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[19]Home : [20]Experiments : [21]Seven Experiments : Fundamental
Constants

The Variability of Fundamental Constants

_Do physical constants fluctuate?_

The 'physical constants' are numbers used by scientists in their
calculations. Unlike the constants of mathematics, such as ¼, the
values of the constants of nature cannot be calculated from first
principles; they depend on laboratory measurements.

As the name implies, the so-called physical constants are supposed to
be changeless. They are believed to reflect an underlying constancy of
nature. In this chapter I discuss how the values of the fundamental
physical constants have in fact changed over the last few decades, and
suggest how the nature of these changes can be investigated further.

There are many constants listed in handbooks of physics and chemistry,
such as melting points and boiling points of thousands of chemicals,
going on for hundreds of pages: for instance the boiling point of
ethyl alcohol is 78.5°C at standard temperature and pressure; its
freezing point is -117.3°C. But some constants are more fundamental
than others. The following list gives the seven most generally
regarded as truly fundamental.

_CAPTION:_ _The Fundamental Constants_

Fundamental quantity Symbol
Velocity of light c
Elementary charge e
Mass of the electron me
Mass of the proton mp
Avogadro constant NA
Planck's constant h
Universal gravitational constant G
Boltzmann's constant k

All these constants are expressed in terms of units; for example, the
velocity of light is expressed in terms of meters per second. If the
units change, so will the constants. And units are [arbitrary],
dependent on definitions that may change from time to time: the meter,
for instance, was originally defined in 1790 by a decree of the French
National Assembly as one ten-millionth of the quadrant of the earth's
meridian passing through Paris. The entire metric system was based
upon the meter and imposed by law. But the original measurements of
the earth's circumference were found to be in error. The meter was
then defined, in 1799, in terms of a standard bar kept in France under
official supervision. In 1960 the meter was redefined in terms of the
wavelength of light emitted by krypton atoms; and in 1983 it was
redefined again in terms of the speed of light itself, as the length
of the path traveled by light in 1/299,792,458 of a second.

As well as any changes due to changing units, the official values of
the fundamental constants vary from time to time as new measurements
are made. They are continually adjusted by experts and international
commissions. Old values are replaced by new ones, based on the latest
'best values' obtained in laboratories around the world. Below, I
consider four examples: the gravitational constant (_G>_); the speed
of light; Planck's constant; and also the fine structure constant a,
which is derived from the charge on the electron, the velocity of
light, and Planck's constant.

The 'best' values are already the result of considerable selection.
First, experimenters tend to reject unexpected data on the grounds
that they must be errors. Second, after the most deviant measurements
have been weeded out, variations within a given laboratory are
smoothed out by averaging the values obtained at different times, and
the final value is then subjected to a series of somewhat arbitrary
corrections. Finally, the results from different laboratories around
the world are selected, adjusted, and averaged to arrive at the latest
official value.

_Faith in eternal truths_

In practice, then, the values of the constants change. But in theory
they are supposed to be changeless. The conflict between theory and
empirical reality is usually brushed aside without discussion, because
all variations are assumed to be due to experimental errors, and the
latest values are assumed to be the best.

But what if the constants _really_ change? What if the underlying
nature of nature changes? Before this subject can even be discussed,
it is necessary to think about one of the most fundamental assumptions
of science as we know it: faith in the uniformity of nature. For the
committed believer, these questions are nonsensical. Constants _must_
be constant.

Most constants have been measured only in this small region of the
universe for a few decades, and the actual measurements have varied
erratically. The idea that all constants are the same everywhere and
always is not an extrapolations from the data. If it were an
extrapolation it would be outrageous. The values of the constants as
actually measured on earth have changed considerably over the last
fifty years. To assume they had not changed for fifteen billion years
anywhere in the universe goes far beyond the meager evidence. The fact
that this assumption is so little questioned, so readily taken for
granted, shows the strength of scientific faith in eternal truths.

According to the traditional creed of science, everything is governed
by fixed laws and eternal constants. The laws of nature are the same
in all times and at all places. In fact they transcend space and time.
They are more like eternal Ideas--in the sense of Platonic
philosophy--than evolving things. They are not made of matter, energy,
fields, space, or time; they are not made of anything. In short, they
are immaterial and non-physical. Like Platonic Ideas they underlie all
phenomena as their hidden reason or logos, transcending space and
time.

