The Foundations of Unification Thought in Quantum Mechanics

by Dr. Jin Sung-bae, head of the Unification Thought Institute,

Translated from the original Korean into English by William Stoertz

OUTLINE

    I.  Scientific realism and empiricism in quantum mechanics

     1.  Realism in classical physics and realism in quantum mechanics

        a.  The realism of particle and wave theory in classical physics

        b.  The realism of particle/wave theory in quantum mechanics

     2.  The Standard Model of quantum mechanics and empiricism

        a.  Heisenberg's uncertainty principle

        b.  Bohr's complementarity principle

   II.  The Unification Thought interpretation of quantum mechanics and its foundations

     1.  The Inner Sung-Sang and the Standard Model of quantum mechanics

     2.  The Inner Hyung-Sang and mathematical principles of quantum mechanics

     3.  The paradox of quantum mechanics from the standpoint of Unification Thought

        a.  The Unification Thought view of matter and the wave-particle duality

        b.  The Unification Thought view on the Schrödinger wave equation

In this paper, we treat issues of peace, generally perceived as a subject of sociology, from the perspective of the natural sciences. We strive to apply the logic and wisdom gleaned through research and through the process of debate down through the history of science to the concept of peace and studies of peace. There have been many attempts to utilize the scientific method in the pursuit of peace, but in the course of the history of struggle in the sciences, efforts to realize a peaceful world are not uncommon, so we are bound to draw some limits as to the framework of this discussion. Thus of course our discussion can hardly do justice to the fine sensibilities of the pure sciences or the issues of peace as such; rather, recognizing the practically insurmountable wall between the natural sciences and the social sciences, it strives to treat the subject of quantum mechanics, at least in part, as a model for how this challenge can be tackled.

     First of all, Einstein and the Copenhagen School, standing at the vanguard of the 20th century scientific revolution, managed to tame the controversy raging in the field of quantum mechanics. With historical hindsight, we can truly appreciate the sublime epistemological balance between scientific realism and empiricism which has been achieved in quantum physics. By resolving the issues in that discussion, they sought to synthesize a brand-new epistemological paradigm in modern physics.

     Secondly, taking in stock the paradox left over in quantum physics in the form of the dialectic of the new view of reality and the Standard Model born in the heat of the debate; when we analyze the character of the scientific revolution -- through analyzing the process by which unity and peaceful coexistence emerged from a state of tension and conflict, we can also derive a new perspective for peace.

     Let us begin by first establishing a definition, posing the question “What is this thing we call science?” The English word “science” is in widespread use; the German term “Wissenschaft” conveys broadly the concept of systematized understanding for the purpose of discovering universal truth and principles. Then this knowledge is partitioned into the humanities or social sciences, and the natural sciences, being further classified into various fields of expertise. Also the word “science” is commonly used to refer to the “natural sciences.” In this paper we will also be using the term “science” in the sense of “natural science”; more specifically we will be concentrating on physics for the most part. “The natural sciences” refers to those scholarly pursuits which investigate theories of the lawfulness of natural phenomena in the areas of physics, chemistry, biology, astronomy, earth sciences, etc.

     In the beginning Aristotle denoted “metaphysica” as the “first philosophy,” where “physica” was the “first natural science” and “meta” meant “right after”, thereby arranging the first philosophy immediately following the first science in his classification scheme. Later on his disciples reinterpreted the prefix “meta” to mean “transcendental”, whereby we obtain the contemporary understanding of “metaphysics”. Looking at it in this light, as long as with Aristotle natural “science was regarded as a this-worldly science, until people acknowledged natural science as an independent discipline, physics and the other branches of natural science were still relegated to the over-arching category of “natural philosophy.” Until the title of “physics” was conferred, we find as with Newton's “Philosophiae naturalis principia” (“The Principle of Natural Philosophy”), that the term “principle” was widely applied to classical mechanics, and that the study was not awarded the title of “physics” but rather was published under the name of “natural philosophy.”

In contemporary philosophical treatises we distinguish and employ the concepts “metalanguage” and “object language.” When we speak of the philosophy of a particular discipline of the natural sciences, it goes hand in hand with an object language referring to the natural phenomena peculiar to that field. Then that field is entitled to be called a scientific discipline in its own right when there is a complete metalanguage dealing with the object language describing the field. Though we do not apply the typical method of Bertrand Russell (1872-1970), separating object language and metalanguage, the “humanities” are in fact classified along with the sciences; therefore we would recommend setting out the task of according them the designation of “the human sciences”; we note that the object languages of the natural sciences differ from those used in philosophy or the humanities.

I.  Scientific realism and empiricism in quantum mechanics

     1.  The realism of contemporary physics and quantum mechanics

     By means of the laws and other scientific trappings of physics, natural phenomena are described in a unified and ubiquitous way as an exact quantitative science. Physics ― whether we speak of classical mechanics or quantum mechanics ― observes measurable physical quantities corresponding to material reality, and seeks the laws and theories to explain these physical quantities. The reason physics is recognized as an exact science is because, when the theoretically calculated physical quantities and the quantities obtained through experiments are not in agreement within specified bounds of statistical error, then either the theory itself is subject to rational modification, the experimental conditions must be refined, or the process is gone over in detail, until the theory agrees with the observed phenomena. The reason physics has established itself as the leading field of scholarly research in our modern civilization is that the theoretical predictions it posits agree more precisely with empirically measurable observations than we see in other disciplines, and because those natural phenomena which adhere to the principle of causality lend themselves readily to rational explanation. On the other hand biology, which explains the origin of species by way of evolution theory, has been thus far unable to experientially corroborate a definitive cause-effect relationship; likewise psychology, dealing with human actions and mental processes, is unable to quantitatively measure motions ― thus these areas of pursuit are necessarily saddled with a certain limit. In quantum mechanics, the controversy still underway at present is over the issue of discrepancies between the theory and observations, and various approaches to resolving such problems.

It was pointed out by Albert Einstein (1879-1955) that quantum mechanics, which lies at the foundation of modern physics, presents an incomplete theory, while the Standard Model of quantum mechanics, the theoretical system promulgated by the Copenhagen School, has been recognized as comprising a complete theoretical structure in and of itself. The sharp dispute between Einstein and the Copenhagen School over quantum mechanics caused unprecedented tension in the history of science, yet this debate yielded magnificent reward in the successful paradigm shift it occasioned in quantum mechanics. The issues which Einstein pointed out in the Standard Theory lay in the principle of causality, the continuity of matter, etc. ― the problem underlying the fact that the quantum mechanical interpretation of the Standard Model ran counter to everyday experience lay in an apparent schism in quantum mechanics itself, namely the so-called particle/wave duality in the fabric of reality of the particle, the discrete quantum steps, etc. The conversation between Einstein and the Copenhagen School led the Copenhagen school to produce a complete explanation of its famous “interpretation,” with the result that the Standard Theory of quantum mechanics was firmly established. The problem Einstein called attention to is being disputed to this day; meanwhile scientific research is steadily working toward a more refined theoretical model to better explain observed quantum phenomena. In a standard physics textbook we read about “the Copenhagen interpretation” where it explains that Werner Heisenberg (1901-1976) realized the concept of the particle/wave duality on the framework of Bohr's complementarity principle, achieving the standard interpretation of quantum mechanics we know today. The main thrust of the present treatise likewise reflects the debate of these two titans, i.e., it examines the Standard Theory of the Copenhagen School represented by Niels Bohr (1885-1862) versus contrasting conceptualizations in the person of Einstein.

The first textbook that appeared on quantum mechanics distinguished Einstein's realism and the Copenhagen School's empiricism, viewing it as a problem of ontology and epistemology. These two viewpoints differed in the question of whether the ultimate substance constituting nature were made of one and the same material, or were divided according to our perception of material reality. In the medieval debate over universals, philosophical realism and the scientific realism classified into categories, Einstein's realism, even in quantum mechanics as in classical mechanics, took the position of recognizing the reality of particles, the principle of locality, cause and effect, continuity, and even the possibility of predicting particle motion in accordance with hidden variables associated with them. At this point (in the 1920s) de Broglie, Planck, Einstein, Schrödinger, Bohm and others came to scrutinize the quantum mechanical position of realism.

        a.  Realism and the particle/wave theory in modern physics

In classical mechanics the special property of the particle is that its changing position and motion vectors are determinate in the dimensions of mass and time. This Newtonian mechanical system represents a complete deterministic view of the world, by means of which the motions of all material objects can be explained ― whether the fall of an apple, the ebb and flow of the tide, even the paths of the celestial bodies. Isaac Newton (1643-1727) believed that light was composed of minute particles that are able to move in a vacuum. He was convinced the light and heat from the sun were actually material entities. However Thomas Young (1773-1829) conducted the experiment of passing light through two slits (in 1801), and discovered that if the two fans of light overlapped one another, they produced interference fringes, leading him to conclude that light is in fact a wave phenomenon. Meanwhile Michael Faraday (1791-1867) demonstrated (in 1831) that if one rotates a bar magnet inside a coil of conducting wire, the magnetic field induces a current flow; and James Maxwell (1831-1879), in the process of formulating Faraday's discovery mathematically (1860-1871), realized that electricity and magnetism are mutually interchangeable effects, and saw in light an electromagnetic vibration propagating at exactly the speed of light ― at which he could not restrain his amazement. In their heyday they superseded the Newtonian concept of interactive forces among particles with the concept of a spatial field which manifests properties such as wavelength and electric charge.

