Quantum Mechanics: Fact and Theory, Physics and Philosophy

From this thou mayest conjecture of what sort
The ceaseless tossing of primordial seeds
Amid the mightier void- at least so far
As small affair can for a vaster serve,
And by example put thee on the spoor
Of knowledge. For this reason too ’tis fit
Thou turn thy mind the more unto these bodies
Which here are witnessed tumbling in the light:
Namely, because such tumblings are a sign
That motions also of the primal stuff
Secret and viewless lurk beneath, behind.
For thou wilt mark here many a speck, impelled
By viewless blows, to change its little course,
And beaten backwards to return again,
Hither and thither in all directions round.
Lo, all their shifting movement is of old,
From the primeval atoms; for the same
Primordial seeds of things first move of self,
And then those bodies built of unions small
And nearest, as it were, unto the powers
Of the primeval atoms, are stirred up
By impulse of those atoms’ unseen blows,
And these thereafter goad the next in size:
Thus motion ascends from the primevals on,
And stage by stage emerges to our sense,
Until those objects also move which we
Can mark in sunbeams, though it not appears
What blows do urge them.

—Lucretius, from De rerum natura, circa 50 BC

In the century since its discovery in the early twentieth century, quantum mechanics* has been employed as evidence for most extraordinary array of conclusions. Aside from inspiring at least a dozen competing interpretations amongst contemporary physicists, quantum mechanics has also permeated the contemporary Zeitgeist and incited innumerable revolutions in popular culture. Despite that nearly a century has elapsed since its formulation, the implications of quantum mechanics remain uncertain. Must we accept such uncertainty as an essential facet of the post-modern era, or might we win through to a comprehension that is not subject to Jeff Bridge’s notorious enunciation of the post-truth condition, “that’s just your opinion, man”? Any eventual understanding will depend on sound logic, and an hallmark of the latter is that the conclusion ought not to precede the reasoning. Let us, therefore, explore the question and accept whatever conclusions may result.

Quantum mechanics was developed to describe the behaviour of minute particles, which were discovered to obey laws that were at odds with any explanation that classical physics could offer. Specifically, Max Planck hypothesised in 1900 that under certain ideal conditions,† a body energy did not emit thermal energy in a continuous stream, but rather in discreet packets. The latter were latter to be called “quanta.” Albert Einstein soon related Planck’s notion of quanta to light, thereby to explain the photoelectric effect. The light quantum was later named “photon.” Quantum mechanics emerged in its recognisable form in 1925 when two separate mathematical systems were formulated to calculate the behaviour of photons (and electrons, after they were later discovered to obey similar laws). Niels Bohr, Werner Heisenberg, and Pascual Jordan developed the equations for matrix mechanics, which described the quantum leaps of electrons about the valences of atomic nuclei. In the same year, Erwin Schrödinger formulated the equations for wave mechanics to describe the wave-like behaviour of particles in a given system, which equations he published a year later in 1926. The Schrödinger wave equations are, without a doubt, amongst the most extraordinary equations in the history of physics. The former allows for the calculation, from specified initial conditions, of the wave-function for subatomic particles in that system. The wave-function represents the probability-distribution of the all of possible states that a particle will be in at any moment.

Given the accuracy of the predictions that the Schrödinger wave equations provide, as well as those of matrix mechanics, it was natural for physicists to conclude that they had hit upon the truth of the matter. “Truth,” in this case, has a very definite meaning: it refers exclusively to the ability to construct a mathematical model to predict the outcomes of a given experiment. It does not include the conceptual understanding that would explain those outcomes. Truth refers to accuracy, not to understanding. But understanding being a natural impulse of the human spirit, physicists immediately set about an attempt to elucidate their findings with the conceptual element which observational data alone does not provide.