Of course, everyone agrees that the laws of nature as formulated by
scientists change from time to time, as old theories are partially or
completely superseded by new ones. For example, Newton's theory of
gravitation, depending on forces acting at a distance in absolute time
and space, was replaced by Einstein's theory of the gravitational
field consisting of curvatures of space-time itself. But both Newton
and Einstein shared the Platonic faith that underlying the changing
theories of natural science there are true eternal laws, universal and
immutable. And neither challenged the constancy of constants: indeed
both gave great prestige to this assumption, Newton through his
introduction of the universal gravitational constant, and Einstein
through treating the speed of light as absolute. In modern relativity
theory, c is a mathematical constant, a parameter relating the units
used for time to the units used for space; its value is fixed by
definition. The question as to whether the speed of light actually
differs from c, although theoretically conceivable, seems of
peripheral interest.

For the founding fathers of modern science, such as Copernicus,
Kepler, Galileo, Descartes, and Newton, the laws of nature were
changeless Ideas in the divine mind. God was a mathematician. The
discovery of the mathematical laws of nature was a direct insight into
the eternal Mind of God. Similar sentiments have been echoes by
physicists ever since.

Until the 1960s, the universe of orthodox physics was still eternal.
But evidence for the expansion of the universe has been accumulating
for several decades, and the discovery of the cosmic microwave
background radiation in 1965 finally triggered off a great
cosmological revolution. The Big Bang theory took over. Instead of an
eternal machine-like universe, gradually running down toward
thermodynamic heat death, the picture was now one of a growing,
developing, evolutionary cosmos. And if there was a birth of the
cosmos, an initial 'singularity', as physicists put it, then once
again age-old questions arise. Where and what did everything come
from? Why is the universe as it is? In addition, a new question
arises. If all nature evolves, why should the laws of nature not
evolve as well? If laws are immanent in evolving nature, then the laws
should evolve too.

Today these questions are usually discussed in terms of the anthropic
cosmological principle, as follows: Out of the many possible
universes, only one with the constants set at the values found today
could have given rise to a world with life as we know it and allowed
the emergence of intelligent cosmologists capable of discussing it. If
the values of the constants had been different, there would have been
no stars, nor atoms, nor planets, nor people. Even if the constants
were only slightly different, we would not be here. For example, with
just a small change in the relative strengths of the nuclear and
electromagnetic forces there could be no carbon atoms, and hence no
carbon-based forms of life such as ourselves. 'The Holy Grail of
modern physics is to explain why these numerical constants . . . have
the particular numerical values they do.'

Some physicists incline toward a kind of neo-Deism, with a
mathematical creator-God who fine-tuned the constants in the first
place, selecting from many possible universes the one in which we can
evolve. Others prefer to leave God out of it. One way of avoiding the
need for a mathematical mind to fix the constants of nature is to
suppose that our universe arose from a froth of possible universes.
The primordial bubble that gave rise to our universe was one of many.
But our universe has to have the constants it does by the very fact we
are here. Somehow our presence imposes a selection. There may be
innumerable alien and uninhabitable universes quite unknown to us, but
this is the ony one we can know.

This kind of speculation has been carried even further by Lee Smolin,
who has proposed a kind of cosmic Darwinism. Through black holes, baby
universes may be budded off from pre-existing ones and take on a life
of their own. Some of these might have slight mutations in the values
of their constants and hence evolve differently. Only those that form
stars can form black holes and hence have babies. So by a principle of
cosmic fecundity, only universes like ours would reproduce, and there
may be many more or less similar habitable universes. But this very
speculative theory still does not explain why any universes should
exist in the first place, nor what determines the laws that govern
them, nor what maintains, carries, or remembers the mutant constants
in any particular universe.

Notice that all these metaphysical speculations, extravagant though
they seem, are thoroughly conventional in that they take for granted
both eternal laws and constant constants, at least within a given
universe. These well-established assumptions make the constancy of
constants seem like an assured truth. Their changelessness is an act
of faith. ...If measurements show variations in the constants, as they
often do, then the variations are dismissed as experimental errors;
the latest figure is the best available approximation to the 'true'
value of the constant.

