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Abstract.
Note: After publication of this paper, an experiment was performed during the 2017 solar eclipse using a high performance CCD camera and star positions from the USNO UCAC5 star catalog. Light deflection by the sun is demonstrated and agrees with relativity within 3% uncertainty.
See: D.G. Bruns, "Gravitational Starlight Deflection Measurements during the 21 August 2017 Total Solar Eclipse", arXiv:1802.00343.
- The estate of Paul Marmet
1 - Introduction.
According to general relativity(1)
(page 179), light emitted from a source far away from the Sun
and passing near the Sun should be deflected by an angle d :
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2 - The Viking Relativity Experiment.
The deflection of electromagnetic radiation by
the solar gravity is now claimed to be real because of an
experiment using radar signals called the Viking Relativity
Experiment(2). (Other less
accurate experiments were also done involving Venus and
Mercury(3)).
In
those experiments, physicists did not measure the deflection
of light (or of a radio signal) by the Sun. All they measured
was the time taken by a radio signal to travel between the
Earth and another planet when grazing the Sun’s surface. This
observed time was then compared with the time taken by light
moving in a straight line at velocity c to travel the same
distance in the absence of the gravitational potential. A
delay was reported between those two times.
It
is
recognized
that
when
radio
signals
travel
through
the
plasma
around
the
Sun,
a delay is produced. This contribution to the reduced velocity
of light was taken into account and subtracted accordingly
(see appendix I). In the case of the Viking Relativity
Experiment, this contribution was measurable because two
different frequencies were used and the delay in the plasma is
frequency dependent.
General
relativity
predicts
that
the
solar
gravitational
potential
must
also
produce
a
delay
in the transmission of the radio signal. The same relativistic
phenomenon which produces the predicted deflection of 1.75" is
also responsible for the slowing down (compared with the
absolute velocity of light c) of the radiation between Mars
and the Earth. However, no direct deflection is measured in
the Viking Relativity Experiment.
Let us consider the delay Dt
predicted by general relativity in the case of a round trip
between the Earth and Mars, respectively at distances r1 and r2 from the
Sun. Using Einstein’s theory, using Schwarzschild's metric,
the delay(1)
for a radio signal making a return trip from Earth to Mars is:
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4 |
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3 - Physical Causes for
the Delay.
Let us study three causes that could be
responsible for the delay in the transmission of radiation
between the Earth and Mars:
a) an increase of the
geometrical distance between the extremities of a bent
trajectory;
b) general relativity;
c) the interaction with the
plasma around the Sun.
3 - a) Delay Due to the
Geometrical Bending of Light.
We have seen above that general relativity
predicts that light passing near the solar limb is deflected
by an angle of 1.75". The same theory predicts that due to the
same gravitational potential, the radiation takes a longer
time to travel the distance between the Earth and Mars. Figure
1 illustrates how light is deflected when grazing the Sun.
Geometrical Time Delay
Figure 1
One can see on figure 1 that if the trajectory of light is not a straight line (dotted line), it takes a longer time to travel between Mars and the Earth. The increase of time Dtb due only to the geometrical bending of light by d = 1.75" is given by the relationship:
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3 - b) Physical Meaning
of the Relativistic Equation.
In order to get a better understanding of the
physics implied by equation 3, let us simplify the problem and
apply the equation to the case of a single passage of the
radiation from Mars to the Earth when grazing the Sun. The
time delay D tE-M(1) is then half of equation 3:
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7 |
3 - c) Delay Due to the
Plasma around the Sun.
It is well known that the Sun is
surrounded by a plasma and that the velocity of
electromagnetic radiation is reduced when moving through such
a medium. Radio signals have been observed while going through
the solar corona and a corresponding delay has been measured(2).
Furthermore, it is well known that the velocity of
transmission of a radio signal is also slowed down when
traveling through neutral gases, even if that contribution is
frequently neglected. The fact that many spectral lines are
observed in the solar corona proves that the plasma is not
fully ionized. Since the delay produced and observed due to
the plasma in the solar corona is not due to general
relativity, it must have a different origin. An analysis of
that phenomenon is presented in appendix I of this article.
4 - Relativistic Delay
on Earth and Double Value of the Velocity of Light.
Equation 7 gives the Einstein's delay
of transmission of radiation between any two locations r1 and r2 (see figure 1).
