Transcript Santilli’s IsoRedShift and IsoBlueShift: A Brief Review Ritesh L.Kohale Department of Physics, R.

Santilli’s IsoRedShift and IsoBlueShift: A Brief Review
Ritesh L.Kohale
Department of Physics, R. T. M. Nagpur University, Nagpur-440033,
India
Email: [email protected]
Workshop on Isomathematics and its applications
September 25, 2013,
ICNAAM 2013, Rhodes Palace Hotel, Rhodes, Greece
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ACKNOWLEDGMENTS
o The author has no words to express his deepest gratitude to Prof. R.
M. Santilli for encouragements and providing an opportunity to get
initiated in this field of research.
o The financial support from the R. M. Santilli Foundation is gratefully
acknowledged for getting exposure to work in this interesting field
of research at this initial stage .
o Additionally, the author would like to gratefully acknowledge Prof.
A. A. Bhalekar and Prof.V.M.Tangde for their guidance during the
one day motivational workshop on Santilli’s new mathematics held
on 6th April 2013 at Smt. Bhagwati Chaturvedi College of
Engineering, Nagpur-09 (INDIA) and for reading this manuscript
and providing suggestions.
The present workshop was also sponsored by R. M. Santilli Foundation .
This Presentation Reports
 The theoretical, mathematical and physical
foundation of hypothesis presented by R. M. Santilli
regarding IsoRedShift (IRS) and IsoBlueShift (IBS), we
have concentrated on the compatibility of Santilli’s
IRS and IBS with the axioms of special relativity
under their appropriate mathematical formulations.
 Reports the innovative experimental confirmations
of IRS by Santilli in 2010 for a blue laser light in a
tube containing air pressure up to 2,000 psi ≈ 1137
bars at his IsoShift Testing Station.
 The mathematical concepts and physics of
IsoRedShift and IsoBlueShift proposed by Prof.Santilli
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Overviews
 Introduction
 History of light at glance
 Basic physical assumptions regarding Interior and exterior
dynamical problems
 Inapplicability of special relativity for interior dynamical problems
 Evidences on inapplicability of special relativity within our
atmosphere
 Santilli 1965 no reduction theorem:
 Dismissal of the absorption and scattering hypotheses by prof
santilli
 Origin of the redness of the sun at sunset and sunrise
 First experimental confirmation of santilli isoredshift
 Santilli isomathematics
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 Conclusions
Introduction
IN THE BEGINNING - (c 4.5 Billion BC)
Let There Be Light!
In the beginning it was dark and cold.
There was
No sun, No light, No earth, No solar system.
There was nothing, just the empty void of space.
Then slowly, about 4.5 billion years ago,
a swirling nebula, - a huge cloud of gas and dust was formed.
Eventually this cloud contracted and grew into a central molten mass that became
our Sun.
At first the sun was a molten glow.
As the core pressure increased, and the temperature rose to millions of degrees –
a star was born.
Through the process of thermonuclear hydrogen fusion, the sun began to shine
(Light).
This was the nebular hypothesis, first proposed in 1755 by the great German
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philosopher, Immanuel Kant.
THE SUN - (c 4 Billion BC)
 The sun is approximately 93,000,000 (9 crore,30 lacks) miles
from the earth, 864,000 miles in diameter, and is only an
'average' star in size, brilliance and age.
 There are more than 100 billion other stars in our sun's own
galaxy, the Milky Way. Energy, with a color temperature of
approximately 6500 degrees Kelvin, is received on earth,
from the sun.
 It takes light from the sun approximately 8 minutes to reach
the earth. The illumination on the earth's surface by the sun
may exceed 100,000 lux, (10,000 fc) in mid summer.
THE EARTH - (c 4 Billion BC)
 About 4 billion years ago, soon after the Sun was formed, the
Earth and our other planets were formed from violent
explosions and byproducts from the process that created the
Sun.
 The nine planets created are now known as Mercury, Venus,
Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto,
(arranged in order, from the sun).
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Light
 For centuries the nature of light was disputed.
 In the 17th century, Isaac Newton proposed the “corpuscular
theory” stating that light is composed of particles.
 Other scientists, like Robert Hooke and Christian Huygens,
believed light to be a wave.
 Today we know that light behaves as both a wave and as a
particle.
Robert Hooke
Christian Huygens
Isaac Newton
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HISTORY OF LIGHT AT GLANCE
 1021 - Alhazen initiated the conception of light as,
•made up of particles,
•supported by numerous scientists,
 1873 - Maxwell's equations supported the alternative interpretation of
light as,
•made up of (transversal) electromagnetic waves,
•propagated by a universal substratum (ether),
 Nevertheless, with the discovery of the black body radiation, the wave
interpretation of light resulted in being insufficient to represent all data.
Particularly, the discrete character of the absorption and emission of light
by atoms.
 1905 - Einstein resolved the latter standoff with his conception of light as,
•being made up of basic quantum particles called photons
•with energy E = hν
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wavelength
What is light really?
Electromagnetic radiation waves
Generally, electromagnetic waves and particles propagate inside the
anisotropic and inhomogeneous physical media.
• Electromagnetic waves can be described as a stream of photons.
• Each photon traveling in a wave-like pattern, moving at the
speed of light and carrying some amount of energy.
• The only difference amongst radio waves, visible light, and
gamma-rays is the amount of energy of the photons.
• Radio waves have photons with low energies.
• Microwaves have a little more energy than radio waves. Gammarays and cosmic rays have highest energy waves.
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10
The Doppler Effect
• You will know the Doppler effect as the falling note
of a car or train horn as it approaches, passes, and
then goes away from you.
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Equation
• For any object that is moving with a speed much less
than that of light, it can be shown that the change in
frequency is given by:
•
•
•
•
∆f - change in frequency (Hz)
f - original frequency (Hz)
v - speed of object (m/s)
c - speed of light (m/s)
f v

f
c
for v  c only!
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The equation in terms of wavelength is:

v


c
•
•
•
•
∆λ - change in wavelength (m)
λ - original wavelength (m)
v - speed of object (m/s)
c - speed of light (m/s)
for v  c only!
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Conventional Doppler contributions
 The conventional Doppler law does indeed contribute to the
redness of the Sun at the horizon for the evident reason
that,
 Even though the distance between Earth and Sun can be
assumed as remaining constant during the few hours of the
measurements, Earth rotates and, therefore, an observer on the
surface of Earth moves away from the Sun at Sunset and toward
the Sun at Sunrise, thus causing a conventional Doppler shift.
 However, simple calculations from well-known data (radius of
Earth and rotation time) show that the Doppler contribution is
quite small. In fact, the approximate tangential speed of Earth at
the equator has the value
vtang ≈ 430 km/s.
