Tuesday, March 28, 2017

Peculiarities of the Fine Structure Constant

Spacing of spectral line shifts depends on the fine structure constant. It's been found that different spectra are obtained in the lab vs. obtained from distant quasars with light passing through gas clouds.

In the table presented in my March 18th post, the fine structure constant is shown on the last line with a value of  a   =  1/ 137.035999139 or approximately, 1/ 137.   Note the value is the same irrespective of the system of measurement because this constant is a pure number - there ate no units attached- unlike the other constants I covered.  Indeed,  a    is an amalgamation of several other constants including the electron, the speed of light and the Planck constant. We can write, for example,

 a   =  1/ 4p e    { e2 / ħ c }   where:     ħ  =   h/ 2p

Physicists keep track of the fine structure constant by using quasars. Also called "QSOs" for quasi -stellar objects, these are active galactic nuclei of extremely high luminosity powered by supermassive black holes. As shown in the diagram above, on its way toward Earth the QSO's light passes through gas clouds which absorb light of particular frequencies producing gaps - also called absorption lines - in the otherwise continuous spectrum.  The typical profile of such an absorption line is shown below, this one centered at a wavelength of 5889.95 angstroms:

As can be seen from the absorption line profile there is a variation in the line "darkness"  with the maximal degree at line center where the absorption coefficient is greatest. This then falls off in what we call the "line wings".   (Note here that  D uD  is the Doppler half-width of the line.)  The point is that the locations of these absorption lines depend on the fine structure constant. Thus, variations in the spacing of the lines in space or time might indicate the value of  a    has changed.

Is there evidence for such variations? In 2011, in a paper appearing in Physical Review Letters, John Webb of the University of New South Wales and colleagues reported the fine structure constant increases in one direction in the sky and decreases in the opposite direction. Almost if some special axis was running through the universe. Of course, no physicist would be content with such "specialness" or uniqueness. By the cosmological principle such behavior of a   ought not depend on directions. (And in this regard even Webb counts himself as a skeptic, as he should).

In fact, a compelling alternative explanation has been put forward by Michael Murphy of Swinburne University of Technology in Melbourne, Australia.  He suggests the logical take that telescope calibration issues are to blame for the apparently changing value of a.   Using measurements free of calibration issues, the value of  stays put, as Murphy et al reported in the Monthly Notices of the Royal Astronomical Society.   See also:


It should be noted, however, that Murphy et al's findings do not rule out actual variations in  with respect to the part of the sky observed by Webb in 2011.

Here's an interesting side thought to ponder: What if, instead of a   = 1/137 (approximately) it had been 1/ 130? Say during the birth of the universe. Then it seems clear the cosmos would have been set on a path to being barren, empty.

As an interesting historical aside, Sir Arthur Eddington arrived at a value of a   = 1/136 by taking the ratio of two "naturally occurring units of action". ('Great Ideas and Theories of Modern Cosmology', 1961, p. 178).  He chose one unit of action as the quantum for radiation, or  ħ  =   h/ 2p  and the second as the action for elementary particles, or e2 / c.   Then, taking:

{e2 / c}/  ħ  =  1/ 136

Curiously, Eddington wasn't bothered by the divergence (from a   = 1/137 )  , and just introduced a "fudge factor". This "was for obscure reasons that are difficult to understand". Perhaps, in the end, he was simply mesmerized by a kind of 'numerology' . Eddington also came up with a quadratic equation: 10x2  +    136x +  1 = 0,  linking his  fine structure result with the mass ratio of the proton to electron, i.e. in terms of the ratio of its two roots. From there, Eddington parlayed his fine structure and other pure number results into a kind of "universal theory" linking every aspect of the cosmos in a kind of romantic quest. Much like Kepler before him, with his "harmonic geometry"  in which the five Pythagorean regular polyhedra dictate the structure of the universe and reflect God's plan through geometry.

We shouldn't be too hard on Sir Arthur  (or Johannes Kepler) as he wasn't the first scientist to be taken in by numerical relationships, "harmonic" ratios, and "precision" theoretics. Nor will he likely be the last.  Even today we behold "scientists" seriously working on the so-called "anthropic principle". This  nonsense is based on the fallacy (due to a misunderstanding of physics units, dimensions) that there is an implicit "fine tuning". This in turn depends on a putative "fine precision" - but that is almost always based on the choice of units.

Thus, saying stupidity like "if the neutrino mass were 1 part in 10 35  smaller there'd be no expansion of the universe" is like saying that if Lebron James were 1 part in 10 16  shorter he'd not have been a great basketball player! 

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