Some variations may well be due to errors, and such errors decrease as
instruments and methods of measurement improve. All kinds of
measurements have inherent limitations on their accuracy. But not all
the variations in the measured values of the constants need
necessarily be due to error, or to the limitations of the apparatus
used. Some may be real. In an evolving universe, it is conceivable
that the constants evolve along with nature. They might even vary
cyclically, if not chaotically.

_Theories of changing constants_

Several physicists, among them Arthur Eddington and Paul Dirac, have
speculated that at least some of the 'fundamental constants' may
change with time. In particular, Dirac proposed that the universal
gravitational constant, G, may be decreasing with time: the
gravitational force weakening as the universe expands. But those who
make such speculations are usually quick to avow that they are not
challenging the idea of eternal laws; they are merely proposing that
eternal laws govern the variation of the constants.

The proposal that the laws themselves evolve is more radical. The
philosopher Alfred North Whitehead pointed out that if we drop the old
idea of Platonic laws imposed on nature, and think instead of laws
being immanent in nature, then they must evolve along with the nature:

Since the laws of nature depend on the individual characters of the
things constituting nature, as the things change, then consequently
the laws will change. Thus the modern evolutionary view of the
physical universe should conceive of the laws of nature as evolving
concurrently with the things constituting the environment. Thus the
conception of the Universe as evolving subject to fixed eternal laws
should be abandoned.

I prefer to drop the metaphor of 'law' altogether, with its outmoded
image of God as a kind of law-giving emperor, as well as an omnipotent
and universal law-enforcement agency. Instead, I have suggested that
the regularities of nature may be more like habits. According to the
hypothesis of morphic resonance, a kind of cumulative memory is
inherent in nature. Rather than being governed by an eternal
mathematical mind, nature is shaped by habits, subject to natural
selection. And some habits are more fundamental than others; for
example, the habits of hydrogen atoms are very ancient and widespread,
found throughout the universe, while the habits of hyenas are not.
Gravitational and electromagnetic fields, atoms, galaxies and stars
are governed by archaic habits, dating back to the earliest periods in
the history of the universe. From this point of view the 'fundamental
constants' are quantitative aspects of deep-seated habits. They may
have changed at first, but as they became increasingly fixed through
repetition, the constants may have settled down to more or less stable
values. In this respect the habit hypothesis agrees with the
conventional assumption of constancy, though for very different
reasons.

Even if speculations about the evolution of constants are set aside,
there are at least two more reasons why constants may vary. First,
they may depend on the astronomical environment, changing as the solar
system moves within the galaxy, or as the galaxy moves away from other
galaxies. And second, the constants may oscillate or fluctuate. They
may even fluctuate in a seemingly chaotic manner. Modern chaos theory
has enabled us to recognize that chaotic behavior, as opposed to
old-style determinism, is normal in most realms of nature. So far the
'constants' have survived unchallenged from an earlier era of physics:
the vestiges of a lingering Platonism. But what if they, too, vary
chaotically?

_The variability of the universal gravitational constant_

In spite of the central importance of the universal gravitational
constant, it is the least well defined of all the fundamental
constants. Attempts to pin it down to many places of decimals have
failed; the measurements are just too variable. The editor of the
scientific journal Nature has described as 'a blot on the face of
physics' the fact that G still remains uncertain to about one part in
5,000. Indeed, in recent years the uncertainty has been so great that
the existence of entirely new forces has been postulated to explain
gravitational anomalies.

In the early 1980s, Frank Stacey and his colleagues measured G in deep
mines and boreholes in Australia. Their value was about 1 percent
higher than currently accepted. For example, in one set of
measurements in the Hilton mine in Queensland the value of G was found
to be 6.734 ± 0.002, as opposed to the currently accepted value of
6.672 ± 0.003. The Australian results were repeatable and consistent,
but no one took much notice until 1986. In that year Ephrain
Fischbach, at the University of Washington, Seattle, sent shock waves
around the world of science by claiming that laboratory tests also
showed a slight deviation from Newton's law of gravity, consistent
with the Australian results. Fischbach proposed the existence of a
hitherto unknown repulsive force, the so-called fifth force (the four
known forces being the strong and weak nuclear forces, the
electromagnetic force, and the gravitational force)

The possible existence of a fifth force is not particularly relevant
to possible changes in G with time. But the very fact that the
question of an extra force affecting gravitation could even be raised
and seriously considered in the late twentieth century serves to
emphasize how imprecise the characterization of gravity remains more
than three centuries after the publication of Newton's Principia.