As a consequence, the following approximate value (similarly at
the equator) of the Doppler shift term
But actuality it is unsatisfactory to provide a numerical
representation of the redness of the Sun at Sunset and Sunrise.
It is interesting to note that, despite its small value, the
conventional Doppler shift is certainly visible to the naked eye.
By remembering that such a contribution is a redshift at Sunset
and a blueshift at Sunrise,
the comparison of the redness of the Sun at Sunset and Sunrise
shows certain a difference visible to the naked eye which is exactly
due to the opposite Doppler contributions.
Quantitative and time invariant representation
of IsoRedShift (IRS)
The representation of the IRS of the Sun verifying the conditions
1) Being capable of representing the increase of the IRS with the
increase of the distance d traveled by light in our atmosphere;
2) Being capable of representing as a limit the IRS of the light
wavelength from the blue, λblue ≈ 450 nm, to the red, λred ≈ 650 nm;
3) All representations being invariant over time in the indicated
logic.
Basically the selected value of 200 nm for the IRS is an
upper limit selected to illustrate the representative
abilities of IsoRelativity.
By reminding that the Doppler effect contributes to the redness of
the Sun at the horizon, we can use the Doppler-Santilli isolaw
for the wavelengths one can write the above equation as
where:
λirs is the increase of λblue due to the IRS for a given distance d;
ns is the space characteristic quantity of the atmosphere in the selected
direction s;
n4 is the local index of refraction of light in air;
The local speed of electromagnetic (e.g., radio) waves is the familiar
expression
C = c/n4;
v is the tangential speed of the observer due to the rotation of Earth;
c is the speed of light in vacuum;
and the minus sign is selected because of the dominance of the IRS,
Basic Physical Assumptions Regarding
Interior and Exterior Dynamical Problems
Until the early part of 20th century, there was a clear distinction
between Interior and Exterior Dynamical Problems.
Interior Dynamical Problems:
 Referred to extended particles and electromagnetic waves
propagating within physical media.
Exterior Dynamical Problems:
 Referred to systems of point-particles and electromagnetic waves
propagating in empty space
 Difference Between Interior and Exterior Dynamical Problems.
A primary difference between interior and exterior systems is appearance in the
form of contact, non-linear, non-local and non-potential interactions that cannot
be consistently represented via a Hamiltonian or a Lagrangian formulation.
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During the past fifty years,
Research conducted by large number of researchers, has identified
mathematical, experimental, physical, chemical and industrial
confirmation that,
 The Minkowskian geometry and special relativity are not
precisely applicable [1] for interior dynamical problems (e.g.,
electromagnetic waves propagating within physical media and
extended-deformable particles) [2].
 The Minkowskian geometry and special relativity is valid only for
exterior dynamical problems (e.g., electromagnetic waves
propagating in vacuum and point particles)
 The Lorentz symmetry is not exactly applicable within a physical
media and it needs consistent simplification for exterior
dynamical problems
 Special theory of relativity was not precisely applicable [1] for
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interior dynamical problems.
Inapplicability of special relativity for Interior dynamical
problems
By 20th century with the arrival of special and general relativities these
inadequacies were removed by means of the reduction of light to photons.
The distinction between exterior and interior
dynamical problems was eliminated via the
reduction of interior problems to a finite number of
point-particles
And put
forward the
facts that,
• Photons (light) travels in empty space
• It experiences scattering,
• It undergoes absorption and reemission by the
atoms of the medium
• Thus recovering the conditions of exterior
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problems
Diversified evidences on inapplicability of special
relativity within our atmosphere
Contrary to the case of galaxies,
o In case of the Sun we have visual evidence of the
absence of an appreciable relative motion between Sun
and Earth during the short duration of the Sunset.
o Consequently, the redness of the Sun at Sunset
constitutes visual evidence of the violation of the
Doppler shift law in our atmosphere, with consequential
inapplicability of special relativity, as it is the case at
large within all physical media
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Independently
from
previous
visual
evidence,
There are numerous additional reasons according to which
special relativity cannot possibly be exactly valid in our
atmosphere, Some of them are :
1. Our atmosphere is Inhomogeneous (because of the variation of the density with
the elevation from the sea level) and Anisotropic (because of the rotation of
Earth).Implies the inapplicability of the geometric foundations of special
relativity, the Minkowskian spacetime, since they requires homogeneity and
isotropy;
2. As it is well known, special relativity can only be defined with respect to inertial
reference systems, that is, reference frame moving in empty space along a
straight line without acceleration. Evidently, such inertial frames cannot exist in
our atmosphere, with consequential impossibility of properly formulating the
basic axioms of special relativity.
3. The strict application of special relativity within our atmosphere implies the
violation of interconnection. In fact, particles such as cosmic rays can travel in
our atmosphere at speeds bigger than the local speed of electromagnetic (e.g.,
radio) waves, thus implying a violation of interconnection.
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Contd…………….
4.
When the speed of light in vacuum is assumed as the maximal causal speed
within our atmosphere ,we have the violation of the relativistic laws of
addition of speeds because the sum of the speeds of two electromagnetic
(again, e.g., radio) waves in our atmosphere does not yield the local speed of
electromagnetic waves;
5.
Dynamics in our atmosphere, such as a satellite during re-entry, requires
contact, zero range, nonpotential interactions (e.g., of resistive type) that are
beyond any hope of representation via a Lagrangian or a Hamiltonian, thus
being beyond the analytic foundations of special relativity,
Additionally, the reduction of macroscopic objects moving in our atmosphere
to their elementary particle constituents (for the evident purpose of regaining
special relativity at the particle level), has been disqualified as being
inconsistent
by
the
No
reduction
Theorems
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•Santilli 1965 No Reduction Theorem:
“Non conservative and irreversible classical systems cannot be
consistently reduced to systems characterized by a finite number of point
particles all in conservative conditions and, vice versa, the latter systems
cannot consistently reproduce the former under the correspondence or
other principles.”
•This theorem establishes that, Einstein's theories and Quantum
mechanics are only valid under the physical conditions for which
they were considered and experimentally verified
(i.e. Reversible, Conservative, Hamiltonian, Exterior dynamical
problems of point-particles and Electromagnetic waves propagating
in vacuum).
•No Reduction Theorem was proved on the basis of violation of
thermodynamical laws due to the evident loss of entropy when
passing from a real physical system to an ideal collection of pointparticles moving in empty space all in conservative conditions,
•Because it was necessary to verify special relativity, quantum
mechanics and the conventional scattering theory.
