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The Planck Length: Ubiquity and Meaning (Article)

In the years 1899, and 1900, a German physicist by the name of Max Planck, with the use of two variables, *h* and *v*, felled a problem, that began the domino show that would come to be known as the development of quantum theory.

I. The Man Behind The Mechanics.

Max Karl Ernst Ludwig Planck, born in 1858, Kiel Germany, was the descendant of a long line of public servants and scholars, professors of Law and Divinity at Göttingen, an ancestry which indicates traits which are not at all absent from his character as a scientist, but rather ingrained deeply within it. These traits expressed themselves in the nature of his research, and very well may have enabled him to make the discoveries he did, with the traits being chiefly, dedication, steadfastness, belief in the beautiful simplicity of the natural world, and a burning desire to adhere to the logical and orderly.

> "What led me to my science and from my youth filled me with enthusiasm, is the fact...that our laws of thinking conform with the lawfulness in the passage of impressions which we receive from the outer world, thus making it possible for man to gain information about that lawfulness by mere thinking. In this it is of the highest significance that the outer world represents some­ thing independent of us and absolute...and the search for the laws which govern this absolute has appeared to me as the most fascinating work of a lifetime." (Planck, 1948)

Surprisingly enough, despite his early introduction to the mathematical sciences via Hermann MĂĽller, at age 9, in the Maximilian Gymnasium, he was not necessarily predestined to go into physics. Considering his lineage, his father being a Professor of Law in his hometown, and his having deep interest and curiosity about language, and musical composition, he very well could have taken a number of different paths. Despite this, he dedicated his life to the physical sciences, though he maintained a musical streak, possessing an acknowledgeable skill as a pianist, a hobby he continued throughout the entirety of his life.

He received his doctorate in physics at the age of 21, in 1879, from the University of Munich, delivering a thesis largely focused on thermodynamics, the deep and rigorous study of which, combined with a staunch but respectful intellectual rivalry with Ludwig Boltzmann over its nature, would lead him to the discovery that would eventually send reverberations throughout the deepest foundations of physics: *the quantum of action*. This discovery, and the endless toil it required would, a little under two decades later, reward him with the greatest honor in the field of physics, the Nobel Prize.

It is a well known, stunning, and absurdly ironic fact that he was advised by his professor at Munich, Philipp von Jolly, to pursue a study other than physics, telling him "*In this field, almost everything is already discovered, and all that remains is to fill a few holes*."

One could say that Ph. von Jolly was correct, with the caveat that of the few remaining "holes" in physics, one of them, the filling of which Max Planck would be responsible for initiating, was absolutely several orders of magnitude more vast, deep, and wide than either of them could have fathomed.

In many ways, while reaching the apogee of achievement in his working life, his personal life was be beset with deep misfortune, contiguously buffeted by the gale-force winds of tragedy, losing his wife, and three children in a decades time. Perhaps experiencing a respite from this after the First World War ended, the Second World War would bring such vicissitudes back to the forefront of his life, with him losing his home in an ally air raid. Furthermore, having been adamantly against the Nazi regime in both public in private (Goebbels in fact, mentioned him in his Diary, finding it "...a great mistake that we failed to win science over to support the new state. That men such as Planck are reserved...in their attitude towards us...is irremediable."), he suffered greatly at the hands of it, with his last living child of his first marriage, Erwin, being sentenced to execution by hanging as a result of the direct order of Hitler, for being involved in a plot for his assassination.

While it is said that this last tragedy sapped his will to live, he was already well into his twilight years, and it seems also that he found some modicum of peace, through his unwavering and thoroughly ingrained religious sense, having said to a friend Anton Kippenberg a month after the loss of his son:

> "If there is consolation anywhere it is in the Eternal, and I consider it a grace of Heaven that belief in the Eternal has been rooted deeply in me since childhood. God protect and strengthen you for everything that still may come before this insanity in which we are forced to live reaches its end." (Planck, 1945)

His religiosity, while seeming counterintuitive to the nature of his work, fueled his perspective greatly, such that he in fact felt as if the two were not only complementary, but necessary in tandem in order for man to operate at his highest level:

> “The one does not exclude the other; rather they are complementary and mutually interacting. Man needs science as a tool of perception; he needs religion as a guide to action.” (Planck, as cited in Eggenstein 1984, Part I; see “Materialistic Science on the Wrong Track)

While not the most prolific teacher, Planck did leave a legacy in terms of doctoral students, the most well recognized being Nobel laureate Max von Laue, and Lise Meitner, who spearheaded the discovery of X-ray diffraction, and nuclear fission, respectively. Of course, were it not for the generally misogynistic attitude of the day, and cowardice on the part of her collaborator Otto Hahn, Lise Meitner, referred to by Einstein as the "German Marie Curie:", would be the second Nobel Laureate who studied under and attended lectures by Planck.

While one may see, when looking at pictures of Planck, something resembling a caricature of the by the book scientist, unconcerned with matters outside of the domain which his field is capable of assessing, or falsifying, however, Planck was more than willing to accept and contemplate ideas that scientists have more recently been known to eschew as unworthy of consideration. In his opinions one can find hints of panpsychism, with him stating rather openly "I regard consciousness as fundamental. Everything...that we regard as existing, postulates consciousness." (Planck, as cited in Purucker, 1940, p. 206, The Esoteric Tradition), belief in life after death, which he refers to as “another world, exalted above ours, where we can and will take refuge at any time" (Planck to Neuberg, 1946).In his later years, he turned a large portion of his focus towards philosophical endeavors, interweaving strands from several schools of thought in order to explicate his perspective on the tenuous, yet symbiotic relationship between physics, religion, and absolute truth, considering the the former two necessary tools in the never-ending quest for the latter. For Planck, the scientific endeavor was necessarily imbued with the same faith required for religious belief, for him, faith was "an unpretentious but essential principle", a notable echo of Maxwell before him, also a devout Christian who spearheaded a new era of Physics. Faith however, was not the only prerequisite extended from religious tradition to the scientific, as he placed deep importance on the moral imperative of truthfulness, as the premiere quality of a scientist, a quality which he possessed in spades, which, among others, as before mentioned, seem to be key in his path to unearthing the astounding revelation about physical reality that he's known for.

> "Under no circumstances can there be in this domain the slightest moral compromise, the slightest moral justification for the smallest deviation." (Planck. Scientific autobiography, p. 79, 1949)

II. Planck's Units & Constant

The road to Planck's constant begins during his study at the University of Munich, where, by way of the writings of Helmholtz, Kirchhoff and Clausius on thermodynamics, he found himself being called by his fascination, particularly with its first law: the conservation of energy.

The conservation law, as put forth by Émilie du Châtelet, simply states that energy cannot be created or destroyed, but rather only transmuted between different forms, such as kinetic, chemical or potential energy, and that for an isolated system, the sum of the energy released from the system, and still present at the end of some process, can be no greater, or less than was existent in the system at the beginning of the process. This law can be rigorously proved via, and seen as a result of Noether's theorem, which shows that for any conservation law, there is a symmetry, and vice versa. In the case of the conservation of energy, the symmetry is observed under time translation, or the time that has passed from the beginning, to the end of the aforementioned process undergone by some isolated system (or the section of time during which the process is observed).

III. The Planck Length

IV. Implications for Physics and Ubiquity.

“It would seem that the shortest scale, in fact, has the longest reach.”