At the same time, Louis de Broglie (1892-1987) proposed (in 1924) the concept of the “wave packet”, speculating that both light and matter exhibit the duality of particle and wave properties. He proved that so-called “particles” could be described in terms of the famous “Broglie wavelength,” calculated by the formula λ = h/p. It was established that the wavelength λ and momentum p of a particle are circumscribed by Planck's constant h, and are mutually coupled according to this formula. He also showed that wavelength and particle are mutually interchangeable; their correspondence can be calculated with this mathematical equation. Moreover, by inserting into this formula the energy of Bohr's discrete quantum steps, the model of the hydrogen atom was replaced by the form of a stationary wave in three dimensions. De Broglie's concept of the material wave resurrected Newton's realism along with the concept of dynamic continuity in quantum mechanics. This development was certainly welcomed by Albert Einstein.

        b.  Realism and the particle/wave duality in quantum mechanics

Einstein's Special Theory of Relativity unified Newton's mechanics and Maxwell's electromagnetism after the pattern of Lorentz symmetry, with temporal dilation and spatial contraction, and last but not least the famous mass/energy equivalence E = mc². With his General Theory of Relativity he denied the objective existence of gravity, replacing it with a Riemannian curvature of space, and predicted the bending of light owing to the curvature of space in the vicinity of the sun. From now on what we observe is not gravity but only materially existing bodies moving in accordance with spacetime which exists as a conceptual reality, and energy “granules” which comprise what we call “particles.” All this amounted to introducing a new conceptual turning point.

     Light may manifest as a wave or as a particle flux. Max Planck observed that the thermal radiation emitted by a hot body exhibits a characteristic color spectral pattern, and the heat energy is released as electromagnetic waves according to a certain formula which he elaborated. The function expressing the energy at each wavelength ― called “Planck's Formula”: E = hf, where h is Planck's Constant and f is the frequency ― pointing to a surprising fact. Namely, the energy emission from matter following any energy input such as sound pitch or mechanical wave is not continuous but is released in discrete increments as energy bundles in integer multiples of the quantity hf. At any rate it was established that matter radiates energy only in the form of discrete quanta.

Einstein thought the cause of the discontinuity lay not in the material particle, but in the light energy itself. In 1921 he presented a paper on the photoelectric effect, studying electrons emitted by a cold metal surface, for which he received the Nobel Prize. Based on the particle theory of light, he first came up with the concept of the photon. A light wave is a bundle of energy granules (photons); he discovered that the units of measure of these granules are quanta of energy in discrete multiples of Planck's Constant E = hf, and the energy of this particle is in direct proportion to the frequency. Next he observed that, despite the discontinuous release of energy from the particle, the light wave behaves like a material particle with energy and momentum. As ever, Einstein remained a staunch advocate and guardian of causality and determinism, scientific objectivity and realism. In Einstein's photon hypothesis the mutual relation of the energy E and the frequency ν may be calculated using the equation ν = E/h, derived from de Broigle's formula λ = h/p, where λ is the wavelength and p is the momentum; when we compare the two formulas, we gain new insight into quantum mechanics.

“Einstein assumed that light always manifests in the form of wave packets, i.e. light quanta or photons, and the formula E = hν represented the energy of a single photon.”

     Whereas Heisenberg started out from the traditional electronic particle theory in his Interpretation of quantum mechanics, Erwin Schrödinger (1887-1961) started out from de Broglie's wave theory. Karl Popper (1902-1994) believed in the existence of Schrödinger's particles, but he is considered to be the first person who felt the need to explain the particle in some other way. De Broglie's concept of the matter wave came to assume a more refined mathematical structure through Schrödinger's wave mechanics. The Schrödinger equation is a differential equation for calculating the wave function which contains the data on the physical quantities representing particles like electrons. Niels Bohr (1885-1962) understood that the reason the electron produces light from radiant heat is that in the electronic model the electron jumps to a different orbit in discrete quantum leaps. On the other hand, following de Broglie, Schrödinger expressed the quantum leap using a mathematical function in a manner similar to the beat pattern of a sound wave. By handling the wave function using this technique, he managed to preserve continuity in quantum mechanics. In his view, the reason the atom emits light was not because the electron makes a quantum jump from one orbital to another; rather, he interpreted it as the manifestation of a beat harmony of a continuous standing wave set up between two orbital levels. When this happens, the beat note corresponding to the wave number of the difference between two frequencies would agree with the frequency of the radiated light. In this way the continuity and verisimilitude of the scientific model of reality was upheld.

     However, Schrödinger's wave equation could only be “seen” by the particles themselves; in other words we seem to be dealing with merely a statistical probability curve here. The particle could in fact be observed only through experiments ― only by using light of a sufficiently short wavelength could the position of the particle be determined. Paradoxically, Schrödinger's wave equation actually revived the concept of discontinuity in quantum mechanics, giving rise to the quip “collapse of the wave function” on the part of observers of the Copenhagen School. So the Copenhagen School ended up denying the continuity and objectivity of the real world. A new worldview had arisen in which all one could be certain of was the empirical reality observed by a given observer. In other words, a new positivism or empiricism had sprung up.

     From the wave equation Schrödinger reasoned through Heisenberg's uncertainty formula and came to the conclusion that his wave mechanics was mathematically equivalent to particle mechanics. The wave function Ψ(r, t) (where t is time and r is position) is at the core of the quantum wave equation depicting the quantum state associated with the wave packet ― yet the value of this function cannot be directly measured in an experiment. However, using statistical analysis, Bohr was able to experimentally determine ∣Ψ∣² , the square of the absolute value of the wave amplitude. Popper, applying the same statistical method as Bohr, interpreted this probability in terms of the square of the amplitude of the quantum wave function. Supporting the substantial existence of the particle, Bohr, based on his statistical analysis, interpreted Schrödinger's wave equation to mean the probability of discovering the particle within a given location and volume of space. If we adhere to Bohr's rule, the value of ∣Ψ∣² for a certain time interval t and a certain region of space r gives the probability of finding the particle there at that time. To generalize Bohr's rule, we can calculate the probability distribution for any physical quantity. Bohr's approach to statistical probability analysis was rejected in Heisenberg's interpretation.

     In a sense, it would be no overstatement to observe that the issue in the many struggles over quantum mechanics is over Schrödinger's wave equation and its interpretation. Even once quantum theory was completed, the conceptual structures underlying the mathematics were not transparent and easy to accept, in connection with the character of the wave function. The wave function Ψ expressed in Schrödinger's mathematical formulation is not something that manifests plainly, but a probability that shows merely “a tendency to occur,” related to the quantitative wave form. It is not a substantial wave like a sound wave or an ocean wave. To solve the particle/wave duality, Popper introduced the concept of the “quantum field,” which is mathematically equivalent in the abstract sense, containing all the features of the wave of the quantum wave function, which was in turn seen as reflecting the probability of finding the particle within a specific time and space. Thus it is impossible to predict precisely where a subatomic particle will be found in time and space; only the likelihood of it turning up there can be estimated. Schrödinger supported this interpretation of the quantum wave function, holding fast to the substantial existence of the particle.

However the Copenhagen School's interpretation was different. For them the wave-like probability pattern was not the probability of a physical object being somewhere at a certain moment; rather it should be interpreted it as conveying the probability of an interaction occurring in the process of observation. The reason for this is that the particle, as an independent physical entity, can only be observed and defined based on interaction with another physical object. For the first time, centered on this probabilistic interpretation, the issue distinguishing Schrödinger and the Copenhagen School became a difference of opinion between scientific realism and logical positivism (empiricism).

