On the Origin of Natural Constants

Here’s what Hans Peter Good says in the book’s Preface: “Is there a connection between the natural constants or are they all just man-made?  For what reason do these invariant quantities emerge in all experiments? … Is there a mathematical structure behind it?”  Down the page he states, “The existence of the natural constants is probably not a coincidence, but the consequence of internal connections.  The constant themselves have the greatest potential to tell us something about it.”

 

Then Good goes on to describe what he is up to.  “The book begins with the radical interpretation that the mass scale cannot be chosen independent of the time and length scales,” this being due to an idea of the redoubtable (and controversial) quantum physicist, David Bohm, which is really something of a leitmotif for his entire enterprise.  The original thesis, or observation, which Good refers to as “the David Bohm analogy,” entailed “[a comparison] of the formulas of the electromagnetic energy of a cavity with the energy of a harmonic mass oscillator and [the discovery] that the formulas for the energy have in both cases an analogous mathematical structure.”  It is this philosophical point that perhaps sets the entire discussion in motion: “If it is demanded that the formulas for the corresponding quantities are not only formally but numerically equal, it follows that the mass unit can be reduced to the dynamic units of length and time.”  So, right off the bat, we are dealing with the interplay of rather subtle physics themes.  Here’s Good one more time: “It … enables an innovative bridging between gravitation, quantum mechanics, and statistical thermodynamics.” 

 

“The next three chapters concern universal lengths.”  This is ambitious stuff, but Good introduces it in a disarmingly innocuous way: “… fundamental length scales must exist because it is important in physics to know how big things are.  By multiplication with the dimensionless Sommerfeld or fine-structure constant … values were … scaled so that they came close to lengths playing a role in … physics.  The choice of the fine-structure constant may seem arbitrary, but as a scaling factor itself it is almost mandatory, since it is the only dimensionless quantity given by physics itself.”  Good then invokes none other than Werner Heisenberg as an ally.

 

The tone is set:  we are dealing with an exceedingly interesting enterprise which Good himself characterizes with the by-line, “Axiomatic Ideas with References to the Measurable Reality.”  With the above remarks as an indication of what it’s all about, and with the David Bohm analogy (or philosophy) leading the way, we get a glimpse of what’s next as Good continues with his very revealing Preface.  He suggests that the mass of the electron as well as Newton’s constant of universal gravitation are definable in terms of just Planck’s constant and the speed of light.  This is pretty wild stuff: “Possibly, this procedure provides an explanation for the fundamental problem [of] why the electron in the hydrogen atom loses no radiant energy in its ground state despite its motion.”  Manifestly, Good does not shy away from turning his attention to mysteries of physics that reside at the very core of the subject: the foregoing question is what vexed the original pathfinders themselves, including Max Planck, Albert Einstein, and Niels Bohr.  Make no mistake: Good is suggesting something very dramatic and far-reaching.

 

The reader should peruse the book’s table of contents (or the Preface, of course) to get more of an idea of what Good covers, but here, anyway, is a small sampling: Chapter 9 deals with “The classical concept of electrostatic field energy”; Chapter 10 takes on “The radiation formula of Max Planck”; Chapters 11 and 12 take on astronomical themes; and Chapter 16, coinciding with Part II of the book, concerns itself with “an attempt … to gain an alternative perspective [on ‘carefully conducted measurements of thin resistive layers’ whose ‘interpretation is difficult or impossible with established models’] by means of length and energy scales [presented and discussed] in the first part [of the book].”  

 

All this having been said, the book under review is hard to classify: it does not lend itself to comparison with other sources or texts.  It is clear, however, and praiseworthy, that Good is going after such big game with an approach orthogonal to that of the mainstream: “This book is an explicative attempt to see the construction of matter through a different optic than the predominant doctrine.  Although every single observation can lead to a discussion, the combined results of many independent tests are not to be dismissed.  The conjectures are proved by the fact that they often lead to outstanding agreements with results of experiments that can be verified in the literature.”  Here’s a caveat, however: “[m]any things have been worked out intuitively without heavy math by simple merging or by heuristic manipulation with the aid of ‘non-mathematical’ dimensional analysis.”

  

So, Good is listening for the music of the spheres with an ear to a different tuning of the celestial orchestra.  He does not present his meditations as definitive, however: “The book does not claim to have recognized everything in the description of atomic structures, but only shows that there exist amazingly simple quantitative relationships to which seemingly complicated processes can be attributed.  However, many connections are unclear and misunderstood, and a deeper understanding is still needed.”  Ambitious, yes, but also refreshingly modest.  

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Michael Berg is a Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.