By 1927, the “the Copenhagen interpretation” had begun to take form. This was an heroic attempt, piloted by Bohr and his lieutenant Heisenberg, to comprehend the apparent mysteries of quantum phenomena. In its essence, the Copenhagen interpretation acknowledged the probabilistic nature of the equations which describe physical interactions at the quantum scale. It took this as evidence that reality itself at this scale, which is the elementary basis of all other scales, was indeterminate until an actual observation. Heisenberg’s “uncertainty principle,” Bohr’s principle of “complementarity,” and “the observer effect,” are key notions that the Copenhagen interpretation postulated in an attempt to conceptualise such unexpected results as superposition, the wave-function collapse, and the interference pattern in the double slit experiment. Albert Einstein famously rejected the anti-realist, anti-determinist assertion of the Copenhagen interpretation with his affirmation that “God does not play with dice,” suspecting instead that the experiments contained hidden variables that might later come to light. Bohr notoriously responded, “Einstein, stop telling God what to do.” Bohr offers an alternative perspective to Einstein when he writes that “physics is not about how the world is, it is about what we can say about the world,” thereby seeming to imply the actual existence of a real world but only questioning our knowledge of it. This makes for an interesting pluralism of viewpoints when he contradicts Einstein’s deterministic realism and also when he contradicts his own anti-realism. Simply put, the Copenhagen interpretation both affirms and denies the actuality of the physical world. Unless we are willing to deny the reality and intelligibility of the world, to reject the fundamental principle of logic is not a viable solution to the quantum paradoxes.

Given the stakes of this question, is not altogether surprising that some physicists have simply refused to consider it. The physicist David Mermin captured this sentiment in the most expressive manner with the phrase “shut up and calculate!” Given the predictive success of the equations, this way of thinking would see no reason to inquire into their meaning. Still, such an exclusively instrumentalist notion of science will strike many as distinctly unsatisfying. Aristotle capture the natural curiosity of the human being in the opening sentence to Metaphysics when he wrote that “All men, by nature, desire to understand.” Without a doubt, to reduce physics to equations and data-collection will never satisfy this desire. Thus, in respect to quantum mechanics, we must conclude that an understanding still awaits us. A recent survey amongst physicists attending a conference on the foundations of quantum mechanics in 2013 highlighted this lack of understanding. Roughly 40 percent favoured the Copenhagen interpretation and the remainder were distributed amongst a plethora of alternative interpretations. That the Copenhagen interpretation does not seem consistent with itself again emphasises that we have yet to understand the implications of quantum mechanics.

It is important to note that the lack of understanding that the survey above revealed is not a question of experimental results, but of an inability to conceptualise them. In other words, what we lack is not “knowledge that,” but “knowledge why.” Indeed, Schrödinger’s wave equations leave little to be desired in their ability to predict the behaviour of particles. What physicists have failed to agree upon, however, is a coherent account for why the particles behave in the way that they indeed do. An epistemological distinction that Aristotle presents in Posterior Analytics may help to illuminate the situation. The Stagirite famously contrasted scientific knowledge with sophistic knowledge when he wrote that the former can explain the causes by which a thing is while the latter can only say that a thing is. Evidently, quantum mechanics has not met the criterion of scientific knowledge that Aristotle set forth. Although some may question the relevance of an Ancient Greek philosopher to questions of contemporary particle physics, no one should question Aristotle’s capacity to think in clear concepts. Once the data has been collected and the equations formulated, thinking in clear concepts is just the capacity that is necessary if we are ever to understand the nature of quantum mechanics. Indeed, what we lack today is just what mere calculation and experiment can not provide. In the most general sense, the question around quantum mechanics hinges on a conception of what happens between measurements. Such a conception would provide the necessary account of actual observations, without which the latter can only appear enigmatic or arbitrary. Obviously in this case it begs the question to say that the particles behave in the manner that they do because of the equations, since the issue at hand is precisely why they behave in the way that the mathematical model indeed predicts they will. A model is derived from an actual phenomenon and thus it makes no sense to explain the phenomenon with the model that was derived from it.

Given the situation as we have characterised it above, we may wonder whether physics, by the very nature of the discipline today, can provide the account of quantum phenomena that we seek. It may be that modern physics only concerns “knowledge that,” and not “knowledge why.” The data do not provide their own explanation any more than a text reads itself. Historically, physics benefitted from a license to draw on other disciplines of human inquiry to form a coherent world-conception. René Descartes famously compared Philosophy to a tree: “The roots are metaphysics, the trunk is physics, and the branches emerging from the trunk are all the other sciences.” By “metaphysics,” Descartes means first principles which cannot themselves be empirically verified but which provide a basis for empirical verification. Being, space, time, identify, non-contradiction, causality and God are examples of such first principles. It should be clear that, though not every one of these principles is necessary for science, it is just as true that science would be inconceivable without some of them. With the scientific revolution in the seventeenth century, physics gradually began to distance itself from its metaphysical roots. Nevertheless, a tacit metaphysical inheritance continued to ground new advances in science. Thus, physicists were able to draw their premises, more or less consciously, from religious and philosophical traditions of the past to ground their conclusions. Isaac Newton, for instance, invoked the monotheistic notion of a supreme being to lend lawfulness and sensibility to the cosmos. Thus in the General Scholium, he famously declares:

This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent Being…This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called “Lord God” παντοκρατωρ [pantokratōr], or “Universal Ruler”…The Supreme God is a Being eternal, infinite, [and] absolutely perfect.

