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Referenced
Articles:
Relativistic
Mass-Energy and Relativistic Space-Time Continuum
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Baseless Attack on
Einstein's Relativity
#P-A1
December 29,
1998
To
the Editor:
The
two (2) critical-view articles on
Einstein's Special Theory of Relativity (STR)
posted on your site should be removed as they
have no merit. The attack and the so-called
refutations of Relativity have stood time and
time again over the past 90 years. Anyone
interested in learning WHY relativity is
accepted should look at the Relativity FAQ site
at http://math.ucr.edu/home/baez/physics/relativity.html
and particularly at the page where the
experimental verification of STR is fully
documented, http://math.ucr.edu/home/baez/physics/experiments.html.
Putting aside that all
arguments presented therein are based on lines
of attack that were long dismissed, I take
additional issue with your entire site which
indicates that arguments should be made "using
Rational Thinking and only Rational Thinking".
Physics is not based on "Rational Thinking", but
instead is focused on achieving consistency with
observation. What is "Rational" takes a
back-seat to being able to explain observation
and predict the results of future experiments.
That means that any reasonable refutation will
not only make statements contradicting the
assertions of the author of these articles, but
will also cite published works in which said
observations were made or in which a line of
reasoning was first shown to prove a conjecture.
I would hope that such citations would add
weight to any such argument, and not be glossed
over as is often the case with others who feel
that "Thinking" is superior to observation,
logic, and mathematics.
Edward M.
Schaefer
schaefer@plansys.com
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STR
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STR
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STR
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December 29, 1998
Editor's
Reply:
#PER-A1
While
it is true that during its 90-year existence STR
had plenty of opposition (see, for instance, the
recently released book of Professor Arthur I.
Miller from the University College in London,
England, entitled Albert Einstein's Special
Theory of Relativity, Springer-Verlag New
York, 1998), this in itself cannot constitute a
ground for dismissing outright a critical
examination of STR. Surely Einstein did not seem
too concerned to challenge after some 220 years
Newton's theory of gravitation!
As for your remark pointing out that Physics
does not, as a matter of fact, employ
exclusively "Rational Thinking and only Rational
Thinking", to that regrettably I have to agree
with you. I say regrettably because this is the
source of so many problems that Theoretical
Physics is facing today most notably the ones
from Quantum Theory. It is our experiment here,
never employed anywhere, to see how far we can
go using, in exclusivity, our most precious
commodity --Rational Thinking, to an absolute
extreme. We may call our endeavor Rational
Physics to separate it, if you will, from the
traditional methods of Physics that you have
described.
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#P-A2
December 29, 1998
To
the Editor:
Edward M.
Schaefer
schaefer@plansys.com
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January 2, 1999
Editor's
Reply:
#PER-A2
With
respect to your point that in Science "it is
easy to attack something", this is true only if
the attack is based on beliefs or speculations
as anybody can indeed believe and speculate in
whatever he or she may want. However, when the
attack is done from a sound physical foundation
and carried out not through beliefs and
speculations but through rigorous logical
inferences --that is an entirely different
proposition altogether and may not be as easy as
you think.
In regard to your point
that a credible attack needs, in addition, to
have "something to replace it with" --this, in
general, is also not correct. In Mathematics,
for instance, proofs of various theorems are
rejected all the time by finding an aberration
of logic without finding a substitute proof. One
of the most celebrated and publicized such
theorems was Fermat's "Last Theorem." Pierre de
Fermat, some 350 years ago scribbled his result
on the margin of a book stating that he did not
have space to write the proof for his theorem.
Ever since, mathematicians have tried to prove
or to disprove that theorem. Numerous proofs
were given on both sides: for showing that
Fermat's Last Theorem was true and for showing
that it was not. Each time a "perfect" proof was
claimed to exist, a subtle error in rationale
was shown to exist. It was not until a couple of
years ago, that Fermat's Last Theorem was
finally proved, but not without several
revisions, by the now famous mathematician,
Professor Andrew Wiles of Princeton University,
USA. Because of the sensation that this proof of
Professor Wiles created, a PBS "Nova"
documentary was made highlighting the drama and
the turmoil of this discovery which was aired in
1997 on most of the PBS stations. For those who
missed this fascinating documentary or are not
residents of the US and may wish to visit or
revisit this subject and see an interesting
interview with Professor Wiles, they may want to
"hit" the PBS website, at http://www.pbs.org/wgbh/nova/proof/wiles.html
But now to come back to
Physics and to the subject at hand, it is worth
mentioning that the famed Dutch physicist
Hendrik A. Lorentz in attempting to prove the
null or negative result of the Michelson-Morley
experiment, which eventually lead Einstein to
his Relativity Theory, created an elaborate
theory of the electron (see, The Theory of
Electrons by H. A. Lorentz, Second Edition,
Dover Publications, 1952) which later was
refuted by others without an alternative theory
being provided. In fact, as of now we still do
not have a complete theory of the electron.
