| Topic: |
Science > Physics |
| User: |
"Dengised28" |
| Date: |
28 Dec 2003 11:04:22 AM |
| Object: |
The Nature of Mass |
The Nature of Mass
We have all been taught in our physics classes that mass is one of the
fundamental entities of our reality and that all of the effects occurring in
our Universe are dependent on interactions between masses. It behooves us then
to examine what we know of mass.
About 40 years ago the writer came across the observation in a Scientific
American article that, in the equation E=M*C^2 there can only be two
independent variables. One of those variables, E, M, or C must be dependent
upon the other two. If we look at the velocity of light, C, it is obvious that
it must be one of the independent variables. Since velocity involves only
length and time, we can measure the velocity of light under conditions that are
independent of either mass or energy. Similarly, it is obvious that energy, E,
is an independent variable since energy involves only force and length, we can
also measure it under conditions that are independent of the velocity of light
and of mass. There remains only mass to be examined.
If one wished to determine the mass of an object, one could weigh it
(gravitational mass), shake it (inertial mass) or observe the amount of energy
released if it where annihilated. Weighing a mass provides a measurement of its
mass but the observation is made in terms of a reference mass (e.g.- the mass
of the Earth) and, in effect, we would then be defining the mass in terms of
another mass. This is hardly an acceptable solution since it leads to a dead
end. Annihilating the mass is a legitimate solution providing one can measure
the energy content of the end products without relying on a measurement of
their mass (such a reliance would be a form of circular reasoning). The
remaining possibility is to measure the inertial properties of the mass by, for
example, shaking it and measuring the force required to produce an a given
acceleration. This type of measurement involves force, length, and time, all of
which are directly observable and does not suffer form the limitations of the
other methods. What we would then be doing is measuring mass as the incremental
impulse required to produce an incremental change in velocity. (In the case of
photons and neutrinos it might be desirable to remove the word "incremental"
from the measurement since these particles exist only at the velocity of
light). Seen in this light, what we consider to be mass is actually a property
which is an indication of the energy required to change the velocity of the
quantity of energy defined by E=M*C^2. With this definition, the Lorentz
Transformation for Mass becomes equal to the cube of the accepted value and
allows problems involving STR to be solved without resorting to momentum. This
conclusion is consistent with STR because the conventional Lorentz
Transformation results when one integrates this transformation between the
limits of 0 and V.
An intellectual difficulty occurs when one considers the so-called
"massless" particles. They have this name because they have no "rest mass". A
reasonable man would consider such a terminology to be frivolous because these
particles exist only when traveling at the velocity of light. They have no
"rest mass" because they don't exist at rest. These so called "massless"
particles do however, possess inertial mass as evidenced by the radiation
pressure they exert when their velocity vectors are altered, either by
reflection or absorption. They provide the same reaction force as would a
material particle of the same relativistic mass that was traveling
infinitesimally close to the velocity of light. They also experience
gravitational forces that are twice the force that would be experienced by a
material particle of the same energy. A simple “thought experiment” as
outlined in Part 4 of http://members.aol.com/einsteinhoax/gravity.htm easily
shows this. (The writer has received a rather cryptic E-mail from someone who
apparently is associated with the physics establishment to the effect that the
photon imparts momentum because its energy is equal to the product of its
frequency and Plank's Constant and it is traveling at the velocity of light.
The sender denied vehemently that the expression E=M*C^2 and the idea that even
though the photon contains energy and imparts a momentum equivalent to a mass
of that energy traveling at the velocity of light, means that the photon has
mass. Bertrand Russell is reported to have said that the sign of a great mind
is the ability to hold two mutually exclusive beliefs at the same time. The
writer disagrees with him. That ability is the sign of a mind which is too lazy
to resolve the contradiction and/or is too damn lazy or too damn stupid to
resolve it)
The inertial and gravitational masses of the so-called "massless"
particles have a significant effect on our understanding of cosmology. A back
of the envelope calculation suggests that the inertial mass of these particles,
as evidenced by the 3 degree Kelvin radiation temperature of space, exceeds the
inertial mass of the matter in our Universe by a factor of 10. When we consider
that neutrinos are formed in nucleons that have 1800 times the energy content
of the source of photons (electrons), it may be possible that the mass of
neutrinos outweighs the mass of photons by a factor of 1800! Looked at it in
this light, our Universe may actually be a gasbag of photons and neutrinos
filled with a miniscule amount of the dust we call matter. Rather than being
the King of the Universe, what we call as matter may actually be only a
miniscule contaminant.