Gradually, however, the success of the sciences encouraged physicists to assert their discipline’s independence of its metaphysical roots. Thus the centuries following the scientific revolution saw increasing attempts to account for experimental results without appealing to anything outside of physics. Thus by 1796, the physicist Pierre Laplace could reply to Napoleon Bonaparte’s question as to the role of the Creator in the universe that the former had proposed in his Exposition du systeme du monde with the assertive reply: “Je n’avais pas besoin de cette hypothèse-là.” (“I had no need of that hypothesis.”)

The late physicist Stephen Hawking offers an insight into the contemporary perspective in his 2010 book The Grand Design, in which he definitively rejected the notion that any appeal to principles outside of physics was necessary to explain the origin of the physical world. “Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist,” he wrote in, and concluded, “It is not necessary to invoke God to light the blue touch paper and set the universe going.” Hawking clarified his statement in an interview in March 2018 (https://www.elmundo.es/ciencia/2014/09/21/541dbc12ca474104078b4577.html): “Before we understand science, it is natural to believe that God created the universe. But now science offers a more convincing explanation.” The explanation to which Hawking refers is of course “spontaneous creation,” which strikes one as a feasible explanation until one recognises that it is no explanation at all. Everything must initially strike us as spontaneous until we have understood it. In other words, spontaneous creation cannot itself be a reason, or an explanation, because that is precisely the thing we seek a reason, or an explanation, for. This is a simple fact about the nature of scientific knowledge, and a return to the subject of quantum mechanics will render it immediately apparent. The quest for a coherent interpretation of quantum mechanics is just to explain why the phenomena that the Schrödinger equations and matrix mechanics describe, behave in the manner that they in fact do.

As we indicated above, Bohr and Heisenberg attempted to do exactly this with the Copenhagen interpretation. In order to explain such surprising phenomena as the wave-function collapse, and the interference pattern in the double slit experiment, the Copenhagen interpretation posits that particles as such have no definite location until an actual observation. Instead, they subsist in superposition, which is described as being “smeared out” across space along the parameters of the wave-function, until the act of observation collapses the wave-function and the particle assumes a definite position. The apparent influence of observation on physical reality the has been called the “observer effect.” By now in our exploration, we have learned we cannot expect to achieve an understanding of quantum mechanics without thinking about it. Let us therefore think about whether “the observer effect” actually means what it suggests. What is the observer affecting? The standard answer is that the observer collapses the wave-function, or “forces” the particle to assume a definite location. To reiterate from above, the wave-function is a mathematical calculation to describe, from given initial conditions, the behaviour of particles at any time during an experiment. As the wave-function indicates, subatomic particles like photons and electrons follow a wave-like pattern. If a particle is observed, however, the continuous wave-function instantly collapses and gives way to a discreet particle with definite location. Let us here distinguish between the wave-function as a description of potential outcomes to an eventual measurement, and an actual observation that yields an actual measurement. The source of confusion can now begin to reveal itself, since potentiality and actuality are not substantially commensurate. The wave-function is not a physical wave, it is a wave of possibility. “The observer effect,” in its application to interpretations of quantum mechanics, is an expression of the mistake of regarding a probability wave—a wave in abstract, non-physical Hilbert space—in the same manner as the observed particle in actual physical space.

From this realisation, it should follow as self-evident why the “mere” act of observing a particle collapses the wave-function. Again, the wave-function is a statistical description of possible outcomes. Thus it is a description of the experimenter’s knowledge of the entire system. Obviously, an actual observation affects this knowledge by fixing the possible outcomes to a specific one. From initial conditions, a weather forecast might predict a 40% chance of rain in a given location, but that is not the same as it actually raining there. To actually observe rain instantaneously resolves the probability of precipitation from .4 to 1, but no one recognises “the observer effect” in this phenomenon, nor supposes that before the observation, the weather was in a state of superprecipitation.

