Fine structure constant (idea)

Evolution of the Fine Structure Constant

An old idea...

The idea that the constants might evolve over time is an old one, Paul Dirac first took these constants and combined them together to form dimensionless numbers. One example is the magnitude of the ratio of the universe's age and the time it takes light to travel across an electron, is very similar to the magnitude of the electrostatic and gravitational forces present in the hydrogen atom. (10⁴⁰ compared to 10³⁹) As the universe has of course got older, to keep this relationship constant, the values of the fundamental forces would have to change over time.

But Why?

It has long been known that the most correct theory of physics is incomplete, the standard model relies on certain arbitrarily determined constants as inputs, as 'givens'. New formulations of physics such as superstring theory an M-theory do allow mechanisms where these constants can arise from the underlying model.

One problem with these new theories is that they postulate the existence of extra dimensions, that are said to be 'compactified' down to (most likely) about the Planck length, where they have no impact on the visible world we live in. Saying these extra dimensions must exist, but on a scale we can't observe is presumably part of the reason Richard Feynman was heard to refer to superstring theory as nonsense.
Another problem is that is these extra dimensions are not fixed in size, the ratio between the compactified dimensions and our normal 4 space-time ones could cause some of the fundamental constants to change! If this could happen then it might lead to physics that are in contradiction to the universe we observe.
Of course the flip side to this is the problem of the constants not being fixed provides a means by which you can test part of the predictions of superstring and m-theory.

Another reason having the fine-structure constant change over time is that it allows you to postulate the speed of light might not be constant. This would explain the flatness, horizon and monopole problems in cosmology.
Recent work has shown the universe is expanding at an ever faster rate, and there may well be a non-zero cosmological constant after all. (Einstein said his inclusion of the constant to balance the books was his "worst mistake".) There is a class of theories where the speed of light is determined by a scalar field (the force making the cosmos expand, the cosmological constant) that couples to the gravitional effect of pressure. Changes in the speed of light convert the energy density of this field into energy. The basic upshot being when the universe was very young and hot during the radiation epoch, this prevented the scalar field dominating the universe, as the universe expands pressureless matter dominates, variations in c decrease (and therefore alpha becomes fixed and stable) and the scalar field begins to dominate, driving a faster expansion of the universe.

Whether the variation of the fine-structure constant claimed exists or not, putting bounds on the rate of change puts tight constraints on new theories of physics, making it very valuable research.

Measuring the Dimensionless

The fine-structure constant is of course one of those dimensionless numbers, and is actually one that it is possible to measure (or observe) to calculate any time variance of. By examining the natural nuclear reactor in Oklo, Gabon constraints can be put on the rate of change of alpha. This does not reach far enough back in time really though to really pin down any changes, and by the same token current laboratory measurements of alpha have to be so incredibly precise, experimental error is nearly impossible to rule out. Although one such experiment, based on comparing two clocks formed from 2 different atoms (a H-maser and a Hg⁺ maser) over 3 and a half months, gave the result alpha did not change by more than 3.7x10^-14.

It turns out that by looking at the spectra of light from quasars that has passed through intervening dust clouds, the fine-structure constant can be calculated from the atomic absorbance lines in the spectra. By observing quasars of different redshift, the fine-structure constant can be calculated for different periods in the history of the universe. This experiment has been performed for sources 23-87% of the age of the universe by J.K. Webb (et. al.), and the results suggest that &delta ; ;alpha/alpha = -0.72 (+- 0.18)x10^-5 (Over the redshift range 0.5 < z < 3.5, to 4 standard deviation)
A rough schematic of the system is shown below :-

               *     *     *                     __
                   * *  *                        __
###              M+    *  *
###~~~~~~~~~~~~~~~~~~>M+~~~~~~~~~~~~~~>@         ==
###             *   *  *              
                  *      M+                      __

Quasar         Gas Cloud            Detector   Spectra

 

The devil is in the details....

So the way it works is you measure the atomic spectra of a beam of light from a quasar that has been absorbed and re-emitted from a metal ion in an intervening gas cloud, and compare this spectra to a reference one obtained in the lab. Any difference between the two indicates a change of Ν.
The dependence of the wavenumber (w_z) you observe to alpha is given by :-

w_z=w₀+q₁x+q₂y

Where x=( (alpha_z/alpha₀)² - 1 ) and y=( (alpha_z/alpha₀)⁴ - 1 )
alpha₀ is the present day value, and alpha_z is the value at redshift of the absorption.
q₁ and q₂ are terms necessary to correct the relativistic effect of the electrons orbiting a given atom in a given electronic configuration. (Please see my write up in gold for a bit more on this.)

Originally measurements were made by looking at one doublet in the spectra of one species, e.g. MgII or SiIV (the alkali doublet method), but recent work has shown a ten fold increase in precision can be obtained using several species. Magnesium and Iron for instance, where the lighter magnesium provides an "anchor" point for the heavier elements. This "many multiplet" method allows the comparison of any combination of transitions from different species; usually a heavy and a light metal ion. This both increases the amount of data you can get from your spectrums, (which helps the statistics) and it eliminates a potential source of error, as the relativistic corrections can be both positive and negative. If your calculations were not complete for q₁ and q₂, then this helps compensate for errors.
In the Physics review letters paper, 87 091301, 2001 by J. K. Webb et. al. further sources of systematic, experimental error were identified; such as the variation of isotopic abundances, but all could either be discounted, or shown to increase the effect.

This is potentially Nobel prize winning stuff here I feel, if the work can be followed up and independently verified.

Cosmology Matters

Whenever you start messing with the fundamentals of physics, you can expect to see changes in the world around you, often this happens not on just the small scale, but of the largest scale possible, over the entire universe; changing alpha is no exception.
After the universe underwent cosmological inflation and cooled, the energy began to convert to matter, and nucleosynthesis formed the lighter elements. (Up to Lithium I believe; heavy elements need stars or even supernova to form.). Initially this was a super-heated plasma, and opaque to light, it's this "surface" that gives rise to the cosmic background radiation.
Any change in alpha would firstly alter the proportion of elements formed in the primordial post-big bang nucleosynthesis, and secondly affect the time it took the electrons to couple with the nucleons in the plasma, changing the "distance" to this surface.(i.e The redshift of the cosmic microwave background radiation.) Also the ratio of baryons to photons at the last-scattering surface. (Described above). Such effects could be observed on a universal scale.
Looking at the ⁴He abundance over the cosmos, it's been calculated by Kolb, Perry and Walker in 1986 that &delta ; ; alpha/alpha < 9.9x10⁵, at the time of big-bang nucleosynthesis. (Corresponding to a redshift, z ~ 10⁸ - 10⁹).
The effect of a different fine structure constant should give rise to changes to both the amplitude and position of features in the cosmic microwave background radiation, that the next generation of space-based instruments should be able to detect.
Whilst studies of both of these studies have shown that perhaps the fine structure constant could have been smaller in the past, the results are not statistically significant.
One reason observations of the CMBR might not give significant results with respect to varying alpha, is that if dark energy exists, it's density moderated by a scalar "quintessence" field, then bounds on the amount of change of alpha imposed by the observations might have to be widened.

Where are we now

Well, the jury is still out on this one, there is quite simply not enough evidence to prove the fine-structure or any other fundamental constant changes with time.
If the constants can be proven to change however, it could possibly validate new theories of physics, and help confirm other hypothesis such as the existence of dark energy and quintessence; scalar fields involved in a varying cosmological constant.