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Abstract.Return to the book: Einstein's Theory of Relativity Versus Classical Mechanics
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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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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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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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®
,
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 millions 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 millions » 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 a 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.
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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).
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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.
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A-4 |
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A-5 |
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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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