Quality of Life:    

The Quantum Myth of Sisyphus: Change and Sustainability

Nature adapts to meet new challenges in sustainability by making use of chance on every scale, from the broadest appearance of the entire universe down to the tiniest sub-atomic interaction.  


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The Quantum Myth of Sisyphus: Chance and Sustainability

For thousands of years human beings have wondered, what is life and the surrounding universe all about? Humans have a finite lifetime, infinitesimal compared with the present age of the universe, which appeared 13.7 billion years ago. They just look around in wonder and for most of them, what they see and feel goes beyond their comprehension. What is it all about; what is our place in the universe; what are we doing here; what is the purpose, if any, of existence? These are the most fundamental questions that we need to answer, one way or another.

It is rather amazing and unique in the history of mankind that a bunch of Greeks more than 2600 years ago formulated the “problem” and tried at the same time to solve it. The natural philosophers in Asia Minor: Thales of Miletus, Pythagoras of Samos, Heraclitus of Ephesus, and several others a bit later understood that there are physical laws and universal forces of nature which are responsible for what is “moving” the world, or even better, the universe. That was the first time ever that human beings got rid of myths and nonsensical religious beliefs and moved towards a new era of logic and clear thinking. Let me quote Heraclitus on two issues that prove what great thinkers these philosophers were.On the issue of destiny, Heraclitus said: “A man’s character is his fate”; [1] in other words he killed any notion of a deus ex machina that drives our future. He correctly pointed out that we are responsible for our actions as well as our future.On the creation of the universe Heraclitus said: “The world ( κόσμος ) was made neither by God nor by any man …, it is just there.” [2] This is the central conclusion of today’s cosmogony/cosmology, based on experimental, reproducible, verified facts, as we will see below. Furthermore, if this fact-based conclusion is not the cornerstone of our search for the quality of life, frankly, I don’t know what is.

Clearly, the post-natural philosophers, such as Socrates, Plato, Aristotle, and others, pushed the envelope further—although not always to my taste—essentially creating, out of the blue, what we call today western civilization. It is also quite remarkable that the classical Greek knowledge survived through at least two thousand years of dark ages, despite all kinds of orchestrated efforts from different quarters to send it to oblivion. We are in debt to these great minds, and we have a responsibility to continue in their footsteps and not let their visions be blurred and their dreams be lost. We also need to appreciate the scientific advances in knowledge, made possible only recently by advanced technologies and theory, that give us new perspectives on the universe.

In today’s world, sustainability has been a keyword, sometimes overused, and its connection to our quality of life is rather obvious. Of course, different people, or groups of people, have their own interpretations of “quality of life.” Is it solely to live our finite (~80–100 year) lives healthy and prosperous, using today’s available advanced techno-means, and then die? This is one view of what quality of life means, though for most people it is the only point of view. Or on the other hand, do we also need to make an effort to comprehend our world, in a more advanced way, so that we gain an inner peace by somehow feeling more “connected” to the wholeness of the universe? For readers whose quest is fulfilled by the first point of view, I have nothing more to add. For those whose thinking is characterized by the second point of view, I may have something to offer to help them in their cosmic adventures.

The main thrust of my contribution here, as the title suggests, is that nature makes use of chance—i.e. unpredictable, unexpected random behaviours—on every scale, from the “appearance” of the whole universe down to gene mutations for (self-)adaptability and sustainability. This is not ancilla dei, the ‘handmaid of God.’ It is a result of the fundamental physical laws that determine our universe. In the following pages I discuss the evolution of the universe from the beginning—the real beginning. In order to really understand what is going on in the universe, we need to appreciate the physical laws that govern it.

We know today, based on innumerable experimental results, that the fundamental laws of the universe are based upon the quantum uncertainty principle, formulated in 1927 by the great physicist and Nobel Prize laureate Werner Heisenberg. The uncertainty principle is the epitome, “ la crème de la crème, ” of the quantum theory that describes the microcosmos. Quantum logic runs counter to the “black and white” Aristotelian logic, providing all the intermediate possibilities (e.g. grey). The classical meaning of “trajectory” does not exist in the quantum (micro) world, because the uncertainty principle entails that the position (X) and the momentum (P) of a particle cannot be measured simultaneously:
where ħ = Planck’s constant.[3] (Here and later, ΔX and ΔP, and in general ΔA, indicates the uncertainty in the measurement of the quantity A.) Thus the two initial conditions (X 0 and P 0 ) needed to determine the motion, and thus the trajectory, are unreachable, and instead of a trajectory we get, at best, a “fuzzy” region where it is highly probable we will find the particle. In other words, the certainty of the classic trajectory, Laplace’s hyperon, is replaced by a probability distribution (|Ψ| 2 ), where Ψ(x) is the complex wave function that characterizes the particle. It is now established that all particles in the universe obey characteristic wave equations (Schrödinger, Dirac, Klein-Gordon, etc.). Of course, such a description highlights the dual nature of substance: particle sive wave . It should be emphasized that Heisenberg’s uncertainty principle is an elegant formulation of a fundamental law of nature.

