Posted on February 26, 2021
The Meaning Of A Precise Dimen
sionless Physical Constant
The development of 20th Century physics was intimately interconnected with the ramifications of what constitutes a physical constant or fundamental parameter. Which was first immortalized in Einstein’s special relativity as an invariant constant c = the speed of light. For the best Maths Tutor In Ireland company, call Ace Solution Books. As velocity measures length L divided by time T, c represents a metric or ‘dimensional constant,’ as is mass M or any combination of these quantities. Yet when the SI metric system was formally adopted (firmly …
fine-structure,quark masses,dimensionless physical constants,precision predictions
The development of 20th Century physics was intimately interconnected with the ramifications of what constitutes a physical constant or fundamental parameter. Which was first immortalized in Einstein’s special relativity as an invariant constant c = the speed of light. As velocity measures length L divided by time T, c represents a metric or ‘dimensional constant,’ as is mass M or any combination of these quantities. Yet when the SI metric system was formally adopted (firmly replacing the CGS system), c had acquired new meaning as a defined constant equal to a precise integer 299,792,458 represented in meters per second. However, as explained by Wikipedia (browse “physical constant”), the distinction between a ‘pure’ or ‘dimensionless number’ in mathematics and physics is that the speed of light had to be measured since no theory can predict it; for even then the value would have to be empirically confirmed. .
And though hardly an integer nor yet a ‘defined parameter’ by NIST, a much ‘purer’ number as a dimensionless fundamental physical constant is distinctly embodied by the inverse of the electromagnetic coupling constant ‘alpha’ or “fine-structure (fs-) number” a ~ 137.036. Which essentially equals Planck’s constant h multiplied by c (times 4p times the vacuum permittivity) divided by the square of the electric charge e, though all metric dimensional terms are canceled in this ratio. While even constants such as a fundamental particle’s mass can be expressed as a dimensionless relationship, say, to the ‘Planck scale’ or other mass, the fine structure is uniquely a pure number. Which led to some deep pondering from its inception, culminating in what was chosen as the number one quandary facing physics at the ‘Strings 2000’ conference. As articulated by David Gross this “Millennium Question” is:
“Are all the (measurable) dimensionless parameters that characterize the physical universe calculable in principle, or are some merely determined by historical or quantum mechanical accident and incalculable.”
My first impression upon reading this in a morning paper was utter amazement a numerological issue of invariance merited such distinction by eminent modern authorities. For I’d been obsessed with the fine-structure number in the context of my colleague A. J. Meyer’s model for a number of years but had come to accept it’s experimental determination in practice, pondering the dimensionless issue periodically to no avail. Gross’s question then was the catalyst from my complacency; recognizing a unique position as the only one who could provide an answer in the context of Meyer’s main fundamental parameter. But even then my pretentious instincts led to two months of inane intellectual posturing until one day sanely repeating a simple procedure explored a few years earlier. I merely looked, and the solution and more struck with full heuristic force.
For the fine-structure ratio effectively quantizes (by h-bar) electric charge (of e2) as a coupled to light, in the same sense as an integer like 241 is discretely quantized compared to the ‘fractional continuum’ between it and 240 or 242. As we aren’t talking directly about the integer 137 at all, the result definitively answers Gross’s question. For it follows that the fs-number exactly equals 137.0359996502301…, which here is given to 15, but is calculable to any, number of decimal places.
By comparison, given the experimental uncertainty in h and e, the NIST evaluation varies up or down around the mid (6) of ‘965’ in the invariant sequence defined above. It follows that one can completely and consistently categorically state that this is the exact fine-structure number. For this evaluation is not only independent of any empirical measure of h-bar or e, no matter how ‘precisely’ metric measure attained, it is still infinitely short of ‘literal exactitude!’ Yet once one recognizes this distinction and accepts the exactitude as a pure defined number and literal constant, it’s then possible to use it as a tool that can potentially help hone the relative precision in the respective dimensional constants – not to mention more immediate uses in defining exact dimensionless relations (in equations) between, and precise values of, a number of other fundamental parameters.
Indeed, after facing the embarrassing fact that I’d lost my senses and never entertained employing the empirical fs-constant for the physical scaling of masses within AJ’s model for 5+ years; it took a mere two weeks to derive all six quark masses, which largely utilizes various fine-structured relations. Besides a few other crucial fundamental mass particles and theoretic solutions that burst forth within a couple of weeks of answering Gross’s question, that’s seven or more exact dimensionless or very precise mass constants.
Compare this feat with the available knowledge seven years later concerning the definition, number and values of ‘dimensionless physical constants.’ Basically one will find a chain of input from the present NIST or Particle Data Group’s experimental values that end up for free, easy reference on various websites like marvelous Wikipedia, which goes on to list 26 fundamental constants borrowed from a mathematical theorist, John Baez, with no mention of their largely undetermined experimental values.
Is unresolved theoretical speculation and experimental plodding all one can ‘realistically’ expect? I suppose it would as long as a status quo promotes one’s job aspirations. But wouldn’t it be nice if someone also cared about a complete system of a confirmed fundamental physics backed by an exacting body of data, today, while one’s still alive to enjoy the marvel?