If we examine the radiation pressure produced by the observed level of
photons in space, it is easy to see why space appears to be expanding.
Radiation pressure is counteracting the gravitational pressure. It is also easy
to understand why the dynamics of galaxies appears to be skewed by what is
termed "dark matter". There would seem to be no need to postulate the existence
of "dark matter" until the gravitational and inertial effects of the photons
and neutrinos that populate the Universe have been amply explored. This has not
been done, primarily because these particles have been foolishly defined as
"massless".
The source material for this posting may be found in "Gravity" (1987),
"The Einstein Hoax" (1997), and "Corrections to Residual Errors in Special
Relativity (1999) located at http://www.members.aol.com/einsteinhoax/site.htm.
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.
Please make any response via E-mail as Newsgroups are not monitored on a
regular basis. Objective responses will be treated with the same courtesy as
they are presented. To prevent the wastage of time on both of our parts, please
do not raise objections that are not related to material that you have read at
the Website. This posting is merely a summary.
E-mail:-
The material at the Website has been posted continuously for over 5 years.
In that time THERE HAVE BEEN NO OBJECTIVE REBUTTALS OF ANY OF THE MATERIAL
PRESENTED. There have only been hand waving arguments by individuals who have
mindlessly accepted the prevailing wisdom without questioning it. If anyone
provides a significant rebuttal that cannot be objectively answered, the
material at the Website will be withdrawn.
.
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| User: "Krzysztof Olczyk olczykdotkrzysztofatxldotwpdotpl" |
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| Title: Re: The Nature of Mass - (on relativistic mass) |
29 Dec 2003 02:32:59 PM |
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"Dengised28" <dengised28@aol.com> wrote in message
news:20031228120422.26263.00001853@mb-m06.aol.com...
The Nature of Mass
We have all been taught in our physics classes that mass is one of
the fundamental entities of our reality and that all of the effects
occurring
in our Universe are dependent on interactions between masses. It behoves
us
then to examine what we know of mass.
Hello,
That post is not to be strict response to the quoted above post,
I am going to present my view on relativistic mass.
Generally, I don't like the term "relativistic mass".
For me, it is not a mass, but it is simply the kinematical energy
expressed in mass units. In my opinion, the term mass should be used
only when talking about "rest-mass" and I will do so in that post.
However, mass is (in my own definition) the accumulation
of energy of high density, "disturbing" body movement.
Why am I thinking so? I will show in one of future post.
Before that, I will answer the question the author of the post
"The Nature Of Mass" is for sure, now, stating:
"So why, then, 'massless' particles (i.e. photons) cause
radial pressure during absorption or reflection?".
In classical mechanics, Newton's second law states that force satisfies
the famous equation
F = m * a , (1)
so there must exist mass to cause force.
Of course, due to relativistic laws, it is not true for high velocities.
However, the truthful does the equation F = dp/dt remain,
that says that force is a derivative of momentum over the time.
Both for 'relativistic-mass-enthusiasts' and '-sceptics' true is
the relation:
E*v = p*c^2 (2)
since it does not involve any explicit mass.
Transforming the equation above we have that momentum equals:
p = (E*v)/c^2 (3)
Now, we would like to obtain the equation similar to eq. (1)
but with relativistic correction.
To get that, let us differentiate eq. (3). After trivial calculations we
have:
dp/dt = E/c^2 * dv/dt + v/c^2 * dE/dt (4)
Obviously, dv/dt equals acceleration. Denoting P=dE/dt, we can write:
F = E/c^2 * a + v/c^2 * P (5)
Thus, we obtained (1)-like second law of dynamics and what we can see?
Force is proportional (but not with constant factor) to acceleration.
But, now, the factor is total body/particle's energy (not only
the stationery energy associated with mass).
Therefore, the larger energy is the larger is also the inertia of body
and it is the energy to be considered a measure of inertia.
Now let us take a look on second term in eq. (5).
We have here the speed of alteration of energy multiplied
by velocity and inverse of squared light velocity constant.
How to deal with it? The alteration of energy is the work.
Thus, the derivative dE/dt equals power.
Reassuming, the force appears when there is a alteration
of velocity (acceleration) or when work is performed.
For small velocities (v << c) the total body's energy is almost equal
to stationery energy (in eq. (5) E/c^2 ~= m, '
other' energy divided by c^2 may be neglected)
and v/c^2 is approaching zero and, therefore, second term vanishes.
So, for small velocities we obtain: F = m * a, as we should have.