     2.  The Standard Model of quantum mechanics and empiricism

        a.  The Heisenberg uncertainty principle

     In quantum mechanics, unlike the method of Einstein's deterministic realism, the empirical approach sets as its task to derive the expected values from theory and check the empirical data obtained by observation instruments for coherence, with the aim of establishing a finely attuned theoretical framework. The empirical methodology starts from the premise, “Only that which can be observed can be defined.” This standpoint concurs with the general systematic character of physics, but what is particularly unique about quantum mechanics is that theoreticians have taken the position of abandoning continuity, causality, determinacy, etc., and certainty of the actual existence of material particles themselves is not acknowledged. Thus the empirical standpoint overlooks the issue of the reality of the particle, nonlocality, the discontinuous quantum leap, uncertainty, etc. To deal with such paradoxes as rear their heads in the positivistic (empirical) school of quantum physics, it eventually becomes necessary to forge another theory following in its wake. In the face of these enigmas of quantum mechanics, the Copenhagen School launched a revolution in scientific realism, establishing a new worldview that challenged Descartes' mechanistic philosophy. Now we no longer see the universe as a vast mechanism linked together by continuous motions of material bodies and subatomic particles; instead we have come to comprehend it as a dynamic whole, mutually interacting in discrete quantum steps. The logical positivism which has become the trademark of the Copenhagen School is armed with a very elaborate conceptual structure possessing logical and theoretical strengths capable of handling the portions that the outdated mechanistic worldview is ill equipped to explain. This treatise examines the foundational cornerstones of the Standard Model of quantum physics, focusing on Heisenberg's uncertainty principle and Bohr's complementarity principle.

The problem raised over the two-fold nature of light and matter is not simply an issue of the contradiction of two natures, with a particle occupying space and a wave smeared out ― it demands the far-fetched assumption that, before taking a measurement, the particle is distributed throughout the entirety of cosmic space with a certain probability, and upon measurement it instantly exists in one place only with a probability of 1. As in the well known paradox of Schrödinger's cat, before observation the particle is spread all throughout the universe with a certain probability distribution, and with the event of observation the probability of its presence at one point becomes 1, while at all other locations the probability of its presence becomes 0. This phenomenon is termed the “quantum wave function collapse.” In any case, if we will, with Schrödinger, look at the tendency of the wave with its particle/wave duality to manifest a particle with a certain probability, it is bound to entail a certain inherent limitation in observing an actual physical quantity.

When we observe an electron under a microscope, after the light strikes an electron, the light passes through the microscope and enters the eye, and so we know the electron's position. At this time, if we use light of a short wavelength in order to know the electron's position exactly, then this high-energy light will disturb the electron, so that we cannot measure the electron's motion exactly. In so doing, inevitably the more precisely we try to measure the electron's position, the more the accuracy of our information on the electron's motion falls off. On the other hand, if we use light of a long wavelength to get a more accurate reading of the electron's momentum, since the light has a low momentum it is more diffuse, so we cannot get a precise measurement of the electron's position. Thus it is not possible to obtain an accurate measurement of any particle's material state, both position and momentum; we cannot avoid a certain degree of uncertainty and error. Then in connection with such uncertainty, given the particle/wave duality, the measuring equipment interacting with the experimental state, and the limitations of the classical concept, what we can express by an exact mathematical equation is the uncertainty principle.

     If we trace the process by which the uncertainty formula Δp Δq ≧ h/2π was established, this formula is a theorem that was logically derived from the statistical theory of classical wave mechanics. Contrary to classical mechanics, where if the position and velocity (momentum) of an object are precisely measured, it is possible to predict its future, in quantum mechanics, according to the uncertainty principle, based on the present physical state it is not possible to predict its future state. At this point we have no choice but to amend the deterministic causality of classical mechanics to the probabilistic causality of quantum mechanics.

     In regard to the indeterminacy posed by the uncertainty principle, the basic problem is the event of observation, taking place between a particle as the object under observation and the experimental equipment including the observer. To solve this problem, in the beginning Heisenberg insisted that, in the experimental setting, the act of observing on the part of the observer himself was the cause of the uncertainty. Einstein, Podolsky and Rosen, conducted a thought experiment in which an electron and positron pair are separated between the earth and Andromeda galaxy in the effort to disprove the Copenhagen School's uncertainty and nonlocality. In their experiment, they tried to measure the position and momentum in such a way as not to disturb the particle, and following the observer's intervention, and they ended up encountering a new state ― Heisenberg's observation problem all over again. The EPR experiment initiated by Einstein was deliberately set up with the intention of overthrowing the doctrines of the quantum mechanical uncertainty and discontinuity occasioned by the observer's interference. He maintained that, for quantum mechanics to be a complete theory, under conditions below the threshold of observer interference with the experiment, if the two particles of an original electron-positron pair are separated remotely to where there is no observer at all, the two particles' position and momentum can be precisely measured, since the two influence one another via mutual interaction through EPR.

     With the EPR Einstein upheld the validity of the theory of relativity, that “no object can travel faster than light,” and proposed an experiment free of any observer interference whatsoever, but a new problem was raised: “How could entangled particles respond to one another by exchanging information, without exchanging some kind of signal at light speed?” In connection with this enigma, Einstein insisted that the cause of the uncertainty lay not in the subjective factor attributable to the observer but in local “hidden variables” among the particles' objective properties. From the uncertainty principle, the object of observation and the experimental instruments cannot influence one another based on the principle of locality, but the reason the uncertainty arises is due to local “hidden variables.” If we can know these hidden variables, we can solve the problem of uncertainty, and by solving this, we can uphold the determinist position. Countering this, Bohr held that uncertainty was a problem that could not be solved by “local hidden variables”; rather the observer affects the entire experimental setup; the two particles are joined in a network stretching across the entire universe ― thus nonlocality is a natural principle.

Thirty years later Einstein's idea of “hidden variables” was refuted by Bell's theorem. According to EPR, we postulate “hidden variables”; due to hidden variables both position and momentum cannot be simultaneously measured to the maximum degree of certainty. That the “hidden variables” hypothesis is not equivalent to the “uncertainty principle” is evidenced by the mathematical formulas themselves. Since Heisenberg's uncertainty principle, involved in the whole experimental setup, cannot now be revoked, Einstein's “local” hidden variables hypothesis must needs be subject to reexamination. If the “local” hidden variables conjecture is not to be replaced by a “nonlocal” hidden hypothesis, then we are confronted with the unavoidable situation of pointing out an error in the uncertainty principle. The fierce debate over EPR raged on unabated, splitting scientists into two camps ― those advocating continuity in quantum physics and others supporting discontinuity. Thereafter, Einstein's conviction, championing continuity, realism, and scientific objectivity has been passed on to his followers, while new opponents continually rise up in pilgrim crusades against the Copenhagen School's “Standard Theory” and its “interpretation”, armed with ever new weapons.

        b.  Bohr's complementarity principle

Niels Bohr considered that his uncertainty principle had to be applied to all physical quantities; the uncertainty principle when generalized hinted at the pair concept. Niels Bohr came up with the complementarity principle ― particle/wave, position/momentum, measuring time/energy, and so on. In physics many natural properties exhibit such duality. Then going beyond the observation that duality is a natural property, he pointed out that, based on the uncertainty principle, pairs of complementary quantities are observed to exhibit one of the two more precisely when sampled, showing an across-the-spectrum limitation in measuring particle attributes. Two complementary physical parameters cannot both be sampled accurately in tandem. That is, at the instant of observation, this double complementarity breaks down and only one facet is accessible while the other facet either disappears or is hidden.

In the quantum mechanical world the complementarity principle reigns strictly, whereas in the macroscopic world physical states overlap, and the objects being measured have very large physical quantities, so the uncertainty principle does not manifest. Deterministic causality holds sway in the macroscopic world, where the physical quantities of quantum mechanics average out to those of classical mechanics. Likewise on the average the quantum physical quantities tally up to exactly the values obtained by Newtonian mechanics, and the quantum laws follow those of classical mechanics. This property is termed the “correspondence principle.” The microscopic world is in the domain of the uncertainty principle tied to the Planck constant, but for large masses in the macroscopic realm well beyond the domain of Planck's constant, the uncertainty principle does not apply and the classical physical laws may be applied as is. In this sense, although the laws of quantum mechanics do not contradict the laws of classical physics, it should be kept in mind that they are more comprehensive in application.

     Following the same pattern, the complementarity principle, covering both microscopic and macroscopic worlds, has played a decisive role as umpire in the measurement problem, and the problem of cognition, which is naturally raised by the complementarity principle, could transcend the position of logical positivism, even going so far as to touch upon solipsism, burgeoning with its innovative claims. If we first investigate the logical character of quantum mechanics, we see that quantum mechanics, rather than trailing in the wake of the deterministic causality of classical physics, follows a probabilistic statistical causality instead. Logical reasoning rooted in probability and statistics flies in the face of classical formal logic with its principle of the excluded middle, and the logic of complementarity would seem to pertain to “heads or tails”, to a kind of three-pronged logic. This is because unlike classical mechanics, in quantum mechanics, each pair of attributes ― particle and wave, position and momentum, and so on ― do not coexist as independent variables, but have mutually complementary and at the same time contradictory properties. Heisenberg and Bohr's positions in the debate over how to interpret such a state of complementary coexistence differed.

