Natural Science Forum / Physics / Relativity / April 2006

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- v^2/c^2) , 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 are a static electric and static magnetic field. They are at
rest to you and have no 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 the frequency goes to
zero (and the energy and momentum too) the beam is preceding you at c.

Does that mean 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, E^2 = (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 mc^2. In case one forgets, mc^2 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.

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)