Now, take "massless particles". Note that due to the fact they always travel
with constant velocity, so the acceleration equals 0 and, eventually, the
first term in (5) vanishes and the equation finally becomes:
E = 1/c * dE/dt (6)
and it can be interprated that when light is absorbed or reflected
the energy is transformed and dE/dt gets value.
Coefficient 1/c shows why the strong flux is needed.
Summing up, I consider the energy the measure of inertia.
Mass is to measure the amount of matter and there is no relativistic mass.
When talking about relativistic mass, one is, in fact, talking about energy
expressed in mass units.
--
Regards,
Krzysiek
****************************
!WARNING!
****************************
That post is copyrighted to its author
and no part of it may be reproduced
without explicit acceptance of author.
*****************************
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| User: "Franz Heymann" |
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| Title: Re: The Nature of Mass |
28 Dec 2003 04:45:49 PM |
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"Dengised28" <dengised28@aol.com> wrote in message
news:20031228120422.26263.00001853@mb-m06.aol.com...
[snip]
Dear me, I nearly started reading that crap before I noiticed that it was
yet again that fool retiche.
Franz
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| User: "Sam Wormley" |
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| Title: Re: The Nature of Mass |
29 Dec 2003 12:19:24 AM |
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Dengised28 wrote:
The Nature of Mass
Ref: http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html
Physics FAQ] - [Copyright]
Addendum added by DK 2002.
Updated by Jim Carr 1998.
Original by Philip Gibbs 1997.
Does mass change with velocity?
There is sometimes confusion surrounding the subject of mass in
relativity. This is because there are two separate uses of the term.
Sometimes people say "mass" when they mean "relativistic mass",
mr but at other times they say "mass" when they mean "invariant
mass", m0. These two meanings are not the same. The invariant
mass of a particle is independent of its velocity v, whereas
relativistic mass increases with velocity and tends to infinity as the
velocity approaches the speed of light c. They can be defined as
follows:
m_r = E/c^2
m_0 = sqrt(E^2/c^4 - p^2/c^2)
where E is energy, p is momentum and c is the speed of light in a
vacuum. The velocity dependent relation between the two is
m_r = m_0 /sqrt(1 - v^2/c^2)
Of the two, the definition of invariant mass is much
preferred over the definition of relativistic mass. These
days, when physicists talk about mass in their research,
they always mean invariant mass. The symbol m for
invariant mass is used without the subscript 0. Although
the idea of relativistic mass is not wrong, it often leads to
confusion, and is less useful in advanced applications such
as quantum field theory and general relativity. Using the
word "mass" unqualified to mean relativistic mass is
wrong because the word on its own will usually be taken to
mean invariant mass. For example, when physicists quote
a value for "the mass of the electron" they mean its
invariant mass.
At zero speed, the relativistic mass is equal to the invariant mass.
The invariant mass is therefore often called the "rest mass". This
latter terminology reflects the fact that historically it was relativistic
mass which was often regarded as the correct concept of mass in the
early years of relativity. In 1905 Einstein wrote a paper entitled
Does the inertia of a body depend upon its energy content?, to
which his answer was "yes". The first record of the relationship of
mass and energy explicitly in the form E = mc2 was written by
Einstein in a review of relativity in 1907. If this formula is taken to
include kinetic energy, then it is only valid for relativistic mass, but it
can also be taken as valid in the rest frame for invariant mass.
Einstein's conventions and interpretations were sometimes
ambivalent and varied a little over the years; however an
examination of his papers and books on relativity shows that he
almost never used relativistic mass himself. Whenever the symbol
m for mass appears in his equations it is always invariant mass. He
did not introduce the notion that the mass of a body increases with
velocity--just that it increases with energy content. The equation E =
mc2 was only meant to be applied in the rest frame of the particle.
Perhaps Einstein's only definite reference to mass increasing with
kinetic energy is in his "autobiographical notes".
To find the real origin of the concept of relativistic mass, you have to
look back to the earlier papers of Lorentz. In 1904 Lorentz wrote a
paper Electromagnetic Phenomena in a System Moving With Any
Velocity Less Than That of Light. There he introduced the
"longitudinal" and "transverse" electromagnetic masses of the
electron. With these he could write the equations of motion for an
electron in an electromagnetic field in the Newtonian form F = ma
where m increases with mass. Between 1905 and 1909 Planck,
Lewis and Tolman developed the relativistic theory of force,
momentum and energy. A single mass dependence could be used
for any acceleration if F = d/dt(mv) is used instead of F = ma. This
introduced the concept of relativistic mass which can be used in the
equation E = mc2 even for moving objects. It seems to have been
Lewis who introduced the appropriate velocity dependence of mass
in 1908, but the term "relativistic mass" appeared later. [Gilbert
Lewis was a chemist whose other claim to fame in physics was
naming the photon in 1926.]