The meaning of all this is that the microcosmos (molecules, atoms, nuclei, protons, quarks, leptons, etc.) obey fundamental rules based on the idea of probability. Thus randomness and chance are deeply rooted in the most fundamental physical laws! Furthermore, nature has chosen to quantize not only position and momentum but also energy and time: (ΔΕ ·Δt≥ħ); in other words, it is possible for some time interval Δt to get variations in the energy content (ΔE), as long as the above uncertainty principle is satisfied. Even more amazing, nature has applied the quantization rule to the wave function itself Ψ(x,t) and its time derivatives
[[See Figure 1, Equation 1]]
[[See Figure 2, Equation 2]
]clearly implying something really incredible, at first sight: that there is really no vacuum, in its Platonic meaning. The real or quantum vacuum is full of “virtual particles” that appear and disappear all the time, since the beginning. But why? Because of this “second quantization,” or the wave function and its time-derivative uncertainty principle. Imagine at one instant that Ψ(x,t) = 0. At this instant
[[See Figure 3, Equation 3]]
has to be “infinite,” so that the product must be ≥ħ. But because
[[See Figure 4, Equation 4]
] is not zero, Ψ(x,t) will not be zero, and thus we will naturally have a quantum fluctuation of the particle under consideration. In other words, the particle will appear and disappear continuously, ad nauseam, a micro-Sisyphean task, or closely related, a micro-Tantalean task . If Albert Camus had only known (more on this later)! It is of great importance to stress here that these quantum fluctuations are observable, and do produce measurable quantities. It is a real triumph of the human mind that in Feynman’s quantum electrodynamics—i.e. the quantum version of classical electromagnetism—the agreement between theory and experiment is better than one part in a billion! Incidentally, both the words electricity and magnetism go back to Thales of Miletus, around 600 BC, illustrating that fundamental knowledge is an evolutionary process, also ruled by uncertainties in time and space.

With this brief introduction, let us now go back to the origin of time, the real beginning of everything. We know that we live in an expanding universe. Our universe is so vast today because it has been expanding for 13.7 billion years. If we go back in time, extremely close to the origin, the universe would have been even smaller, say, than an atom, and the quantum laws would be at work. At this early time, we can discuss without apology the wave function of the universe Ψ UNIV , which must also be subject to the uncertainty principle. Thus quantum-fluctuating universes occurred all the time, not unlike the multiverse point of view of modern string and M-theories. The “conventional” point of view, then, is that one of those quantum fluctuations made it, and survived a very rapid early expansion, the so-called inflationary period, and voilà, our observable universe was born. What I have done here is to unveil what we usually refer to as “the universe starting from a Big Bang.” We should pay attention to the fact that the origin of the universe, as described in the beginning by Ψ UNIV , is probabilistic, and thus random and due to chance. There is no raison d’être attached to it; neither does it have any higher meaning. We try, a posteriori, to give it some (necessarily subjective) meaning, but it has to be Baccarat clear that there is no τέλος (‘purpose’) in the universe. This is Albert Camus’ philosophy of the absurd on a grand scale.

The above view of the universe is not just theoretical speculation; it is also based on experimentally observed facts that are worth mentioning, in order to avoid the pitfall of scientific dogmatism—which is as bad as any other dogmatism, εξ αποκαλύψεως (‘revealed’) or not. Grosso modo, the majority of these facts are rather recent, though they extend all the way back to Edwin Hubble in the 1920s. During the last twenty years, an amazing amount of cosmological information has enabled us to trace the history of the universe all the way to its origin (see Figure 5).

