June 11, 2005

THERE are some 20 universal constants which are believed to be so finely tuned that life as we know it became possible in our universe because of them. Were these constants even slightly different, “the universe might never have amounted to more than a formless morass of matter and energy.”

Yet, scientists are now looking at the possibility that some, or perhaps all, of them might be varying with time. Such a variation, however, would probably be small. One of the constants, which is being revisited, is the “fine structure constant.”

Enigma of 137

Indeed, as Feynman has said, physicists ought to put a special sign up in their offices to remind themselves of how much they don’t know. The message on the sign would be very simple. It would consist entirely of one word, or one number: 137. (Charles C. Mann)

Fine structure constant is represented by the Greek letter alpha and is equal to the square of the charge of an electron divided by the speed of light times the Planck’s Constant. In the words of Charles Mann: “…(T)his one little number contains in itself the guts of electro-magnetism, relativity (the speed of light), and quantum mechanics (the Planck’s Constant).”

The currently accepted value of alpha is 1/137.03599976. Alpha is a dimensionless number, which was introduced by the celebrated physicist Arnold Sommerfeld in 1915. Originally, the value of alpha was held to be 1/136. This number had its own charm and attraction.

Sir Arthur Eddington was “possessed” by alpha and other universal constants. The famous scientist gave a formula for alpha in terms of the whole numbers 16 and 2. His formula was: 16+(16^2-16)/2 = 136.

However, the magic from 136 was stolen in due time by 137. He then added 1 to his formula to obtain 137. The Punch magazine dubbed him “Sir Arthur Adding One” for that.

More seriously, Paul Dirac expressed his views on alpha and other large constants in 1970 in an interview with the IOP magazine. Speaking of alpha, Dirac said, “There is another dimensionless number which connects Planck’s Constant and the electronic charge. This number is about 137, quite independent of the units. When a dimensionless number like that turns up, a physicist thinks there must be some reason for it. Why should it be, well, 137 and not 256 or something quite different. At present, one cannot set up a satisfactory reason for it, but still people believe that with the future developments a reason will be found.”

Hopes for such further developments are pinned on unified theory, which is being investigated at present intensively, using various viable theoretical approaches. Of these, the string theory involving branes seems most promising.

String theory (the M version) works in eleven dimensions; ten of them are of space and one of time. Einstein’s theory of general relativity works in four-dimensional space-time. Scientists wonder if the laws developed for four-dimensional space-time will remain valid for an eleven-dimensional universe.

Fortunately, the additional dimensions are infinitely small and compactified. Einstein’s theory doesn’t remain valid in the microscopic subatomic world in which the theory of quantum mechanics applies. The question then is: Will the theory of quantum mechanics hold good in the eleven-dimensional world? It is hoped that the unified theory will answer this question and predict the universal constants and explain their numerical magnitudes too.

The constants’ mutability

The idea that the fundamental laws of physics and the constants might be changing with time is not new. Milne and Dirac independently surmised on such a possibility in the 1930s.

The philosopher Alfred North Whitehead wrote in 1933: “Since the laws of nature depend on the individual characters of the things constituting nature, as the things change, then correspondingly 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 regulating all behaviour should be abandoned.

“Having said that let me also say that no revolutionary change has so far been reported that might impact the foundations of physics. Efforts are going on to check if the laws and the constants of physics are showing signs of mutability. One of the universal laws that is under investigation to determine whether it changes with time or other physical conditions, is the ‘inverse square law’ that was first given by Newton. According to this law, the force of attraction between two point masses separated by a distance r is directly proportional to the product of the masses and inversely proportional to the square of the distance r. The constant of proportionality is denoted by G and is called the constant of gravitation or the gravitational constant.”

Einstein’s theory of relativity did not change this law and since relativity is the “theory of the large” in four-dimensional space-time, it is believed that the inverse square law holds good for such conditions. Dirac believed that since the universe is constantly expanding, it might affect the force of gravitation (reduce it). But more about that later.

Many experimental investigations are currently in progress to determine the limit of the applicability of the inverse square law for short distances — of the order of a few micrometres. Although there is no definite evidence to show that the law doesn’t hold good in experiments that have been performed, there is a hint that the gravitational force might vary inversely to the fourth power of r at extremely short distances of the order of Planck’s scale. At present, this is only a conjecture without any experimental evidence.

Dirac’s argument for a variable G, in his own words, is as follows: “If you have an electron and a proton, the electric force between them is inversely proportional to the square of the distance; the gravitational force is also inversely proportional to the square of the distance; the ratio of those two forces does not depend on the distance. The ratio gives you a dimensionless number. The number is extremely large, about ten to the power thirty-nine… . It’s a number provided by nature and we should expect that a theory will some day provide a reason for it… .