Heisenberg's matrix function is a mathematical parallel dispersion function centered on the particle theory. Bohr, in contrast, viewed the position of the electron as a particle state and interpreted the momentum using de Broglie and Planck's wave function with rotating complementarity, different from Heisenberg's parallel complementarity. After fierce debate Heisenberg accepted Bohr's interpretation, though they differed in dimension, and the notion of particle and wave bonding together in a cyclical relationship became established in quantum mechanics. According to Bohr, the complementarity of particle and wave, position and momentum, observer and observed object, and the rest does not mean parallel complementarity but rotating complementarity. That is, the complementary relationship is not a parallel relationship on the same plane or dimension, but rather a serial or cyclical relationship in which the two attributes of one complementary pair rotate through two mutually perpendicular planes or dimensions.

This cyclical complementarity principle caused the paradigm shift in our understanding of quantum mechanics. Thus an instrument was prepared enabling us to see the world of everyday experience by our normal senses as “real”, and at the same time, against the background of one visible plane, hinting of the existence of another hidden, complementary plane of reality. In the world of our normal sense perception we are used to the dualism of subject and object. The overall character of reality ― the “big picture” ― is not readily visible, yet we tend to believe the shapes that appear to our five senses is “reality.” Namely, we are accustomed to seeing only one facet of the complementary nature of things. According to the uncertainty principle, the more precisely we measure a particle's position, the more diffused is the wave's momentum and it becomes increasingly impossible to measure; on the other hand, the more accurately we try to determine the momentum, the particle's position becomes smudged and we can no longer get an accurate fix on it. Through our act of observation, the complementarity thus engendered leads to either the one or the other side of the duality being amplified, and its counterpart being concealed, and this succession proceeds in a cyclical manner. As if the momentum were hidden, even though we try to disclose it, by our act of observing it the momentum is concealed, reverting to a state of latency, of being only potentially extant. The hidden information on the momentum must indeed be hidden somewhere within the complementary structure of the “Weltall”, but in any case this information is required to be hidden under the formalism of de Broglie's formula P = h/L.

     In Young's experiments, the interference fringes of light particles appear even without any observer interference, while in Heisenberg's thought experiment on the indeterminate particle/wave duality another problem crops up in Young's experiment due to the observer effect. In particular, as an example of the paradoxes inherent in quantum mechanics, at the time of observation, the uncertainty issue first shows up, and then the quantum wave collapse. All these effects stem from the observer's interference. Existing up to the moment of sampling as complementarily entangled modes of existence, if the particle/wave duality appears as a particle by being discovered to be such by the observer, the wave component starts getting blurred, and finally it ends with the wave collapse. Try though we might, we cannot mathematically describe the collapse of the quantum wave function. In the interval before and after the event of observation, the observer has interfered; at the instant the experimenter discovers the experimental object the quantum wave collapse takes place ― a problematic event which classical mechanics is hard put to solve. Respecting this enigma, Bohr focused on the role of the observer, and pointed out that the observer him/herself is not the sole exterior factor impinging on the laboratory setup; through the experimenter's choice only one facet (dimension) indeed manifests itself, but this is patently not the totality of its existence, as he asserts in his interpretation. As if Plato's philosophy were being revived, a particle the moment it is caught appears in the guise of a particle, while in reality another dimension is hidden from view, the quantum wave form, all together constituting the totality of the entity being observed.

In the microscopic realm of quantum mechanics what we call the “particle” is not some kind of granule, but probability patterns within an indivisible universal web and exerting influences on one another, while the human being along with human consciousness, which we call “the observer” are all included within this ubiquitous web. Understanding it this way, the universe of quantum physics cannot be decomposed or analyzed into separate components; rather it is a dynamic whole, exhibiting the intrinsic property that all its parts are connected mutually to one another. With the EPR experiment Einstein nailed down the legitimacy of the complementarity theory: He had been unable to resolve the problem of information exchange between two partners of an entangled particle pair almost infinitely remotely separated from each other, in other words he could not solve the nonlocality problem. Thus Einstein with his thought experiment intentionally, unexpectedly, opened the way for the holistic worldview of the Copenhagen School.

     The whole picture still had to be clarified, and now, thanks to Bohr, the portion of the deterministic worldview which required understanding in light of the big picture was now confronted with the nondeterministic Weltanschauung. Whereas in classical mechanics those portions governing overall character and behavior are mechanistic structures, in quantum mechanics the portions that determine character and behavior are organic structures so to speak. Such a holistic model can just as well be synthesized from the Standard Model too. In this systemic shift in perspective and way of thinking, it is now the human act of observation which takes the center position. In the microscopic realm, unlike the macrocosmic world, the object of observation is both determined and interpreted by the observer. Thus the paradox that crops up stems from the mode of interpretation of quantum mechanics, which itself becomes the empirical circumstances and arrangement. This cannot be grasped with Cartesian dualism, the position Einstein took; but only when we regard subject and object of cognition, or observer and object under observation, as merging together in a holistic state of oneness, can it be encompassed.

     What the complementarity principle contends is that when we select the “reality” we desire to see as the object, then that is the form which will manifest. By choosing one out of the many possibilities in our mind, then that is the reality which will take form. The way Kant looked at it, what we call “reality” is hidden within matter itself, but to the observer it takes the form of reality in the “form that is seen” ― this is none other than the form constructed by the observer himself or herself. As a corollary of this interpretation, the deeds which take place moment by moment in our normal everyday lives are themselves the acts which construct reality, and on each occasion as we choose the object and method of observation, reality manifests itself in a different form. Thus “reality” as we call it is not an existing something; if it were not for our perceptual “method”, if we did not even take it upon ourselves to perceive, what we call “reality” would not even exist at all. To take an example, when one photon emitted by a star many years ago now enters my eye, I state that this photon is a “reality”, but if I were not standing there, it wouldn't exist.” Because we cannot perceive the precise choice we call down within the domain of a photon or an atom, all that is revealed is the “mathematical reality” which we call the quantum wave function. In such a way what we call “the world” is not that which objectively exists “outside myself”, but just one plane or facet of the overall complementarity manifesting itself to me. For such a reason that quantum mechanics is characterized as “logical positivism” or “empiricism” lies here in the way the world reveals itself to me. We choose the object to observe, and when we observe that object, the particle-wave continuity breaks down and discontinuous uncertainty is what manifests. Simultaneous with the act of observation, all the continuity associated with the object breaks down and just one dimension of the complementarity reveals itself to us. In this sense, at least in the microscopic world, the observer constructs and creates reality. In going through this process, quantum mechanics transcends empiricism to where in quantum theory we can make the solipsistic observation that “The world is I.”

     Bohr explained the quantum paradox in terms of the complementarity of the observer's “seen world” vs. the “hidden world.” Heisenberg, linking this dormant reality with the uncertainty principle, came up with the idea of a “third reality” or “intermediate reality.” The wave of the mathematical formula bears with it the potential for existence, and the moment the observer turns up a particle, this event causes the collapse of the wave function, and its probability drops to zero ― this is a perplexing fact that can only be understood if we suppose the existence of at least three different levels of reality. Bohr, also a proponent, postulated at least three levels of reality, namely the real world of the discovered particles, the realm of the quantum wave function as the world of potentialities, and the realm of management of the observation process along with other assorted functions. The totality of reality (the “Weltbild”) is pictured as holistically blended by the mutual interaction of these three realms of reality, through the complementarity principle.

�U. Foundation of Quantum Mechanics based on Unification Thought

“Unification Thought as a Universal Science” recounts how many philosophers from Plato up to Husserl and then the Encyclopedists of the Enlightenment and the Unified Sciences Movement of the Vienna School, along with others, have attempted to bring unity among the fields of knowledge, with various methodological approaches and their own unique theoretical foundations. In connection with the topic of today’s discussion, in light of such a background, the present paper advocates the position of Unification Thought as a Universal Science, in support of the overall context of this forum. First of all, let me cite some passages from my dissertation, “Unification Thought as a Universal Science.”

This paper was able to secure the subjective condition of universal science from the evidence of spiritual apperception, which executes the role of the rational intuition through the epistemological foundation of universal science, and from the intentionality of the consciousness or the spiritual apperception. In regard to the problems in the construction of experience, Unification Thought has obtained the objective condition of universal science by proposing the inner hyungsang in the internal sungsang as the objective world within consciousness in regards with the intentionality of spiritual apperception. Universal science demands a logical basis through which all aspects of the experiential world as well as intellectual studies can be guaranteed. This may be the reason why philosophical groups such as the Enlightenment and the Unity of Sciences Movement, which sought to establish the foundation of universal science on individual studies such as mathematics and physics, etc., were discouraged.