Most of the information has poured in from the Wilkinson Microwave Anisotropy Probe, or WMAP , a NASA satellite that has detected, in nitty-gritty detail, the cosmic background radiation all the way back to 380,000 years after the start of the Big Bang. These detailed studies indicate that the scenario I described above seems to be at work here as well. More specifically, the cosmic background temperature anisotropies expected since the late 70s and observed in the 2000s are in spectacular agreement both in shape and magnitude with the inflationary universe. It is exactly these minute (~10 5 ) fluctuations in temperature
[[See Figure 6, Equation 5]]
or equivalently energy density (δρ/ρ), let loose around 380,000 years after the Big Bang got a chance to grow, that created all the large-scale structures that exist in our universe. In other words, random energy-density fluctuations at cosmic scales built up the stars, the galaxies, and so on. It is the attractive nature of the gravitational force that is at work here, at cosmic scales and masses that provide for the sustainability of these systems, for at least billions of years. Isn’t this a wonderful example of chance and sustainability at the roots of the large-scale structures of the universe, of which our local terrestrial environment is κόκκος άμμου (‘a speck of sand’)? These conclusions are all based on accepted fundamental laws of science.

But the story gets even more interesting. One may naturally ask “what orders the energy-density fluctuations at cosmic scales?” Here the answer has far-reaching consequences. These are quantum energy-density fluctuations. Oh, yes! Those quantum fluctuations again, that have been frozen in amplitude at
[[See Figure 7, Equation 6]]
that is a calculated and naturally expected number! They were stretched from quantum gravitational scales (~10 33 cm) to cosmic scales during the initial exponential expanding phase, the so-called inflationary phase. In plain language, the seeds of the large-scale structures observed in the universe were planted by random quantum fluctuations of certain specific fields or particles at the beginning, which I have called inflatons, which were then translated into quantum energy-density fluctuations that resulted in a tremendous increase in their wavelength, while maintaining their amplitude, during the inflationary phase. So here we have another case of chance and sustainability: the random quantum inflaton field fluctuations—“chance”—and at the same time the preservation (“freezing”) of their amplitude (~10 5 , very essential for galaxy formation)— “sustainability”! Nature is trying to tell us something, rather loudly and explicitly, about the roles of chance and sustainability.

But it gets even better. It is an experimental fact, discovered during the last ten years, that we live in a “flat” universe, i.e. at every given instant the universe looks Euclidean. This lack of cosmic space curvature implies that the “forces” that might curve the universe cancel each other. In other words, the attractive gravitational force is counterbalanced by the expansive thrust, so that at every given moment the total energy of the universe is zero. Yes, a big zero (0)! It couldn’t be otherwise, if the picture I have just painted makes any physical sense. Otherwise, where does the net positive (or negative) energy come from?

To recapitulate: We are a redistribution and reshuffling of the ( quantum ) nothingness . Actually, this cosmic description of our universe avoids the pitfall of questions about the beginning of the universe, what was before, and the like. It is worth stressing here that the reality of Nothingness was mentioned by Democritus twenty-five centuries ago. As Samuel Beckett, one of the creators of the Theatre of the Absurd, wrote in his novel Murphy : “…the Nothing, than which in the guffaw of the Abderite naught is more real.” This phrase refers of course to “the laughing philosopher” Democritus of Abdera, who is quoted as having said “Nothing is more real than nothing,” a very condensed form of his philosophy of atomism. Amazingly enough, in this Democritean materialistic point of view, the world consists of atoms, and between them is void or nothing. Both atoms and the void, or nothing, exist; therefore they are real. This is a very advanced point of view, indeed. Today, Democritus’ “atoms” are perhaps replaced by superstrings,that emerge from the quantum vacuum.