No Reduction Theorem proved that the nonlinear, nonlocal and
nonpotential forces experienced, for instance, by a spaceship during
reentry in our atmosphere originate at the most primitive possible level,
that of elementary particles,
When exposed to interior dynamical problems (extended objects moving within a
physical medium), such as a satellite during reentry or a proton in the core of a
star, a general position is that their irreversibility, nonconservative and nonHamiltonian characters are seems true or possible but in fact it is not possible
("illusory" ) because,
 when the satellite is reduced to elementary particles and the proton is reduced
to its (claimed) point-like constituents - so the position says - Einstein's theories
continued…..
and quantum mechanics are recovered exactly.
THE OUTCOMES OF SANTILLI 1965 NO REDUCTION
THEOREM :
• No Reduction Theorem disproved that that total
conservation laws for an isolated system are only verified
by a system of particles in conservative conditions.
• Since they have no potential energy, neoconservative
forces are in essence exchange forces, as a result of which
they cancel each other when the system is isolated,
resulting in the full verification of the conventional total
conservation laws.
• The scattering region is an interior dynamical system, thus
characterized by a nonlinear (in the wavefunction),
nonlocal (integral) and nonpotential (nonunitary) time
evolution.
• No Reduction Theorem prohibit the exact reduction of the
scattering region to a finite set of isolated points, which is
considered a mere first approximation of a rather complex
reality.
• No Reduction Theorems are not bypassed by the
reduction of the scattering particles to point-like quarks,
since elementary constituents with a point-like
wavepacket do not exist.
Dismissal of the absorption and scattering hypotheses
by Prof. Santilli
Despite the above diversified evidence on the inapplicability of
special relativity in our atmosphere, the absorption and scattering
hypotheses have been formulated as the primary origin of the
redness of the Sun at Sunset and Sunrise.
But they were successfully dismissed by Prof. Santilli with his
experimental confirmations.
View of the experimental set up
used for the measurement of the
IRS of the entire visible spectrum of
Sunlight showing the telescope and
the Yokogawa analyzer AQ6373 set
for the detection at the horizon.
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1. Dismissal of the Absorption Hypothesis
 The hypothesis that absorption is the origin of the redshift of the Sun at
Sunset and Sunrise has no scientific foundations
 Visual evidence establishes beyond reliable doubt that the sky is blue
because redlight is absorbed by our atmosphere following a maximal
effective vertical travel of about 49 miles ≈ 80km.
 The trajectory of Sunlight at Sunset or Sunrise, that is, the trajectory along a
tangent to Earth at the horizon, is of the order of 4 356 miles ≈ 7 000 km
(given by Earth’s radius of 3, 968 miles ≈ 6, 384 km plus the atmosphere
along said tangent).
 Therefore, the trajectory of Sunlight at the horizon is about 875 times bigger
than that for the Sun at the Zenith.
 since red light cannot reach us when the Sun is at the Zenith, the same red
light cannot possibly reach us when Sunlight covers a trajectory 875 times
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longer than that at the Zenith
Eventually Prof. Santilli Proposed that,
 Had the Sun been dark blue at Sunset or Sunrise !!!!!! …..........,
then the absorption conjecture would be scientifically valid.
 But the Sun is red at Sunset and Sunrise,
 Thus providing visual evidence that the absorption hypothesis here
considered is essentially a non-scientific attempt to adapt physical
reality to the preferred Einsteinian theories.
And in the Dismissal of the absorption hypothesis
 It is addressed that, the absorption of individual spectral lines by our
atmosphere positively cannot cause any frequency shift because said
absorption is set by the atomic structure of our atmosphere.
 Therefore, the sole possibility for a frequency shift due to absorption
is that of changing the chemical composition of our entire
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atmosphere.
An electronically created composition to illustrate the definition of the IRS for the
spectrum of Sunlight, rather than that for monochromatic wavelengths as in Fig. showing:
1) The spectrum of actual Sunlight at the Zenith (top);
2) The same spectrum electronically shifted by 47 nm (bottom); and 3) Both spectra being
cut from 480 to 580 nm.
The main feature illustrated in this picture is that a visual comparison of the two
spectrograph shows no apparent frequency shift, while in reality we have a shift of about
47 nm.
This illustrates the impossibility to identify the IRS of individual wavelengths when dealing
with a spectrum,
and the consequential need to measure the IRS of the entire spectrum of Sunlight in the
transition from the Zenith to the horizon.
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2.
Dismissal of the Scattering Hypothesis
It should be recalled that Prof. Santilli rejected scattering as the
origin of the redness of the Sun at Sunset and Sunrise on grounds
very similar to those used for the rejection of scattering as the
origin of the cosmological redshift of galaxies, that is,
 scattering cannot possibly occur along a straight line for all
frequencies,
 scattering cannot possibly generate a redshift of the entire Solar
spectrum,
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The Physical Evidences That Supports to
Dismissal of the Scattering Hypothesis
1. The color of our atmosphere is precisely due to scattering
because, in its absence, our sky would be black day and night;
2. Scattering of some of direct Sunlight in our atmosphere is the
origin of the loss of intensity of Sunlight;
3. The color of our atmosphere surrounding the Sun at Sunset or
Sunrise is due precisely to scattering of red light;
4. A component of the redness of the atmosphere surrounding the
Sun at Sunset does indeed contribute to the detected redness of
the Sun at Sunset and Sunrise in our instruments, such as a
telescope (Fig. below).
5. Our atmosphere is blue during the day and red at the horizon at
Sunset and Sunrise, thus establishing that scattering occurs for all
frequencies and cannot possibly be the origin of the shift from,
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blue to red.
The view of the spectrograms of direct Sunlight at the Zenith (top) and at the
horizon (bottom) obtained on July 19, 2011, with the Avantes analyzer model
3648-FCPC and cut from 470 to 550 nm.
 As one can see, the comparison of the two spectrograms shows no apparent
IRS, except for an irrelevant change in intensity.
 This occurrence is fully in line with the definition of large IRS for a spectrum
(rather than for a monochromatic wavelength) because a shifted segment of
a spectrum must essentially coincide with the original spectrum segment.
 Hence, the use of the Avantes analyzer model 3648-FCPC, while being
excellent for the detection of the IRS of monochromatic wavelengths, was
inconclusive for the measurement of the IRS of the Sun at Sunset because its
range from 470 to 550 nm was insufficient to cover the entire spectrum of
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direct visible Sunlight
Origin of the redness of the sun at sunset and sunrise
Declaration of the problem
As it is well known,
Sunlight at the Zenith is predominantly yellow but at Sunset is
predominantly red, with a redness that increases with the
increase of the distance traveled by light in our atmosphere,
That is, with the decrease of the elevation of the Sun over the
horizon without any appreciable relative motion between the
Earth and the Sun,
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Acceptable Representations
The redness of the Sun at Sunset and Sunrise has been observed by
mankind since the dawn of civilization, and its scientific study has
been conducted since Galileo’s time. During this long period of
time, numerous hypotheses have been formulated on the origin of
the indicated redness, the most important ones deserving
consideration being nowadays reduced to three:
o Absorption,
o Scattering and
o IsoRedShift.