The suggestion by Paul Dirac and other theoretical physicists that G
may be decreasing as the universe expands has been taken quite
seriously by some metrologists. However, the change proposed by Dirac
was very small, about 5 parts in 1011 per year. This is way below the
limits of detection using conventional methods of measuring G on
Earth. The 'best' results in the last twenty years differ from each
other by more than 5 parts in 104. In other words, the change Dirac
was suggesting is some ten million times smaller than the differences
between recent 'best' values.

In order to test Dirac's hypothesis, a variety of indirect methods
have been tried. Some depend on geological evidence, such as the
slopes of fossils and dunes, from which the gravitational forces at
the time they were formed can be calculated; others depend on records
of eclipses over the last 3,000 years; others on modern astronomical
methods.

The problem with all these indirect lines of evidence is that they
depend on a complex tissue of theoretical assumptions, including the
constancy of the other constants of nature. They are persuasive only
within the framework of the present paradigm. That is to say that if
one assumes the correctness of modern cosmological theories,
themselves presupposing the constancy of G, the data are internally
consistent, provided that all actual variations from experiment to
experiment, or method to method, are assumed to be a result of error.

_The fall in the speed of light from 1928 to 1945_

According to Einstein's theory of relativity, the speed of light in a
vacuum is invariant: it is an absolute constant. Much of modern
physics is based on that assumption. There is therefore a strong
theoretical prejudice against raising the question of possible changes
in the velocity of light. In any case, the question is now officially
closed. Since 1972 the speed of light has been fixed by definition.
The value is defined as 299,792.458 ± 0.001 # 2 kilometers per second.

As in the case of the universal gravitational constant, early
measurements of c differed considerably from the present official
value. For example, the determination by Römer in 1676 was about 30
percent lower, and that by Fizeau in 1849 about 5 percent higher.

In 1929, Birge published his review of all the evidence available up
to 1927 and came to the conclusion that the best value for velocity of
light was 299,796 ± 4 km/s. He pointed out that the probable error was
far less than in any of the other constants, and concluded that 'the
present value of c is entirely satisfactory, and can be considered as
more or less permanently established.' However, even as he was
writing, considerably lower values of c were being found, and by 1934
it was suggested by Gheury de Bray that the data pointed to a cyclic
variation in the velocity of light.

From around 1928 to 1945, the velocity of light appeared to be about
20 km/s lower than before and after this period. The 'best' values,
found by the leading investigators using a variety of techniques, were
in impressively close agreement with each other, and the available
data were combined and adjusted by Birge in 1941 and Dorsey in 1945.

In the late 1940s the speed of light went up again. Not surprisingly,
there was some turbulence at first as the old value was overthrown.
The new value was about 20 km/s higher, close to that prevailing in
1927. A new consensus developed. How long this consensus would have
lasted if based on continuing measurements is a matter for
speculation. In practice, further disagreement was prevented by fixing
the speed of light in 1972 by definition.

How can the lower velocity from 1928 to 1945 be explained? If it was
simply a matter of experimental error, why did the results of
different investigators and different methods agree so well? And why
were the estimated errors so low?

One possibility is that the velocity of light really does fluctuate
from time to time. Perhaps it really did drop for nearly twenty years.
But this is not a possibility that has been seriously considered by
researchers in the field, except for de Bray. So strong is the
assumption that it must be fixed that the empirical data have to be
explained away. This remarkable episode in the history of the speed of
light is now generally attributed to the psychology of metrologists:

The tendency for experiments in a given epoch to agree with one
another has been described by the delicate phrase 'intellectual phase
locking.' Most metrologists are very conscious of the possible
existence of such effects; indeed ever-helpful colleagues delight in
pointing them out! . . . .Aside from the discovery of mistakes, the
near completion of the experiment brings more frequent and stimulating
discussion with interested colleagues and the preliminaries to writing
up the work add fresh perspective. All of these circumstances combine
to prevent what was intended to be 'the final result' from being so in
practice, and consequently the accusation that one is most likely to
stop worrying about corrections when the value is closest to other
results is easy to make and difficult to refute.