The quantum vacuum, by its very nature, is always there, and the universe emerged as a quantum fluctuation. This is all that we can say. So questions like who, or when, or what for, are moot—it is all in the quantum . I will dare to say that even if we didn’t have a clue about quantum physics and used only plain logic, which should include the fact that there is a scientific explanation of the universe, we would have discovered it. Concerning the nature of physical laws, they are always, like the quantum vacuum, sub specie aeternitatis ‘under the aspect of eternity’. Spinoza’s Deus sive natura becomes natura sive leges naturalis . This is apparent in the deep connection that exists between aesthetics , expressed in the exact sciences as symmetries ( συν - μετρο- ), and the precise form of the physical laws. General relativity and gauge theories, the total sum of our physical laws as we know them today, are the result of grand symmetries, equivalent principle and gauge symmetry correspondingly. The first one is based upon the fact that “free fall” is independent of the mass of the body—confirmed in Galileo’s experiments from the Pisa tower—while the second refers to the fact that our fundamental interactions should be locally invariant in space-time transformations. Applying these “big principles,” the form of the physical laws follows directly. Clearly, nature teaches us something very profound about the rather ubiquitous involvement of aesthetics in the natural laws! We have found our own ways to express them, but even though our description of nature is admittedly incomplete at any given moment, we have finally decoded it. Let’s hear once more what Heraclitus has to say precisely about the origin of the universe:
κόσμον τόνδε, τὸν αὐτὸν ἁπάντων, οὔτε τις θεῶν οὔτε ἀνθρώπων ἐποίησεν, ἀλλ’ ἦν ἀεὶ καὶ ἔστιν καὶ ἔσται πῦρ ἀείζωον, ἁπτόμενον μέτρα καὶ ἀποσβεννύμενον μέτρα.
Heraclitus Fragments 30 n.4
This world, the same for all, neither any of the gods nor any man has made, but it always was, and is, and shall be, an ever living fire, kindled in due measure, and in due measure extinguished.[5]
Ἡ. φησι τοῖς ἐγρηγορόσιν ἕνα καὶ κοινὸν κόσμον εἶναι, τῶν δὲ κοιμωμένων ἕκαστον εἰς ἴδιον ἀποστρέφεσθαι.
Heraclitus Fragments 89 n.6
Heraclitus says: To those who are awake, there is one world in common, but of those who are asleep, each is withdrawn to a private world of his own.[7]
All of these postulates were written at the end of the sixth and the beginning of the fifth century BC. No further comments are necessary.

Nature’s game of chance and sustainability extends beyond the large cosmic structures in an island universe, down to the scale of living creatures. The very structure and function of the agent of heredity, the DNA macromolecule, also makes use of quantum probabilities. It is the so-called H(ydrogen)-bond, plainly quantum in nature, that is responsible for the “attraction” between a(denine) and t(hynine) and c(ytosine) and g(uanine), i.e. the fundamental basis, through the formation of the double-helix construction, of heredity. Here chance and sustainability act in multiple ways. It is chance that determines the sequence of A, T, C, and G, for every triplet (a random combination of A, T, C, and G) that determines the resulting amino acid that builds up the proteins, etc, etc. While the H-bonds are rather resilient to an aggressive environment—e.g. high temperatures cannot destroy them—nevertheless, during the copying of one helix to another quantum “errors,” and thus mutations, are possible. These mutations may be good for a species, or they may destroy it. Thus, we can see that the whole rich genetic space is a result of chance and sustainability. At the most fundamental quantum level we discover an explanation for a central Darwinian principle: evolution by natural selection, expressed more generally as “survival of the fittest.” We see that chance and necessity drive the evolution of living species, from their first steps as single-celled structures (e.g. bacteria) all the way to Homo sapiens.

Nature exhibits several examples of links between chance, fitness, and sustainability. At the molecular level, the evolution of proteins has been quite conservative, perhaps indicating that life has a very limited biochemical domain of fitness on Earth. There are respected researchers who question why homologous protein sequences have not evolved and diverged more quickly. This example of limited evolution may just be a matter of time and the robustness of the protein fitness space within living systems.

Macrobiological systems on Earth exhibit increased diversity and complexity on evolutionary time scales, but also seem conservative in the relatively limited number of taxa. Again, these questions may be best resolved with better understanding of the fitness space, which changes both rapidly (e.g. sudden extinctions following asteroid impacts) and gradually (e.g. degradation of a supporting ecosystem due to climate change).

Where did sapient thinking and reasoning come from? Today we often see the human brain characterized as a mind machine. In other words, the brain structure, with its daedalic hundred billion interconnecting neurons, the neural network, provides a framework that is responsible for the hierarchical emergence of the mental world. This central thesis of neuroscience, based upon experimental facts, was a remarkable discovery. Democritus wrote about twenty-five centuries ago “nothing goes to the mind that has not gone through the senses.” The first atomist also got it right on the great matter-versus-mind problem. Dualism and the like are now completely eclipsed, gone from today’s scientific lexicon. Today the scientific challenge is to try to understand the specific structures and mechanisms in the brain that are responsible for all our mental capacity, memory, feelings, and emotions, and eventually for the sum total of human thought that is called consciousness !