Thus, your point that for a credible attack on a
theory "like Relativity, you need something to
replace it with" is plain nonsense.
You are absolutely
correct in the analysis of your point #2.
Unfortunately or fortunately, depending on the
side that one is taking with respect to
Einstein's Special Theory of Relativity in
general and the relativistic mass formula in
particular, the correctness of this critique of
yours does not affect an iota, one way or the
other, the debate on the validity or invalidity
of Einstein's mass formula. Indeed, let us take
a closer look at what is involved here.
The author, clearly
overstated his case when he wrote in Part VIII
of his article refuting Einstein's relativistic
mass formula the following:
"Imagine what
would have happened with particle
accelerators around the world if Einstein's
mass formula
were to hold! Since particles in modern
accelerators can reach speeds comparable to
the speed of light, their mass, by this
formula, would have been increased so much
that the structures holding such accelerators
would have had to collapse by their own
enormous weight creating in the end
earthquakes! No such a thing ever happened,
and the architects designing the foundational
structures of such accelerators never put in
their calculations the weight effects of the
accelerated particles that may result from
Einstein's mass formula."
As you correctly have
shown even at "a trillionth less than
c
itself, a speed for all practical purposes
indistinguishable from
c,
the mass of a particle is still less than a
million times its rest mass." Thus, what you
have proven beyond dispute was how negligible
the relativistic mass effect is in a particle
accelerator, so negligible in fact, that for all
practical purposes it can be neglected
altogether! It is surprising therefore when you,
out of the blue, made this leap in your
concluding remark:
"The simple
fact of the matter is that particle
accelerator operators live and breath
Relativity. Without using Einstein's
insights, they cannot get the things to
work."
Aside from its
gratuitous nature, this statement defies exactly
what you have just proved: that in particle
accelerators the relativistic "influence" to the
overall mass result is so small that for all
practical purposes it is nonexistent. Why would
anyone care, in practical terms, for such an
infinitesimal and imperceptible influence? Thus,
ironically your calculations helped the author's
conclusion to stand, namely that
"the
architects designing the foundational
structures of such accelerators never put in
their calculations the weight effects of the
accelerated particles that may result from
Einstein's mass formula."
But with this being
said, let us make no mistake that the author's
passage in question cannot stand as it is, being
incorrect, and accordingly, it has to be either
removed or modified to take into account your
valid criticism. Of course, it goes without
saying, that this, in itself, has no effect on
the challenge and the potential threat that the
new mass formula
introduced in the
posted article and derived from Classical
Physics may pose to Einstein's relativistic mass
formula.
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Not So Baseless
Attack on Einstein's Relativity
#P-CA1
January 2, 1999
To the Editor:
First,
I take strong exception to the framework under
which this entire discussion takes place.
Respectfully, the title "Baseless Attack on
Einstein's Relativity" is without merit as there
is nothing, in the discussion presented to
warrant, as of now, such a title. When and if a
credible challenge can be found based on
Rational Thinking and only Rational Thinking
free of "beliefs, speculations, or analogies" as
posted in your welcoming page, http://www.NatureQuest.net/home.html,
then and only then can such a title have any
meaning, merit, or consideration.
Now with this being
said, let me be allowed to respond in kind to
some of the issues that have been raised by
Edward Schaefer in his second letter (#P-A2),
and divide my response in
two (2) parts.
Part
I
In the first paragraph
of the stated letter, Mr. Schaefer is arguing,
in brief, two points:
i) one,
that through Einstein's Special Theory of
Relativity "the rules of physics better fit
observations" and,
ii) two,
that the attack on Einstein's theory is due
to its success! As Mr. Schaefer put it,
Einstein "succeeded, and therefore his work
remains the focus of debate and attacks."
