ScienceWeek

THEORETICAL PHYSICS: ON THE FUNDAMENTAL CONSTANTS OVER TIME

The following points are made by K.A. Olive and Y-Z. Qian (Physics Today 2004 October):

1) Are any of nature's fundamental parameters truly constant? If not, are they fixed by the vacuum state of the Universe, or do they vary slowly in time even today? To fully answer those questions requires either an unambiguous experimental detection of a change in a fundamental quantity or a significantly deeper understanding of the underlying physics represented by those parameters.

2) At first glance, a long list of quantities usually assumed to be constant could potentially vary: Newton's constant G(subN), Boltzmann's constant k(subB), the charge of the electron e, the electric permittivity epsilon-0, and magnetic permeability mu-0, the speed of light c, Planck's constant h-bar, Fermi's constant G(subF), the fine-structure constant alpha = e^(2)/(h-bar)c and other gauge coupling constants, Yukawa coupling constants that fix the masses of quarks and leptons, and so on. One must, however, distinguish what may be called a fundamental dimensionless parameter of the theory from a fundamental unit. Dimensionless parameters include gauge couplings and quantities that, like the ratio of the proton to electron mass, are combinations of dimensioned quantities whose units cancel. Their variations represent fundamental and observable effects.

3) In contrast, variations in dimensioned quantities are not unambiguously observable.(1) To point out the ambiguity is not to imply that a universe with, say, a variable speed of light is equivalent to one in which the speed of light is fixed. But no observable difference between those two universes can be uniquely ascribed to the variation in c. It thus becomes operationally meaningless to talk about measuring the variation in the speed of light or whether a variation in alpha is due to a variation in c or h-bar. It is simply a variation in alpha.

4) Lev Okun(2) provides a nice example, based on the hydrogen atom, that illustrates the inability to detect the variation in c despite the physical changes such a variation would cause.(2) Lowering the value of c lowers the rest-mass energy of an electron, E(sube) = m(sube)c^(2). When 2E(sube) becomes smaller than the binding energy of the electron to the proton in a hydrogen atom, E(subb) = m)sube)e^(4)/2(h-bar)^(2), it becomes energetically favorable for the proton to decay to a hydrogen atom and a positron. Clearly, that's an observable effect providing evidence that some constant of nature has changed. However, the quantity that determines whether the above decay occurs is the ratio E(subb)/2E(sube) = e^(4)/4(h-bar)^(2)c^(2) = alpha^(2)/4. Therefore, one cannot say which constant among e, h-bar, and c is changing, only that the dimensionless alpha is.(3-5)

References (abridged):

1. M. J. Duff, L. B. Okun, G. Veneziano, J. High Energy Phys. 2002(03), 023 (2002).

2. L. B. Okun, Sov. Phys. Usp. 34, 818 (1991)

3. B. Bertoti, L. Iess, P. Tortora, Nature 425, 374 (2003)

4. J. K. Webb et al., Phys. Rev. Lett. 82, 884 (1999); M. T. Murphy et al., Mon. Not. R. Astron. Soc. 327, 1208 (2001) ; J. K. Webb et al., Phys. Rev. Lett. 87, 091301 (2001); M. T. Murphy et al., Mon. Not. R. Astron. Soc. 327, 1223 (2001)

5. M. T. Murphy, J. K. Webb, V. V. Flambaum, Mon. Not. R. Astron. Soc. 345, 609 (2003)

Physics Today http://www.physicstoday.org

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ASTROPHYSICS: ON THE FINE STRUCTURE CONSTANT

The following points are made by L.L. Cowie and A. Songaila (Nature 2004 428:132):

1) The physical constants might not be so constant. If any variation in their values were measured, it could give us profound constraints on a long-sought quantized theory of gravity. So it is no surprise then that a claim(1,2) to have measured a variation over time in the value of the fine-structure constant, alpha, has led to a spate of papers incorporating this result into a wide range of theories. Chand et al(3) have used the same technique of measuring radiation from distant quasars but reach the opposite conclusion -- there is no significant variation in alpha . What should we believe?

2) The fine-structure constant was originally uncovered in studies of the closely spaced spectral lines of atoms such as hydrogen and helium. This "fine structure" reflects the quantization of electron energies within the atom. The constant is defined as the product 2(pi)e^(2)/hc (where e is the charge of the electron, h is Planck's constant and c is the speed of light) but is perhaps more familiar in its numerical form: alpha = 1/137.

3) Curiously enough, the most stringent limits on the variation of alpha come not from laboratory or astronomical measurements but from a natural nuclear reactor in Africa. About 1.8 billion years ago, in what is now the Oklo mine in Gabon, a spontaneous chain reaction began, involving the fission of the uranium isotope U-235. The capture of thermal neutrons from the fission process by other elements can be related to alpha . The best recent analysis of data from Oklo shows that any fractional change in the fine-structure constant (delta-alpha/alpha) has been less than 10^(-7) over nearly two billion years(4).