When light grazes the Sun during its transmission from Mars to
the Earth, equation 7 shows that it must also be delayed
during each extra kilometer, after it has reached the Earth.
This extra delay is given by the derivative of equation 7 as a
function of the distance r1:
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8 |
Figure 2
Fraction of Reduction of
Velocity of Light versus Distance from the Sun.
The shaded area on figure 2 shows, according to general relativity, how much the velocity of light is reduced with respect to c. This delay is more important in the solar neighborhood (c is reduced by 4.24×10- 6) but light is still noticeably delayed in the Earth neighborhood (c is reduced by 1.97×10-8) and the phenomenon is not negligible even very far beyond the Earth orbit. For example, according to equation 3, light traveling between Jupiter and the Earth is still notably delayed, even when Jupiter is in opposition with the Sun so that light does not pass in the Sun's neighborhood. Considering that the velocity of light is defined as c on Earth, the new reduced value (i.e. (1 - 1.97×10-8) c) means that there is a double value of velocity of light on Earth.
5 - Importance of the
Delay in the Earth Neighborhood.
We have seen above that general relativity
predicts that light does not move at the speed of light c when
traveling in a gravitational potential. Therefore, since the
Earth is located inside the solar gravitational potential, the
velocity of light predicted on Earth is not the same as c.
According to relativity, that velocity of light should be
corrected due to the solar gravitational potential at Earth's
distance from the Sun.
Bowler(6)
(page 57) states that in general relativity "the local
velocity of light must depend on the local gravitational
potential". Since equation 3 predicts that the velocity
of light is reduced on Earth by as much as 1.97×10-8, using Earth parameters, one must conclude that
general relativity leads to an incoherence on the value of the
velocity of light on Earth. The fundamental definition
requires an absolute velocity c while general relativity
requires the use of a velocity reduced by a factor of 1.97×10-8 on Earth. Furthermore, since we know that a
standard meter on Earth is defined as the number of
wavelengths of a spectral line of light moving at the exact
velocity of light c, we see that there is also an incoherence
to the length of the standard meter. We have now two values
for the velocity of light on Earth: the definition of c, and
the one predicted with the delayed value. How can light know
which velocity to choose?
This incoherence also appears clearly in Bowler's book(6). On page 58, he
calculates (equation 5.1.5) the velocity of light predicted on
Earth as a function of the distance r from the Sun using the
"index of refraction" of the gravitational field. Bowler
states: "As r tends to 
,
we want the velocity of light to be c." This result is
compatible with a new definition of c at infinity and not with
the international definition of the velocity of light c on
Earth. Consequently, Bowler's equation 5.1.5 does not give the
correct value of c at the Earth distance from the Sun at it
should. A variation of 1.97×10-8 in the velocity of light is a very large error
since atomic clocks are considered to be accurate within about
10-12 to 10-14. One must conclude that general relativity leads to
a disastrous incoherence about the velocity of light and the
length of the standard meter on Earth.
Finally,
we
have
seen
that
the
delay
predicted
by
general
relativity
is
equivalent
to a reduced velocity of light in vacuum, in the Sun’s
gravitational potential. Consequently, photons are slowing
down when approaching the Sun. In fact, the velocity of the
photons can be reduced to zero when they reach the surface of
an extremely massive body. This is surprising, since this
prediction is contrary to what happens to particles which are
speeding up when falling in a gravitational potential. One can
see that these predictions of general relativity lead to
serious difficulties when we consider momentum and energy
conservation.
6 - Consequences of the
Viking Relativity Experiment.
As seen in section 2, Shapiro et al.(2)
report an experiment in which they measured the round trip
time of flight of radio signals transmitted between the Earth
and the Viking spacecraft in order to test Einstein's general
theory of relativity. Theoretically, using Fermat's principle,
one can see that the time delay (reduced velocity of light) is
related to the deflection of light by the Sun. The
differential slowing down of the speed of light as a function
of the distance from the Sun tilts the wave front and changes
its direction by d = 1.75".
This differential velocity predicted by general relativity
produces a deflection of light just as the differential
velocity in a plasma produces a bending as explained in
appendix I (and figure 1A). According to general relativity,
the radio signal grazing the solar surface is delayed by up to
72 km corresponding to 250 ms.