[sic!]
Let me state
emphatically, as this point was made in my two
articles, that there is not one single
observation or experiment that "fits better"
through the predictions of Einstein's Special
Theory of Relativity. I challenge
Mr. Schaefer or anyone else to document in
detail only one such observation or experiment.
As part of our collective brainwash, we were
indoctrinated by our educators with a myth of
how wonderful Einstein's Special Relativity
predicts certain observations of Nature better
than before when in fact, at a closer and more
meticulous scrutiny, no such thing exists. The
harm of this brainwash, which has a life of its
own, is of a monumental proportion as it
deprives generation after generation of students
from getting acquainted with the real
Physics embodied in a 2000-year
history.
The current success of
Einstein's Special Theory of Relativity rests
not in its ability to predict certain
observations better, as the preachers of this
theory led us to believe, but in its speculative
nature and in the difficulty to acknowledge how
wrong, how impatient, and how desperate we have
been in finding quick solutions to our most
vexing problems. As I have alluded, in one of my
posted articles, keeping alive Einstein's
Special Theory of Relativity was essential for
the birth of Quantum Mechanics, and if an
opportunity is given to me to present this
linkage through a full-fledged article, I most
certainly shall take advantage of such an
offer.
Part II
Much was made of my
blunder in the ostracized passage given in my
article on the relativistic mass. In Einstein's
Special Theory of Relativity, it is postulated
that nothing can travel faster than the speed of
light. For the purpose of this argument (and
only for this purpose), let us assume this to be
true. Nothing in the relativity theory prohibits
an object reaching the speed of light; the only
prohibition is that it cannot exceed the
speed of light. Thus, in theory, nothing
prohibits a particle, in an accelerator, to
actually reach the speed of light. And in such a
hypothetical situation, we get, by Einstein's
mass formula, the absurd result that the
respective particle will have an infinite mass.
My point was that we need not worry about such
absurdity ever materializing! Thus, for the sake
of clarity and accuracy, I am suggesting that
the said passage in question be replaced with
this one below:
Anonymous
Author
(Code: #AA050144-552)
Email: AnonymousAuthor@NatureQuest.net
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Editor's
Reply:
#PER-CA1
We
have noted your protest and displeasure with our
heading "Baseless Attack on Einstein's
Relativity" but that heading will stay as it
represents a point of view, and in fact, as you
must be aware, it represents the current
prevailing point of view. But, on the other
hand, being sensitive to your criticism, we have
added a second title, as you can see, more in
"tune" with your vantage point, under which your
response is being published. We are not here to
judge or to endorse a particular point of view.
Our job is simply to create a proper and
balanced "atmosphere" for airing different, and
sometimes clashing, points of view. If we fail
in that objective, we clearly fail in our
responsibilities.
We are happy to
commission you for the article that you have
alluded to. If our understanding is correct, you
have some ideas regarding a possible linkage
between Einstein's Special Theory of Relativity
and the "birth" of Quantum Mechanics. We would
love to have your thoughts formalized in an
article which, depending upon its nature, could
be posted either in our Historical Scrutinies
section for Physics, or in our Foundational
Inquiries.
Finally, we are
allowing the modification that you have
requested, although we have a feeling that this
may not be the last revision that needs to be
made. You see, your rhetorical question posed of
what would have happened if a particle in an
accelerator would have reached the speed of
light may not even be a realistic question since
implicitly it implies that a particle will not
disintegrate before it reaches the speed
of light. Why and when a particle disintegrates
is a fair question to be posed for examination
and elucidation.
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#P-CA2
JJanuary 10, 1999anuary
2, 1999
To the Editor:
In
Part II of my letter above (#P-CA1), I stated
the following:
"Nothing in
the relativity theory prohibits an object
reaching the speed of light; the only
prohibition is that it cannot exceed
the speed of light. Thus, in theory, nothing
prohibits a particle, in an accelerator, to
actually reach the speed of light."
You, in your response
to my rationale, in a subtle way, took issue
with the inference made by me, i.e., with
my "Thus" throwing a monkey wrench into it. You
in effect argued, perhaps not in these exact
words, that just because from STR we do not have
a direct prohibition that a particle
cannot reach the speed of light this does not
mean that in fact such a prohibition does not
exist dictated perhaps by other theories or
principles of Physics. You then continued, with
your critical analysis, by noting that for this
matter to be settled we need to have, at the
very least, an understanding of "why and
when a particle disintegrates." Well, it is my
pleasure to provide you with such an
understanding from the principles enunciated in
my article attacking Einstein's relativistic
mass concept.