“As the object of consciousness in Unification Thought, the inner hyungsang is accorded priority as the basis making experience possible, and possesses the logical basis that can encompass moral laws, mathematical systems, ideological laws, scientific laws and the entire world of life. Through such work, the subject condition and object condition making up the logical structure to establish the basis for universal science were secured.”

The task that stands before us is to establish firm philosophical grounding based on the structure of the Original Image for all the rational foundations of Unification Thought. As I mentioned above, in establishing “mind” and “the world is I” as foundational principles of Universal Science, we are not speaking of the egocentric human mind; we are speaking of the mind that shines forth in the structure of the Original Image — the internal structure of the Original Sung-sang. The sung-sang which is the human mind stands in an analogous, ontological relationship with the Original Sung-sang in the structure of the Original Image; above all its root is to be found in the Original Image. Once we can understand the inner structure of the human sung-sang, then we gain a glimpse into the form of the Original Image — the reason being that particles likewise resemble one another, as they stand in an ontologically analogous relationship. The structure of the Original Image never directly appears to our human eyes, but this realm is accessible to the human mind. And so paradoxically, it is for this very reason that we can even fathom it at all. In Unification Thought the structure of the Original Image is the ultimate rational and ontological foundation for all existing things, and our human mind is capable of grasping it by way of analogy based on the structure of our own consciousness. Now that we have such a frame of reference firmly in our grasp, let us turn our attention to look at the inward nature of modern physics with particular reference to quantum mechanics.

1. Foundation of Quantum Mechanics based on Unification Thought

The speaker intends not only to clarify a paradox that has cropped up in quantum physics and to uphold the general consistency of the theory, but also to carefully consider whether, from the systematic standpoint of Unification Thought, we may somehow comprehend and acclaim the vivacity and coherence that is apparent in quantum physics.

First, let us critically examine the solipsism evident in quantum mechanics. In Unification Thought, the structure of the Original Image abides as the ontological and rational cornerstone for the entire structure of existence. Thus when we view the structure of the Original Image in Unification Thought and the levels of existence in its ontological system, the existence and interactions of particles are uniformly regarded from an analogical perspective. For this reason, the egocentrism apparent in quantum mechanics, where “The world is I” in particle theory, finds a parallel in Unification Thought in terms of the structure of the Original Image, though of course the structure of the Original Image summons up an entirely different level of significance. The most signal feature of particle physics is its treatment of the dubious reality of particles and waves, so markedly at odds with classical physics; moreover we ourselves as the observer are given to know that we form an integral participant in the reality of our object. The patent solipsism of the particle theory, empowered by the uncertainty principle, is no logical contradiction but in fact is the strong point of the hypothesis. On the other hand, its glaring weak point is that it runs directly counter to our everyday experiential reality and common sense. The subjectivity of the observer in the quantum physical paradigm leads us to wonder if perhaps the real existing world of common sense, experienced through our five senses, is after all ephemeral — nothing but a phantom. In the quantum physics laboratory environment there is a tendency to doubt the surroundings as something created by the observer. Without the quantum leap, there could not be the phenomenon of the observer “seeing” the object of his observation; therefore only by virtue of the so-called “quantum leap”, that discrete and indeterminate state, can the world be seen at all. Thus blind, hands-off observation that does not attain the stage of cognition cannot be afforded the status of concrete existence; truly “To see is to know.” Therefore from the standpoint of the egocentrism of quantum theory, we can affirm that it is through my consciousness that this world, “seen” through my five senses and proceeding through my cognitive processes, takes shape and is constructed. Thus the world is truly “I”. The new physics has developed into a new scientific movement where the inherent solipsism of quantum theory shares common ground with Oriental philosophy.

In Unification Thought what we know as the world is classified into the world in its original state and the presently existing world; human beings are the mediator between the two worlds. In contrast to the observer-centered Weltanschauung of quantum theory, Unification Thought portrays a cosmos comprising the world of existence and the human world – a perspective that joins the existing world and the subjective world centered upon “I”.

In an overview of the history of philosophy, we would place quantum theory with its solipsism squarely in the category of subjective idealism. A weak point in its philosophical system shows up in its rather detached attitude to the real world, where a person can trip and fall over a jagged stone on the way to work. The protruding rock in the path didn’t know passersby would stumble on it, it was there as a “reality call.” But if in his self-delusion he denies its reality, gets a knock on the head, and calls that an illusion — is he going to call the pain an illusion too? The difference here between subjective idealism and quantum theory is that in the former view that “The world is my emblem,” we come to question the emblem (concept) of the individual as subject; in the latter, quantum theory, the individual and the whole go hand in hand, and the egocentric concept of existence in the “World is I” paradigm comes into question.

In the microscopic world the uncertainty principle comes to the fore by virtue of the non-localized wave function. Then does this impinge on macroscopic phenomena in the realm of classical physics? According to Niels Bohr’s complementarity principle, the answer is in the affirmative. Hugh Everett III and Eugene Wigner usher us into even more counter-intuitive paradoxes in the observer-centered paradigm of quantum physics: their theory of parallel universes, the multiverse, dispenses with the problem of consciousness. With a touch of humor Professor Wigner went on to pose the famous “Paradox of Wigner’s Friend.” Figuring out a way to shunt this troublesome egocentric “I” out of the picture in quantum theory, Everett postulated an infinity of potential worlds of the non-localized quantum wave function, each budding or rupturing off into a multiplicity of all the possible substantial worlds “like this world” — in other words, parallel universes, which he also termed “quantum machines.”

Meanwhile Noble prize winning physicist Eugene Wigner, with his trademark conundrum “Wigner’s Friend,” worked ardently to shore up the “I” of quantum theory. Together with his professor and friend, Wigner “created” the particle, while his friend of friends assembled a universe of boxes, endlessly packing boxes within boxes, boxes within boxes…..boxes within boxes — until he reached the final observer, which was “I”. Here, the solipsism of quantum theory had reached its final terminus. As Wigner explained based on the solipsism of the quantum theory, this means that when we see one and the same flower, we each have different sensations and realizations based on our everyday experiences. In Wigner’s quantum mechanics, ultimately we reach the point where we “see”; but this is not an outward, accommodating act. Rather, looking at things from the observer’s standpoint, the observer himself/herself forms the object of cognition and he or she undertakes the active step of creation.

From the standpoint of the observer, outside of the act of “seeing”, he/she cannot perceive, recognize, or acknowledge the reality of any other object — in this sense no outward existence is real. Wigner’s view differs from Bohr in this point. Furthermore, regarding the act of “seeing”, the observer him/herself contains the act of creation; in this stepwise inference process the final, ultimate observer is decided. As for the observation act of “seeing” the flower, the act of “seeing” the flower includes the final observer and simultaneously a countless number of Wigner’s friends. Through such a serial process, our experience of “seeing” occurs to ourselves and is shared together with the final observer, attaining “consciousness” as the subject of quantum mechanics. At this point Leibniz’s determined compatibility theory comes to mind. Actually Wigner’s paradox differs from the determined compatibility theory in the fact that free consciousness intervenes in the observer’s choice, namely because in all sorts of circumstances our “seeing” implies that we “made a choice.” Thus quantum mechanics’ uncertainty means that free will, i.e. the observer’s so-called “choice”, finds a place in its worldview of discontinuous nondeterminism.

The reason Unification Thought takes a close look at quantum mechanics is because the observer’s choice posited in its uncertainty principle upholds the doctrine of “free will.” The observation by Wigner’s friend of a subatomic particle, Wigner’s particle observation including his friend, the friend of Wigner’s friend……. In final analysis, all his friends are included in the act of observation by that final observer in achieving the observation of an elementary particle, so in final conclusion the observation of a subatomic particle for the first time ever is a simultaneous event. Our conclusion is that the very first person to observe the particle and the very last one in line all count as simultaneous observers, and this completes it! This is Wigner’s definitive quantum physical answer to the act of “seeing.”

Considering this from the standpoint of Unification Thought, this entire succession of acts of quantum mechanical observation alludes to the combined process of intentionality in the structure of the Original Image and intentionality in the human mind. The point where Unification Thought differs from quantum mechanics is that, whereas in the solipsism of the quantum theory my observation is exactly simultaneous with the final observation, in Unification Thought, the intentionality of the original sung-sang in the Original Image is of a level qualitatively different than that of the intentionality of the human sung-sang. Unlike the solipsism of quantum theory, where the consciousness of “I” and the consciousness of the “final observer” possess one and the same “choice” and one and the same “free will”, according to Unification Thought, the free will of the human sung-sang is not regarded as having the same conscious intentionality as the free will of the original sung-sang of the Original Image; rather each ontological or developmental level is considered to have its characteristic degree of independent free will.