Shapiro et al.(2) claim an agreement with general relativity to
within 0.5%. This means that the delay must be measured with
an accuracy of 0.36 km.
The Viking Relativity Experiment(2) involves corrections that take into account the
delay due to the plasma composed of an erratic electron
density surrounding the Sun. Since the claimed accuracy of
0.36 km in the round trip distance is extremely small compared
with ~760 million km traveled by
light during that same round trip (ratio equal to 4.7×10-10), it is necessary
to know, with a comparable accuracy, all of the other
contributions of error in the delay. The errors originate
primarily from two sources: (1) the orbits of the planets and
of the spacecraft around Mars and the positions of the
tracking stations on Earth and (2) the solar corona which
increases the delay significantly for signal paths that pass
near the Sun. We have seen that the increase of path length
due to the geometrical bending is negligible (section 3a).
It is certainly not clear in Shapiro’s team’s paper(2) how the elements of
orbit of Mars and the Earth can be reliably obtained with the
claimed accuracy of 4.7×10-10. When calculating the data, one has to decide
whether those elements of orbit have been corrected for
general relativity. At the Earth distance from the Sun,
general relativity predicts that time and lengths are changed
by about 10-8 due to the
orbital velocity of the planets and the solar gravitational
potential. Have the data taken by radar to determine the
orbital elements been all corrected for the reduced velocity
of light? One can expect that general relativity has been
taken into account since extremely accurate elements of orbit
of Mars and of the Earth are required. This indispensable
information is missing in Shapiro’s team’s paper(2).
Calculations
show
that
the
expected
relativistic
correction
that
are
needed
to
be
applied
to
Newton's elements of the orbit is much larger (~2×10-8) than the relative error claimed in the distances
of the planets (0.36÷760 million ~5×10-10). Consequently, the delay claimed by Shapiro’s team(2) is necessarily
dominantly dependent on the relativistic correction previously
introduced in his calculation. They cannot find that the
relativistic correction exists if they have already introduced
that correction in the elements of orbit leading to the
distance between Mars and the Earth. When a relativistic
correction in introduced in a calculation, we cannot be
surprised to find in the final calculation, a difference in
delay caused by that same relativistic correction.
Consequently,
due
to
the
above
uncertainties
in
the
elements
of
orbit
of
the
planets,
the delay reported is meaningless and does not prove any
fundamental agreement with general relativity. Anyhow, the
method used by Shapiro et al.(2) is not coherent and uses non-coherent (double)
values for the velocity of light in vacuum. Therefore, it is
erroneous to believe that Shapiro's team's experiment proves
that the velocity of light is reduced in the solar
neighborhood since this is not compatible with the corrected
velocity of light measured on Earth.
7 - Measurement of
Gravitational Deflection Using Very Long Baseline
Interferometry.
Another kind of experiment(3,7)
using radio signals has been claimed to measure the deflection
of radio signals near the Sun. Since no angle is measured and
only time delays are studied, those are indirect measurements.
One of those measurements(7) uses VLBI observations of the extragalactic radio
sources 3C273B and 3C279 passing near the Sun every year. The
article starts with: "There is a wide recognition of the
importance of testing theories of gravitation". This is a
clear manifestation that these theories have not yet been
properly tested. In that experiment, the radiation issued from
a galactic radio source is detected simultaneously at two
different receiving stations located in California and in
Massachusetts and recorded on magnetic tapes with the signal
generated by local atomic clocks.
Let
us
consider
a
deflection
of
the
extragalactic
signal
due
to
the
solar
gravity.
Since the radio signal originates from extremely far behind
the Sun, after a deflection in the solar neighborhood the
radio signal reaching California will remain nearly parallel
to the deflected ray reaching Massachusetts. Nearly only the
direction (of both rays) has changed near the Sun by an angle
d , with respect to the initial
direction, as seen on figure 3. However, geometrical
considerations show that, for a pair of distant stations
located in the plane perpendicular to the initial incoming
direction of the radio signal, the ray which passes further
away from the Sun will arrive slightly before the other one.
Figure 3
Differential Delay after
Deflection of Light by the Sun.
8 - Origin of the
Fluctuations of the Radio Source.
General relativity predicts that the velocity
of light is reduced in the solar gravitational potential.
Furthermore, the solar plasma adds a supplementary delay to
the transmission of radiation, but more importantly, it adds
important fluctuations to the original extragalactic signal.