To "see" why, when, and
how a particle disintegrates, you need to follow
my LOOM method of discovering 'things' in
Nature, and thus, if you do not mind, follow me
in this journey. We are going to "descend" to a
Level Of Organization Matter (i.e., to a
LOOM) from where we can "see" the
interrelationship or interrelationships which an
accelerated particle establishes with its
immediate environment. In fact, we are
going to "descend" to the lowest LOOM possible
reaching thus the "bottom" of the
Universe! I shall employ the simplest
visualization possible so that absolutely anyone
who wants to can join us, in this rather
fascinating journey, without difficulty or
special training. The only thing that you need
is to keep yours eyes "open". Well, if you are
ready, let me begin by setting up the stage.
As noted in my article, Einstein's renunciation
and abolishment of a material medium filling up
the space of the Universe is, as so eloquently
was put by Isaac Newton, "so great an
absurdity, that I believe no man, who has in
philosophical matters a competent faculty of
thinking, can ever fall into it". Yes, the
old and troubled ether concept (as the
hypothetical, prevailing and underlying
substance within which all material perturbances
of the Universe are being transmitted and
propagated) which was thrown out by Einstein
needs to be restored, perhaps under a new name.
For a number of years, in my studies, the name
that I have been using in lieu of the ether or
æther concept is xenofluid
("xeno" in Greek means "strange"). To fully
appreciate this concept, I have to present a
full-fledged cosmological article, but for here,
to continue, it is suffice to say that the ether
concept is back and fully reinstated and being
"reincarnated" as xenofluid. We need this
fundamental and underlying concept to explain
what we are going to "see" in our journey about
to begin.
The name 'particle' in this journey shall have a
completely different meaning than the one
employed in Quantum Mechanics. Here by
'particle' we will mean simply a minuscule
"hard" ball, which anybody can visualize and
thus be able to "see", formed of a "hard shell"
whose interior is vacuum. We will view such
particles as the primordial particles of the
Universe and we shall called them
masstrons. Without going into any
detail how masstrons of the Universe are being
formed or the kinds or types of masstrons that
may exist, what we need to know about them is
that notwithstanding their "hard" shell, they
can eventually break. And when they do break,
their hard shell substance, called
xenorigid (XR), will
transform back into
xenofluid (XF). The capacity
of xenorigid to transform into xenofluid shall
be called energy. If this
xenorigid's capacity is able to manifest its
existence, then we shall call it active
energy, if not we shall call it
dormant energy. The actual flow of
this transformation from xenorigid to xenofluid
shall be called the energetic
field.
The xenofluid
(aka the old ether concept) is considered
to be the pervading substance of the Universe
which obeys a so-called DownLevel
Law (or Downward Law)
--the grand master law of the Universe from
within which all physical phenomena and laws of
Nature can be derived and understood in a
coherent way. In its simplest form of
expression, the DownLevel Law, states
that:
xenofluid
has always the tendency to flow towards its
less dense parts.
Xenofluid should be
viewed as the primordial matter of the Universe
and, from an analysis that is not going to be
given here, considered to be an unstructured
"perfect" compressible fluid within the meaning
employed in Continuum Mechanics or in Fluid
Mechanics. The density of the xenofluid can vary
between
a maximum low
level value, transforming it into a new
state, called
xenobase (XB), which can
be viewed as a state in which xenofluid is at
its maximum "stretch",
and
a maximum high
finite level value, transforming it into a
new state, called
xenorigid (XR), which can
be viewed as a state in which xenofluid is at
its maximum "compression", and regarded as an
"absolute" unstructured rigid in the sense
employed in the mathematical Theory of
Elasticity.
All these three states, xenofluid, xenobase, and
xenorigid, can be incorporated under the
collective name xenosubstance
(XS). With this terminology introduced, we state
that the objective of the
DownLevel Law is that
of leveling
down the entire energy of the Universe to the
energy level of the xenobase.
