reason: The net time differential when the movement of the
clock is complete is the same as though the dilation time was operative
throughout.
What then? What is the explanation for the "effect", but not the
actuality? Particle accelerator operators and Ives & Stillwell claim to
have "directly observed" time dilation. What they have observed is
transverse Doppler rates. And it so happens, by some extraordinary
coincidence, that the transverse Doppler rate is the same as the time
dilation rate.
And now to display the Doppler time resolution of the Twins Paradox:
What is displayed here is the round trip Twins experience with no
paradox. The upward arrow signifies outward bound, the downward arrow
signifies inward bound. The double arrows signify the ship being
observed going outbound while it in actuality is traveling inbound.
(second chart). This, of course, is due to the time it takes light to
travel. The observed velocity is v(.75c). At this velocity the so
called time dilation rate is 1/2 . The distance to far-point is sqrt(3
light seconds). So the elapsed time for the ship's transit is one
second due to the fact its actual velocity is sqrt(3 light seconds/sec)
( See The Dual VelocitiesTheory of Relativity.)*
( For seconds or years, the figures hold.)
This means that four years on earth would be only two years on ship.
The time rates shown in the second chart are the time rates of the ship
as observed by earth. They are Doppler rates.
They have to be. Any invariable frequency -- clock or atom -- will be
observed at Doppler rates. The same is true for observations of earth
by the ship (first chart). So there is a parity of rate observations as
required by the principle of relativity.
Notice, there is no time dilation rate observed (1/2 in this case) --
but when the trip is concluded the difference in the clock readings is
as though the ship clock had run at half time to the earth clock, i.e.
, run at dilation time. When Einstein saw that in his calculations
(1905 paper) he said the A clock "ran slow" by ... . This created the
impression that time really ran slower for the ship's clock. The table
below shows this isn't so. It runs at the normal (proper) rate but is
observed to run at the Doppler rate.
It is worth mentioning that according to the Special Theory of
Relativity a clock in the approach mode runs slow - but astronomers
observe clocks in the approach mode, and they are running fast.
Consequently, there is no time dilation observed. There is, however, a
time dilation effect, i.e., the transit time differential on the two
clocks -- and these were created by Doppler time.

OBSERVE:

ASTRONAUT'S TABLE

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TO SEE THE TABLE CLICK THIS LINK --- THEN LOOK FOR THE PULLDOWN "LIST
OF AUTHORS" AND FIND VERTNER VERGON -- THEN CLICK ON THE MARCH  5 ENTRE
http://www.wbabin.net    THE TABLE IS IN THAT ARTICLE.

So we see that although the final time differential is as though time
dilation were operating - in fact it is the Doppler time-frequency
that operates.

Note: Not only is there a parity of rate observations, but the length
of time each twin is an observer is equal to the time he is observed.
Thus there is a time commonality of observation. This, in a space-time
chart given in Space-time Physics (by Taylor and Wheeler), is labeled
the "line of simultaneity".

·    This article may be found at http://www.wbabin.net . Go to the pull
down "List of Authors" and click on Vertner Vergon. Then click on
the March 10 insertion

·    To calculate the Astronomer's observation of the outgoing trip,
we note the following:The distance to far point is 1.732 light seconds.
The velocity of the ship to the astronomer is the relativistic .866 c.
Thus it will take two seconds for transit. But Astronomer will not
observe that until light recording that event arrives at earth. This
will take 1.732 seconds. Adding the 2 seconds and the 1.732 seconds
yields the 3.732 seconds of observation (upward arrows).
Regarding the return trip: Even though the ship is traveling at a
(Newtonian) speed greater than c, it does not surpass the light
recording its journey. Instead, the waves pile up (condense) in front
of it and are observed by Astronomer at the rate of 3.732 times norm.
This phenomenon indicates that light can travel faster than c but the
manifestation of that is an increased frequency (shorter wavelength)
- with the observation of c as the velocity.