Unfortunately, the density of that plasma as well as its short
time fluctuations are totally unpredictable. Signal
fluctuations have been observed lasting a few minutes. They
were measured(7) to vary by as much
as 500%. Since random variations of the intensity of that
plasma are taking place very rapidly and are totally
unpredictable, a parameterized correction cannot give an
accurate prediction. The fluctuations in the plasma density
even vary within one period of accumulation of data.
Consequently, even if three different frequency components are
measured, the theoretical inverse quadratic correction (as a
function of frequency) introduced to determine the density of
the plasma cannot provide the picosecond accuracy stated in
the paper. One must recall that the change of distance
corresponding to one picosecond is equal to only a difference
of 0.3 millimeter (at light velocity) between the receiving
antennas on Earth.
Lebach’s et al.(7) experiment is based on the condition that the
fluctuations of intensity of the radio signal (from the radio
sources 3C273B and 3C279), used for synchronization in
California and Massachusetts, originate at a cosmological
distance, well before radiation approaches the solar
neighborhood. When any extra fluctuation is added to the rays
crossing the solar corona, the receivers located in California
and in Massachusetts can no longer synchronize correctly the
phase relationship (identified by a specific pattern of
fluctuation) required for the experiment. Any interference by
the plasma is a serious obstacle to the experiment, since
there is no way to recognize the strong random noise generated
by the solar corona from the original fluctuations necessary
to synchronize the radio signals. Furthermore, when the noise
from the corona (added to the signal), is later filtered by a
narrow band filter (used in Lebach’s et al. experiment), the
addition of that filter changes the phase of the signal.
It
is
well
known
theoretically
and
previously
observed,
that
when
a
radio
signal
is
transmitted through a plasma, (here the plasma of the solar
corona), very important fluctuations are added. Even Lebach et
al.(7)
report that in some data: ". . . large, rapid
plasma-density fluctuations in the solar corona would make
the coherence time of the signals from 3C279 at 2 GHz too
short to allow detection ". Therefore, Lebach et al.(7)made an arbitrary
selection to what appeared to be acceptable data. The
noise generated by the solar plasma gets so intense that it
can block completely the cosmic signal. For example, when the
radio signal of Pioneer VI(8-13) passed through the solar corona, it was observed
that the fluctuations due to the interaction with the plasma
became so important that the initial signal became
undetectable well before reaching the solar limb vicinity.
Signal distortion due to the increase in the frequency
bandwidth is quite evident(8-13). In his abstract, Goldstein(8) states: "The spectral bandwidths increased
slowly at first, then very rapidly at 1 degree from the
Sun". It is well known theoretically how a plasma
generates fluctuations while increasing the bandwidth. A
computer program cannot identify small statistical
fluctuations in the extra galactic radio source from the
intense wide band noise fluctuations generated by the plasma
surrounding our sun. Radiation emitted by the extra galactic
radio source fluctuates after passing through the solar corona
just as starlight twinkles after passing through the Earth
atmosphere. Genuine starlight fluctuations (in the radio
range) cannot be identified through the intense twinkling
caused by the intense million-degree furnace of the sun's
corona.
9 - From Amateur Size
Telescopes to Multi-Billion Dollar Space Technology.
One must conclude that the theoretical model
used and leading to the reported delay, is no longer
acceptable when there is such an unstable plasma, because much
larger noisy fluctuations are added by the plasma in the Sun’s
neighborhood. The delays measured by Lebach et al.(7)
cannot prove the deflection of light by the Sun, because of
the impossibility of demonstrating a reliable synchronization.
It is well known statistically, that with a gigantic amount of
data automatically recorded in that experiment, combined with
the astronomical number of fits tested by the computer,
coupled with a large amount of noise reaching sometimes the
level of saturation as reported in their paper, some data
can always be found to fit the expected theoretical
model. This is specially true when it is felt that nobody
might challenge the result obtained with a multi-billion
equipment used to find an agreement with an extremely popular
theory. Unfortunately, the observation of the deflection of
visible light by the sun seems to have been abandoned some
years ago because the phenomenon appeared impossible to detect
in visible light.