The reason that the uncertainty principle has come to the fore in quantum mechanics is in support of the all-important free will as expressed in the intentionality of consciousness in Unification Thought — namely it was disclosed for the sake of “observer choice” in the experimental setting. Then the reason the Unification Thought analysis of quantum mechanics is so persuasive is that it is able to secure the continuous objectivity of the real world which quantum theory with its solipsism is unable to grasp. In stark contrast to quantum mechanics which denies the reality of the world “outside of myself”, asserting that the rock I trip over on my busy way to work does not really exist but is merely a phantom — according to Unification Thought, the stumbling block definitely exists and is ready to wake us up to its experiential reality.

2. Inner Hyung Sang in UT and the Mathematical Principles of Quantum Physics

In the process of searching for scientific formulae, what is emphasized above all is the scientists’ ambitious quest for truth. In Unification Thought this is expressed as the directivity of consciousness in the inner sung-sang. This conscious intentionality is the very source and basis driving the scientific civilization to progress at an ever quickening pace. When they encounter a scientific or technical roadblock, the researchers devote untold efforts racking their brains and conducting experiments in their search for clues to solve the challenge. At such a time the scientists put themselves through rational and experimental contortions, mobilizing all means at their disposal, absorbing themselves toward solving the problem. All this behavior stems from the intentionality of the consciousness. In such a way, at the scene of scientific investigation, whether empirical (inductive) or rational (deductive), the work is expedited on the practical level; relations of junior and senior and such impediments are brushed aside — you do not see one coworker trying to dominate another unilaterally, or undermining another’s work, or putting his colleague to shame. In scientific research, inductive and deductive methods mutually support each other. Therefore, regarding all this from a Unification Thought perspective, the spirit of scientific research in its quest for natural laws stems from the directionality of consciousness (inner sung-sang), and corresponding to this, the scientific laws (inner hyung-sang) that come up in the scientist’s mind. These harmoniously interact with one another in a rational, systematic structure.

Then, what actually are these scientific laws, as the object of scientific research? If these scientific laws do not exist as experiential realities in our everyday world; then are they presented to our human mind pure and unadulterated through experimentation? The question of how we gain access to the scientific laws, whether by going through an inductive process, or occasionally they just suddenly pop up in our mind through an educated guess — lately has risen as an important issue in the philosophy of science, leading to a renewed controversy between the empirical and rational approaches. Isaac Newton pored over Kepler’s studies in the motions of the celestial bodies, observed the phenomena, and worked out the law of gravitation. Ampere likewise, through careful observation of electric current, inductively, discovered many laws governing electricity.

Meanwhile Immanuel Kant, learning of Newton’s new discoveries, considered universal gravitation as a law that could be deduced from certain a priori principles. Whether the groundwork for discovering scientific laws is experience or reason, in either case the human mind can appreciate and understand such laws. The Unification Thought system considers the scientific laws not simply as factually existing laws regulating an exterior, inanimate natural world, but as principles which take their place among the pre-existing norms immanent in the internal hyung-sang within the structure of the inner sung-sang of the human mind. So then the scientific principles that come up in the scientist’s mind are not something created by the scientist; instead a whole intrinsic world of order concealed somewhere within rises up in the scientist’s mind. This hidden order is the inner hyung-sang of the Original Sung-sang in the structure of the Original Image. With the human mind standing in a relationship of existing (projected, outward) analogy to the Original Sung-sang, the scientific laws conceived in the theoretician’s mind are a reflection of the underlying order in the inner hyung-sang of the Original Sung-sang.

Just as Newton understood the law of gravitation as a real principle governing the world of phenomena, and in the same way that Kant considered this as a principle constituting the material world and residing as a pre-existing law in our mind, Unification Thought does not view the scientific laws from a myopic, one-sided perspective. If scientific laws were not instituted as principles governing the phenomenal world, the entire world order around us with its assemblages of matter would collapse into a tangled chaos.

And if the scientific laws were not imprinted a priori within our minds, we would have no basis enabling us to recognize these principles operating in the world about us, and no matter how much professors would try to drum them into the heads of students, they simply could not relate to scientific principles. Within the inner hyung-sang of our mind, pre-existing scientific principles are already implanted, which when presented with the scientific principles imbued in the phenomenal world for the first time, are able to acknowledge and comprehend them. In such a way, the task of researchers investigating the laws of the natural world is none other than to fulfill the act of discovering and cognizing the scientific principles bestowed in the inner hyung-sang realm of the internal sung-sang. Let us now set out to examine more closely some of the mathematical principles of this theory which have been elaborated in the process of establishing the theoretical underpinnings of quantum mechanics.

Before work on quantum mechanics began in earnest, the leading paradigm of physics was the model of dynamic systems based on Newtonian determinism and mechanism. Up till the time that the dynamic systems paradigm was perfected, there was an era of scientific revolution lasting 150 years, during which period the “giants” whom Newton spoke of — Copernicus, Bruno, Kepler, Galileo, Descartes, and others — were on everybody’s lips. These figures to a man were sworn to the dogma of continuity and causality. On the foundation of this worldview, the influence of Descartes’ analytical geometry and the mechanistic ideal reached all the way to Einstein. At this point, let us trace the foundational issues all the way up to Einstein, following Descartes’ model standing upon mathematical continuity.

Differing from the properties of material oscillations such as sound waves, ripples on water, and other types of matter waves — light had to be explained in a different way if it were to be viewed as a wave. When the phenomenon of interference was discovered in 1801, the classical mechanical particle theory of light was overturned. This was Young’s double slit experiment. At that time, when Young came out with his wave theory in contradiction to Newton’s corpuscular theory of light, inevitably he was mocked and snubbed. But Faraday discovered electromagnetic induction, and Maxwell presented mathematical equations, so that by the 1860s they had begun to see the light. In 1900, conducting experiments in black body radiation, Planck revealed that light was emitted discontinuously in discrete quantities of energy, and issued “Planck’s formula” E = hf (where h is Planck’s constant and f is the frequency). The quantity h was discovered to be 6.62607 x 10^-34 joule-second—an extremely tiny amount. Each type of light has different radiant energy bound up in its energy packets (particles) according to its frequency. As we can see through this, the particle concept took on the character of a theory, but when Planck’s formula first appeared everything turned around. Then along comes Einstein with his photon hypothesis, contemplating taking quantum mechanics as his Ausgangspunkt, and assuming he could apply it in his research on light. But already by that time, based on Planck’s constant and the concomitant particle model, the photon was discovered.

In 1922 de Broglie put forth his matter wave as a solution to the evident particle-wave duality of light. He predicted the stationary wave — de Broglie’s matter wave; it was up to Bohr to calculate the orbit and present it in his atomic model. The trajectory and the electron’s momentum P were in agreement with the value h/λ, conforming to Planck’s constant and the light wave aspect of the matter wave. Thus P = h/λ. In this way we behold Bohr’s orbital in the form of a standing wave, the problem of the “quantum leap” was solved, and we could preserve “continuity” in quantum mechanics. The de Broglie formula lent new prospects to the particle theory through the formula E = hf which agreed with v = E/h, describing the correlation of the energy E from Einstein’s photon hypothesis and the frequency v. Now they came to realize that, according to Planck’s formula E = hf, the frequency of the matter wave could be determined by the particle energy; using de Broglie’s formula λ = h/P the wavelength could be calculated from the particle momentum. Actually the wave of the matter wave is well within 1 Å, the dimension of the atom, which would be the maximum breadth of the trajectory, so if a light wave has 1/5000 of that wavelength; it is indeed an extremely tiny wave. Following close in the heels of de Broglie was Schrödinger, the champion of “continuity” in quantum mechanics. Skeptical of the Copenhagen School’s “Interpretation,” Schrödinger adopted de Broglie’s matter wave concept to complete his “wave mechanics.” Next we must turn our discussion to examine Schrödinger’s wave mechanics in detail.

Before examining the mathematical formulations supporting “continuity” in quantum mechanics, let us first present a brief overview of some fundamentals of Unification Thought which we will refer to in addressing these matters. First we take a closer look at the autonomous “four position foundation” of the original sung-sang. Unification Thought sees that all things possess two categories of aspects, namely, an aspect perpetually seeking to maintaining one’s own identity, and an aspect striving to change and develop. We divide these two types of aspects into what we call the “autonomous four position foundation” and the “developing four position foundation.” The autonomous four position foundation and the developing four position foundation each comprise four elements: center, subject, object, and result. A point to this: although they are similar, the difference is that at the center of the autonomous four position foundation is “heart”; at the center of the developing four position foundation is “purpose.”

