[Paleopsych] Scientific American: Inconstant Constants
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Inconstant Constants
http://www.sciam.com/print_version.cfm?articleID=0005BFE6-2965-128A-A96583414B7F0000
5.5.23
Do the inner workings of nature change with time?
By John D. Barrow and John K. Webb
Some things never change. Physicists call them the constants of
nature. Such quantities as the velocity of light, c, Newton's constant
of gravitation, G, and the mass of the electron, m[e], are assumed to
be the same at all places and times in the universe. They form the
scaffolding around which the theories of physics are erected, and they
define the fabric of our universe. Physics has progressed by making
ever more accurate measurements of their values.
And yet, remarkably, no one has ever successfully predicted or
explained any of the constants. Physicists have no idea why they take
the special numerical values that they do. In SI units, c is
299,792,458; G is 6.673 X 10^-11; and m[e] is 9.10938188 X
10^-31--numbers that follow no discernible pattern. The only thread
running through the values is that if many of them were even slightly
different, complex atomic structures such as living beings would not
be possible. The desire to explain the constants has been one of the
driving forces behind efforts to develop a complete unified
description of nature, or "theory of everything." Physicists have
hoped that such a theory would show that each of the constants of
nature could have only one logically possible value. It would reveal
an underlying order to the seeming arbitrariness of nature.
In recent years, however, the status of the constants has grown more
muddled, not less. Researchers have found that the best candidate for
a theory of everything, the variant of string theory called M-theory,
is self-consistent only if the universe has more than four dimensions
of space and time--as many as seven more. One implication is that the
constants we observe may not, in fact, be the truly fundamental ones.
Those live in the full higher-dimensional space, and we see only their
three-dimensional "shadows."
Meanwhile physicists have also come to appreciate that the values of
many of the constants may be the result of mere happenstance, acquired
during random events and elementary particle processes early in the
history of the universe. In fact, string theory allows for a vast
number--10^500--of possible "worlds" with different self-consistent
sets of laws and constants [see "The String Theory Landscape," by
Raphael Bousso and Joseph Polchinski; Scientific American, September
2004]. So far researchers have no idea why our combination was
selected. Continued study may reduce the number of logically possible
worlds to one, but we have to remain open to the unnerving possibility
that our known universe is but one of many--a part of a
multiverse--and that different parts of the multiverse exhibit
different solutions to the theory, our observed laws of nature being
merely one edition of many systems of local bylaws [see "Parallel
Universes," by Max Tegmark; Scientific American, May 2003].
No further explanation would then be possible for many of our
numerical constants other than that they constitute a rare combination
that permits consciousness to evolve. Our observable universe could be
one of many isolated oases surrounded by an infinity of lifeless
space--a surreal place where different forces of nature hold sway and
particles such as electrons or structures such as carbon atoms and DNA
molecules could be impossibilities. If you tried to venture into that
outside world, you would cease to be.
Thus, string theory gives with the right hand and takes with the left.
It was devised in part to explain the seemingly arbitrary values of
the physical constants, and the basic equations of the theory contain
few arbitrary parameters. Yet so far string theory offers no
explanation for the observed values of the constants.
A Ruler You Can Trust
Indeed, the word "constant" may be a misnomer. Our constants could
vary both in time and in space. If the extra dimensions of space were
to change in size, the "constants" in our three-dimensional world
would change with them. And if we looked far enough out in space, we
might begin to see regions where the "constants" have settled into
different values. Ever since the 1930s, researchers have speculated
that the constants may not be constant. String theory gives this idea
a theoretical plausibility and makes it all the more important for
observers to search for deviations from constancy.
Such experiments are challenging. The first problem is that the
laboratory apparatus itself may be sensitive to changes in the
constants. The size of all atoms could be increasing, but if the ruler
you are using to measure them is getting longer, too, you would never
be able to tell. Experimenters routinely assume that their reference
standards--rulers, masses, clocks--are fixed, but they cannot do so
when testing the constants. They must focus their attention on
constants that have no units--they are pure numbers--so that their
values are the same irrespective of the units system. An example is
the ratio of two masses, such as the proton mass to the electron mass.