Relativistic mass came into common usage in the relativity text
books of the early 1920s written by Pauli, Eddington and Born. As
particle physics became more important to physicists in the 1950s,
the invariant mass of particles became more significant, and
inevitably people started to use the term "mass" to mean invariant
mass. Gradually this took over as the normal convention, and the
concept of relativistic mass increasing with velocity was played
down.
The case of photons and other particles that move at the speed of
light is special. From the formula relating relativistic mass to
invariant mass, it follows that the invariant mass of a photon must
be zero, but its relativistic mass need not be. The phrase "The rest
mass of a photon is zero" might sound nonsensical because the
photon can never be at rest; but this is just a side effect of the
terminology, since by making this statement, we can bring photons
into the same mathematical formalism as the everyday particles
that do have rest mass. In modern physics texts, the term mass
when unqualified means invariant mass, and photons are said to be
"massless" (see Physics FAQ What is the mass of the photon?).
Teaching experience shows that this avoids most sources of
confusion.
Despite the general usage of invariant mass in the scientific
literature, the use of the word mass to mean relativistic mass is still
found in many popular science books. For example, Stephen
Hawking in A Brief History of Time writes "Because of the
equivalence of energy and mass, the energy which an
object has due to its motion will add to its mass." and
Richard Feynman in The Character of Physical Law wrote "The
energy associated with motion appears as an extra mass,
so things get heavier when they move." Evidently, Hawking
and Feynman and many others use this terminology because it is
intuitive and useful when you want to explain things without using
too much mathematics. The standard convention followed by some
physicists seems to be: use invariant mass when doing research and
writing papers for other physicists but use relativistic mass when
writing for non-physicists. It is a curious dichotomy of terminology
which inevitably leads to confusion. A common example is the
mistaken belief that a fast moving particle must form a black hole
because of its increase in mass (see relativity FAQ article If you go
too fast do you become a black hole?).
Looking more deeply into what is going on, we find that there are
two equivalent ways of formulating special relativity. Einstein's
original mechanical formalism is described in terms of inertial
reference frames, velocities, forces, length contraction and time
dilation. Relativistic mass fits naturally into this mechanical
framework, but it is not essential. If relativistic mass is used, it is
easier to form a correspondence with Newtonian mechanics, since
some Newtonian equations remain valid:
F = dp / dt
p = m_r v
Also, in this picture mass is conserved along with energy.
The second formulation is the more mathematical one introduced a
year later by Minkowski. It is described in terms of spacetime,
energy-momentum four vectors, world lines, light cones, proper
time and invariant mass. This version is harder to relate to ordinary
intuition because force and velocity are less useful in their
four-vector forms. On the other hand, it is much easier to generalise
this formalism to the curved spacetime of general relativity where
global inertial frames do not usually exist.
It may seem that Einstein's original mechanical formalism should be
easier to learn, because it retains many equations from the familiar
Newtonian mechanics. In Minkowski's geometric formalism, simple
concepts such as velocity and force are replaced with world lines
and four vectors. Yet the mechanical formalism often proves harder
to swallow, and is at the root of many people's failure to get over the
paradoxes that are so often discussed. Once students have been
taught about Minkowski space, they invariably see things more
clearly. The paradoxes are revealed for what they are and
calculations also become simpler. But it is debatable whether or not
the relativistic mechanical formalism should be avoided altogether.
It can still provide the correspondence between the new physics and
the old, which is important to grasp at the early stages. The step
from the mechanical formalism to the geometric can then be easier.
An alternative modern teaching method is to translate Newtonian
mechanics into a geometric formalism, using Galileian relativity in
four dimensional spacetime, and then modify the geometric picture
to Minkowski space.
The preference for invariant mass is stressed and justified in the
classic relativity textbook Spacetime Physics by Taylor and Wheeler
who write
"Ouch! The concept of `relativistic mass' is subject to
misunderstanding. That's why we don't use it. First, it
applies the name mass--belonging to the magnitude of a
four-vector--to a very different concept, the time
component of a four-vector. Second, it makes increase of
energy of an object with velocity or momentum appear to
be connected with some change in internal structure of
the object. In reality, the increase of energy with velocity
originates not in the object but in the geometric properties
of space-time itself."
