Einstein's Theory of Relativity
versus
Classical Mechanics
by Paul Marmet
( Last
checked
2009/11/7 )
Appendix II
The Deflection of Light by the Sun's
Gravitational Field:
An Analysis of the 1919 Solar Eclipse
Expeditions.
Note:
After
the publication of this book, a much more complete study of the
observations of the deflection of light and radio waves by the Sun has
been published under the title:
Relativistic
Deflection
of
Light
Near
the
Sun Using Radio Signals and Visible Light.
This paper can be read direcly on the Web.
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 deviated 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 1911, using Newton's
gravitational law (half deflection). 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 [1].
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 [1,2]. This test
was crucial to the general approval that Einstein's general theory of
relativity enjoys nowadays.
However, this experimental result is obviously not in accordance with
the result found in chapter ten. This is not a problem, as we will show
that the deflection was certainly not measurable. We will see that the
effect of the atmospheric turbulence was larger than the full
deflection, just like the Airy disk. We will also see how the
instruments could not give such a precise measurement and how the stars
distribution was not good enough for such a measurement to be
convincing. Finally, we will discuss how Eddington's influence worked
for Einstein's full displacement and against any other possible result.
ABOUT THE EXPERIMENTAL RESULTS -
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 [3]
(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 the afternoon due to the heat of the
ground. Tentative solutions to this seeing problem have only recently
been experimented [4].
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 10') is due to the
heat coming from the barbecue.
Eddington,
an astronomer, was certainly aware of this problem. If it was difficult
in 1995 [3],
to see details finer that 1'', how much more difficult was it 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 [1].
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'' [2].
How could Eddington and Dyson claim to observe that if at best, their
precision due to atmospheric turbulence in daytime heat was several
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 telescopes that were
less than ideal.
The error
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 means perfect correction for sphericity and
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'' [2]
(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 focus of
the telescopes was determined and fixed many days before the eclipse [1] (page 141). But the elements
of a telescope are very sensitive to temperature [1]
(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".
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 astrograph, but what about the the mirrors and
the 4-inch telescope?
The
photographs of the eclipse taken with the astrograph were very
disappointing [1]
(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.
What about
the 4-inch
telescope? The Sun’s heat could have affected its scale without
blurring the images. We know that there is a zone around the focal
length where the image will look as if it were in focus but where the
scale will be changed. To the best of our knowledge, nothing has ever
been said about that possible problem.
If we plot
the value of Einstein's deflection against the angular distance of the
star from the Sun (as done in [5]
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. These observations (and most of the others studied in
von Klüber's article which reviews all observations done before
1960)
could easily be fitted by a straight line instead of Einstein's
deflection equation. Therefore they do not prove any of Einstein's
deflections (full or half).
In one of
the meetings of the Royal Astronomical Society [6]
(page 41), Ludwik Silberstein pointed out that the displacements found
were not radial, as Einstein's theory states, but sometimes deviated
from the radial direction by as much as 35°! Nothing was said about
that in Dyson's article. 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.
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 [2]
(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 [2]
(page 391). Some of the displacements presented were very small,
sometimes of the order of 0.01''. In another meeting [6]
(page 40), Oliver Lodge asked if it were possible to measure a
deviation 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 favour of the full
deflection before doing the experiment. Writing about the results of
the expedition, he said [7]
(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 [8]
(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 [8]
(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 [9]
(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 [9]
(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 shifts 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 shift [9] (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.
Jamal Munshi in reference to his ² Weird but True²
reports on the internet at:
http://munshi.sonoma.edu/jamal/physicsmath.html:
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 was close to being declared a "conscientious objector"!
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 deviation 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.
REFERENCES
[1] Dyson, F. W., A. S.
Eddington and C. Davidson, A
Determination of the Deflection of Light by the Sun's Gravitational
Field, from Observations Made at the Total Eclipse of May 29, 1919,
in Philosophical Transactions of the Royal Society of London,
series A, 220, p. 291-333, 1920. (See also: Annual
Report of the Board of Regents of the Smithsonian Institution Showing
the Operations, Expenditures, and Conditions of the Institution for the
Year Ending June 30 1919, Government Printing Office, Washington,
p. 133-176, 1921.
[2] Joint Eclipse Meeting
of the Royal Society and the Royal Astronomical Society, 1919, November
6, The Observatory, 42, 545, p. 389-398, 1919.
[3] MacRobert, Alan M., Beating
the
Seeing, Sky & Telescope, 89, 4, p. 40-43,
1995.
[4] Fischer, Daniel, Optical
Interferometry:
Breaking
the
Barriers, Sky & Telescope,
92, 5, p. 36-41, 1996.
[5] von Klüber, H., The
Determination
of
Einstein's
Light-Deflection
in
the Gravitational Field
of the Sun, Vistas in Astronomy, Pergamon Press, London, 3,
p.
47-77,
1960.
[6] Meeting of the Royal
Astronomical Society, Friday, 1919, December 12, in The
Observatory, 43, 548, p. 33-45, Jan. 1920.
[7] Eddington, A., Space,
Time and Gravitation: An Outline of the General Relativity Theory,
Cambridge University Press, Cambridge, 218 pages, 1959.
[8] Chandrasekhar, S., Eddington:
The
Most
Distinguished
Astrophysicist
of
His Time, Cambridge
University Press, Cambridge, 64 pages, 1983.
[9] Earman, J. and C. Glymour,
Relativity and Eclipses: The British Eclipse Expeditions of 1919 and
Their Predecessors, in Historical Studies in the Physical
Sciences, 11, p. 49-85, 1980.
=========================
Appendix
1 Contents
Appendix3
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========== ==========
========== ==========
Einstein's Theory of Relativity
versus
Classical Mechanics
by Paul Marmet
Appendix III
Physical
Constants.
Bohr Radius ao = 5.29×10-11 m
Coulomb constant k =1/4pe0=8.988×109 N·m2/C2
Eccentricity of Mercury’s orbit e = 0.2056
Electronic charge e =1.602×10-19 C
Electron mass me = 9.109×10-31 kg
Gravitational acceleration on Earth g = 9.8 m/s2
Gravitational constant G = 6.6726×10-11 N·m2/kg2
Mass of the Earth M(E) = 5.9742×1024 kg
Mass of the hydrogen atom mo =
1.6727406×10-27 kg
Mass of Mercury M(M) = 0.33022×1024 kg
Mass of the Sun M(S) = 1.9834×1030 kg
Muon mass mm =
207me = 1.886×10-28 kg
Planck constant h = 2p
= 6.626×10-34 J·s
Semi-major axis of Mercury a = 5.791×1010 m
Sommerfeld fine structure constant a
= 7.297×10-3 @ 1/137
Velocity of light c = 2.99792458×108 m/s
Appendix
1 Contents
Appendix2
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Where to get a: Hard
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