ON THE CO-DEPENDENCE OF TIME DILATION, SUPERLUMINAL VELOCITIES, AND RELATIVISTIC MASS

ON THE CO-DEPENDENCE OF TIME DILATION, SUPERLUMINAL VELOCITIES, AND
RELATIVISTIC MASS
Vertner Vergon

ABSTRACT:
The special theory of relativity is a quintessential example of
mathematical physics at work. There is no doubt as to its veracity or
accomplishments but unfortunately it leaves one disoriented when trying
to interpret its mathematical results in terms of every day experience.
This has led to the philosophy that we should disregard what our senses
dictate as reality. In turn physics theory has gone awry, engaging in
flights of fancy with no constraint as long as it is supported by
esoteric mathematics.

It is time to set the record straight, to interpret correctly the
misinterpretations of Einstein. The areas that need clarification are
Time Dilation, Relativistic Mass, and c as a limit (Superluminal
Velocities). These three are all tied together, one dependent upon the
other.


THE IMPORTANCE OF SUPERLUMINAL VELOCITIES.

Not to discuss whether UFOs really exist but rather if there were
intelligent life elsewhere in the universe -- and they had a high
technology -- could they reach us considering the vast distances, the
limiting speed of light, and the time it would take for voyagers to
transit? Is there a velocity/time barrier surrounding us that forever
places us in isolation? Fortunately (or maybe unfortunately) the answer
is no for superluminal velocities are possible and the only limit
placed on interstellar travel is the technology of transit, i.e., the
technology of attainable velocity.

As a consequence, this dissertation will deal firstly with the
existence of superluminal velocities. To do this we will summarize the
Dual Velocity Theory of Relativity. It seems everybody agrees
*observed* longitudinal length in an observed frame decreases with an
increase in relative velocity.

Postulate 1: Longitudinal length and "distance" are the same thing as
longitudinal length is also a distance.

Postulate 2: Velocity is distance per unit time.

Conclusion: Since longitudinal length reduces with an increase in
velocity, then *observed* velocity reduces with an increase in velocity
of the moving frame. Restated: The velocity of the moving frame is
greater than the observed velocity. Thus we have two velocities, the
observed velocity -- and the true velocity of the moving frame. The two
velocities are Lorentz variant. That is true velocity times the Lorentz
transform equals the observed velocity.

Where V is the velocity of the moving frame, v the observed velocity,
and R the Lorentz transform

v ( 1- v2/c2) , --- then V x R = v

Thus there are two velocities, that which is extant -- and that which
is observed. It will be found that as V goes to infinity, v goes to c.
Therefore we conclude that superluminal velocities exist. We also
conclude that in p = mv/R, the R applies to v not to m. So there is no
such thing as relativistic mass. The mass is invariable and v is the
observation of V that goes to infinity as R goes to zero.

PURSUING A BEAM OF LIGHT

Scenario 1

If you pursue a beam of light, your velocity has to be relative to the
emitter. As you gain in velocity the frequency reduces. At c it is
zero. No "spatial oscillation". Also, at c, the energy of the photon is
zero -- and the momentum is zero. Zero frequency, zero energy, zero
momentum = there is nothing to observe. But how can that be? The photon
must have consisted of something. The only conclusion is that what you
behold is a static electric field, i.e., a coulomb field. It is at rest
to you and has no kinetic energy, momentum or frequency.

Scenario 2

There is a problem with our posit. The speed of light is c to all
frames. We state you pursue a beam of light. Forgotten is that that
beam of light will *always* precede you at c -- thus you can never
attain a velocity equal to the photon. So even as you attain c and the
frequency goes to zero (and the energy and momentum too) the beam is
preceding you at c.

Does that mean that when you attain c the velocity of the photon is 2c?
Consider the spatial contraction aspect. At c *all* the space up front
is apparently contracted to zero. That means the photon is everywhere
up front at once. That is why time in the photon's frame is considered
stopped. It can cover any distance with no lapse in time. With a little
cogitation one realizes that fits the description of infinite velocity.


Since the space does not really contract, we are drawn to the
conclusion that the velocity of light is really infinite (or infinitely
great). In section 4 of his famous paper Einstein states: "... the
velocity of light in our theory plays the part, physically, of an
infinitely great velocity".


Interpretation of Mathematics

We should not be so enamored about the accuracy of mathematics. Whereas
the procedures and operations may be more or less accurate, the
failings come in the interpretations of the results.

Examples:

In his clock gedanken experiment, Einstein saw his moving clock was
"behind" (his word) the at rest clock and concluded that the moving
clock ran slower. Wrong.