Researchers’ scientific quest and their succeeding outcome, the mathematical equations of quantum mechanics which arise in the minds of the investigators, stand in an internal give-and-receive relationship. The mathematical formulae, part of the hidden order governing nature, are latent in terms of objective information in the internal hyung-sang of structure of the Original Image, but through the labor of the scientists who discover this latent order, this information rises to the surface in our minds and is given expression. Thus, to explain the process of scientific research in terms of a rational structure, it proceeds as follows: center—scientist (subject)—mathematical formula (object)—realization of the goal (result). This process forms a four position foundation. In the process of forming such a four position foundation, those mathematical formulas which uphold the continuity of quantum mechanics direct the “pre-eminence” of nature and their “self-identity”; as such these formulas must contribute toward such an end.

Even if the particles enter into a relationship with other substances and experience change, the former term and the latter term of the quantum mechanical mathematical formula functionally maintain the same equivalence, and the physical quantities that follow them will be experimentally verified. For this reason the equations preserve their overall “self-identity”. If such natural striving for “pre-eminence” and “self-identity” were denied, then the autonomous four position foundation would be destroyed and the continuity and causality of nature could no longer be validated. For this reason the autonomous four position foundation of Unification Thought is maintained, for the sake of the foundation of “self-identity” and “continuity”; therefore the basis of the mathematical formulas of quantum mechanics which insist on continuity maintains its autonomous four position foundation. That is, the mathematical formulas upholding continuity in quantum mechanics, as entities that have forged their own four position foundation in the structure of the Original Image of Unification Thought, stand as fundamental principles maintaining “continuity” and “self-identity” in nature.

Next let us examine the mathematical patterns of the Copenhagen School positing discontinuity in quantum mechanics. In the following discussion we look at the Cartesian model as it applies to physics, emphasizing continuity and causality in nature. This is elaborated through the system of algebraic (analytical) geometry; if we perfectly establish this mathematical body, mathematics’ qualification as a universal science will be confirmed and Descartes’ ideal can be realized. However, this holy grail of the universal field of knowledge has been challenged and it has begun to rupture on account of the standard interpretation of quantum mechanics in regard to “uncertainty” (“indeterminacy”). As a universal science, Unification Thought’s model of the Original Image and the solution derived from it resolves the most difficult problems of quantum mechanics and presents a new model which is capable of handling the troubling issues of “indeterminacy” and the standard interpretation. Since Heisenberg’s uncertainty principle, formulated as △p·△q≥ h/2π, was examined in detail earlier, we will proceed to Bohr’s “quantum leap.”

Bohr compiled the atomic orbitals, starting with the electrons’ momentum according to Planck’s Constant, with integral multiples of h (1h, 2h, 3h, …), which number is called the “quantum number.” Then the electron orbits, in order as the mean radius of their ellipse, were arranged by their mean squares (1 : 4 : 9 : …). All this was conceived in order to build the “atomic model.” Then when matter is heated, the reason characteristic colors of light that are emitted is because the atoms enter an excited state, and when the electron makes a “quantum leap” back to a more inward orbit, it releases a quantum of radiated energy. Taking this one more step forward, he viewed emission spectra from the standpoint of classical electromagnetic dynamics, seeing in the spectrum of light a Fourier series, as the electrons revolve around the atom, synchronizing their frequencies with one another, and by induction he came up with the correspondence principle ν = τω. That is, when the electrons in their normal state experience orbital perturbations, they climb to a new orbital representing a higher energy level. The optical frequency ν is its normal ground state, which must be restored by the number of electronic orbital motion shifts (n⁻) through the Fourier series a τ number of times along the harmonic function until it conforms to the frequency τω. By so doing, with his correspondence principle, Bohr avoided relegating quantum mechanics to a classical mechanical field; rather what he was striving for was to generalize classical mechanics.

Working toward a standard theory of quantum mechanics, Heisenberg with his uncertainty principle △p·△q≥ h/2π together with Bohr’s correspondence principle forged the two pillars of the Copenhagen Interpretation of quantum mechanics. A special feature of the Copenhagen Interpretation is their tools for observing the ultramicroscopic world of subatomic particles — but what’s most special of all is their willingness to include other observers together with their First Observer.

In all the above the presenter brought in several general mathematical formulas or equations which he explained. The presenter has expounded “Realism”, asserting the “continuity” of quantum mechanics, and likewise introduced “Epistemicism” which upholds “discontinuity” in quantum physics. First, we need to try to evaluate Realism and its associated mathematical patterns. As for the position of Realism, while the particle/wave duality of light and matter is universally acknowledged. While quantum mechanics itself is split on these issues, the theoreticians by and large have interpreted quantum mechanics using these same mathematical patterns in favor of continuity and causality. Among these, Young and Einstein advocated the particle position, while Planck, de Broglie, Schrödinger, et al. took the side of wave theory, each developing their ideology in separate directions, basically leaving out the differences, yet they all likewise supported quantum mechanical continuity and determinism. The formulae they invoked in order to support their theories pertain to the inner hyung-sang of the Original Image in Unification Thought. The quantum physical formulae following Plato’s method are universals of the realm of Idealism, and the quantum mechanical phenomena following this method are individual cases.

In this respect Plato’s Idealism would definitely belong to the inner hyung-sang in the Unification Thought structure of the Original Image. The presenter, taking after Plato’s model more than Descartes’ model, lays the groundwork for Universal Science; though I consider it has validity, I would venture that is because he makes an excellent case for Plato’s idealism. Then in keeping with the rationalist tradition, we call upon Plato and Descartes, the entire mathematical deductive system of reasoning, the Scholastic ideal, along with the objective realm of forms of the Ideal which Plato advocated, without laying down the premises for it, the reason being that the Scholastic ideal of Universal Science had never been attained. In this respect he promotes mathematics as a universal science; unlike Descartes, he holds that all academic fields can be reduced to mathematics. Calling to his support the realm of Idealism, the world of the objective concept, based on the foundation of the Scholastics, and even Plato — he would be seen as promoting the genuine Scholastic Ideal. In this regard, Plato’s Idealism has contributed immensely to the foundations of the Universal Science of Unification Thought. To speak in analogical fashion, the Inner Hyung-sang in the structure of the Original Image in Unification Thought may be said to belong squarely in the realm of Plato’s Ideals.

Maxwell’s mathematical equations, de Broglie’s formulae, Planck’s formulas, Einstein’s tensor equations, all the way up to Schrödinger’s wave equations — the challenges of this entire scientific quest, in a word, to pack all these together in one and explain it all through mathematical formulations, in support of natural causality and continuity, [All this] must be relentless and untiring labor! Viewing this from the perspective of Unification Thought, the quantum mechanical mathematical formulae, as principles bestowed a priori in the Internal Hyung-sang of the structure of the Original Image, the scientists had to discover these pre-existing natural laws and, operating purely upon Principle, explain them to the world at large. The pre-existing laws and principles hidden in the Inner Hyung-sang, once upon a time or at some time yet to come, by way of scientific wizards and geniuses, this Image shall finally make it to the surface. No matter how we look at it, by Divine Providence and the natural order of things, whether the mathematical formulations hitherto hidden buried deeply in the Inner Hyung-sang of the Original Image should remain forever hidden to the secular system of this world, we could only wonder. The titanic successor of Albert Einstein’s commitment to continuity, Nobel Prize recipient David Bohm of the “hidden order” a.k.a. “the implicate order” introduced these concepts to the field of quantum mechanics.

     3. The Paradox of Quantum Mechanics from the Unification Thought Perspective

        a.  The Unification Thought View on Matter and the Particle/Wave Duality

Unification Thought views the universe as the harmonious synthesis of the dual essentialities of Sung-sang and Hyung-sang. The Sung-sang and the Hyung-sang of the universe are of the same substance and same elements as the Original Essence and as such are “One”, with the difference that the two essentialities composing the universe are individually embodied; therefore all beings in the universe are united bodies incorporating the dual essentialities of Sung-sang and Hyung-sang. This hearkens back to Aristotle's hylomorphism; however, it differs from the dualism of Aristotle's world of rational possibilities, whereby the first form is separate from prime matter, and is also to be distinguished from Descartes' dualism of mind and matter. In Unification Thought Sung-sang and Hyung-sang exchange information, interact with each other, and can unite to form an individual being, owing to the essential homogeneity of Sung-sang and Hyung-sang. Simply put, “Sung-sang” pertains to the world of the mind while “Hyung-sang” refers to the realm of the body which we often call the universe. In the Unification Thought view, matter arises from the Original Hyung-sang which is an aspect of the Original Structure; Original Hyung-sang comprises a material component and an energetic component. This point is an area where Unification Thought and the scientific understanding of matter are in agreement; the scientific explanation of physical processes comes neatly under the Hyung-sang of Unification Thought and they share the goal of investigating material reality and developing scientific theory.