But if changes in the values of constants in the past are attributed
to the experimenters' psychology, then, as other eminent metrologists
have observed, 'this raises a disconcerting question: How do we know
that this psychological factor is not equally important today?' In the
case of the velocity of light, however, this question is now academic.
Not only is the velocity fixed by definition, but the very units in
which velocity is measured, distance and time, are defined in terms of
light itself.

The second used to be defined as 1/86,400 of a mean solar day, but it
is now defined in terms of the frequency of light emitted by a
particular kind of excitation of caesium-133 atoms. A second is
9,192,631,770 times the period of vibration of the light. Meanwhile,
since 1983 the meter has been defined in terms of the velocity of
light, itself fixed by definition.

As Brian Petley has pointed out, it is conceivable that:

(i) the velocity of light might change with time, or (ii) have a
directional dependence in space, or (iii) be affected by the motion of
the Earth about the Sun, or motion within our galaxy or some other
reference frame.

Nevertheless, if such changes really happened, we would be blind to
them. We are now shut up within an artificial system where such
changes are not only impossible by definition, but would be
undetectable in practice because of the way the units are defined. Any
change in the speed of light would change the units themselves in such
a way that the velocity in kilometers per second remained exactly the
same.

_The rise of Planck's constant_

Planck's constant, h, is a fundamental feature of quantum physics and
relates the frequency of a radiation, v, with its quantum of energy,
E, according to the formula E=hv. It has the dimensions of action
(energy x time).

We are often told that quantum theory is brilliantly successful and
amazingly accurate. For example: 'The laws that have been found to
describe the quantum world. . . are the most accurate and precise
tools we have ever found for the successful description and prediction
of the workings of Nature. In some cases the agreement between the
theory's predictions and what we measure are good to better than one
part in a billion.'

I heard and read such statements so often that I used to assume that
Planck's constant must be known with tremendous accuracy to many
places of decimals. This seems to be the case if one looks it up in a
scientific handbook--so long as one does not also look at previous
editions. In fact its official value has changed over the years,
showing a marked tendency to increase.

The biggest change occurred between 1929 and 1941, when it went up by
more than 1 percent. This increase was largely due to a substantial
change in the value of the charge on the electron, e. Experimental
measurements of Planck's constant do not give direct answers, but also
involve the charge on the electron and/or the mass of the electron. If
either or both of these other constants change, then so does Planck's
constant.

Millikan's work on the charge on the electron turned out to be one of
the roots of the trouble. Even though other researchers found
substantially higher values, they tended to be disregarded.
'Millikan's great renown and authority brought about the opinion that
the question of the magnitude of e had practically got its definitive
answer.' For some twenty years Millikan's value prevailed, but
evidence went on building up that e was higher. As Richard Feynman has
expressed it:

It's interesting to look at the history of measurements of the charge
on the electron after Millikan. If you plot them as function of time,
you find that one is a little bigger than Millikan's, the next one's a
little bigger than that, and the next one's a little bit bigger than
that, until finally they settle down to a number that is higher. Why
didn't they discover that the new number was higher right away? It's a
thing that scientists are ashamed of--this history--because it's
apparent that people did things like this: When they got a number that
was too high above Millikan's, they would look for and find a number
closer to Millikan's value when they didn't look so far. And so they
eliminated the numbers that were too far off, and did other things
like that.

In the late 1930s, the discrepancies could no longer be ignored, but
Millikan's high-prestige value could not simply be abandoned either;
instead it was corrected by using a new value for the viscosity of
air, an important variable in his oil-drop technique, bringing it into
alignment with the new results. In the early 1940s, even higher values
of e led to a further upward revision of the official figure. Sure
enough, reasons were found to correct Millikan's value yet again,
raising it to agree with the new value. Every time e increased, so
Planck's constant had to be raised as well.

Interestingly, Planck's constant continued to creep upwards from the
1950s to the 1970s. Each of these increases exceeded the estimated
error in the previously accepted value. The latest value shows a
slight decline.