One ratio of particular interest combines the velocity of light, c,
the electric charge on a single electron, e, Planck's constant, h, and
the so-called vacuum permittivity, [varepsilon.gif] [0]. This famous
quantity, [alpha.gif] = e^2/2 [varepsilon.gif] [0]hc, called the
fine-structure constant, was first introduced in 1916 by Arnold
Sommerfeld, a pioneer in applying the theory of quantum mechanics to
electromagnetism. It quantifies the relativistic (c) and quantum (h)
qualities of electromagnetic (e) interactions involving charged
particles in empty space ( [varepsilon.gif] [0]). Measured to be equal
to 1/137.03599976, or approximately 1/137, [alpha.gif] has endowed the
number 137 with a legendary status among physicists (it usually opens
the combination locks on their briefcases).
If [alpha.gif] had a different value, all sorts of vital features of
the world around us would change. If the value were lower, the density
of solid atomic matter would fall (in proportion to [alpha.gif] ^3),
molecular bonds would break at lower temperatures ( [alpha.gif] ^2),
and the number of stable elements in the periodic table could increase
(1/ [alpha.gif] ). If were too big, small atomic nuclei could not
exist, because the electrical repulsion of their protons would
overwhelm the strong nuclear force binding them together. A value as
big as 0.1 would blow apart carbon.
The nuclear reactions in stars are especially sensitive to [alpha.gif]
. For fusion to occur, a star's gravity must produce temperatures high
enough to force nuclei together despite their tendency to repel one
another. If [alpha.gif] exceeded 0.1, fusion would be impossible
(unless other parameters, such as the electron-to-proton mass ratio,
were adjusted to compensate). A shift of just 4 percent in would alter
the energy levels in the nucleus of carbon to such an extent that the
production of this element by stars would shut down.
Nuclear Proliferation
The second experimental problem, less easily solved, is that measuring
changes in the constants requires high-precision equipment that
remains stable long enough to register any changes. Even atomic clocks
can detect drifts in the fine-structure constant only over days or, at
most, years. If [alpha.gif] changed by more than four parts in 10^15
over a three-year period, the best clocks would see it. None have.
That may sound like an impressive confirmation of constancy, but three
years is a cosmic eyeblink. Slow but substantial changes during the
long history of the universe would have gone unnoticed.
Fortunately, physicists have found other tests. During the 1970s,
scientists from the French atomic energy commission noticed something
peculiar about the isotopic composition of ore from a uranium mine at
Oklo in Gabon, West Africa: it looked like the waste products of a
nuclear reactor. About two billion years ago, Oklo must have been the
site of a natural reactor [see "A Natural Fission Reactor," by George
A. Cowan; Scientific American, July 1976].
In 1976 Alexander Shlyakhter of the Nuclear Physics Institute in St.
Petersburg, Russia, noticed that the ability of a natural reactor to
function depends crucially on the precise energy of a particular state
of the samarium nucleus that facilitates the capture of neutrons. And
that energy depends sensitively on the value of [alpha.gif] . So if
the fine-structure constant had been slightly different, no chain
reaction could have occurred. But one did occur, which implies that
the constant has not changed by more than one part in 10^8 over the
past two billion years. (Physicists continue to debate the exact
quantitative results because of the inevitable uncertainties about the
conditions inside the natural reactor.)
In 1962 P. James E. Peebles and Robert Dicke of Princeton University
first applied similar principles to meteorites: the abundance ratios
arising from the radioactive decay of different isotopes in these
ancient rocks depend on [alpha.gif] . The most sensitive constraint
involves the beta decay of rhenium into osmium. According to recent
work by Keith Olive of the University of Minnesota, Maxim Pospelov of
the University of Victoria in British Columbia and their colleagues,
at the time the rocks formed, was within two parts in 10^6 of its
current value. This result is less precise than the Oklo data but goes
back further in time, to the origin of the solar system 4.6 billion
years ago.