With this simple
preparation, we are hopefully ready to begin our
journey, so let us not waste any more time as a
vista of phenomenal splendor and incredible
depth is just in front of us about to open. As a
final reminder before we proceed, let us not
forget the magic secret provided by the LOOM
method of discovering "things" in Nature:
to always look
at the relationship(s) that the studied
object (in our case, our particle vested into
the masstron concept) establishes with its
immediate environmental medium, as each such
relationship will manifest its existence
through a concrete physical
phenomenon.
As
stated, we begin our extraordinary journey by
"descending" all the way to the absolute
"bottom" LOOM of the Universe. Here, at this
ultimate "bottom", the corresponding loomtrons
are the ultimate particles of the Universe --the
masstrons, and the surrounding environmental
medium is the underlying matter of the Universe
--the xenofluid.
As a masstron moves
through its environmental xenofluid, we "see"
with ease two (2) interesting things that
happen simultaneously --one in the back of the
masstron, the other in its front:
FIG.1
A moving masstron leaving behind
it a low-density xenofluid tail and, in
front a high-density coat deposited on
the frontal side of the masstron's
surface. By the DownLevel Law, the
environmental xenofluid will "rush"
towards the masstron's low-density
xenofluid tail left behind.
i). In the
back of the masstron, we see that a "tail" of a
lower density xenofluid is being formed
following the moving masstron.
ii). In the
front of the masstron, we see that a xenofluid
"coat" of a higher density xenofluid is being
accumulated on the masstron's surface on its
frontal part.
Now, let's see what is
happening next. In the back of the masstron, the
environmental xenofluid, by the DownLevel Law,
will "rush" towards the masstron's tail from all
sides generating an IN-going xenofluid flow. Let
us note that
the IN-going
xenofluid flow will push from behind the
masstron offsetting the resistivity that the
masstron will encounter from its surrounding
xenofluid medium. This is the Principle of
Inertia! first enunciated by Galileo. We
have for the first time an understanding of
the Principle of Inertia. We have the big WHY
in our pocket, we know WHY, for the very
first time, inertia exists, we understand and
are able to "see" its machinery at work!
Let's stop for a minute here and reflect. And
as we do this, you may want to perhaps read
what the late distinguished Professor Richard
P. Feynman had to say about Galileo's
Principle of Inertia in his celebrated
Lectures on Physics (Addison-Wesley
Publishing, 1963, vol. I, p. 7-2):
"Galileo
discovered a very remarkable fact about
motion ...
That is the principle of inertia --if
something is moving, with nothing touching
it and completely undisturbed, it will go
on forever, coasting at a uniform speed in
a straight line. (Why does it keep
on coasting? We do not know,
but that is the way it is.)"
Now, we do
know and "see" how inertia works. Let us look
one more time at FIG. 1
before we move on.
As a result of the
IN-going xenofluid flow created, the masstron's
tail will be squished transforming its current
shape into a hot-dog shape of high-density
xenofluid. Then, by the same, DownLevel Law, the
high-dense xenofluid hot-dog will decompress,
generating a burst of an OUT-going xenofluid
flow (FIG. 2), until it reaches the level
of its environmental xenofluid
medium.
FIG.2
The masstron's tail being
transformed, by the DownLevel Law, into
a dense hot-dog shape xenofluid which
in turn, by the same DownLevel Law,
generates an outburst of an outgoing
xenofluid flow.
As for the frontal
xenofluid coat of the masstron, its density will
increase until the DownLevel Law shall "take
over" generating an OUT-going xenofluid
flow.
In a theory which we
shall not pursue or elaborate here, called
The Rational Unified Theory Of Nature
(TRUTON), the IN-going xenofluid flows are
called gravitational fields and,
the OUT-going xenofluid flows are called
caloric fields. This is another
momentous point which we have reached in our
journey, so let us stop again for a minute and
reflect on the extraordinary vista that has
opened in front of us. For the first time ever
we are actually able to "see" the origin of
gravity and its association with the caloric
field. This, in itself, is truly extraordinary.
Let's stay here for another moment or so and
grasp these two stunning revelations:
a masstron
by simply moving generates an ingoing
gravitational field!
and,
a masstron
by simply moving generates an outgoing
caloric field!
From this vantage
point, we see the path which needs to be
followed for studying and understanding gravity.