“There is a definite age when the big bang occurred. The most recent observations give it to be about 18 billion years ago. Now, you might use some atomic unit of time instead of years, years is quite artificial depending on our solar system. Take an atomic unit of time, express the age of the universe in this atomic unit, and you again get a number of about ten to the power thirty-nine, roughly the same as the previous number… .

“Let us assume that these two numbers are connected. Now, one of these numbers is not a constant. The age of the universe, of course, gets bigger and bigger as the universe gets older. So the other one must be increasing in the same proportion. That means that electric force, compared with the gravitational force, is not constant, but is increasing proportionally to the age of the universe. The most convenient way of describing this is to use atomic units, which make the electric force constant; then, referred to these atomic units, the gravitational force will be decreasing. The gravitational constant, usually denoted by G, when expressed in atomic units is not a constant any more but is decreasing inversely proportional to the age of the universe.”

If Dirac’s argument is correct, then G should be decreasing with the age of the universe regardless of whether the universe is four-dimensional as required by Einstein’s theory of relativity or eleven-dimensional as required by the M-theory.

Dirac also observed: “The ordinary Einstein theory demands that G shall be a constant. We thus have to modify it in some way. We don’t want to abandon it altogether because it is so successful.” His thesis that G should change with the age of the universe is quite novel because nobody else has challenged the theory of relativity from that perspective.

Eric Adelberger et al have suggested a method to check if there are deviations in the inverse square law at large distances. This consists of measuring the Moon’s precession of its orbit much more accurately than the present measurements to detect if the actual precession is significantly different from the predicted value. They asserted, “When the effects of general relativity and the influence of the Sun and the other planets are included, the predicted value for the precession of the Moon’s orbit (19 milliarcseconds per year) is in very good agreement with the measurements, and any discrepancy caused by a possible breakdown of the inverse square law must be less than 270 milliarcseconds per year.”

Variability of alpha

The particular question that I have been vigorously pursuing with colleagues at the University of New South Wales, Sydney, and elsewhere can be stated as follows: Is the fine structure constant really constant, or has its value changed over the history of the universe? (John Webb)

The fine structure constant is a dimensionless number and that “makes it even more fundamental than the other constants such as the strength of gravity, the speed of light or the charge on the electron.” The gravitational constant, speed of light, and the charge on the electron are all dimensional constants; they have different numerical values in different units of measurement.

According to Webb, there are several different ways of measuring possible changes in alpha with time: “We can measure the absorption spectra of quasars (shortened from ‘quasistellars’) at different red shifts, as we (Webb and his associates) have done at UNSW. We can compare the ticking rates of atomic clocks made of different elements… .”

The first method, however, that physicists used for the purpose of checking the variability of alpha was to study the so-called “natural nuclear reactor” at Oklo in central Africa. In 1972, some scientists from the French Atomic Energy Commission collected some soil samples from a uranium mine in Gabon in central Africa. Analysis of these samples showed a strange result, namely, the relative abundance of U235 (Uranium 235) had a factor that was 2 points lower than expected. Ruling out several other possibilities, Webb postulated that over time a natural nuclear reactor came into being which “would have burnt uranium 235, thus explaining the low levels of the isotope found at Oklo”. This observation, however, did not direct attention to alpha by itself.

Alexander Shlyakhter made the connection to alpha via the relative abundance of samarium 149, in 1976, which had a factor that was 45 lower than in the other terrestrial samples. Without going into the details of the calculations here, it was found that any fractional change in the value of alpha since the time that Oklo was active cannot be greater than 10^-7. This affects the numerical value of alpha only in the seventh place of decimal.

This result was confirmed by Freeman Dyson who did his calculations also on the Oklo samples. He came up with the rate of change in alpha to the tune of 0.5x10^-16 per year, which gives a total rate of 10^-7 in a period of 2 billion years.

The rate of change of alpha obtained from investigations with atomic clocks — by H. Marion et al in France and James Bergquist et al at the National Standards Institute and Technology in Boulder, Colorado — is between 7x10^-15 and 7x10-16 per year.

The current investigations show a change in the numerical value of the fine structure constant with respect to time but the actual change is quite small. More investigations are underway to firm up the estimates of the variability of alpha. There is still no reliable indication if the measured or the calculated rate of change of alpha will affect physics in any fundamental way.

Feynman had asserted, “We do not imagine, at the moment, that the laws of physics are somehow changing with time, that they were different in the past than they are at present.” His assertion is still good. However, it is hoped that new insights will be gained in the subatomic world with the unified theory. Whether it will have any fundamental effect on the physics of the macroscopic world is at best only a matter for speculation at present.

The writer akramgill@yahoo.com is a US-based engineer who did his PhD from the University of London

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