There is a desperate situation among scientists for not
being able to show, with the most sophisticated
technology, what is considered to be the basic principle of
general relativity on which rely most of modern science, while
this was claimed to be demonstrated by Eddington in 1919 using
a simple four inch amateur size telescope. Of course, a
trillion or quadrillion dollar equipment will never reveal
clearly the deflection of light if such a deflection does not
exist. It is hard to predict for how many more decades this
race will last and how much money has to be wasted before
scientists, at last, admit that there is no deflection.
Let
us
recall
that
Einstein’s
predictions
of
light
deflection
is
based
on
an
unverified variable velocity of light and on the double value
of the velocity of light in the Earth neighborhood, as
explained above. This incoherence of general relativity must
be added to the fact that general relativity is not compatible
with the principle of mass-energy conservation as demonstrated previously.---
(14).
The internal contradiction about having two different values
of the velocity of light at the same location does not exist
when we use a rational description, agreeing with the
principle of mass-energy conservation (14).In that case, the
advance of the perihelion of Mercury given by Newton's physics
is explained independently and is also perfectly identical to
the equation predicted by general relativity. Furthermore,
length contraction and the change of clock rate can now
logically be explained(14).No reliable observation has ever been able to prove
such a deflection of light by the sun after 80 years.
Therefore, it is much more logical to believe that such a
deflection does not exist at all, and be compatible with the
principle of mass-energy conservation.
10 - Acknowledgments.
The authors wish to acknowledge the personal
encouragement and financial contribution of Mr. Bruce
Richardson, which helped to pursue this research work. We are
also grateful to Dr. I. McCausland, University of Toronto, for
bringing his attention to some interesting historical
information.
Shapiro(5) has observed that, due to the density of the plasma in the medium surrounding the Sun, the velocity of transmission of the radiation is reduced with respect to the speed of light c. Then, a delay D tm appears (with respect to the speed of light) between the emission of a pulse of a radio signal from Earth, and the reception of its echo through the interplanetary medium. This delay(5) is:The Deflection and Delay of Radio Signals in the Solar Plasma.
 |
A-1 |
) is the electron density expressed in
electrons/cm3, f is the
frequency of the radiation in hertz, c is the velocity of light
in cm/sec, is the path length in cm and e and p
respectively refer to the Earth and the other planet (i.e.
Mars).  |
A-2 |
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A-3 |
Deflection of Radiation
Due to the Plasma.
Figure A1 illustrates the propagation
of radio waves emitted from Mars in which relativity is
momentarily ignored but for which we take into account the
solar plasma distributed around the Sun. Each radio wave
emitted travels in space forming a spherical front expanding
around the emitter. The wave front expands and the light rays
move in the radial direction away from the source. Some of the
rays pass near the Sun so that the velocity of propagation of
the radio signal is reduced by an amount that depends on the
electron density of the plasma. Just near and above the Sun,
two rays a and b are drawn on figure 1A.
Figure 1A
Delay Due to the Solar
Plasma
in a given time interval.
Consequently, the upper part of the wave front travels faster
and the wave front becomes tilted due to the difference of
velocity in the plasma. Once the wave has passed the plasma
region, this wave front maintains its tilted direction until
reaching the Earth without any other perturbation. This is the
reason for which the radio beam is deflected by the solar
plasma.  |
A-4 |
 |
A-5 |
 |
A-6 |
Appendix II
The Gravitational
Deflection of Light by the Sun during Solar Eclipses.
A - Introduction.
According to Einstein's general theory of
relativity published in 1916, light coming from a star far
away from the Earth and passing near the Sun will be deflected
by the Sun’s gravitational field by an amount that is
inversely proportional to the star’s radial distance from the
Sun (1.745'' at the Sun's limb). This amount (dubbed the full
deflection) is twice the one predicted by Einstein in 1908(16) and in 1911(17) using Newton's
gravitational law (half deflection). In 1911, Einstein wrote:
A ray of light going past the Sun would accordingly undergo
deflexion to an amount of 4×10-6 = 0.83 seconds of arc.
Let us note that Einstein did not clearly explain which
fundamental principle of physics used in the 1911 paper and
giving the erroneous deflection of 0.83 seconds of arc was
wrong, so that he had to change his mind and predict a
deflection twice as large in 1916.