Correct interpretation: The moving clock traveled faster than measured
-- and therefore made its transit in less time than experienced by the
inertial clock. Therefore, with both clocks keeping the same rate, the
moving clock makes its transit in *less time*. Thus we see the moving
clock keeping proper time but being behind the inertial clock at the
end of its journey. There is no slowing of the clock. Thus we see time
dilation as proposed by Einstein does not exist. (Nor does the Twin
Paradox.)


Relativistic mass

Einstein's math showed that as a body approached c, its energy
requirements, approached infinity as did its momentum. His conclusion:
This was due to an increase in inertial mass -- thus the bugaboo of
relativistic mass was born. His math also showed that as a body
approached c, its transit time of a longitudinal distance approached
zero. The transit time approaching zero was offered as time dilation.

Both wrong. There was given no cause and effect reason for the mass
increase and time dilation. Time dilation was already indicated as not
existing due to the fact it created a reductio ad absurdom known as the
Twin Paradox. Such a condition is a wildly waving flag that something
is wrong with a theory and that it has to be reworked. Such was not
done.

Correct interpretation:

The longitudinal length of a moving system *appears* to contract due to
the measurement being made by the use of light which has an invariant
velocity of c. Einstein could have concluded that as the apparent
length of a moving system contracted, so would the velocity itself
undergo a foreshortening. This would result in the following: As the
velocity of a body approached infinity, the foreshortened *measured*
velocity would approach c -- the maximum velocity of the measuring
tool.

As a matter of fact, if one does the arithmetic, they will find that
the energy requirements, the momentum and the transit time of a body do
not fit the relative velocity but DO fit the corresponding actual
(Newtonian) velocity. Thus we see the parameters of the Newtonian
velocity in the company of the measured corresponding relative
velocity.

Then there is the general (mis)interpretation of the energy-momentum 4
vector equation. This equation is nothing more or less than the
combination of Einstein's equations for the energy and momentum of
moving *bodies* -- "bodies", not radiation. The general interpretation
of the equation, E2 = (mc2)2 + (pc)2 is as follows: "If we set the m in
the right hand first term to zero, then we get E = pc which we know is
true. This shows that the mass of the photon is zero."

Wrong.

The first term is the square of mc2. In case one forgets, mc2 is REST
energy -- and the m is REST mass. Do we agree that the REST mass of the
photon is zero? Of course. A photon brought to rest (by absorption) is
no longer a photon -- so its REST mass is zero. The second RH term is
pc, the energy of a photon IN FLIGHT. The p is momentum - which we
know the photon in flight has.

In addition, we recognize that the equation represents ONE particle,
that is both RH terms represent the same particle. If the rest mass is
zero, then the particle is at rest. If the particle is at rest, it can
have no momentum --- so the second RH term is zero, i,e, no p.
Therefore pc does not
exist (is zero).

Every equation for momentum contains MASS and motion. Therefore E = pc
states that the photon in flight has mass. When faced with that fact,
the poor souls who misinterpreted the equation try to maintain their
position by declaring a new physics whereby there exists momentum with
no mass. The problem is, they cannot substantiate that.

"When you can measure what you are speaking about and express it in
numbers, you know something about it." Lord Kelvin (1824-1907)

DUAL VELOCITIES

Einstein's thesis is entitled "On the Electrodynamics of Moving
Bodies". So what does that actually mean? It is on the interaction of
light and moving systems. It might well be titled "The observation of
fast moving systems". Note, the operational word is OBSERVATION.

A rod in the system does not contract (along the line of motion) -- a
clock does not change the rate of its ticking -- the mass of any object
in the system does not change -- -- everything in the system stays the
same, it is the OBSERVATION that is distorted. In short, there is an
ABERRATION due to the fact that light -- the message carrier -- travels
at an invariable velocity (c). Observe the fact that light creates two
aberrations, (1) the aberration caused by refraction, and (2) the
aberration caused by the constancy of velocity.

In the first instance, the fish in the river pool is not where it
appears to be -- and in the second the condition of items in the moving
system are not undergoing the changes they appear to. If one keeps that
in mind they will avoid a lot of wrong conclusions.

One of the errors assumed from the theory is that c is the limiting
velocity of the universe. The correct conclusion is that c is the
limiting OBSERVED velocity in the universe -- because that is the limit
of the message carrier. The message carrier can be "tricked" into
revealing superluminal velocities. Here is one way.

Assume two points one light year apart -- A and B. Assume there is an
observer equidistant from both points. Next, we have an object expend
sufficient energy to attain a velocity of 12 c. Thus it will transit
the 12 light months in one month. The observer, being equidistant from
both A and B can disregard the transit time for light to carry the
messages of departure and arrival. He will receive these signals one
month apart. Thus he will measure a superluminal velocity of 12c.

(Note, in the 1960's astronomers at Caltech announced they observed
"blobs" receding from exploding galaxies at nine c.)