In the final analysis the issue is a debate over whether or not
relativistic mass should be used, and is a matter of semantics and
teaching methods. The concept of relativistic mass is not wrong: it
can have its uses in special relativity at an elementary level. This
debate surfaced in Physics Today in 1989 when Lev Okun wrote an
article urging that relativistic mass should no longer be taught (42
#6, June 1989, pg 31). Wolfgang Rindler responded with a letter to
the editors to defend its continued use. (43 #5, May 1990, pg 13).
The experience of answering confused questions in the news groups
suggests that the use of relativistic mass in popular books and
elementary texts is not helpful. The fact that relativistic mass is
virtually never used in contemporary scientific research literature is
a strong argument against teaching it to students who will go on to
more advanced levels. Invariant mass proves to be more
fundamental in Minkowski's geometric approach to special
relativity, and relativistic mass is of no use at all in general
relativity. It is possible to avoid relativistic mass from the outset by
talking of energy instead. Judging by usage in modern text books,
the consensus is that relativistic mass is an outdated concept which
is best avoided. There are people who still want to use relativistic
mass, and it is not easy to settle an argument over semantic issues
because there is no absolute right or wrong; just conventions of
terminology. There will always be those who post questions using
terms in which mass increases with velocity. It is unhelpful to just
tell them that what they read or heard on cable TV is wrong, but it
might reduce confusion for them in the longer term if they can be
persuaded to think in terms of invariant mass instead of relativistic
mass.
In a 1948 letter to Lincoln Barnett, Einstein wrote
"It is not good to introduce the concept of the mass M =
m/(1-v^2/c^2)^1/2 of a body for which no clear definition can be
given. It is better to introduce no other mass than `the
rest mass' m. Instead of introducing M, it is better to
mention the expression for the momentum and energy of
a body in motion."
The viewpoint above, emphasising the distinction between mass,
momentum, and energy, is certainly the modern view. Fifty years
later, can relativistic mass be laid to rest?
Addendum: What is the relativistic version
of F = ma ?
For this last section, we'll write down the relativistic version of
Newton's second law, F = ma. In Newton's mechanics, this
equation relates vectors F and a (hence the bold script) via the mass
m of the object being accelerated, which is invariant in Newton's
theory. Because m is just a number, in Newton's theory the force on
a mass is always parallel to the resulting acceleration.
The corresponding equation in special relativity is a little more
complicated. It turns out that the force F is not always parallel to
the acceleration a! To express this fact, we need to use matrix
notation. Letting m be the invariant mass, v be the velocity as a
column vector, and 1 be the 3 x 3 identity matrix, the actual result
turns out to be
F = gamma m (1 + gamma^2 v v^t) a
and
a = (1 - v v^t) F / (gamma m)
(As an aside, there's a nice correspondence to the one dimensional
case here. Just as gamma^2 can be written as 1 + gamma^2 v^2, and its
inverse (i.e. reciprocal) is 1 - v^2, so the matrix 1 + gamma^2 v v^t has
inverse 1 - v v^t, as well as determinant gamma^2.)
Looking at this relativistic version of F = ma, we might say that
when the (invariant) mass m appears, it's accompanied by a factor
of gamma, so that really it is the relativistic mass that's appearing.
Isn't this then, a good reason why we might want to give the notion
of relativistic mass more credence? Not really. Notice that now the
acceleration is not necessarily parallel to the force that produced it.
It's not hard to see from the above equations that it's easier to
accelerate a mass sideways to its motion, than it is to accelerate it in
the direction of its motion. So now, if we still want to maintain some
meaning for relativistic mass, then we'll have to realise that it has a
directional dependence--as if the object somehow has more mass in
the direction of its motion, than it has sideways. Evidently the idea
of relativistic mass is becoming a little more complicated than at first
we might have hoped! And this is another reason why, in the end,
it's so much easier to just take the mass to be the invariant quantity
m, and to put any directional information into a separate, matrix,
factor.
References:
Arguments against the term "relativistic mass" are given in the
classic relativity text book Space-Time Physics by Taylor and
Wheeler, 2nd edition, Freeman Press (1992).
The article Does mass really depend on velocity, dad? by Carl
Adler, American Journal of Physics 55, 739 (1987) also discusses
this subject and includes the above quote from Einstein against the
use of relativistic mass.
Einstein's original papers can be found in English translation in The
Principle of Relativity by Einstein and others, Dover Press.