No longer does the Copenhagen interpretation’s assertion of ontological nebulosity appear like an altogether satisfactory conclusion to draw. Let us inquire further, however, for there may be other reasons for it. Another riddle of quantum mechanics that lent credence to the notion of ontological indefiniteness was the discovery that the position of an electron could not be measured at the same time as its momentum. Heisenberg postulated his “uncertainty principle,” and Bohr the principle of “complementarity” in response to this fact. Because the uncertainty principle is not a function of the measuring device, but of the equations themselves, the future appeared to offer no promise of its resolution with technological advances of the equipment. This appeared to some to support the conclusion that “reality” is fundamentally uncertain. Bohr, for instance, when Erwin Schrödinger attempted to challenge this ontological assertion of uncertainty with his famous cat-paradox, maintained that the cat was actually in a superposition of life-death until the box was opened. As we discovered in our investigation of the observer effect, however, no observational data supports such a conclusion as Bohr felt compelled to draw. Indeed one cannot help but conclude that Bohr’s reasoning was driven by motives ulterior to the scientific nature of the situation. Simply stated, momentum implies a changing—which is to say, a non-definite—position. The former implies the latter by the very meaning of those respective concepts. This conceptual complementarity is expressed mathematically as the fact that momentum is proportional to the time-derivative of position. In other words, momentum is calculated by the rate by which the position changes: if the position is fixed, then its time-derivate cannot be calculated and neither can its momentum. Accurate knowledge of an electron’s position precludes accurate knowledge of its momentum, and the converse. In other words, certainty about one aspect condemns one to uncertainty about the other. To extrapolate this epistemological fact into a metaphysical principle strikes one as distinctly unwarranted by the current evidence.

What does seem safe to extrapolate from the current evidence is that the disagreement over interpretations of the quantum experiments will never be resolved by the methods of modern physics. For anyone who considers the nature of the disagreement and the history of modern physics, the fact that physicists have reached no consensus in an hundred years will not come as a surprise. Indeed, the only semblance of progress comes about when physicists smuggle in metaphysical principles that are sufficiently naturalised in the contemporary Zeitgeist so as to be unnoticed. Science deserves more than back-door philosophy, however, which is all that it will receive as long as physicists insist on sustaining the illusion that their discipline can provide its own foundations. The Copenhagen interpretation distinctly undermines its own foundations with the assertion that particle subsists in a superposition of mutually exclusive states. Such an assertion flouts the principle of non-contradiction upon which the very equations that were its source depend. Nobody would use wool to deny sheep and nobody should make inferences that contradict the methods from which those inferences were drawn. Specifically, an interpretation that rejects the principles of the mathematics that underly the experiments which the interpretations are meant to explain is an interpretation that has sawed off the branch on which it had meant to perch.

Mercifully, Heisenberg himself offered a path towards resolution of the quantum muddle, revealing that he could draw from the roots that support his discipline when he was not being bullied into adopting Bohr’s idiosyncratic ontological notions. In his 1958 work Physics and Philosophy, Heisenberg characterises the nature of the situation in a clear manner:

The probability wave of Bohr, Kramers, Slater… was a quantitative version of the old concept of “potentia” in Aristotelian philosophy. It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality.

Thus we encounter the name of Aristotle for the third time in this exploration. Heisenberg did not pursue this notion further, and perhaps it is not his role. His contributions to human knowledge are sufficient to warrant our admiration regardless of whether he fully elaborated their philosophical implications. It may be that Heisenberg left the clue to resolve this riddle, however, with his mention of Aristotle in the quote above. Aside from the characterisations of knowledge and innate wonder that we made use of earlier in this exploration, could it be that Aristotle also offers us conceptual framework to understand the natural world? This seems to be just what Heisenberg suggested. In the specific context of this inquiry, we can make use of Aristotle’s reciprocal notions of dynamis (δύναμις) & energeia (ἐνέργεια). Latin translators during the Middle Ages rendered these terms as “potentia” and “actualitas,” respectively. Indeed this is the phrase that was familiar to Heisenberg. Each of these four words has at least one cognate in English: “dynamite,” “energy,” “potential,” “actual.” Dynamis denotes a specific power while energeia refers to the active working of that power, it’s “being-at-work.”** The concpets of potential and kinetic energy exemplify, but do not exhaust, the meaning of dynamis and energeia. Potential-kinetic energy is a species of which dynamis-energeia is the genus.