That the gravitational field and the caloric
field are part of the same underlying process is
an astonishing connection to have discovered. In
fact understanding this deep connection will
lead us to understanding, in a rational fashion,
the most stunning cosmological results in regard
to the evolution of the Universe. The
realization that gravity is not the only
dominant force in the Universe and that that
there is an other force equally dominant
opposing gravity, vested in the caloric field,
is the underlying motor for all work in
Theoretical Astronomy. The checks and balances
that the caloric field continuously imposes on
the "influence" of the gravitational field is
the secret for understanding the great harmony
and global equilibrium that exists in the
Universe. And this study, is without doubt, one
of the most fascinating paths that one can
undertake. Also from the same vantage point but
looking slightly into a different direction, we
"see" the path that we need to enter for
studying the energy concept. Also from here, we
can "see" the path which we need to enter for
studying and understanding light and other
electromagnetic radiation. The wave-corpuscular
duality associated with the properties of light
or the de Broglie wavelike postulate associated
with particles in general are straightforward
consequences derived from the interrelationship
that a masstron establishes with its surrounding
environmental xenofluid. In fact, because we are
at the "bottom" of the Universe from where all
physical laws of Nature have their origin
implanted, we can pursue from here to any
desired subject of studies covered by Natural
Sciences.
But what about the
subject at hand which is to understand and "see"
why and how an accelerated particle will
eventually disintegrate as it cannot increase
its speed indefinitely, you may ask. Well, we
are coming to it right now, but it was
irresistible for me not to point out the
stunning vistas that are available for
exploration from this vantage point where we are
now situated.
As we stated and
stated, the key to discovering the origin of any
property of Nature is through an analysis
deciphering the relationship which the object of
study establishes with its immediate
environment. Let us therefore continue looking
at the evolving relationship that a masstron
whose speed continuously accelerates establishes
with its surrounding xenofluid medium. Well,
first let us note, that because of the "perfect"
elastic property of the xenofluid, the masstron
is able to advance through space as the
xenofluid in front of it will always "open up"
through its stretch. However, if the masstron's
speed continuously increases, then it will exist
a moment, called the critical
moment, when the masstron's speed
will be so great, called the universal
critical
speed û,
that the masstron can no longer be able to
advance through its surrounding xenofluid as it
hits the "bottom" of the facing xenofluid, i.e.,
it will hit its xenobase.
FIG. 3
A masstron reaching its maximum
critical speed before disintegrating
into a burst of energy by hitting the
xenobase "wall". The energy is released
in the form of electromagnetic
radiation (light) that is propagating
perpendicular (red arrows) to the
masstron's direction of
motion.
And this xenobase will
act as an impenetrable wall: the masstron will
be crushed transforming into a burst of energy
which we call light. We note that radiation of
light always propagates perpendicular to the
direction of motion. Thus, not only that were we
able to understand why an accelerated particle
cannot increase its speed indefinitely, but we,
as a bonus, were able to "see" how an
accelerated particle actually transforms into
light. And this, as you undoubtedly will
recognize, is a tremendous bonus as it opens to
us the vista toward the road for studying light
and the rest of electromagnetic radiations. I
will stop here for now hoping that you have
enjoyed this journey which took us to the
"bottom" of the Universe.
Anonymous
Author
(Code: #AA050144-552)
Email: AnonymousAuthor@NatureQuest.net
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Editor's
Reply:
#PER-CA2
If
I am to understand correctly from your dazzling
journey, you have a theory entitled The
Rational Unified Theory Of Nature (TRUTON)
employing as its primordial element the
masstron. Since you stated that
"without going
into any detail how masstrons of the Universe
are being formed or the kinds or types of
masstrons that may exist ..."
I am wondering how and
through what principles and mechanism your
masstrons are being formed and if there is more
than one type of masstron, how can you
differentiate them qualitatively?
We would be extremely
interested to have and publish as much material
as possible from your TRUTON theory. In the
interim, we are creating an Appendix to your
critical view article on Einstein's mass formula
where your entire letter is being
published.
Finally, we cannot help
but wonder, whether in fact, as you have alluded
in your letter, you have mastered all the detail
in explaining the origin of gravity. If this is
so, then you are not only the first known human
to understand why gravity exists, but also the
only one in possession of that understanding and
this, must be a truly awesome feeling!
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E n d
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...
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[as
of
now]
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..
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~ S p e c i a l
T h e o r y
o f
R e l a t i v i t y ~
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