Some other historical details can be found in Concepts of mass by
Max Jammer and Einstein's Revolution by Elie Zahar.
.
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| User: "Uncle Al" |
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| Title: Re: The Nature of Mass |
28 Dec 2003 02:12:27 PM |
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Dengised28 wrote:
The Nature of Mass
[snip]
Psychotic ineducable boring spammer retic (Ernest Wittke),
You see yourself this way,
http://www.mazepath.com/uncleal/effete6.jpg
The entire remainder of the planet sees you this way,
http://www.mazepath.com/uncleal/effete7.jpg
http://b5.sdvc.uwyo.edu/bab5/snds/argcstpd.wav
http://w0rli.home.att.net/youare.swf
http://www.mazepath.com/uncleal/sunshine.jpg
http://www.you-moron.com/
http://groups.google.com/groups?q=group%3Asci.physics+author%3Awittke
http://www.mazepath.com/uncleal/effete0.jpg
http://www.mazepath.com/uncleal/effete1.png
http://www.mazepath.com/uncleal/effete2.png
http://www.mazepath.com/uncleal/effete3.png
http://www.mazepath.com/uncleal/effete4.png
http://www.mazepath.com/uncleal/effete5.jpg
http://www.apa.org/journals/psp/psp7761121.html
http://insti.physics.sunysb.edu/~siegel/quack.html
<http://www.firehead.org/~jessh/film/kubrick/Kubrick-Psycho.html>
<http://www.naturalchild.com/elliott_barker/prisons.html>
The source material for this posting may be found in "Gravity" (1987),
"The Einstein Hoax" (1997), and "Corrections to Residual Errors in Special
Relativity (1999)
[snip]
Hey, stooopid spammer Ernest Wittke - Do you want EVIDENCE? Each of
the 24 GPS satellites carries either four cesium atomic clocks or
three rubidum atomic clocks in orbit, with full relativistic
corrections being applied.
http://arXiv.org/abs/hep-th/0307140
GR structure, especially Part 4/p. 7
<http://rattler.cameron.edu/EMIS/journals/LRG/Articles/Volume4/2001-4will/index.html>
Experimental constraints on General Relativity.
<http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf>
Nature 425 374 (2003)
<http://rattler.cameron.edu/EMIS/journals/LRG/Articles/Volume6/2003-1ashby/index.html>
http://www.eftaylor.com/pub/projecta.pdf
Relativity in the GPS system
Special Relativity is physics on a topologically trivial Lorentzian
manifold with a metric whose curvature tensor is zero. This is a
perfectly diffeomorphism-invariant condition and does not require
any particular coordinate choice. It is invariant under
the full group of diffeomorphisms. The Poincare group is
the group of *isometries* of the metric in special relativity.
The Special Relativity metric is *non-dynamical* (unlike GR). It
defines the coupling *constants* of your theory. If you change the
metric in any nontrivial way you are changing your theory. An
operation can only be called a "symmetry" of a special-relativistic
(non-gravitational) theory if it preserves the metric, and therefore
the symmetry of special-relativistic theories is the Poincare group
only. General Relativity (gravitation) has a dynamic metric.
NIM A 355 537 (1995)
Physics Letters B 328 103 (1994)
Physical Review Letters 64 1697 (1990)
Physical Review Letters 39 1051 (1977)
Physical Review 135 B1071 (1964)
Physics Letters 12 260 (1964)
Europhysics Letters 56(2) 170-174 (2001)
General Relativity and Gravitation 34(9) 1371 (2002)
http://fourmilab.to/etexts/einstein/specrel/specrel.pdf
<http://www.geocities.com/physics_world/sr/ae_1905_error.htm>
<http://www.physics.gatech.edu/people/faculty/finkelstein/relativity.pdf>
http://users.powernet.co.uk/bearsoft/Paper6.pdf
http://users.powernet.co.uk/bearsoft/LPHrel.html
Longitudinal and transverse mass
http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf
http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm
http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm
http://www.trimble.com/gps/index.html
http://sirius.chinalake.navy.mil/satpred/
http://www.phys.lsu.edu/mog/mog9/node9.html
http://egtphysics.net/GPS/RelGPS.htm
http://www.schriever.af.mil/gps/Current/current.oa1
http://edu-observatory.org/gps/gps_books.html
<http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html>
If anyone
provides a significant rebuttal that cannot be objectively answered, the
material at the Website will be withdrawn.
Right, like your head has ever been withdrawn from your ***** - even
when you *****.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
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