To probe possible changes over even longer time spans, researchers
must look to the heavens. Light takes billions of years to reach our
telescopes from distant astronomical sources. It carries a snapshot of
the laws and constants of physics at the time when it started its
journey or encountered material en route.
Line Editing
Astronomy first entered the constants story soon after the discovery
of quasars in 1965. The idea was simple. Quasars had just been
discovered and identified as bright sources of light located at huge
distances from Earth. Because the path of light from a quasar to us is
so long, it inevitably intersects the gaseous outskirts of young
galaxies. That gas absorbs the quasar light at particular frequencies,
imprinting a bar code of narrow lines onto the quasar spectrum.
Whenever gas absorbs light, electrons within the atoms jump from a low
energy state to a higher one. These energy levels are determined by
how tightly the atomic nucleus holds the electrons, which depends on
the strength of the electromagnetic force between them--and therefore
on the fine-structure constant. If the constant was different at the
time when the light was absorbed or in the particular region of the
universe where it happened, then the energy required to lift the
electron would differ from that required today in laboratory
experiments, and the wavelengths of the transitions seen in the
spectra would differ. The way in which the wavelengths change depends
critically on the orbital configuration of the electrons. For a given
change in [alpha.gif] , some wavelengths shrink, whereas others
increase. The complex pattern of effects is hard to mimic by data
calibration errors, which makes the test astonishingly powerful.
Before we began our work seven years ago, attempts to perform the
measurement had suffered from two limitations. First, laboratory
researchers had not measured the wavelengths of many of the relevant
spectral lines with sufficient precision. Ironically, scientists used
to know more about the spectra of quasars billions of light-years away
than about the spectra of samples here on Earth. We needed
high-precision laboratory measurements against which to compare the
quasar spectra, so we persuaded experimenters to undertake them.
Initial measurements were done by Anne Thorne and Juliet Pickering of
Imperial College London, followed by groups led by Sveneric Johansson
of Lund Observatory in Sweden and Ulf Griesmann and Rainer Kling of
the National Institute of Standards and Technology in Maryland.
The second problem was that previous observers had used so-called
alkali-doublet absorption lines--pairs of absorption lines arising
from the same gas, such as carbon or silicon. They compared the
spacing between these lines in quasar spectra with laboratory
measurements. This method, however, failed to take advantage of one
particular phenomenon: a change in [alpha.gif] shifts not just the
spacing of atomic energy levels relative to the lowest-energy level,
or ground state, but also the position of the ground state itself. In
fact, this second effect is even stronger than the first.
Consequently, the highest precision observers achieved was only about
one part in 10^4.
In 1999 one of us (Webb) and Victor V. Flambaum of the University of
New South Wales in Australia came up with a method to take both
effects into account. The result was a breakthrough: it meant 10 times
higher sensitivity. Moreover, the method allows different species (for
instance, magnesium and iron) to be compared, which allows additional
cross-checks. Putting this idea into practice took complicated
numerical calculations to establish exactly how the observed
wavelengths depend on [alpha.gif] in all different atom types.
Combined with modern telescopes and detectors, the new approach, known
as the many-multiplet method, has enabled us to test the constancy of
[alpha.gif] with unprecedented precision.
Changing Minds
When embarking on this project, we anticipated establishing that the
value of the fine-structure constant long ago was the same as it is
today; our contribution would simply be higher precision. To our
surprise, the first results, in 1999, showed small but statistically
significant differences. Further data confirmed this finding. Based on
a total of 128 quasar absorption lines, we found an average increase
in [alpha.gif] of close to six parts in a million over the past six
billion to 12 billion years.
Extraordinary claims require extraordinary evidence, so our immediate
thoughts turned to potential problems with the data or the analysis
methods. These uncertainties can be classified into two types:
systematic and random. Random uncertainties are easier to understand;
they are just that--random. They differ for each individual
measurement but average out to be close to zero over a large sample.
Systematic uncertainties, which do not average out, are harder to deal
with. They are endemic in astronomy. Laboratory experimenters can
alter their instrumental setup to minimize them, but astronomers
cannot change the universe, and so they are forced to accept that all
their methods of gathering data have an irremovable bias. For example,
any survey of galaxies will tend to be overrepresented by bright
galaxies because they are easier to see. Identifying and neutralizing
these biases is a constant challenge.