In
order
to
test
which
theory
is
right
(if
any),
an
expedition
led by Eddington was sent to Sobral and Principe for the
eclipse of May 29, 1919(18). The purpose was to determine whether or not there
is a deflection of light by the Sun's gravitational field and
if there is, which of the two theories mentioned above it
follows. The expedition was claimed to be successful in
proving Einstein's full deflection(18,19). This test was crucial to the general approval that
Einstein's general theory of relativity enjoys nowadays.
However, this experimental result is not in accordance with
mass-energy conservation(14)
. This was not a real problem in those years, as
we will show that the deflection was certainly not measurable.
We will see that the effect of the atmospheric turbulence was
much larger than the full deflection, just like the Airy disk.
We will also see how the instruments could not possibly give
such a precise measurement and how the stars distribution was
not good enough for such a measurement to be convincing or
even measurable. Finally, we will discuss how Eddington's
influence worked for Einstein's full displacement and against
any other possible result.
B - Observational Data.
There is a long list(20)
of papers reporting observations of stars in the neighborhood
of the Sun during solar eclipses. A general survey of the
eclipse results, with some discussions, has been published(20). Consequently, it
is not possible to discuss them all in detail. However, it is
the observations of the 1919 eclipse which first convinced the
scientific community that the relativistic deflection really
exists and that established the belief in Einstein’s theory.
Therefore, we will examine these data in more detail though
some information will also be given about observations of
other eclipses. These observations were not successful, but
they were considered as such until they were substituted by
experiments using space probes. The 1919 paper gives an idea
of the kind of measurement that convinced the world to the
most spectacular theory accepted by modern science: the theory
of general relativity. The problem of observing the deflection
of light by the Sun is submitted to numerous experimental
difficulties. Let us study those difficulties.
Atmospheric
turbulence
is
a
phenomenon
due
to
the
atmosphere
which
causes
images
of
stars
as seen by an observer on Earth to jump, quiver, wobble or
simply be fuzzy. This is a well-known phenomenon to any
astronomer, amateur or professional. In fact(21) (page 40), "Rare
is the night (at most sites) when any telescope, no matter
how large its aperture or perfect its optics, can resolve
details finer than 1 arc second. More typical at ordinary
locations is 2- or 3-arc-second seeing, or worse."
The
problem
becomes
even
worse
during
afternoons
due
to
the
heat
of
the ground. Tentative solutions to this seeing problem have
only recently been experimented(22). For anyone unacquainted with atmospheric
turbulence, an easy way to observe a similar phenomenon is by
looking over a hot barbecue. In this case, the distortion of
the images (of the order of several minutes of arc) is due to
the heat coming from the barbecue.
Eddington,
an
astronomer,
was
certainly
aware
of
this
problem.
If
it
was
difficult
in
1995(21)
to see details finer that 1'' at a professional site at night,
how much more difficult was it with an amateur size telescope
in the jungle in 1919? The supposed effect (full and half
deflection) decreases with the distance of the star from the
Sun. During the 1919 eclipse, the stars closest to the Sun's
limb were drowned in the corona and could not be observed(18). Of the stars that
were not drowned in the corona, Einstein’s theory predicts
that k2 Tauri should have the largest displacement, with
0.88''. In Sobral, the displacement for that star was reported
to be 1.00''(19). How could Eddington and Dyson claim to observe
that if at best, their precision due to atmospheric turbulence
in daytime heat was several arc seconds? And they were not at
best, near noon at Sobral and 2 p.m. at Principe, when the
seeing is the worst, with small amateur-size telescopes that
were less than ideal. The instability caused by the
atmospheric turbulence is large enough to refute any
measurement of the so-called Einstein effect. However, there
are other reasons.
Two
object
glasses
were
used
during
the
expedition
at
Sobral,
a
4-inch
object
glass and an astrographic object glass. Assuming a perfect
optical shape, which includes perfect chromaticity, for the
4-inch telescope, the size of the central spot (which is
surrounded by the ring system of the diffraction pattern) can
never be smaller than 1.25''. This central spot is called the
Airy disk. Since some of the results were presented with a
claimed accuracy of the order of 0.01''(19) (page 391), that
relatively big diffraction ring pattern (125 times the claimed
accuracy) should have been easily seen. Since no mention is
made of it, we must understand that it was not observable
because various aberrations (chromatic of spheric) were larger
than 1.25'' and/or because, as expected, the atmospheric
turbulence was larger than 1.25'', which is the theoretical
limit of resolution of that telescope when there is no
aberration and no turbulence.