However, an observer at A will measure the velocity as given by
Einstein - for A, B is along the x axis. So we see there are two
velocities -- the velocity extant, and the velocity observed. (Just as
there is the actual location of the fish -- and where it appears to
be.) We shall call the Einstein velocity the relative velocity -- and
the superluminal velocity Newtonian (because that's what it is.)

In the present example the relative velocity is .9965458 c and the
Lorentz factor is .08304548.

Now if one calculates the kinetic energy and relative momentum for unit
mass they will discover that it is the same for 12c using Newtonian
equations. In other words the parameters for the Newtonian velocity are
to be found accompanying the relativistic velocity. There is one
caveat, however. The equation E = mv2/2 is only good for low
velocities. The correct equation for all velocities is E = mv2/(R + R2
) (which degenerates to mv2/2 at low velocities). It will be found
that this is exactly equal to Einstein's E = (1/R -1)mc2.


Examining this dual velocity further, we see it dissolves the Twin
Paradox. The Earth twin measures the relativistic velocity. The
Astronaut twin experiences the Newtonian velocity. Since the Newtonian
velocity is faster than the relativistic , the astronaut accomplishes
it in less time than that observed on Earth by the Earth twin.


DOPPLER TIME AND THE NON-EXISTENCE OF TIME DILATION

There is a saying, "If he fell in a sewer, he'd come up with a gold
coin. Einstein (whom I admire) was such an individual. He was 25 when
he wrote his theory, 26 when it was published. His concept was
impeccable, his mathematics correct. However, he fumbled in the
interpretation of the mathematical results. This created a mystique
haunting a theory that was basically correct but that played havoc with
our intuitive concept of the universe -- one that was neatly
categorized by Newton.


Rather than dealing only with the relativity of moving bodies he
brought in the electrodynamics also -- to some brilliant conclusions.
Had he interpreted his mathematics correctly, what would have
transpired was the creation of a theory that neatly packaged various
concepts of the *principle* of relativity that had been around for a
while. People would say, "That's nice." and put it on the shelf along
with other accepted theories of how our universe works and he would
have taken his place in equal standing alongside many other brilliant
physicists.


But Einstein misfired. He made interpretive errors that made his theory
- and him -- super famous because the concepts were bizarre and
resolution elusive. Perhaps the main one was the interpretation that
led to the Twin Paradox -- the concept of time dilation. How many
millions of hours have been spent discussing that? He discusses two
identical clocks, one of which goes on a journey and returns to the
stationary one. He notes that the clock that journeyed was "behind"
(his word) the stationary clock, i.e., showed less time.

Error number one. He assumed that the moving clock had kept slower
time. Since the moving clock showed less time when returned it must be
assumed that the loss of time was real, not an aberrated observation.
That in turn means the clock had to run slower in its own coordinate
system -- and that in turn is a contradiction for the STR maintains
that clocks keep proper time in their respective coordinate systems.
Einstein should have known that and worked on the solution.


This declaration of slower time led physicists, great and small to
recount that if one were to observe a space ship at high velocities,
one would observe the on board clock to run at dilation time -- t' = t
v(1-v2/c2). This we know is not so. Astronomers observe moving
emitters, i.e., clocks every night -- and what they see is Doppler
time. Any known constant emitter is a clock. The cesium atom is an
arbitrary choice. The variation of its frequency is the variation of
*observed* time. In recession, the time is slower than norm -- in
approach the time is faster than norm. Following this precept, the Twin
Paradox never appears. The correct explanation of the "behind" clock is
that it traveled At Newtonian velocities and thus completed the course
in less time than measured by the inertial clock which measured the
velocity as relativistic, i.e., slower.


Another oversight by Einstein was that he did not make perfectly clear
that mass increase and longitudinal foreshortening were *hypothetical
observations* only, and not real.(He assumed his readers would have the
intelligence to realize that. He was also stymied when his mathematics
showed infinite requirements for momentum and energy as a body
approached c. Rather than just forge ahead and toss that on the public,
he should have realized that his work was not done and that he had to
go back to the drawing board to get it right.


He might have cogitated that since longitudinal length seemed to
contract, that maybe velocity along that path might observationally
contract also. In which case it could be assumed that Newtonian
infinite velocity was possible -- and as that velocity approached
infinity, its *measurement* approached c. This would account for the
inordinate energy and momentum that accompany the *measured*
velocities. It will be found that those parameters fit exactly the
corresponding Newtonian velocities. This would lay to rest the bugaboo
"relativistic mass" because that was created to explain the excess
momentum.


There were other mistakes in aberration but they were not serious and
were quietly patched up by those who came after him. All in all, he can
be forgiven for in the final analysis the STR is a brilliant piece of
work -- and no one is infallible.

.

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