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First Experimental Confirmation of Santilli IsoRedShift
Santilli et al [R] conducted spectroscopic analyses of the entire spectrum of visible
Sunlight in the transition from the Zenith to the horizon (top view) because it is
equivalent to the cosmological redshift of distant galaxies (bottom view).
Therefore, experimental measurements of the Sun redshift have direct relevance
for the cosmological redshift.
[R] R. M. Santilli, G. Amato and G. West, ”Experimental Confirmation of the IsoRedShift at Sun at Sunset and Sunrise with Consequential
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Absence of Universe Expansion and Related Conjectures,” Journal of Computational Methods in Sciences and Engineering, Vol. 12, pages
165-188 (2012). http://www.santillifoundation.org/docs/Confirmation-sun-IRS.pdf
The transition from yellow to red implies an anomalous
shift
of
about
55
nm.
However, by recalling that only blue light can reach us
at the horizon, the anomalous redshift for both Sunset
and Sunrise is expected as being of the order of 100
nm. Bigger values of the anomalous redshift are then
expected (up to 200 nm) by inspecting the event for
infrared frequencies.
Consequently it became necessary
 to achieve an experimental verification of the representation of the redshift of the
Sun in the transition from the Zenith to Sunset which is quantitative,
 invariant over time and increases with the increase of the travel of Sunlight in our
atmosphere.
The term “quantitative” is referred to a numerical representation of the increase of the
redness with the increase of the travel of Sunlight in our atmosphere;
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The Italian-American scientist Ruggero Maria Santilli has dedicated
decades of mathematical, theoretical and experimental research for the
representation of Interior Dynamical Problems.
His studies have established that the presence of energy (or matter)
causes a transformation of spacetime .
In 1991 he has predicted and experimentaly confirmed that the Redshift of the sun
at sunset and sunrise is due to loss of energy by light to our atmosphere without
any relative motion between the source, the medium and the observer (Santilli
1991 IsoRedShift), and without any reliable contribution from photon
decomposition of light, absorption or scattering.
F. Zwicky 1929 hypothesis (cosmological redshift is due to loss of energy by light to intergalactic gases without any need for the
expansion of the universe) (Zwicky 1929 Tired Light), have successfully confirmed according to Santilli's IsoRedShift (Zwicky-Santilli
effect) and not according to the 1929 scattering origin (which has been dismissed at the astrophysical and laboratory levels).
Santilli's mathematical, theoretical and all experimental results entirely dismiss
• The Expansion of The Universe,
• The Acceleration of The Expansion,
• The Big Bang and
• The Expansion of Space Itself,
All indicating a return to Middle Ages with Earth at the center of
the universe.
Because the cosmological redshift and its increase are the same for
the same distance from Earth in all directions in space,
A conclusion that stick at also for the hyperbolic assumption that
space itself is expanding due to the claimed acceleration of the
expansion.
Santilli IsoRedShift provides an exact representation of ,
• The lack of existence of dark matter and dark energy
• All irregularities in cosmological redshifts
• Direct experimental information on innergalactic and intergalactic media.
RETURN TO THE MIDDLE AGES WITH EARTH AT THE CENTER OF THE UNIVERSE
•
•
RETURN TO THE MIDDLE AGES WITH
EARTH AT THE CENTER OF THE UNIVERSE.
We reproduce a diagram by R. M. Santilli
illustrating that Earth at the center of the
universe is a necessary consequence of the
acceleration of the expansion.
•
•
In fact, for galaxies G2 and G1 we have the
cosmological redshifts z2 = 2 z1 with
consequential speeds v2 = 2 v1 because d2 = 2
d1 radially from Earth E.
However, when the same two galaxies G2 and
G1 are examined from the galaxy G, they have
the same cosmological redshift z2 = z1, and
consequently the same speeds v2 = v1 because
d2 = d1 from G, thus establishing evident
physical inconsistencies of conjecture (2), while
Hubble's experimental law (1) remains valid for
all observers.
In this way, Santilli illustrates the historical
rejection of the expansion of the universe by E.
Hubble, F. Zwicky, L. de Broglie and other
famous scientists, due to the inherent return
to the Middle Ages with Earth necessarily at
the center of the universe.
Contrary to popular beliefs, the far reaching
conjecture of the expansion of space itself also
implies Earth at the center of the universe
because the expansion accelerates with the
radial distance in all directions, specifically and
solely, from Earth.
Historical
Proceedings
Edwin Hubble’s
discovery of the
cosmological
redshift.
Hubble's law establishes that
the cosmological redshift is
the same for all galaxies
having the same distance
from Earth in all directions in
space.
Consequently, the presumptions on
• the expansion of the universe,
• the acceleration of the expansion and
• the big bang
• Pointed towards a return to the Middle Ages with
Earth at the center of the universe and unfortunately
Edwin Hubble, as well as distinguished scientists such
as the Nobel Laureates Louis de Broglie and Enrico
Fermi as well as others, died without accepting the
expansion of the universe because they could not
accept its direct consequence [1]
1929
Fritz
Zwicky’s
hypothesis of
the "Tired Light”
In 1929 Fritz Zwicky
[2] submitted the
hypothesis of the
"Tired
Light”
by
following the Edwin
Hubble’s [3] discovery
of the cosmological
redshift.
• Light loses energy during the
long travel to reach Earth due to
scattering with intergalactic
gases without any need for the
expansion of the universe.
• However, it was known since
that time, and it has been
recently confirmed at the
astrophysical
as
well
as
laboratory levels, that scattering
cannot cause redshift.
• Consequently, the exact validity
of Einsteinian axioms was
assumed
throughout
the
universe,
with
particular
reference to the Doppler shift
law, resulting in the modern
chain of sequential assumptions
on expansion of the universe,
acceleration of the expansion,
big bang, etc.
2. Santilli isomathematics
The Italian-American scientist R. M. Santilli initiated his studies at,
• the Center for Theoretical Physics of MIT From 1974 to 1977,
• Department of Mathematics of Harvard University under DOE
support from 1977 to 1981
• completed at the Institute for Basic Research in Florida.
• The objective of these studies was a solution of the historical
Lorentz problem,
Namely, the universal invariance of all locally varying
speeds of electromagnetic waves propagating within a
physical medium (think of radio, infrared and other
waves for which the reduction to photons has no sense,
as shown below)
•C = c / n(t, r, v, d, ω, ...)
where the familiar index of refraction n has the known
functional dependence on time t, distance r, speed v,
density d, frequency ω, and other variables.