To borrow a concept from physics, the material portion of Unification Thought pertains to physical matter. Original Hyung-sang in Unification Thought does not convey the pantheistic sense of Aristotle's prime matter in contradistinction to pure mental substance, with the realm of potentiality as the logical antipode of prime matter. Original Hyung-sang joins in a reciprocal relationship with Original Sung-sang, responding to its direction, and is the root cause of matter in the phenomenal world.

Light is seen as both a particle and a wave, but when material radiates light it emits it in a discrete form as particles in accordance with Planck's formula E = hf. Keeping this point in mind, Einstein was able to discover the particles of light which had no mass and could interfere with each other, namely photons. As mentioned above, Hyung-sang in Unification Thought consists of a material component and an energetic element, where the material portion possesses the nature of material particles having mass and the energetic element exhibits the wave quality of matter. Then according to Einstein's formula E = mc² for ordinary matter having mass, we can understand that energy is another state of matter ― thus matter and energy are mutually interchangeable.

     So to summarize the quantum concept, the particle is not made up of matter but rather it is viewed as a lump of energy; and the rigidity of matter is owing to the electric forces of attraction and repulsion within and between the atoms, circled by electrons whirling at the phenomenal speed of 1,400 miles/second. By constructing matter out of nuclei, atoms and molecules, the energy patterns of the subatomic world aggregate to exhibit the firm solidity we experience in the macroscopic world. Unification Thought likewise views the material component of this material world as ultimately constituted by energy patterns, while the universe as a whole is filled with energy waves sloshing in all directions and crisscrossed by a network of fields. Therefore the Unification Thought view on material is that particles relate in an overall universal matrix making up an organic, holistic world. The particle, the basic unit of matter, exists through being integrated into the whole universe by energy patterns; it cannot exist in isolation as a concrete entity in three dimensions. In Unification Thought, which espouses organic holism, the overall structure of existence takes precedence over the individual, and this is yet another reason why [UT] is opposed to the position of mechanism which reduces the whole to its parts.

        b.  The Unification Thought View on the Schrödinger Wave Equation

     At the same time it was discovered that the particle and wave properties of light in classical mechanics are identical to its electromagnetic properties, it was not difficult to comprehend these two complementary properties in a unified fashion. From the standpoint of Unification Thought, the wave property of matter is a manifestation of the energetic component of Hyung-sang; at the same time that energy takes on a wave-like character and propagates continually through space. Unlike electromagnetism, the light wave is conveyed by the vibration of a medium, and when this wave oscillates, it exhibits interference phenomena. In quantum mechanics, the core problems are Heisenberg's uncertainty principle and the collapse of the wave function when an object is observed. Quantum mechanics has been branded with the opinions and theories that have been propounded in the course of struggling to resolve the problems cropping up in the wake of these two paradoxes. Since the standpoint of Unification Thought in regard to the paradox caused by the observer and the uncertainty principle has already been discussed in the previous chapter, in this section let us address the problems raised by the Schrödinger wave equation.

     As we have already described, the equivalence was discovered between Schrödinger's wave equation, centered on the wave, and Heisenberg's particle-centered matrix equations. Because Schrödinger's wave equation is a splendid model which superbly explains every feature of the atomic model, using it, de Broglie's concept of the material wave was challenged by Schrödinger's wave equation, which became the model by which the wave concept could be best understood. Then if we seek to integrate Schrödinger's wave equation into the conceptual system of Unification Thought, whereas the material wave is seen as an external component of Universal Prime Force, the wave equation is regarded as an internal component of prime energy. Original Hyung-sang consists of a material aspect and an energetic aspect; the energetic dimension of Original Hyung-sang is called “prime energy.” Universal Prime Force, as the root energy constituting all things, itself has the constituents of Universal Prime Force and prime energy, in the position of subject and object, i.e. cause and effect. The basis for the wave equation being considered as an internal component of prime energy in Unification Thought has nothing to do with it being a concrete three-dimensional wave in a medium (as an ocean wave or a sound wave); rather it is owing to the fact that it is a “probability wave” expressed as an abstract mathematical quantity. The wave equation has all the characteristics of a wave, but in fact it is a probability which shows up as a “tendency to want to exist” as a particle that can be detected. While this “tendency to strive to be embodied” is expressed in mathematical form as a probability, it quantitatively resembles a wave state. Furthermore the probability pattern of the wave function is not merely that of an isolated, independent particle. It represents the probability of it making a connection to the observer and the observation apparatus.

     Viewing the issue from the standpoint of Unification Thought, as a mathematical formula, the probability patterns of the wave function belong to the “Inner Hyung-sang” of the Original Sung-sang, and the probability wave itself, which appears in accordance with the wave function probability pattern, pertains to prime energy in the Original Hyung-sang. At any rate the wave function is not an existing entity, but a kind of information pattern in mathematical terms. This information pattern, stored in the Inner Hyung-sang, operates as a probability pattern governing the probabilities by which particles manifest. For any particle’s wave function, its mathematically quantified tendency to exist corresponds to the specified probability pattern, so that what we observe is the probability wave. It was Max Born (1882-1970) who first interpreted the square of the absolute value of Schrödinger’s wave function ψ, |ψ|², as the probability density function, the probability that the particle will actually be found at any given place. He believed that a wave which satisfies Schrödinger’s wave equation would by no means reveal a particle’s actual motion, but only the probable state of the particle’s movement and position. [Max Born] disagreed with Schrödinger who insisted on continuity, and in part interpreted the probability density function in such a way as to elaborate and establish Heisenberg’s uncertainty principle and the doctrine of the particle’s actual existence.

From the standpoint of Unification Thought, Schrödinger’s wave function, as the information vehicle of the Inner Hyung-sang, cannot in and of itself be the conscious link to the Original Sung-sang; rather, in the same manner that a blueprint conveys the construction plans for building a house, it serves in a directive sense to govern the probability wave. In agreement with the probability distribution of Schrödinger’s wave function, defining the probability of the particle’s presence, the spot in an electron beam where the electrons show the greatest concentration is where the beam has the highest intensity, at that point in time and space the information intensity of the wave function is at a maximum, and Schrödinger’s pulse narrows down to its minimum. On the other hand, if no observation is conducted, the pulse is spread out as wide as the universe and the likelihood of the particle being detected is at a minimum. The greater becomes the probability of its being discovered, the narrower the pulse becomes, and in the instant of its detection, the wave function collapses, and Schrödinger’s equation becomes meaningless. This contractile behavior of the pulse does not bear mathematical description. Born understood such a decisive contraction of the electron beam pulse to be due to the observer effect; he interpreted it as an index of indeterminacy. If the universe were very small and consisted of nothing but lightweight particles, then only when we looked at the universe would it spring into actual existence. Position and momentum lie dormant in nature; it is only when we set out to measure them that they pop into actual existence for the very first time. And even following observation, they go back to existing only as latent potentials.

Viewing it from the standpoint of Unification Thought, when a pair of physical quantities being observed are complementary, such as particle/wave, position/momentum, time/space, mass/space, energy/time, etc., the moment either one of the pair is detected in this concrete phenomenal world of time and space under the sway of the Universal Prime Force, its counterpart abides in a latent state within the prime energy realm of the Original Hyung-sang. Prime energy and Universal Prime Force respectively stand in the relationship of potentiality vs. actuality, or in other words latency vs. realization. Moreover, prime energy and Universal Prime Force are continually interacting with each other. A particle of matter does not exist as an independent, self-sustaining individual truth body but rather as a holistic connected body. The Universal Prime Force is the fundamental energy which goes to construct the entire universe, on the authority of prime energy. The Universal Prime Force is a consciously directive energy and force ubiquitous throughout the entire universe. Universal Prime Force is not a capriciously acting force nor a mechanistically operating force, but a consciously active force throughout the entire universe, mutually interconnected, organic, holistic force. The internal, transcendental (“Sung-sang type”) essence which underlies and wields the Universal Prime Force is the Inner Hyung-sang which is the conscious, directive nature and the object of consciousness. Thus, to conclude, the mathematically expressed Schrödinger’s wave function pertains to the Inner Hyung-sang of the Original Sung-sang, and Schrödinger’s wave itself, as expressed by the wave equation, is none other than the inward essence of the Universal Prime Force.