Mercury,
July/August 1994 Table of Contents
Jack
Zirker, National Solar Observatory
(c)
1994 Astronomical Society of the Pacific
Could
Einstein be wrong? Only a crank or a very selfconfident physicist
could ask such a question seriously in the middle of the 20th century.
Robert H. Dicke, professor of physics at Princeton University, is
by no means a crank, but one of the foremost experimentalists of
his time, and by the mid1950s he had become very skeptical about
the empirical evidence for Einstein's General Theory of Relativity.
He set out to test the Theory rigorously and to explore alternative
theories.
The
General Theory has been hailed as the greatest single achievement
in physics of this century and possibly of all time. It leads to
an explanation of gravity very different from Isaac Newton's. In
Newton's picture, space is "flat" (the sum of the angles
in a triangle adds to precisely 180 degrees) and time unfolds at
the same rate everywhere, no matter how fast you and your clock
may be moving. Heavy bodies attract each other with a gravitational
force proportional to each body's "mass," (the amount
of matter they contain) and accelerate at a rate inversely proportional
to these same masses. If one body moves relative to the other, the
change in its attracting force propagates at infinite speed.
In
Einstein's Special Theory of Relativity, space and time are merged
into a single medium (spacetime), a fourdimensional "field."
Time is no longer universal, but depends on the location and speed
of the clock that measures it. No object can move faster than the
speed of light, a firm speed limit in nature. These constraints
lead to the famous equality of mass and energy, E=mc^{2}.
In
the General Theory, which includes the results of the Special Theory
as a special case, spacetime becomes curved in the presence
of a massive body. The curvature is proportional to the mass of
the body. In this sense Newton's force of gravity in a flat space
is replaced by the curvature of spacetime.
By
midcentury, the General Theory had taken on the aura of revealed
truth. Even the most prominent physicists were dazzled by its simplicity
and scope. Many young theorists were engaged in working out its
consequences, but few questioned its ultimate validity. Among those
few was Dicke, a softspoken associate professor who was teaching
in the same town as the mythical Einstein.
The
two men differed markedly in their methods. Einstein relied on his
incredible physical intuition and on his aesthetic sense to fashion
representations of reality. He firmly believed that any theory that
describes nature accurately should be simple and elegant. His "experiments"
were purely mental but led him unerringly to correct physical principles.
Dicke,
despite his flair for theory, is the ultimate empiricist, a man
who measures. He has a strong skeptical streak, as befits a man
born in Missouri. He already had a distinguished reputation as he
began to reexamine relativity. In 1948, George Gamow and colleagues
proposed what is now known as the "Big Bang" hypothesis
for the origin of the heavy elements. A consequence of a hot, expanding
universe was the existence of a remnant fireball, the Cosmic Background
Radiation with a presentday temperature of about 3 kelvin above
absolute zero. Dicke and his students, P.J.E. Peebles and D.T. Wilkinson,
built a microwave antenna in 1964 to detect the fireball. But, before
they finished, Arno Penzias and Robert Wilson detected some puzzling
radio noise in their tests of microwave antennas at Bell Telephone
Labs. Dicke and his students identified the noise as the cosmic
radiation. Penzias and Wilson were later awarded a Nobel Prize for
their discovery. Since Nobel prizes are given only for discoveries,
not interpretations, Dicke received only the admiration of his colleagues.
Dicke
began thinking about General Relativity in the mid1950s and was
struck by its weak experimental support. Three quantitative predictions
of the Theory had been confirmed by observations, but none with
the degree of precision Dicke thought convincing. Dicke was also
troubled by the philosophical basis of the Theory. Why, he asked,
should gravity be the only force in nature that is not transmitted
by a particle, as, for example, electromagnetic forces are by photons?
Why are physicists so impressed with the mathematical elegance of
the Theory? Does nature necessarily prefer only beautiful theories,
as Einstein came to believe?
The
Precession of Mercury
Dicke
decided to reexamine the most convincing proof of the Theory, its
exact prediction of the anomalous precession of Mercury's orbit.
The orbit precesses by 5,600 arcseconds per century. Newtonian theory
can account for all but 43 arcseconds. Einstein's theory predicts
this excess 43 arcseconds precisely. Could another explanation be
found, Dicke wondered. For example, if the Sun were not exactly
spherical, but had a slight equatorial bulge due to a rapidly rotating
core, its tidal forces on Mercury could account for the observed
effect.
The
bulge required to account for Mercury's motion is only 0.1 arcseconds,
while the Earth's atmosphere normally blurs the edges of the Sun's
image by as much as two or three arcseconds. Dicke and his students
built a special telescope with a rotating focalplace shutter, to
extract the tiny effect from the noise. They took extraordinary
precautions to rule out the extraneous effects. In 1967, after much
hard work, they reported a significant equatorial bulge, more than
enough to account for Mercury's motion.