Prof. Santilli soon realized that
Lorentz failed to achieve said invariance, and
had to restrict his studies to the case with constant
speed c,
Because of structural insufficiencies of the mathematics of the time
(numerical fields, functional analysis, metric spaces, Lie theory, etc.)
since it was developed to treat linear, local and Hamiltonian systems,
while the historical Lorentz problem is structurally nonlinear, nonlocal
and non-Hamiltonian (i.e., not representable with a Hamiltonian).
In the mid 1960s Prof.Santilli
during his graduate studies in
mathematics,
physics
and
chemistry established that this
posture
is
fundamentally
inconsistent.
When exposed to interior dynamical
problems (extended objects moving
within a physical medium), such as a
satellite during reentry or a proton in
the core of a star, a general position is
that
their
irreversibility,
nonconservative and non-Hamiltonian
characters are seems true or possible
but in fact it is not possible ("illusory" )
because, when the satellite is reduced
to elementary particles and the proton
is reduced to its (claimed) point-like
constituents - so the position says Einstein's theories and quantum
mechanics are recovered exactly.
•Santilli Isomathematics and Genomathematics
•In the late 1970s, After joining the Department of Mathematics of Harvard University Prof.
Santilli started systematic studies to achieve a geometric representation of reversible interior
problems within physical media (such as our atmosphere) which are generally,
•1)Inhomogeneous (because of the variation of the density with the elevation) and
•2)Anisotropic (because of Earth's rotation).
Very soon Prof.Santilli discovered that Minkowskian, Riemannian, Fynslerian, and other
geometries available at departments of mathematics in the U.S.A. could not provide a
quantitative representation of the media considered under the conditions of:
•1)The conventional Minkowskian geometry for the vacuum for null density;
•2)Being invariant over time (predicting the same numbers under the same conditions at
different times);
•3)Being axiom-preserving for necessary scientific permanency earlier to extensive theories
for irreversible conditions; and
•4)the interior conditions referred above cannot be consistently reduced to 20th century
theories because of Santilli 1965 No Reduction Theorem (Figure 1).
Considering all this insufficiencies,
•Prof.Santilli constructed an entirely new mathematics, today known as Santilli
isomathematics, specifically conceived for quantitative representations of reversible interior
dynamical problems.
•And as a particular case the Santilli genomathematics for irreversible interior problems
Santilli’s Isomathematics
•Following prolonged studies in the inadequacies of existing mathematics,
•Prof. Santilli started the construction of a new mathematics specifically
proposed for the representation of Interior Dynamical Problems,(Namely,
nonlinear, nonlocal and non-Hamiltonian systems of extended particles and
electromagnetic waves propagating within generally inhomogeneous and
anisotropic media (for example, our atmosphere).
And for this particular mathematics the conditions were,
•1.The representation must prove the same invariance over time as that of
conventional linear, local and Hamiltonian systems,(namely, calculating the
same numerical values under the same conditions at different times).
•2. Prof. Santilli should have to maintain preservations of the axioms of
20th century mathematics and only search for broader realizations.
For these reasons, he called his methods axiom-preserving isotopies (or
isotopic liftings)
The resulting new mathematics was Isomathematics,
where the prefix "iso" is used in the Greek meaning of preserving the
original abstract axioms.
Among Prof.Santilli’s various publications on isomathematics ,
Some of them in which he summarized his initial results in his two monographs
are,
[3] R. M. Santilli, Foundation of Theoretical Mechanics, Volume I (1978) [3a], and
Volume II (1982) [3b], Springer-Verlag, Heidelberg, Germany,
http://www.santilli-foundation.org/docs/Santilli-209.pdf
http://www.santilli-foundation.org/docs/santilli-69.pdf
Volume [3a] – Includes,
The main mathematical tool,
The conditions of variational self-adjointness,
A vast historical search and
Numerous applications.
Volume [3b] – Includes,
Santilli step-by-step isotopic lifting of the various branches of Lie's theory which
includes,
Associative algebras,
Lie algebras,
Lie groups, etc.
Santilli step-by-step Isotopic Lifting of the various
branches of Lie's theory
1) The lifting of the conventional associative product AB of the
enveloping algebra between generic quantities A, B, into the form
AB => A⊗B = AT*B, T* > 0,
characterized by the most general possible quantity T* called the
isotopic element,
Only restricted by the condition of being positive definite (greater
than zero)
As one can see, the new product A⊗B is still associative, thus called
isoassociative product or isoproduct ;
The significant lifting of the Lie product
[A, B] = AB - BA => [A, B]* = A⊗B - B⊗A = AT*B - BT*A,
that still verifies Lie's axioms, and it is called Lie-Santilli isoproduct;
Santilli step-by-step Isotopic Lifting of the various branches of Lie's
theory
Afterward, Prof. Santilli achieved the much needed invariance by inserting all
nonlinear, nonlocal and non-Hamiltonian effects and interactions in the most
general possible isotopic lifting I* of the trivial unit of 20th century
mathematics, today known as Santilli isounit, which must be the inverse of
the isotopic element and can be written in its simple diagonal form for (3+1)dimensional theories
I* = Diag. (n12, n22,, n32,, n42,) = 1 / T* > 0
where n4 is the index of refraction
It is evident that, under the systematic use of the isoproduct
C = c / n(t, r, v, d, ω, ...,
I* is indeed the left and right unit of the new theory,
I*⊗A = A⊗I* = A for all elements A of the set considered.
The unit was selected for the representation of nonlinear, nonlocal and nonHamiltonian effects because the unit is the only quantity assuring the crucial
invariance over time of the resulting theory.
By contrast, all other representations of nonlinear, nonlocal and nonHamiltonian systems resulted to verify Santilli Theorem of Catastrophic
Mathematical And Physical Inconsistencies of Noncanonical and Nonunitary
Santilli step-by-step Isotopic Lifting of the various
branches of Lie's theory
The isotopic image of Lie's theory based on following laws
(1)AB => A⊗B = AT*B, T* > 0,
(2) [A, B] = AB - BA => [A, B]* = A⊗B - B⊗A = AT*B - BT*A,
(3) U = exp(H t i) => U* = exp(H T* t i)
(4) I* = Diag. (n12, n22,, n32,, n42,) = 1 / T* > 0
(5) d*r* = T* d [r I*(t, r, v, ω, ... ....)],
(6) ∂*/∂*r* = I* ∂/∂ [r I*(t, r, v, ω, ...)] [4]
And today it is known as Lie-Santilli isotheory
[8-14].