It is consummately revealing, in light of our exploration till now, to recognise that modern physics has entirely collapsed Aristotle’s distinction between dynamis and energeia, or potential and actual.†† Thus “energy” is defined irrespective of its actuality. Specifically, in modern physics, “energy” is understood as a conserved quantity of the capacity to do work, expressed in a relation of mass × distance²/time² (MD²/T²) or the like. E=MC² is an example of this relation since the universal constant is meant to represent the speed of causality and, as a velocity, is thus measured in units of distance divided by time. Obviously a system of thought that fails to distinguish between potential and actual cases is not a system of thought that can offer any definite insight into the concrete nature of its object, only probable knowledge. The fruition of actual knowledge from probabilistic knowledge could only be the result of an actual observation of an actual case. Anyone who supposed that probability could serve the same function as actuality has simply misunderstood the nature of both concepts.

Nevertheless, misunderstandings of just this nature haunt the domain of science today, as we have attempted to illustrate in respect to the field of quantum mechanics with the present investigation. The physicist Richard Feynman summed up the general situation today in an elegant manner when he stated, “If you think you understand quantum mechanics, you don’t understand quantum mechanics.” One cannot help but conclude that attempts to interpret the findings of quantum mechanics suffer from a distinct lack of philosophical foundations. The ability to conceptually distinguish between potential and actual appears to offer promise for the future of this field, since to say “a particle is potentially in state α and potentially in state ~α at the same time” does not flout the principle of non-contraction—a pillar of logic that sustains the very edifice of quantum mathematics. Such an understanding would provide for at once a more nuanced and a more rigorous conception of reality than our present notions seem to provide. It should be obvious that the matrix and wave equations are describing the potential behaviour of particles in an experiment, which is related to, but not identical with, a description of those particles in their actuality. It is my hope that this exploration may contribute in some small way to our understanding of physis.

Sandro Botticelli, The Birth of Venus (c. 1484–86)

Thanks to all of the fathers like Aristotle, Einstein, Bohr, Heisenberg, Schrödinger, etc…and also thanks to many others

* I have chosen to treat the phrase “quantum mechanics” as though it were a singular noun, which it is not, since this seems to have become a convention.

† A black body is an hypothetical ideal physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence and radiates it at the highest possible efficiency and also isotropically.

**Aristotelian Scholar Joe Sachs coined this neologism to capture, in English, the native Greek speaker’s experience of that term.

† † Similarly, physics is a kinematic, not a dynamic, study. In other words, it studies only mathematical motion abstracted from the force of that motion. Along similar lines, David Bohm notes the following, though not without displaying some of the same logical inconsistencies as in other theories:

Now, there’s one other thing that modern quantum mechanics doesn’t handle. Oddly enough, physics at present has no contact with the notion of actuality. You see, classical physics has at least some notion of actuality in saying that actuality consists of a whole collection of particles that are moving and interacting in a certain way. Now, in quantum physics, there is no concept of actuality whatsoever, because quantum physics maintains that its equations don’t describe anything actual, they merely describe the probability of what an observer could see if he had an instrument of a certain kind, and this instrument is therefore supposed to be necessary for the actuality of the phenomenon. But the instrument, in turn, is supposed to be made of similar particles, obeying the same laws, which would, in turn, require another instrument to give them actuality. That would go on an infinite regress. Wigner has proposed to end the regress by saying it is the consciousness of the actual observer that gives actuality to everything.

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One Comment Add yours

  1. Thank you for your clarity, Leyf. I am in full agreement with your statement:

    “Science deserves more than back-door philosophy, which is all that it will receive as long as physicists insist on sustaining the illusion that their discipline can provide its own foundations.”

    Heisenberg’s reference to “potentia” goes a long way toward sorting out the complete and utter philosophical mess that is contemporary quantum theory. This is the path Whitehead elaborated upon in his philosophy of organism.

    Other philosophically inclined physicists who would appear to be on the right track here include Lee Smolin. He and Roberto Unger recently published “A Singular Universe and the Reality of Time.” It is not a very readable book, but buried in it are some important arguments attempting to replace mathematics with natural philosophy at the foundation of physics. By putting mathematics at the foundation, 20th century physicists have lost touch with the point of science, which is to provide a coherent account of the natural world of our experience. Mathematics is about pure possibilities and the abstract relations among possibilities. Sometimes it has application for modeling the patterned activities of Nature. Math can thus serve a powerful role in the pursuit of knowledge of Nature, but when it becomes the master, our requests for understanding are met with “shut up and calculate!”

    Liked by 1 person

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