The first one we looked for was a distortion of the wavelength scale
against which the quasar spectral lines were measured. Such a
distortion might conceivably be introduced, for example, during the
processing of the quasar data from their raw form at the telescope
into a calibrated spectrum. Although a simple linear stretching or
compression of the wavelength scale could not precisely mimic a change
in [alpha.gif] , even an imprecise mimicry might be enough to explain
our results. To test for problems of this kind, we substituted
calibration data for the quasar data and analyzed them, pretending
they were quasar data. This experiment ruled out simple distortion
errors with high confidence.
For more than two years, we put up one potential bias after another,
only to rule it out after detailed investigation as too small an
effect. So far we have identified just one potentially serious source
of bias. It concerns the absorption lines produced by the element
magnesium. Each of the three stable isotopes of magnesium absorbs
light of a different wavelength, but the three wavelengths are very
close to one another, and quasar spectroscopy generally sees the three
lines blended as one. Based on laboratory measurements of the relative
abundances of the three isotopes, researchers infer the contribution
of each. If these abundances in the young universe differed
substantially--as might have happened if the stars that spilled
magnesium into their galaxies were, on average, heavier than their
counterparts today--those differences could simulate a change in
[alpha.gif] .
But a study published this year indicates that the results cannot be
so easily explained away. Yeshe Fenner and Brad K. Gibson of Swinburne
University of Technology in Australia and Michael T. Murphy of the
University of Cambridge found that matching the isotopic abundances to
emulate a variation in [alpha.gif] also results in the overproduction
of nitrogen in the early universe--in direct conflict with
observations. If so, we must confront the likelihood that really has
been changing.
The scientific community quickly realized the immense potential
significance of our results. Quasar spectroscopists around the world
were hot on the trail and rapidly produced their own measurements. In
2003 teams led by Sergei Levshakov of the Ioffe Physico-Technical
Institute in St. Petersburg, Russia, and Ralf Quast of the University
of Hamburg in Germany investigated three new quasar systems. Last year
Hum Chand and Raghunathan Srianand of the Inter-University Center for
Astronomy and Astrophysics in India, Patrick Petitjean of the
Institute of Astrophysics and Bastien Aracil of LERMA in Paris
analyzed 23 more. None of these groups saw a change in [alpha.gif] .
Chand argued that any change must be less than one part in 10^6 over
the past six billion to 10 billion years.
How could a fairly similar analysis, just using different data,
produce such a radical discrepancy? As yet the answer is unknown. The
data from these groups are of excellent quality, but their samples are
substantially smaller than ours and do not go as far back in time. The
Chand analysis did not fully assess all the experimental and
systematic errors--and, being based on a simplified version of the
many-multiplet method, might have introduced new ones of its own.
One prominent astrophysicist, John Bahcall of Princeton, has
criticized the many-multiplet method itself, but the problems he has
identified fall into the category of random uncertainties, which
should wash out in a large sample. He and his colleagues, as well as a
team led by Jeffrey Newman of Lawrence Berkeley National Laboratory,
have looked at emission lines rather than absorption lines. So far
this approach is much less precise, but in the future it may yield
useful constraints.
Reforming the Laws
If our findings prove to be right, the consequences are enormous,
though only partially explored. Until quite recently, all attempts to
evaluate what happens to the universe if the fine-structure constant
changes were unsatisfactory. They amounted to nothing more than
assuming that [alpha.gif] became a variable in the same formulas that
had been derived assuming it is a constant. This is a dubious
practice. If [alpha.gif] varies, then its effects must conserve energy
and momentum, and they must influence the gravitational field in the
universe. In 1982 Jacob D. Bekenstein of the Hebrew University of
Jerusalem was the first to generalize the laws of electromagnetism to
handle inconstant constants rigorously. The theory elevates
[alpha.gif] from a mere number to a so-called scalar field, a dynamic
ingredient of nature. His theory did not include gravity, however.