A nice presentation of the above scientific journey, with particular
reference to his stays at MIT and Harvard, is provided by Santilli in Lectures
IIA and IIB available from Level II of the series ,
www.world-lecture-series.org.
As it is well known, but it has not been openly
spoken [5] in graduate schools in physics around
the world, that special relativity cannot be
uniformly defined within a physical medium such
as water for various reasons, such as:
1) Special relativity axioms cannot be defined due
to the impossibility of having inertial reference
systems within water;
2) Electrons can travel in water faster than the local
speed of light (Cherenkov light);
3) The relativistic superposition law is violated
because the sum of two local light speeds does not
yield the local light speed; etc.
When encountered with this previous situation, a common situation is that of
reducing electromagnetic waves to photons scattering among the water molecules
for the generally assumed commitments of recovering Einsteinian theories and
quantum mechanics at the level of photons in vacuum.
From his No Reduction Theorem ,
Prof. Santilli has proved that such a situation is basically unpredictable on serious
scientific grounds because the reduction to photons of all electromagnetic waves:
For the reasons that,
A) The above mentioned situations cannot be accurately attentive for radio waves
with large wavelength (or even for infrared waves) which have the same
phenomenology as light (refraction, etc.);
B) One cannot represent refraction (because at the impact with the water surface ,
photons will obviously scatter in all directions);
C) Such situation would indicate the contradictory consequence that a very large
number of photons must pass through a very large number of nuclei in a straight
line without any significant scattering as a condition to represent the light
propagation
Therefore
Prof. Santilli has established that the "only" way to achieve
a "scientific" (that is difficult and quantitative)
representation of the propagation of light within physical
media is the return to the pre-Einsteinian conception
according to Maxwell, Lorentz and others, according to
which electromagnetic "waves" are transverse "waves" that,
since we cannot have a "wave" within nothing, must be
propagated by the ether as universal substratum.
The Universal Lorentz-Poincare'-Santilli Isosymmetry.
Prof. Santilli has established that the most essential statement
throughout the 20th century, which is still widely adopted in 21-st
century physics around the world, is "the universal constancy of the
speed of light c."
By contrast, Einstein himself stated "the universal constancy of the
speed of light in vacuum”, which is indeed a serious scientific statement
[5] because mathematically rigorous (due to the Lorentz symmetry) and
experimentally established (Michelson-Morley and other experiments).
The crucial words "in vacuum" are removed from the statement for
extending the validity of Einstein theories, from the vacuum, to all
conditions that could conceivably exist in the universe.
The Universal Lorentz-Poincare'-Santilli Isosymmetry.
In fact, by recalling the No reduction Theorem and the impossibility for a
reliable reduction to photons of electromagnetic waves propagating within
physical media (Figure 3), Santilli has established that the speed of light is a
local variable C = c/n, as necessary for a scientific representation of evidence.
The Santilli’s isomathematics based on the locally varying speed of light,
C = c / n (x, υ, ω, δ, T…,),
today known as the Lorentz-Poincare-Santilli (LPS) isosymmetry and the
isotopeis of this special relativity known as Santilli isorelativity [6].
The well-known relativistic equation which is applicable only for point particles
moving in vacuum,
E  m c2
(1)
– this condition was clearly express by Einstein himself.
Therefore, the above relativistic equation (1) is not applicable for
o non-spherical,
o deformable and
o extended particles.
According to Santilli’s new isorelativity theory, under these conditions the above
relation should be replaced by [7],
Eˆ  mC2  mc2 / n 2
(2)
where C represents the image of the speed c within the interior of the medium and
where n is less than one.
In the above equation (4), the terms bμ = 1/nμ are the characteristic quantities of the
medium, which are explicitly positive functions of all probable local variables,
for example distance traveled by light d, temperature τ, frequency of light ν, density ρ,
etc., bμ = bμ(d, ρ, τ, ν,...) = 1/nμ = 1/nμ(d, ρ, τ, ν,. . . ),
they are normalized for the vacuum as bμ = 1/nμ = 1, μ = 1, 2, 3, 4;
the quantity 1/b4 = n4 which is time characteristic is familiar to the confined index of
refraction with corresponding confined speed of electromagnetic waves C = cb4 = c/n4,
the space characteristic quantities bk = 1/nk, k = 1, 2, 3, stands for the anisotropy and
inhomogeneity of the medium considered and their value is set by physical verification
in above case the relative motion is null and known as Santilli IsoShift [9,10,11].
From equation (6) IsoRedShift (IRS), occurring for the minus sign when the
medium is at a sufficiently low temperature and atoms being generally in their
ground state as a result light loses energy E = hν to the medium by means of
significant anomalous redshift [11-13]
Santilli iso-Minkowskian geometry and its universal Lorentz-Poincare'Santilli isosymmetry predict a frequency shift for the propagation of
electromagnetic waves within a (transparent) physical medium without
any relative motion between the source, the medium and the observer.
Consequently, Prof. Santilli introduced the following
hypotheses
I)The IsoRedShift (IRS), occurring with the sign - in isolaw (6) when
light loses energy E = h v to a generally cold medium,
II) The IsoBlueShift (IBS), occurring for N = 0 ion isolaw (6) with the
sign + in isolaw (6) when light acquires energy E = h v from a
generally hot medium; and
III) The NoIsoShift (NIS), occurring when the energy lost by light to
the medium is equal to the energy releases
One of the systematic experimental confirmations obtained by G. West and G. Amato [5] on
the existence of Santilli's IRS via the IsoShift Testing Station used in ( adapted from Fig. 6 of
Ref.14)
A View of Santilli main hypothesis of 1991 [15b] according to which, in the transition from
the zenoith (left) to the horizon (right), the entire spectrum of sunlight is shifted toward the
red due to loss of energy by light to the atmosphere without any appreciable contribution
from absorption or scattering .
One of the systematic experimental
confirmations obtained by G. West and
G. Amato on the existence of Santilli's
IBS via the same IsoShift Testing Station
The first of systematic experimental
confirmations obtained by G. West and G.
Amato on the existence of Santilli's IBS via the
same IsoShift Testing Station.
The central peak indicates the blue laser light
under vacuum; the peak to the right indicates
IRS obtained at night; and the peak to the left
presents the first measured IBS
62
Experimental Verification of Santilli IsoRedShift, IsoBlueShift
and NoIsoShift
In the late 1980s, Following the prediction of the IRS, IBS and NIS Prof. Santilli proposed their
experimental verification to virtually all qualified physics laboratories and institutions around the
world.
In 2009 Prof.Santilli assembled the research facilities of the Institute for Basic Research in Florida .