_CAPTION:_ _Planck's Constant from 1951 to 1988 (Review Values)_

Author Date h(x 10-34 joule seconds)
Bearden and Watts 1951 6.623 63 ± 0.000 16
Cohen et al. 1955 6.625 17 ± 0.000 23
Condon 1963 6.625 60 ± 0.000 17
Cohen and Taylor 1973 6.626 176 ± 0.000 036
1988 6.626 075 5 ± 0.000 004 0

Several attempts have been made to look for changes in Planck's
constant by studying the light from quasars and stars assumed to be
very distant on the basis of the red shift in their spectra. The idea
was that if Planck's constant has changed, the properties of the light
emitted billions of years ago should be different from more recent
light. Little difference was found, leading to the seemingly
impressive conclusion that h varies by less than 5 parts in 1013 per
year. But critics of such experiments have pointed out that these
constancies are inevitable, since the calculations depend on the
implicit assumption that h is constant; the reasoning is circular.
(Strictly speaking, the starting assumption is that the product hc is
constant; but since c is constant by definition, this amounts to
assuming the constancy of h.)

_Fluctuations in the fine-structure constant_

One of the problems of looking for changes in a fundamental constant
is that if changes are found in the constant, then it is difficult to
know whether it is the constant itself that is changing, or the units
in which it is measured. However, some of the constants are
dimensionless, expressed as pure numbers, and hence the question of
changes in units does not arise. One example is the ratio of the mass
of the proton to the mass of the electron. Another is the
fine-structure constant. For this reason, some metrologists have
emphasized that 'secular changes in physical "constants" should be
formulated in terms of such numbers.'

Accordingly, in this section I look at the evidence for changes in the
fine-structure constant, a, formed from the charge on the electron,
the velocity of light, and Planck's constant, according to the formula
the fine structure constant = [charge on the electron, squared]/2
[Planck's constant][the velocity of light][the permittivity of free
space]. It gives a measure of the strength of electromagnetic
interactions, and is sometimes expressed as its reciprocal,
approximately 1/137. This constant is treated by some theoretical
physicists as one of the key cosmic numbers that a Theory of
Everything should be able to explain.

Between 1929 and 1941 the fine-structure constant increased by about
0.2 percent, from 7.283 x 10-3 to 7.2976 x 10-3. This change was
largely attributable to the increased value for the charge on the
electron, partly offset by the fall in the speed of light, both of
which I have already discussed. As in the case of the other constants,
there was a scatter of results from different investigators, and the
'best' values were combined and adjusted from time to time by
reviewers. As in the case of the other constants, the changes were
generally larger than would be expected on the basis of the estimated
errors. For example, the increase from 1951 to 1963 was twelve times
greater than the estimated error in 1951 (expressed as the standard
deviation); the increase from 1963 to 1973 was nearly five tims the
estimated error in 1963.

_CAPTION:_ _The Fine-Structure Constant From 1951 to 1973_

Author Date a x 10-3
Bearden and Watts 1951 7.296 953 ± 0.000 028
Condon 1963 7.297 200 ± 0.000 033
Cohen and Taylor 1973 7.297 350 6 ± 0.000 006 0

Several cosmologists have speculated that the fine-structure constant
might vary with the age of the universe, and attempts have been made
to check this possibility by analyzing the light from stars and
quasars, assuming that their distance is proportional to the red-shift
of their light. The results suggest that there has been little or no
change in the constant. But as with all other attempts to infer the
constancy of constants from astronomical observations, many
assumptions have to be made, including the constancy of other
constants, the correctness of current cosmological theories, and the
validity of red-shifts as indicators of distance. All of these
assumptions have been and are still being questioned by dissident
cosmologists.

_Do constants really change?_

As we have seen with the four examples above, the empirical data from
laboratory experiments reveal all sorts of variations as time goes on.
Similar variations are found in the values of the other fundamental
constants. These do not trouble true believers in constancy, because
they can always be explained in terms of experimental error of one
kind or another. Because of continual improvements in techniques, the
greatest faith is always placed in the latest measurements, and if
they differ from previous ones, the older ones are automatically
discredited (except when the older ones are endowed with a high
prestige, as in the case of Millikan's measurement of e). Also, at any
given time, there is a tendency for metrologists to overestimate the
accuracy of contemporary measurements, as shown by the way that later
measurements often differ from earlier ones by amounts greater than
the estimated error. Alternatively, if metrologists are estimating
their errors correctly, then the changes in the values of the
constants show that the constants really are fluctuating. The clearest
example is the fall in the speed of light from 1928 to 1945. Was there
a real change in the course of nature, or was it due to a collective
delusion among metrologists?