Four years ago one of us (Barrow), with Håvard Sandvik and João
Magueijo of Imperial College London, extended it to do so.
This theory makes appealingly simple predictions. Variations in
[alpha.gif] of a few parts per million should have a completely
negligible effect on the expansion of the universe. That is because
electromagnetism is much weaker than gravity on cosmic scales. But
although changes in the fine-structure constant do not affect the
expansion of the universe significantly, the expansion affects
[alpha.gif] . Changes to [alpha.gif] are driven by imbalances between
the electric field energy and magnetic field energy. During the first
tens of thousands of years of cosmic history, radiation dominated over
charged particles and kept the electric and magnetic fields in
balance. As the universe expanded, radiation thinned out, and matter
became the dominant constituent of the cosmos. The electric and
magnetic energies became unequal, and [alpha.gif] started to increase
very slowly, growing as the logarithm of time. About six billion years
ago dark energy took over and accelerated the expansion, making it
difficult for all physical influences to propagate through space. So
[alpha.gif] became nearly constant again.
This predicted pattern is consistent with our observations. The quasar
spectral lines represent the matter-dominated period of cosmic
history, when [alpha.gif] was increasing. The laboratory and Oklo
results fall in the dark-energy-dominated period, during which has
been constant. The continued study of the effect of changing
[alpha.gif] on radioactive elements in meteorites is particularly
interesting, because it probes the transition between these two
periods.
Alpha Is Just the Beginning
Any theory worthy of consideration does not merely reproduce
observations; it must make novel predictions. The above theory
suggests that varying the fine-structure constant makes objects fall
differently. Galileo predicted that bodies in a vacuum fall at the
same rate no matter what they are made of--an idea known as the weak
equivalence principle, famously demonstrated when Apollo 15 astronaut
David Scott dropped a feather and a hammer and saw them hit the lunar
dirt at the same time. But if [alpha.gif] varies, that principle no
longer holds exactly. The variations generate a force on all charged
particles. The more protons an atom has in its nucleus, the more
strongly it will feel this force. If our quasar observations are
correct, then the accelerations of different materials differ by about
one part in 10^14--too small to see in the laboratory by a factor of
about 100 but large enough to show up in planned missions such as STEP
(space-based test of the equivalence principle).
There is a last twist to the story. Previous studies of [alpha.gif]
neglected to include one vital consideration: the lumpiness of the
universe. Like all galaxies, our Milky Way is about a million times
denser than the cosmic average, so it is not expanding along with the
universe. In 2003 Barrow and David F. Mota of Cambridge calculated
that [alpha.gif] may behave differently within the galaxy than inside
emptier regions of space. Once a young galaxy condenses and relaxes
into gravitational equilibrium, [alpha.gif] nearly stops changing
inside it but keeps on changing outside. Thus, the terrestrial
experiments that probe the constancy of [alpha.gif] suffer from a
selection bias. We need to study this effect more to see how it would
affect the tests of the weak equivalence principle. No spatial
variations of [alpha.gif] have yet been seen. Based on the uniformity
of the cosmic microwave background radiation, Barrow recently showed
that [alpha.gif] does not vary by more than one part in 10^8 between
regions separated by 10 degrees on the sky.
So where does this flurry of activity leave science as far as
[alpha.gif] is concerned? We await new data and new analyses to
confirm or disprove that varies at the level claimed. Researchers
focus on [alpha.gif] , over the other constants of nature, simply
because its effects are more readily seen. If [alpha.gif] is
susceptible to change, however, other constants should vary as well,
making the inner workings of nature more fickle than scientists ever
suspected.
The constants are a tantalizing mystery. Every equation of physics is
filled with them, and they seem so prosaic that people tend to forget
how unaccountable their values are. Their origin is bound up with some
of the grandest questions of modern science, from the unification of
physics to the expansion of the universe. They may be the superficial
shadow of a structure larger and more complex than the
three-dimensional universe we witness around us. Determining whether
constants are truly constant is only the first step on a path that
leads to a deeper and wider appreciation of that ultimate vista.
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