Now it is internationally known IsoShift Testing Station,
consisting of:
 An air conditioned cabin containing a laser;
 A second air conditioned cabin containing the wavelength analyzer; and
 The interconnection of the laser and analyzer via a 60 feet long steel pressure tube.
A View of the IsoShift Testing Station built by Prof. Santilli in 2009.
Experimental Verification of Santilli IsoRedShift, IsoBlueShift
and NoIsoShift
 Prof. Santilli then conducted systematic measurements for about one year of the
wavelength of the (blue) laser light with a vacuum pulled out of the pressure tube and the
wavelength of the laser light with the tube containing air at 2,000 psi.
 And eventually he established the existence of his IRS as well as its increase with
pressure,
 And presented these experimental results as well as the underling mathematical and
physical formulations at the workshop Cosmology, the Quantum Vacuum, and Zeta
Functions, held at the Universitat Autonoma de Barcelona, Spain, March 8-10, 2010 [16].
The historical first measurements of Santilli IsoRedShift in June 2009 (top view) and of its
increase with pressure (bottom view) [17]
Experimental Verification of Santilli IsoRedShift, IsoBlueShift
and NoIsoShift
Afterward , G. West and G. Amato [18] conducted systematic measurements for about one
year that provided final experimental confirmation for the existence of Santilli IRS ,
with air at pressure but at temperature below 70 F, measured for the first time Santilli IBS
for air at pressure over 140 F and confirmed Santilli NIS for air at pressure at temperature
between 70 F and 140 F.
A view of the equally historical measurements establishing the IsoRedShiuft origin of the
redness of the sun at sunset, the main scan being that of the sun at the zenith and the
second scan representing sunlight in decreasing elevation on the horizon [49].
Experimental Verification of Santilli IsoRedShift,
IsoBlueShift and NoIsoShift
 All the above measurements were conducted for one
monochromatic laser light.
The measurements of the IRS for the sun in the transition from the
zenith to the horizon required a telescope (to condense sunlight
particularly at sunset and sunrise) and special analyzers capable of
scanning the entire spectrum of sunlight.
 Prof. Santilli and his technicians secured three different wavelength
analyzers meeting said requirement, conducted comprehensive
measurements from June 2011 to May 2012, and achieved a
systematic confirmation of the IRS origin of the redness of the sun
at sunset and sunrise.
 The results were then published in June 2012 by the Journal of
Computational Methods in Sciences and Engineering [20].
Experimental Verification of Santilli IsoRedShift,
IsoBlueShift and NoIsoShift
Distribution of energy in the solar spectrum and absorbing components of the
Earth's atmosphere (adapted from Fig. 1.3 of monograph [4])
Experimental Verification of Santilli IsoRedShift,
IsoBlueShift and NoIsoShift
An elaboration of the chromatographs of the preceding figure with the entire sunlight
spectrum in yellow and sunlight spectrum at the Horizon in red, with a clear
identification of about 200 nm IsoRedShift [20].
Experimental Verification of Santilli IsoRedShift,
IsoBlueShift and NoIsoShift

when the Sun is at the
Zenith, our atmosphere is
predominantly BLUE not
only toward the Zenith, but
also toward the horizon,

While the atmosphere at
Sunset and Sunrise is
predominantly RED
Views taken by the author in Palm Harbor, Florida, of the horizon when the Sun is at
the Zenith (left), at Sunset (top right) and Sunrise (bottom right), illustrating the
predominant blue color when the Sun is at the Zenith and the predominant red
color at both Sunset and Sunrise[21].
Experimental dismissal of the Universe Expansion, Acceleration of
the Expansion, Expansion of space, big Bang , Dark Matter and Dark
Energy
 As a result of Prof. Santilli’s decades of mathematical, theoretical
and experimental research on the propagation of electromagnetic
waves within physical media,
 Prof. Santilli has established that the redness of the Sun at Sunset as
is direct visual evidence, confirmed by comprehensive
measurements, dismissing the general assumptions on the
expansion of the universe [22]. The same results consequently
dismiss the acceleration of the expansion [23], the big bang [24] and
the expansion of space itself [25].
Experimental dismissal of the Universe Expansion, Acceleration of
the Expansion, Expansion of space, big Bang , Dark Matter and Dark
Energy
Independently from these clear experimental dismissals, 20th century
cosmological conjectures have reached a self-destructive stage due to:
1) Excessively far fetched implications
(E.g., entire galaxies at the edge of the known universe are proffered to traveling
faster than the speed of light in vacuum);
2) Gross internal inconsistencies
(E.g., per very definition of explosions, the big bang would require the universe to
be empty for about 13.7 billion light years from Earth, with galaxies then
decreasing in speed, in dramatic disagreement with astrophysical evidence, while
the background radiation can be easily proved to have been absorbed by galaxies
and intergalactic media billions of years ago); and
3) Large failure in representing the intended conditions
(E.g., dark matter and dark energy cannot possibly provide any measurable effect
when equally distributed, and they demand the contraction of galaxies and of the
universe, respectively, according to Einstein gravitation).
Following decades of mathematical, theoretical and experimental research,
Santilli has established beyond credible doubt that
 The redness of the sun at sunset is visual evidence of the lack of expansion
of the universe (because the redness is due to loss of energy by light to the
medium without relative motion according to the IsoRedShift law.
 The same redness is also visual evidence of the absence of the acceleration
of the expansion (because the redness increases with the decrease of the
elevation, that is, with the increase of the travel by light within the
atmosphere which is also according to the IsoRedShift law).
 Consequently, the same redness is visual evidence on the absence of the
expansion of space itself. Finally, the same redness is visual evidence on the
absence of the big bang, dark energy and dark matter .
CONCLUSIONS
 Prof. R. M. Santilli conducted his mathematical, theoretical and experimental
studies for interior dynamical problems and confirmed that light propagating
within the physical media admits a IsoRedShift (IRS) and IsoBlueShift (IBS),
without any relative motion between the source, the medium and the observer.
 His discoveries regarding (IRS) and (IBS) deal with excitation and de-excitation of
atomic electrons, and independent from known molecular processes, such as
scattering or absorption. According to Santilli the most significant cosmological
inference is that it gives an opportunity to reconsider the status of the current
proposal of the expansion of universe. Further investigations on its cosmological
implications are in progress.
 The physical law leftovers the relativity of the absorption of wavelength for
propagation of light in a medium, consequently the explanation in terms of
scattering causes redshift is released theoretically and experimentally.
 In closing, we recall Santilli’s assertions on IsoRedShift, namely
1) Scattering cannot occur along straight lines for all frequencies since, by
definition, light “scatters” in all directions while we view galaxies straight
directly;
2) The cosmological redshift occurs for all frequencies, thus preventing a
quantitative representation via scattering since the latter is generally believed
to occur for only one frequency of a given gas.