This
result excited a controversy that rocked back and forth over the
next 20 years. First, several astronomers argued that Dicke had
underestimated the effect of solar faculae, bright areas that cluster
near the edges of the Sun and thus could bias his results. Dicke
reanalyzed his data, using his critics' criteria, and reconfirmed
his result. Then, some theorists suggested that a poleequator temperature
difference of only 30 kelvin could account for the apparent oblateness.
Dicke demonstrated that such a temperature difference would result
in serious problems of energy and momentum balance in the solar
interior.
The
facular criticisms would not go away, but with each sally of his
opponents, Dicke was able to refute them with more sophisticated
analyses. Moreover he found a wholly unexpected result: the oblateness
measurements implied that the core of the Sun rotates with a period
of 12.4 days, about half of the surface rotation period.
What
was needed to settle the arguments were new independent data. A
fresh crop of Princeton graduate students was marshaled to build
another version of the oblateness telescope and a new series of
limb brightness measurements was carried out between 1983 and 1985.
Meanwhile,
Henry Hill, a former colleague of Dicke and a superb experimentalist
in his own right, decided to repeat Dicke's important experiment.
In the early 1970s he built his own telescope, similar to the one
he had helped Dicke to build, and with his students showed that
the Sun was indeed flattened, but no more than expected from its
surface rotation, and far less than required to account for Mercury's
anomalous motion.
Hill's
contradictory results drove Dicke to continue his own series of
measurements. In different years his derived oblateness seemed to
vary: from 45 milliarcseconds in 1966, to 18.3 in 1983, to a mere
5.6 in 1984. Moreover, the 12.4day core rotation did not appear
in the new data. Dicke was puzzled by these erratic results, and
suggested they might be varying in phase with the eleven year solar
cycle. The discrepancy between the two independent sets of measures
has never been explained satisfactorily, but most astronomers now
accept Hill's results.
Gradually,
Dicke and his students gave up trying to measure the solar oblateness
and concentrated instead on small, latitudedependent temperature
differences over the solar surface. They found interesting results
with important consequences for the solar interior (a real poleequator
difference of 0.1 degree kelvin), but not the one originally sought.
General Relativity had survived Dicke's test unscathed.
An
Alternative Theory
In
searching for a new theory of gravitation, Dicke was influenced
by the conjectures of Ernst Mach, a 19thcentury physicist and positivist
philosopher. Mach had published a devastating critique of Newton's
notions of absolutely empty space which had strongly influenced
Einstein. Mach also speculated that the resistance a body exhibits
toward a change in its motion (its inertial mass) arises from some
kind of longrange force from very large and distant masses, which
we can now associate with distant galaxies. Einstein rejected this
idea as unnecessarily complicated, and insisted on the predominance
of local forces. Dicke thought that Mach's idea was plausible, however,
and should be rejected only by experiments.
Influenced
by Mach's ideas, and rejecting Einstein's extrapolation of the Principle
of Equivalence [see sidebar on page 26],
Dicke and his student Carl Brans published an alternative theory
of gravitation in 1961. In the BransDicke theory, masses throughout
the universe generate an extra field, in addition to Einstein's
curvature of spacetime, which can influence the strength of gravity
from point to point. This means that Newton's gravitational "constant,"
G, need not be constant either in space or time.
General
Relativity makes two other predictions about gravity. One concerns
the amount of gravitational reddening of starlight. Because of the
equivalence of mass and energy (E=mc^{2}), a photon
of light with energy, E, has an effective mass, m.
As the photon leaves the surface of a star it is pulled back slightly
by gravitational attraction and loses a bit of its energy  it
"reddens." Secondly, when a photon from a distant star
grazes the surface of the Sun, it will be slightly deflected because
of the gravitational pull of the Sun. Such deflections had been
observed during total eclipses.
The
BransDicke theory contains an adjustable dimensionless parameter,
omega. When omega is set at its most probable value, 5, the theorys
predictions for the gravitational redshift and the deflection of
starlight are smaller by only 9 percent and 6 percent, respectively,
than the predictions of Einstein's Theory. Thus a clear choice of
theories could only be made by a radical improvement in the precision
of these experiments.
James
Brault, a student of Dicke, measured the reddening of sodium spectrum
lines in the gravitational field of the Sun, and, in 1962, found
agreement with the General Theory to within 5 percent. Later measurements
by R.V. Pound and his associates improved this agreement to 1 percent.
Decaying nuclei that are embedded in a crystal, emit photons with
a very narrow range of energies. Pounds used this socalled Mossbauer
effect to measure the changes in a photon's energy as it flies up
a test tower in the Earths gravitational field. The General Theory,
which rests on the Principle of Equivalence, was thus confirmed
to higher precision and the BransDicke alternative was shown to
require an uncomfortably large value of omega.
