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Constantly on my mind

"In most fields of discourse [constant] is an antonym of 'variable', but in mathematical parlance a variable may sometimes also be called a constant."
-Wikipedia, the free encyclopedia

Speak constant and enter

By the dictionary definition, a constant is basically an indestructible fact of nature. Constants are supposed to be those absolute--unchangeable figures and numbers that pin down our scientific theories and laws of nature, defining the reliability and accuracy of our view of the world and the nature of its reality. Though, in an absolute scientific sense of fallibility, nothing can be absolute, not even a constant. For all I understand, the very basic principles of scientific inquiry and way of thinking encourage us to yield from strong dogmatic authorities like constants.

Nevertheless, scientific research is most reliable on constants. The National Institute of Standards and Technology provides a listing of recommended values for 326 fundamental physical constants for research use. For the scientific method, it seems, it is convenient to be able to say that there is something that sticks. Constants are essential for parametrization and calculation of fundamental equations defining the basis of most scientific theories. Constants are found so important that they are even given names in the eponymic convention to honor their founders. It is one of the most convenient ways to get your name in the history books; find a species, write a symphony, or come up with a constant of nature.

Was Einstein right?

One of the most famous constants in modern science is not necessarily famous for being important but for the fact that it was found by Albert Einstein. Probably the greatest scientific mind in of the 20th century needed a constant to complement his work, so he just made one up. He was reluctant to use it and could not even tell the precise value of it, but realized it was necessary to make his theory work. This parameter became known as the cosmological constant or the scale factor, whichever you prefer to call it. Einstein himself later called it the biggest mistake of his life. Nowadays the value of this cosmological constant is a matter of great debate and commotion. By telling its precise value, cosmologists could unravel the fundamental structure of the whole universe.

Constantly at the speed of light

Another crucial value of constant nature in Einstein's work was the speed of light. It is a controversial constant, firstly because Einstein's definition of it gave birth to something that is the modern opposite of things absolute, the theory of relativity. Secondly, it has been suggested that there is a slight possibility it is not a constant at all.

Constants of nature also have a peculiar way of being defined by other constants. A practical example can be drawn from the standard definition of the unit of length in the SI system. The unit, meter, was traditionally defined by the French Academy of Sciences as a commonly agreed length marked on a platinum-iridium rod acting as a prototype of a meter. Nevertheless, since 1983 the meter has been defined as the distance light travels in a vacuum in 1/299,792,458 seconds. Here we don't run in to that much of trouble as a meter is not a true constant occurring in nature. It has no physical meaning. It is just a convention that has been defined to unify the practice of measuring distance and length. Right?

A more abstract example of a constant reliant in its definition on the speed of light, from a field more relevant to geochemistry, is the fine structure constant (α). α is defined by three other constants of nature, Dirac's constant (ℏ, which is actually also in turn defined by another constant, the Planck's constant h), charge of an electron (e) and by the speed of light in a vacuum(c0).

α = e2/ℏc0

Peculiarly enough, some studies of the fine structure constant have concluded that its value has not remained constant through time. This in turn has been taken as an indication that some of the other constants defining α must not be constants. The main suspect to have caused the alleged variation has surprisingly been the speed of light. Especially particular studies on the Oklo natural reactor have shown possible variation in α leading to a healthy debate which at the current moment seems to be in favor of constants still retaining their constant status. But we are left with a doubt, is speed of light constant after all. If it has indeed changed it might be responsible for the suggested change in α, which in turn has an effect on other constants that are dependent on the electromagnetic forces in the nucleus of an atom.

1, 2, 3, decay!

One of these constants is crucial for the particular field of isotope geology - the decay constant (λ). Determination of decay constants for different isotopic systems and improvement of their accuracy have been tasks taken very seriously for they define and justify a field of scientific inquiry which has become very prestigious during the last fifty years. The theoretical potential of very powerful isotopic research tools is restricted by the limited knowledge of the fundamental mechanics behind the phenomena of radioactively decaying elements.

Decay constants are actually more than crucial, they are the solid backbone of modern uniformitarianism itself. Macroscopic geological phenomena can be thought of as not being that absolute by geochemists. Changing rate of change is accepted, everyday compromises are done and quantitative models are constantly modified to better explain observed processes. But decay constants, no way! A constant is a constant. Assuming otherwise would bring down the sound basis of geochronology and a whole field of geoscientific reasoning.

Decay constant under fire...

During the recent decades the advancement in ICP-MS technology has revived the analytics of Lu-Hf isotopes which can be used as a tracer method of petrologic processes in much of the same way as the well-established Sm-Nd method. Particularly the laser ablation in-situ study of zircon, which has the capacity to retain detailed petrologic information about the source characteristics and magmatic evolution of its crystallizing melt has proved to be of great interest to igneous petrologists. The method has encountered also several analytical problems but one of the most fundamental dilemmas of these studies is that the decay constant of Lu-Hf system can't be agreed upon. The rising research activity regarding the isotope system has also revived interest in not just obtaining a reasonably justified value for the decay constant but also questions about methodological legitimacy to answer the set challenges. For an isotopic system to deliver reliable and comparable petrologic information, its reference values must be justified.

Several attempts using diverse techniques have been made but the variation between experimental results remains significant and no consensus exists among practitioners on the field. Isochron methods utilized in study of extraterrestrial samples seem to yield consistently higher values for λLu-176 to 176Hf than the determinations done on terrestrial samples. The range obtained in these studies is far greater than what could be expected on the basis of experimental error estimates and has given a cause for much heated debate.

Some researchers argue for terrestrial samples to be used in determining the λ for further study of other terrestrial samples. Some authorities on the other hand question the age determinations - also reliant on a another set of decay constants - of the terrestrial samples used for cross calibration and prefer the λ values obtained from studies of chondritic meteorites. A different approach of direct counting methods can also be used to back up the terrestrial values but still the coincidence of the results is not good enough for most of the skeptics. Some researchers even utilize the average value for the whole range of determined values in their studies arguing that it is the only truly justified value.

So, the rate of decay of 176Lu to 176Hf is under heavy debate but the research is nevertheless going on. Every published study utilizes its own set value for the decay rate and calls it a constant. Can these numbers really be called constants?

A blind trust to a justified belief is as the value of a constant is to a...?

Constants come in many sizes and shapes, most of them are not that important, as some of them mean (literally) the world to someone. Nailing down any constant and relying on it in one's research can in the end be reduced to a justified belief to invariability of a certain natural phenomenon.

The common thing to all constants of nature seems to be, that none of them are absolute in any other than conventional meaning, being culturally defined as one. How do the constants of nature then differ from the man-created meter? What more are natural constants than mere numbers that are agreed (or disagreed) upon? Constants of nature don't really live up to their name... or do they?

Aku Heinonen
Department of Geology
University of Helsinki

Helsinki, Finland