Neuroscience is still very new, and there is a long way to go before we reach satisfactory, objective, universally accepted conclusions about the fundamental question: how do we think what we think? Nevertheless, the basic framework is in place, and we have to fill in all the details. It is like physics at the beginning of the last century, when it was clear that the atom was a reality, a basic material subunit, but it took several decades to come to the crystal-clear view that quantum physics has provided today. Actually, atoms may be a good analogy for the neurons of our brain, in the following sense: we progressed a long way, even as far as Mendeleev’s periodic table, by just assuming the existence of atoms, but science dramatically accelerated when we discovered the subatomic structures—electrons, protons, and neutrons. The periodic table was explained once we understood that chemistry was nothing else but applied quantum atomic physics, involving the exchange of the valence electrons and much more. Case closed!

Neuroscience is advancing along similar lines. Initial understanding has gone a very long way by using neurons as the basic subunits in the brain and the corresponding neural networks, the synapses and the electrochemical potentials that are responsible for signal propagation. Understanding will get even better with a closer look at individual neurons and their substructures. As we will find out, even though the present interpretation of certain results is not universally accepted, once more, chance and sustainability will be at work here, and it will likely have a quantum origin.

Indeed, there are structures in the neuron—the microtubules (MTs), hollow cylinders with an internal radius of 14mm and lengths up to a few millimeters—that play extremely important multifunctional roles in neurophysiology. It may also be that MTs play an equally important role in a different way than the currently accepted conventional understanding. The basic units of MTs are the tubulins, which are characterized by a rather large electric dipole moment (EDM)—about 1740 daltons—that oscillates between two states. Each tubulin unit is a textbook case of a quantum two-state system, and eventually the tremendous number of these dimers becomes locked in specific states, producing a very specific pattern. It has been suggested that we may have here the elements of a bio-quantum computer (BQC) with far-reaching consequences. In this case, we are talking about a bio-qubit , where the standard dyadic system (0,1) is replaced by the qubit that takes values on the continuous segment [0,1] . The power of such a BQC is very difficult to overestimate. Amazingly enough, the structure of MTs is such that they are free to oscillate between different states, but at the same time they are sustainable. Thus, while the end result may be deeply rooted in the probabilistic nature of the quantum world, the whole system is very resilient. Chance and sustainability at work again! It will be really mind-boggling if nature has chosen such a way to give us “free will,” in the sense that similar initial conditions may lead to very different results, owing to the probabilistic nature of quantum physics. There is no better metaphor for this than in Albert Camus’ masterpiece, the fictional version of absurdism (paralogue) L’ Etranger ( The Stranger, 1942), where Meursault, the main character of the book, ponders over pulling or not pulling the trigger and decides that neither has any higher important meaning, it just happens.

At some point in the future, we may hypothesize an aesthetic theory based on the coevolution of the biological and cultural elements of the human brain and nervous system. If the evolution of our sense of beauty is a nonlinear feedback between cultural and biological determinants, recent developments in the theory of chaos, nonlinear processes, and self-organizing systems can point the way to a better understanding of aesthetics. The experience of beauty might be better understood as a reward, analogous to the neurochemical rewards for other adaptive activities such as eating and sex. Beauty itself might be broadly redefined as an objective property of the fundamental generative processes of the universe—thus as possessing a real, not just a subjective, existence. Like our eyes, our aesthetic sense may be designed to perceive objects that are actually out there: systems which show promise for emergent forms of order. The ability to recognize such systems would have adaptive significance for the sustainability of the human species.

I hope that I have provided sufficient evidence that we are going through a real revolution in science (cosmology, biology, and the neurosciences), much bigger even than the one that occurred in the seventeenth and eighteenth centuries (Galileo, Newton), and that the new knowledge cannot be neglected or avoided. I believe that as in the eighteenth century, when the scientific revolution led to the Enlightenment (Locke, Diderot, Voltaire) and eventually brought about the French Revolution (1789) and created a new social order, the present scientific revolution will bring a new Enlightenment—which I call an enphotonment , as light is nothing else but photons.

Our new view of the universe, based on solid experimental and observational facts, suggests rather strongly that there is no higher purpose in the universe. The sooner we get familiarized and make peace with such a notion, the sooner the bondage of the past will end, and we will be able to face the world really free. I consider this contribution of scientific knowledge to the quality of life far more important than any technological application that makes our lives better. We are the first generation ever to have this knowledge, and it is interesting to see how we are going to use it.

