Pedagoguery

In physics, certain values are special. The speed of light. The mass of the electron. Planck's constant. All of these values have special meaning in various equations. However, none of our current theories can tell us why they take on these particular values. In addition, scientists assume that they are truly constant – that they do not vary over space and time. But, is that actually the case?

There is one class of theories that can potentially explain why physical constants have the values that they do, and that is string theory. The problem is, in string theory, the values of these constants depends on the specific topography of the “curled up” 7 extra spatial dimensions. String theory allows over 10⁵⁰⁰ different values for the standard constants, and so far, none of the variations of string theory has been able to satisfactorily single out one set of values. More disturbingly, string theory allows for the possibility that the topology of those extra dimensions can change over time, or that they settled into a different topologies at different places in the universe.

Another problem arises when we try to measure these constants. Many of them are fundamentally built into our measurement systems. How can you accurately measure something when your ruler also changes? For example, atoms could be gradually increasing in size, but we would never know, since our rulers would increase in size along with everything else. So, we have to concentrate on constants that are dimensionless, in other words pure numbers. An example would be the ratio of the electron mass to the proton mass. The constant that most scientists working in this area concentrate on is called the fine structure constant: α. The fine structure constant is a combination of the speed of light (c), the charge on the electron (e), Planck's constant (h), and something called the vacuum permittivity (ε₀). It identifies the relativistic and quantum qualities of the electromagnetic interactions between charged particles in a vacuum. It has been accurately measured to be 1/137.03599976. Slight differences in its value would have quite measurable effects. For example, the larger the value of α, the less stable small nuclei are, because the electromagnetic force repelling the protons would overwhelm the strong nuclear force holding the nucleus together. A value a s high as 0.1 would blow apart a carbon nucleus.

Nuclear reactions are also very sensitive to α. A difference of just 4% would mean that the nuclear reactions responsible for the production of carbon in stars would be impossible, and there would be no elements in the universe heavier than helium (except for trace amounts of lithium produced in the big bang).

Using tests like this, we can rule out drastic changes in α. What about smaller changes? Well, in the 1970s, scientists from the French atomic energy commission noticed some strange things about some uranium ore from a mine at Oklo in Gabon. It appeared to contain the waste products of a nuclear fission reaction. As it turns out, about two billion years ago, conditions in that area were just right for a natural nuclear reactor. Scientists in Russia were able to determine that the existence of the natural reactor depended quite sensitively on the precise value of α, and were thus able to determine that α had not changed by more than one part in 10⁸ over the last two billion years.

It was a start, but the universe is a lot older than two billion years. Are there tests that can reach even further back in time? As it turns out, meteorites can provide the answer. The abundance ratios arising from the radioactive decay of different isotopes depends on the precise value of α. By analyzing the decay products, particularly the result of beta decay of rhenium into osmium, researchers were able to constrain any change in α to no more than two parts in one million over the last 4.5 billion years, or the life of the solar system.

To probe any further back requires us to enter the realm of astronomy. The value of α has an effect on the energy levels of electrons in atoms. The precise value of those energy levels determines the spectral lines emitted and absorbed by that atom. Therefore, by careful analysis of spectra from distant objects, we can see if the spectral lines of elements have shifted. The precise pattern of the shift will vary from element to element, meaning that if enough lines are considered, a very clear picture of the potential evolution of α can be obtained.

Well, a couple of different teams have conducted such research. By looking at the spectra of quasars, some of the brightest and most distant objects in the universe, they find absorption lines caused by gas clouds the light has passed through between the quasar and us. Analyzing the redshift of the lines gives us the distance of the gas cloud and us, and a detailed analysis of the lines can give a limit to the potential change of α. The results have been inconclusive. One team found that the variation must be less than 1 part per million over the last 6 to 10 billion years. Another team, using a larger sample, found that α had been increasing by an average of 6 parts per million over the past 6 to 12 billion years.

While the jury is still out on this, the possibility is rather intriguing. If α can vary over the life of the universe, how about other constants? And since α is based on four other physical constants, how are they changing individually (if they are changing at all)? These and many other questions still remain to be answered.

Next issue: Why does matter have mass?