The
elements
of
a
telescope
are
very
sensitive
to
temperature.
For
example,
it
is
reported that(18) (page 153): "when the [astrographic] object
glass is mounted in a steel tube, the change of scale over a
range of temperature of 10° F. should be insignificant, and
the definition should be very good". However, during
the team’s stay at Sobral, the temperature ranged from 75°F
during the night to 97°F in the afternoon. This change in
temperature must have affected the 4-inch telescope.
Let
us
calculate
the
change
of
scale
on
the
plate
of
the
4-inch telescope due to the thermal expansion of the steel
tube. The expansion coefficient of steel is 1.3×10-5 per degree Celsius. Even if the optical definition
is not much changed by the change of temperature, the change
of scale on the photographic plate is proportional to the
change of length of the tube. For 10 degrees Celsius the scale
changes by 1.3×10-4. Since the size of the plate is 8 per 10 inches (20
× 25 cm),
this gives a change in its angular size of 1.2 arc-sec. It
does not seem that this change of scale has ever been taken
into account. This introduces a very serious error in the
data. How can they claim an accuracy of the order of 0.01''(19) (page 391) when
they admit that the focus of the telescopes were determined
and fixed many days before the eclipse(18) (page 141)?
The photographs of the eclipse taken with the astrograph were
very disappointing(18) (page 153). It appears that the focus had changed
from the night of May 27 to the moment of the eclipse. After
the eclipse, the team left Sobral and came back in July to
take comparison plates. They discovered that the astrograph
had returned to focus! They blamed this change of focus on the
effect of the Sun’s heat on the mirror, but they could not say
whether this effect caused a change of scale or if it only
blurred the images. The Sun’s heat could have affected its
scale without blurring the images. We know that there is a
zone along the focal length where the image looks as if it was
in focus but for which the scale is changed. To the best of
our knowledge, nothing has ever been said about that possible
error.
If
we
plot
the
value
of
Einstein's
deflection
against
the
angular
distance
of
the
star from the Sun (as done in(20) page 50), we see that the part of the hyperbola
where the slope changes the most lies under a distance of two
solar radii from the Sun's center. That part is thus crucial
to a good interpretation of the results. Looking at page 60 of
the same article, we see that only two of the stars used by
the teams at Principe and Sobral are in this area. It is thus
very difficult to fit a hyperbola when only two of the stars
are in that zone. Only a straight line can be logically fitted
through two points. These observations (and most of the others
studied in von Klüber's(20) article, which reviews all observations done before
1960) could easily be fitted by a straight line instead of
Einstein's deflection equation. Therefore, these data cannot
prove any of Einstein's deflections (full or half).
In one of the meetings of the Royal Astronomical Society(23) (page 41), Ludwik
Silberstein pointed out that the displacements found were not
radial, as Einstein's theory states, but sometimes deflected
from the radial direction by as much as 35°! Nothing was said
about that in Dyson's article(18). According to Silberstein: "If we had not the
prejudice of Einstein’s theory we should not say that the
figures strongly indicated a radial law of displacement."
This
brings
us
to
our
next
point,
which
is
to
what
degree
social circumstances influenced the acceptation of Einstein's
theory.
C - About Eddington's
Influence.
The results from the 1919 expedition were
quickly accepted by the scientific community. When preliminary
results were announced, Joseph Thomson (from the Chair) said(19)
(page 394): "It is difficult for the audience to weigh
fully the meaning of the figures that have been put before
us, but the Astronomer Royal [Dyson] and Prof. Eddington
have studied the material carefully, and they regard the
evidence as decisively in favor of the larger value for the
displacement."
Thomson
makes
it
look
like
only
Eddington
and
Dyson
are
able
to
understand
the
results. It seems that they have such a reputation that the
general and the scientific public should blindly believe them.