REFERENCES
1.
R. M. Santilli, G. West and g. Amato. "Experimental Confirmation of the IsoRedShift at Sun at Sunset and Sunrise with Consequential Absence of Universe Expansion and Related Conjectures, "
contributed paper to the 2011 San Marino Workshop in Astrophysics and Cosmology for Matter and Antimatter, Journal of Computational Methods in Sciences and Engineering, Vol. 12, pages 165188 (2012).http://www.santilli-foundation.org/docs/Confirmation-sun-IRS.pdf.
2.
F. Zwicky, "On the Red Shift of Spectral Lines through Interstellar Space," Proceedings of the National Academy of Sciences of the United States of America, 15, 773
(1929)http://www.pnas.org/cgi/reprintframed/15/10/773
3.
E. Hubble, Proceedings of the National Academy of Sciences of the United States of Amer ica, 15, 168 (1929)
4.
R. M. Santilli, "Nonlocal-Integral Isotopies of Differential Calculus, Mechanics and Geometries," in Isotopies of Contemporary Mathematical Structures, P. Vetro Editor, Rendiconti Circolo
Matematico
Palermo,
Suppl.
Vol.
42,
7-82
(1996),
http://www.santilli-foundation.org/docs/Santilli-37.pdf
5.
Richard Anderson ,Experimental Dismissal of The Universe Expansion, Acceleration of The Expansion, Big Bang, Space Expansion, Dark Matter, And Dark Energy,The R. M. Santilli Foundation ,July
4, 2012
http://www.santilli-foundation.org
http://www.world-lecture-series.org
6.
I. Gandzha and J. Kadeisvily, "New Sciences for a New Era", Sankata Printing Press, Kathmandu, Nepal, 2011.
7.
R.M. Santilli, Lie-isotopic Lifting of Special Relativity for Extended Deformable Particles, Lettere Nuovo Cimento 3(1983), 545.
http://www.santilli-foundation.org/docs/Santilli-50.pdf.
8.
R.M. Santilli, Lie-isotopic Lifting of Special Relativity for Extended Deformable Particles, Lettere Nuovo Cimento 3(1983), 545.
http://www.santilli-foundation.org/docs/Santilli-50.pdf.
9.
R. M. Santilli, Isotopic Generalizations of Galilei and Einstein Relativities, Vols. I and II, International Academic Press, Palm Harbor, USA, (1991)
http://www.santilli-foundation.org/docs/Santilli-01.pdf. http://www.santilli-foundation.org/docs/Santilli-61.pdf.
10.
R.M. Santilli, Elements of Hadronic Mechanics, Volumes I and II, 2nd edition, Ukraine Academy of Sciences, Kiev, 1995. http://www.santilli-foundation.org/docs/Santilli-300.pdf,
http://www.santilli-foundation.org/docs/Santilli-301.pdf.
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N. Bloembergen, “The stimulated Raman effect”, Am. J. Phys.., 35 (1967) 989.
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Stanley David Gedzelman, “Simulating colors of clear and partly cloudy skies”, Applied Optics, 44 (2005) 5723.
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M. Vollmer and S.D. Gedzelman, “Colours of the Sun and Moon: the role of the optical air mass”, Eur J Phys 27 (2006) 299.
14.
H. Ahmar, G. Amato, J. V. Kadeisvili, J. Manuel, G. West, and O.Zogorodnia, “Additional Experimental Confirmations of Santilli's Isoredshift and The Consequential Expected Absence of The Universe
Expansion”, J. Comput. Methods Sci. Eng., 13 (2013) 321–357
15.
R. M. Santilli, Isotopic Generalizations of Galilei and Einstein Relativities, Vols. I [15a] and II [15b] (1991), Ukraine Academy of Sciences
http://www.santilli-foundation.org/docs/Santilli-01.pdf
http://www.santilli-foundation.org/docs/Santilli-61.pdf
16.
[R. M. Santilli, "Iso-Minkowskian Geometry For Interior Dynamical Problems," Contributed paper in Cosmology, Quantum Vacuum, and Zeta Functions, Diego Saez-Gomez, Sergei Odintsov Sebastia
Xambo Editors, Springer, 2011.
http://www.santilli-foundation.org/docs/Isominkowskian-Geom
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R. M. Santilli, "Experimental Verifications of IsoRedShift with Possible Absence of Universe Expansion, Big Bang, Dark Matter, and Dark Energy," The Open Astronomy Journal {\bf 3}, 124 (2010),
http://www.santilli-foundation.org/docs/Santilli-isoredshift.pdf
18.
G. West and G. Amato, "Experimental Confoirmation of Santilli's IsoRedShift and IsoBlueShift," contributed paper to the {\it Proceedings of the San Marino Workshop on Astrophysics and
Cosmology for Matter and Antimatter,} Republic of San Marino, September 5 to 9, 2011, Journal of Computational Methods in Sciences and Engineering, Vol. 12, pages 169-188 (2012),
http://www.santilli-foundation.org/docs/Confirmation-IRS-IBS.pdf
19.
R. M. Santilli, G. West and g. Amato. "Experimental Confirmation of the IsoRedShift at Sun at Sunset and Sunrise with Consequential Absence of Universe Expansion and Related Conjectures, "
contributed paper to the 2011 San Marino Workshop in Astrophysics and Cosmology for Matter and Antimatter, Journal of Computational Methods in Sciences and Engineering, Vol. 12, pages 165188 (2012).
20.
R. M. Santilli, G. West and g. Amato. "Experimental Confirmation of the IsoRedShift at Sun at Sunset and Sunrise with Consequential Absence of Universe Expansion and Related Conjectures, "
contributed paper to the 2011 San Marino Workshop in Astrophysics and Cosmology for Matter and Antimatter, Journal of Computational Methods in Sciences and Engineering, Vol. 12, pages 165188 (2012).
http://www.santilli-foundation.org/docs/Confirmation-sun-IRS.pdf
21.
Anderson R. Insufficiencies of special relativity for the color of the sky. 2008. Available from: http://www.santillifoundation.org/Sunset-Sunrise.html
22.
[50] C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation, W. H. Freeman and Company (1973)
23.
P. Riess et al. Astronomical Journal {\bf 116}, 1009 {1998); S. Perlmutter et al. Astrophysical Journal {\bf 517}, 565 (1999).
24.
E. J. Wollack, Edward, "The Study of the Universe: Big Bang Theory," NASA report (2010).
25.
A. B. Whiting, "The expansion of space: free-particle motion and the cosmological redshift," The Observatory, {\bf 124}, 174 (2004)
http://adsabs.harvard.edu/abs/2004Obs...124..174W
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