The scientific point of view presented here is naturally embedded as the fourth component, the scientific version of absurdism ( paralogue ); the other three being represented by Albert Camus’ philosophical essay “The Myth of Sisyphus” (1942), the novel L’ Etranger (1942), and the play Caligula (1944). This is my small contribution to the gigantic opus of Albert Camus, the creator of absurdism, in memoriam of his absurd death fifty years ago, on the fourth of January 1960, with the great hope that it brings absurdism to its completion by showing it to be based in scientific fact.

To sum up, our new, revolutionary quantum world provides us, for the first time ever, with a possible answer for the “appearance” of the universe. A random quantum fluctuation out of infinitely many in the eternal quantum vacuum “made it” to become our observable universe, through an almost instantaneous exponential expansion leading to the inflationary phase, and the rest is history. This is the cosmological component, version, and justification of absurdism. This is the quantum myth of Sisyphus .

A brief history of our universe is shown in Figure 8.

It is worth stressing two things: First, the universe is made up of 73% dark energy, 23% dark matter, and only 4% of our normal matter (protons, neutrons, and electrons). In other words, the Aristarchan-Copernican heliocentric revolution comes to its completion: not only are we not at the center of the universe; the universe has no center anyway, and we are also not made of the stuff that composes most of it.

It is also worth stressing here another connection with classical Greek culture. In Plato’s cosmology, as it is presented in “Timaeus” (c. 360 BC), he associated four of the five possible polyhedra inscribed in a sphere—namely the hexahedron (cube), the octahedron, the icosahedron, and the tetrahedron—with Empedocles’ four classical elements: earth, air, water, and fire respectively. Plato used the fifth remaining polyhedron, the dodecahedron, perhaps influenced by the dodecatheon of his time, to arrange the constellations on the whole sky! No wonder that today the five polyhedra inscribable in a sphere are called Platonic solids. What is even more remarkable is that Aristotle added a fifth ( πέμπτο ) element or πεμπτουσία (‘the quintessence’), and postulated that the heavens were made of this element, without specific reference to Plato’s dodecahedron. Today, twenty-four centuries later, the 73% of the energy-mass of the universe, the “dark energy” discussed above, is also called “quintessence.”

Secondly, according to the majority of our present theories that provide unification of all the fundamental interactions, the so called Theory of Everything (TOE), protons are not forever ! The proton, the most fundamental constituent that the galaxies, stars, planets, and ourselves are made of, is not stable but has a lifetime of about 10 34 –10 35 years. Arguably, this is a long, long, long lifetime, but one way or another these large structures will dissolve on their own due to proton decay. All the above suggests that absurdism—i.e. a benign indifference, a lack of higher purpose—is at work here, but at the same time we should never forget Camus’ final lines in the “Myth of Sisyphus”: “The struggle itself toward the heights is enough to fill a man’s heart. One must imagine Sisyphus happy.” The relevance here of another ancient Greek myth, that of Tantalus, should also not escape our attention here. Tantalus was immersed up to his neck in water, but when he bent to drink, it all drained away; luscious fruit hung on trees above him, but when he reached for it winds blew the branches beyond his reach. Another magnificent allegory of absurdism, like the myth of Sisyphus: something desirable is always just out of reach.

Nevertheless, even if zero is our destiny, our unavoidable final destination, let’s not make it look like the right price to pay.



Note 1
«… ηθος ανθρώπωι δαίμων …» ( Heraclitus Β 119) [ Ο χαρακτήρας του ανθρώπου είναι το πεπρωμένο του ].

Note 2
«κόσμον τόνδε, τὸν αὐτὸν ἁπάντων, οὔτε τις θεῶν οὔτε ἀνθρώπων ἐποίησεν, ἀλλ’ ἦν ἀεὶ καὶ ἔστιν καὶ ἔσται πῦρ ἀείζωον, ἁπτόμενον μέτρα καὶ ἀποσβεννύμενον μέτρα» (Heraclitus Fragments 30).

Note 3
ħ≈ 1 · 10 -34 J-s, a very tiny number indeed, thus practically “innocuous” in our macroscopic world.

Note 5
Trans. G. W. T. Patrick, see, 20.

Note 7
Trans. G. W. T. Patrick; see, 95.

Equation 1

Equation 2

Equation 3

Equation 4

The Cosmic Bell

Equation 5

Equation 6