It is Dyson who presented the results of the Sobral expedition
at a meeting of the Royal Astronomical Society(19) (page 391). Some
of the displacements presented were very small, sometimes of
the order of 0.01''. In another meeting(23) (page 40), Oliver
Lodge asked if it were possible to measure a deflection of
1/60'' (approximately 0.02'') to which Dyson responded: "I
do not think that it would be possible to measure so small a
quantity." We clearly see that Dyson contradicted
himself. Furthermore, Eddington said himself he was in favor
of the full deflection before doing the experiment. Writing
about the results of the expedition, he said(24) (page 116):"Although
the material was very meager compared with what had been
hoped for, the writer (who it must be admitted was not
altogether unbiased) believed it convincing." Moreover,
according to Chandrasekhar(25) (page 25): "had he been left to himself, he
would not have planned the expeditions since he was fully
convinced of the truth of the general theory of relativity!"
Eddington
was
a
Quaker
and
like
other
Quakers,
he
did
not
want
to go to war (WWI). In England, Quakers were sent to camps
during the war, but because of Dyson's intervention(25) (page 25), "Eddington
was deferred with the express stipulation that if the war
should end by May 1919, then Eddington should undertake to
lead an expedition for the purpose of verifying Einstein’s
predictions!". The circumstances of the war forced
Eddington to do an experiment that he would have never done
had he had a choice because he was so convinced of its
outcome. Why was the theory so quickly, widely and easily
accepted? After all, it was radically changing the common view
of the universe, curving space and dilating time. Furthermore,
the British were accepting a theory from a German man, right
after a bitter war with Germany.
It seems that the theory was widely accepted only after the
eclipse expedition(26)(page 50). According to Earman and Glymour, Dyson
and Eddington played a great influential role in the
acceptation of the general theory of relativity by the
British. In fact, it is Eddington who, convinced of the truth
of the theory, convinced Dyson. In the few years before 1919,
they made the measurement of the "Einstein effect" a challenge
and after the expeditions of May 1919, they helped give the
impression that the data had confirmed Einstein’s theory.
Aside
from
the
fact
that
Eddington
was
convinced
that
the
theory
was
right,
another
reason pushed him to advocate it(26) (page 85). He hoped that a British verification of
a German theory might reopen the lines of communication and
collaboration between the scientists of both countries, lines
that had been closed during World War One. Finally, before
1919, no one had claimed to have observed displacements of the
size required by Einstein's theory. Probably because the
theory was thought to be proved by the 1919 eclipse
observations, a lot of scientists, maybe throwing out some of
their data, reported finding the right displacement(26) (page 85). After
1919, other expeditions were undertaken to measure the
deflection of light by the Sun. Most of them obtained results
a bit higher than Einstein's prediction, but it did not matter
anymore since the reputation of the theory had already been
established.
In "Weird but True" Jamal Munshi(27) reports: "Dr. F. Schmeidler of the Munich
University Observatory has published a paper [49] titled
"The Einstein Shift An Unsettled Problem," and a plot of
shifts for 92 stars for the 1922 eclipse shows shifts going
in all directions, many of them going the wrong way by as
large a deflection as those shifted in the predicted
direction! Further examination of the 1919 and 1922 data
originally interpreted as confirming relativity, tended to
favor a larger shift, the results depended very strongly on
the manner for reducing the measurements and the effect of
omitting individual stars.
So
now
we
find
that
the
legend
of
Albert
Einstein
as
the
world's greatest scientist was based on the Mathematical
Magic of Trimming and Cooking of the eclipse data to present
the illusion that Einstein's general relativity theory was
correct in order to prevent Cambridge University from being
disgraced because one of its distinguished members
[Eddington] was close to being declared a "conscientious
objector".
D - Conclusion.
Much of the popularity of Einstein's general
theory of relativity relies on the observations done at Sobral
and Principe. We see now that these results were
overemphasized and did certainly not consecrate Einstein's
theory. It is interesting to think of what would have happened
if the results had been deemed not good enough or if they had
clearly showed that there is no deflection of light by the
Sun. Einstein’s theory might not have enjoyed the popularity
it now does and a new more realistic theory might have been
found years ago.
The
experiments
claiming
erroneously
the
deflection
of
light
near
the
Sun
shows
some
similarity
with the claim by Michelson-Morley
that there is no drift of interference lines in their
experiment data. A recent analysis of data shows that
the drift of the interference fringes actually exists.
This has been published by Héctor Múnera, Centro
Internacional de Física, Bogotá, Columbia. An abstract and further information can be
obtained at this
address. At the macroscopic scale, it seems that,
only the observation of the Advance
of the Perihelion of Mercury can be accepted as a
reliably observed phenomenon.
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