4) Although less sensitive, cosmological measurements can nevertheless probe much longer periods, encompassing much of the 14-billion-year life of the Universe. Gas in and between galaxies that lie along the line of sight from the Earth to quasars scatters the light from these enormously distant sources. Atoms and molecules in the gas absorb certain wavelengths, imprinting absorption lines in the radiation spectra of these objects. Often the lines of many elements, in many ionization states, might be seen from a particular patch of gas. The wavelengths at which the lines occur depend on the distance of the absorbing gas from the observer, because the radiation becomes "redshifted" to longer wavelengths, owing to the expansion of the Universe, as it travels from its source.

5) If there had been any variation in the fine-structure constant over the billions of years of the light's journey, that would have affected the energy levels in the atoms and would therefore have shifted the wavelengths of the absorption lines. We cannot measure absolute shifts in these wavelengths, because we have no way of independently knowing the distance to the source and hence the redshift that the radiation has undergone. But we can measure relative shifts of the wavelengths from all the absorption lines seen for a particular system. Absorption lines have been detected for quasars so distant that the radiation we see from them corresponds to a time when the Universe was only 6% of its present age(5).

References (abridged):

1. Webb, J. K. et al. Phys. Rev. Lett. 87, 091301 (2001)

2. Murphy, M. T., Webb, J. K. & Flambaum, V. V. Mon. Not. R. Astron. Soc. 345, 609-638 (2003)

3. Chand, H., Srianand, R., Petitjean, P. & Aracil, B. Astron. Astrophys. (in the press); preprint at http://arxiv.org/abs/astro-ph/0402177 (2004)

4. Damour, T. & Dyson, F. Nucl. Phys. B 480, 37-54 (1996)

5. White, R. L., Becker, R. H., Fan, X. & Strauss, M. A. Astron. J. 126, 1-14 (2003)

Nature http://www.nature.com/nature

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GENERAL PHYSICS: ON THE VALUES OF THE FUNDAMENTAL CONSTANTS

Notes by ScienceWeek:

In physics, the term "fundamental constants" (universal constants) refers in general to those constants that do not change throughout the Universe. For example, the charge on an electron, the speed of light in a vacuum, the Planck constant, the gravitational constant, are some of the constants considered as "fundamental constants".

In 1931, the physicist F.K. Richtmyer (d. 1939), author of a textbook well-known to an entire generation of physics students, remarked: "Why should one wish to make measurements with ever increasing precision? Because the whole history of physics proves that a new discovery is quite likely to be found lurking in the next decimal place." The essential basis for this view is that accurate values of the fundamental constants are required for the critical comparison of theory with experiment, and it is only such comparisons that enable our understanding of the physical world to advance. A closely related idea is that by comparing the numerical values of the same fundamental constants obtained from experiments in the different fields of physics, the self-consistency of the basic theories of physics can be tested.

The following points are made by P.J. Mohr and B.N. Taylor (Physics Today March 2001):

1) The authors point out that the values of the fundamental constants are determined by a broad range of experimental measurements and theoretical calculations involving many fields of physics and measurement science (metrology). The best value of even a single constant is likely to be determined by an indirect chain of information based on seemingly unrelated phenomena. For example, the value of the mass of the electron in kilograms is based mainly on the combined information from experiments that involve classical mechanical and electromagnetic measurements, the highest precision optical laser spectroscopy, experiments involving trapped electrons, and condensed matter quantum phenomena, together with condensed matter theory and extensive calculations in quantum electrodynamics.

2) Two additional features of the values of the fundamental constants are not evident from a table of numbers: a) The numbers form a tightly linked set -- very few of the values are independent of the others. In general, a change in a single item of the data on which the constants are based will change many of the values. b) The numbers are based only on the information available at a particular time. Therefore, the recommended values change over time, and the type of information from which the values are obtained changes as well. For example, in the distant past, the charge of the electron was determined by the classic oil-drop experiment, but that method is no longer competitive. Now the electron charge is determined indirectly from other constants.

3) The author points out that the basic approach to finding a self-consistent set of values for the fundamental constants is to identify the critical experiments, determine the theoretical expressions as functions of the fundamental constants that make predictions for the measured quantities, and adjust the value of the constants to achieve the best match between theory and experiment. The idea of making systematic study of potentially relevant experimental and theoretical information in order to produce a set of self-consistent values of the constants dates back to Raymond T. Birge, who published such a study in 1929 as the very first article in what is now the _Reviews of Modern Physics_. The Task Group on Fundamental Constants, established by the Committee on Data for Science and Technology in 1969, has published three sets of recommended values of the fundamental constants, one set in 1973, one set in 1986-1987, and the latest in 1999-2000. The most recent set is termed the "1998 recommended values", because it is based on the information available as of 31 December 1998.

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