So far there have been only two main theories about the fundamental
constants. First, they are truly constant, and all variations in the
empirical data are due to errors of one kind or another. As science
progresses, these errors are reduced. With ever-increasing precision
we come closer and closer to the constants' true values. This is the
conventional view. Second, several theoretical physicists have
speculated that one or more of the constants may vary in some smooth
and regular manner with the age of the universe, or over astronomical
distances. Various tests of these ideas using astronomical
observations seem to have ruled out such changes. But these tests beg
the question. They are founded on the assumptions that they set out to
prove: that constants are constant, and that present-day cosmology is
correct in all essentials.

There has been little consideration of the third possibility, which is
the one I am exploring here, namely the possibility that constants may
fluctuate, within limits, around average values which themselves
remain fairly constant. The idea of changeless laws and constants is
the last survivor from the era of classical physics in which a regular
and (in principle) totally predictable mathematical order was supposed
to prevail at all times and in all places. In reality, we find nothing
in the kind in the course of human affairs, in the biological realm,
in the weather, or even in the heavens. The chaos revolution has
revealed that this perfect order was a beguiling illusion. Most of the
natural world is inherently chaotic.

The fluctuating values of the fundamental constants in experimental
measurements seem just as compatible with small but real changes in
their values, as they are with a perfect constancy obscured by
experimental errors. I now propose a simple way of distinguishing
between these possibilities. I concentrate on the gravitational
constant, because this is the most variable. But the same principles
could be applied to any of the other constants too.

_An experiment to detect possible fluctuations in the universal
gravitational constant_

The principle is simple. At present, when measurements are made in a
particular laboratory, the final value is based on an average of a
series of individual measurements, and any unexplained variations
between these measurements are attributed to random errors. Clearly,
if there were real underlying fluctuations, either owing to changes in
the earth's environment or to inherently chaotic fluctuations in the
constant itself, these would be ironed out by the statistical
procedures, showing up simply as random errors. As long as these
measurements were confined to a single laboratory, there would be no
way of distinguishing between these possibilities.

What I propose is a series of measurements of the universal
gravitational constant to be made at regular intervals--say
monthly--at several different laboratories all over the world, using
the best available methods. Then, over a period of years, these
measurements would be compared. If there were underlying fluctuations
in the value of G, for whatever reason, these would show up at the
various locations. In other words, the 'errors' might show a
correlation--the values might tend to be high in some months and low
in others. In this way, underlying patterns of variation could be
detected that could not be dismissed as random error.

It would then be necessary to look for other explanations that did not
involve a change in G, including possible changes in the units of
measurement. How these inquiries would turn out is impossible to
foresee. The important thing is to start looking for correlated
fluctuations. And precisely because fluctuations are being looked for,
there is more chance of finding them. By contrast, the current
theoretical paradigm leads to a sustained effort by everyone concerned
to iron out variations, because constants are assumed to be truly
constant.

Unlike the other experiments proposed in this book, this one would
involve a fairly large-scale international effort. Even so, the budget
would not need to be huge if it took place in established laboratories
already equipped to make such measurements. And it is even possible
that it could be done by students. Several inexpensive methods for
determining G have been described, based on the classical method of
Cavendish using a torsion balance, and an improved student method has
recently been developed which is accurate to 0.1 percent.

One of the advantages of the continual improvement in precision of
metrological techniques is that it should become increasingly feasible
to detect small changes in the constants. For example, a far greater
accuracy in measurements of G should be possible when experiments can
be done in spacecraft and satellites, and appropriate techniques are
already being proposed and discussed. Here is an area where a big
question really would need big science.

But there is in fact one way that this research could be done on a
very low budget to start with: by examining the existing raw data for
measurements of G at various laboratories over the last few decades.
This would require the cooperation of the scientists concerned,
because raw data are kept in scientists' notebooks and laboratory
files, and many scientists are reluctant to allow others access to
these private records. But given this cooperation, there may already
be enough data to look for worldwide fluctuations in the value of G.

The implications of fluctuating fundamental constants would be
enormous. The course of nature could no longer be imagined as blandly
uniform; we would recognize that there are fluctuations at the very
heart of physical reality. And if different fundamental constants
varied at different rates, these changes would create differing
qualities of time, not unlike those envisaged by astrology, but with a
more radical basis."

© 1995 - 2001 Rupert Sheldrake. All rights reserved.
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