Lunar
Laser Ranging
Dicke
recognized that only a careful physical experiment could decide
the issue of General Relativity. In 1965, he and some colleagues
pointed out the feasibility of "optical radar," using
corner reflectors on the Moon. Corner reflectors employ three mirrors
mounted at right angles to each other, like the corner of a cube.
They reflect any incident beam of light in exactly the direction
from which it came.
The
idea was that the Apollo astronauts could place several of these
reflectors on the Moon, that these reflectors would return a small
but detectable part of powerful laser pulses aimed at the Moon,
and that the accurate timing of the return beam would give the distance
of the Moon to within a few meters. Such measurements, carried out
over a sufficiently long time, would pin down the orbit of the Moon
to incredible accuracy. Any departure from the calculated orbit
could reveal relativistic effects. In addition, lunar laser ranging
could reveal the detailed size and shape of the Earth and provide
precise checks on several astronomical methods of measuring time.
The
ranging proposal was funded in 1965, and, after the astronauts placed
reflectors on the Moon, observations began at Lick Observatory and
later at MacDonald and Haleakala observatories. The distance to
the Moon could be determined daily within 40 centimeters out of
400,000 kilometers. As observations accumulated, this limit gradually
shrank.
Shortly
before the first Apollo landing, Ken Nordtvedt, a young theorist
at the University of Montana, predicted that if the BransDicke
theory was correct, the EarthMoon distance should vary by nine
meters with a period of 29.53 days. This effect would arise if the
Moon's gravitational and inertial masses were different. Thus, lunar
ranging could test Einstein's assertion that the inertial and gravitational
masses of a body are identical. By 1976, a sufficient body of lunar
ranging data was in hand to test. Two groups analyzed the data independently
and came to the same conclusion: the Principle was valid, Einstein
was correct in his conjecture, and the extra field that the BransDicke
theory incorporated could account for a few percent at most of the
gravitational force between the Earth and Moon.
At
this point, a scientist less motivated than Dicke might have given
up his searching critique of General Relativity. But as we have
seen, Dicke continued with his solar oblateness experiments into
the mid1980s, tenaciously investigating the puzzling effects he
uncovered.
A
number of critical experiments have validated General Relativity
in recent years. The gravitational reddening of light was demonstrated
to agree within 1 percent of theory. The deflection of microwaves
from quasars by the Sun was also shown to agree with theory to 1
percent. Gravitational delays of radar signals to the planets provided
new evidence in favor of the General Theory. And the spindown, or
gradual slowing, in the rotation of a binary pulsar demonstrates
the existence of gravitational waves in complete accord with the
theory, a result which won the 1994 Nobel Prize for Joseph Taylor
and R. Hulse.
If
Dicke ever feels disappointed in not finding flaws in General Relativity,
he can look back with satisfaction on a career that sparked intense
interest in experimental relativity, that created a theoretical
framework in which all relativistic theories might be compared,
and that trained a corp of brilliant experimentalists. These are
not minor achievements in a lifetime of independent thought and
sustained effort.
Sidebar:
A Critical Test
The
Principle of Equivalence asserts that an objects inertial and gravitational
masses are the same, and is a fundamental assumption underlying
Einstein's General Theory of Relativity. An objects inertial mass
is a measure of its resistance to a change in its velocity: a train
requires a strong pull to get started because it has a large inertial
mass. An objects gravitational mass is a measure of the pull it
feels due to the presence of another body: a train weighs a lot
(near the Earth) because it has a large gravitational mass.
In
principle, these two kinds of mass could be different, but Newton's
experiments with pendulums showed they are equal to about one part
in a thousand. A test by Roland von Eötvös in 1895 found
that the inertial and gravitational masses of a bodyany kind of
bodyare the same within five parts in a billion. Einstein took this
result to mean that they are exactly identical (or "equivalent"),
with the important corollary that no physical experiment of any
kind can distinguish inertial forces (such as centrifugal forces)
from gravitational forces. Robert Dicke thought Einstein had overinterpreted
Eötvös' results.
In
1964, Dicke and his colleagues at Princeton repeated Eötvös'
experiment, confirming that the two masses are the same with an
accuracy of one part in 100 billion. Lunar laser ranging experiments
have confirmed the Principle to even greater accuracy, suggesting
Einstein was correct in his conjecture.
FIGURE
CAPTIONS
Robert
H. Dicke (Courtesy Princeton University)
Consider
a bowling ball lying on a stretched rubber sheet. The sheet represents
spacetime near the ball and is curved because of the balls mass.
A marble rolling toward the ball, is deflected because of the curvature
of the sheet. To anybody watching this event, the ball seems to
attract the marble with a gravitational force. In this way we can
visualize how the curvature of fourdimensional spacetime replaces
the force of gravity.
