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Ephraim Essien, pp.29-36 Annales Philosophici 5 (2012) SCHRODINGER’S CAT-IN-THE-BOX WITH THE COPENHAGEN ONTOLOGY Ephraim Stephen Essien University of Cape Coast Ghana [email protected] Abstract: This paper focuses on the problems of indeterminism and subjectivism inherent in quantum physics. Schrödinger’s thought experiment reinvigorates an observer-created reality, enunciated in the Copenhagen Interpretation of Quantum Mechanics. Schrodinger’s experiment remains compatible with the Copenhagen ontology, given the commonness of their functions: indeterminism, subjectivism, uncertainty. Indeterminism as determinism is an ontological problem, and here in Quantum Mechanics, we see an interface of metaphysics in physics. In this metaphysics in physics, the thing is not there save the observer observes it. Not just that! What the observer observes may not be definite after all! Idealism in Science? Keywords: quantum metaaphysics physics, indeterminism, subjectivism, I. Introduction Although this paper mainly focuses on the philosophical implication of quantum physics, it also compares subjectivism and indeterminism with the so-called scientific objectivity and acclaimed certainty of classical physics. This is especially done in the Copenhagen analysis of the “cat” experiment. As a matter of fact, this paper begins with a discussion on quantum mechanics. This is followed by an analysis on the Copenhagen interpretation of Quantum mechanics. Schrodinger’s cat experiment follows this analysis consistently and compatibly. This is followed by a Copenhagen analysis of the cat experiment. This paper concludes that Schrödinger’s cat-in-the-box experiment is compatible and consistent with the Copenhagen ontology, which is an observer-created reality. The writer is of the view that uncertainty may not be overcome especially in predicting future events. Quantum mechanics “Quantum” is a Latin term meaning “how much”. It refers to a quantity of something, a specific amount. “Mechanics” is the study of motion. “Quantum mechanics”, following this etymological analysis, is the study of the motion of quantities. Quantum theory says that nature comes in bits and pieces (quanta) and quantum mechanics is the study of this phenomenon (Zukav,1979:45) . 29 Annales Philosophici 5 (2012) Ephraim Essien, pp. 29-36 Quantum mechanics is the branch of physics that studies phenomena of the microcosm. Quantum mechanics has made it more apparent that a researcher cannot have adequate knowledge of a system of interacting objects without active interference in it . This theory holds that energy exists in units that cannot be divided. Max Planck ushered in quantum theory into the epistemological corpus when he offered a solution to the problem of black body radiation in 1900. While working on the thermodynamic theory of thermal radiation, Max Planck introduced ‘quantum of action’ (Frolov, 1984: 327) . According to Planck, light was radiated and absorbed directly, by definite portions-quanta (h=6.62.10=27erg./sec.). This discovery was a turning point in the history of thought. A transition was made from macrocosm to microcosm. This was the birth of quantum theory, which established the fact of discreteness in the energetic processes and thus extended atomism to all phenomena of nature. Planck demonstrated that the experimental observations in radiation could be explained on the basis that the energy from such bodies is emitted in discrete packets known as energy quanta of amount ‘hv’, where ‘v’ is the frequency of radiation and ‘h’ is a constant known as the ‘Planck constant’(Okeke,1989:253). Planck’s breakthrough was an apparent solution to the problem of black body radiation. ‘A black body is a body that absorbs and emits wave-length and temperature. A black body does not necessarily connote a solid body that is black. It is non-reflecting, perfectly absorbing, non-glossy. According to Alozie (2003:98-99), A metal box that is completely sealed, but with a tiny hole pierced would appear black if you look into the interior of the metal box through the hole. If the metal box is subjected to intense heating by probably a blacksmith to a glowing red colour, the hole will be showing a red colour. This was the type of phenomenon that Max Planck studied . Black bodies are physical abstraction and have no concrete existence. According to Alozie, Planck conceptualized a model of an ideal black body as a large number of atomic oscillators that emit and absorb electromagnetic waves. Planck assumed that the energy of E, of an atomic oscillator could have discrete value of E=O, hf, 2hf, 3hf, 4hf, etc. This implies that E=O, hf, 2hf, 3hf, 4hf, etc. are the only permitted values of the energy “E”. Energy quantum is “hf” of “hv” and “n” is the quantum number of the oscillator. For Planck E =nhf, where n=0.1,2,3,4,etc. h =constant (6.6260755 x 10-34 J.S.) f =frequency of vibration (measured in Hertz) There are no energies with discrete values. Thus they are quantized. Hence energy quanta. Following quantum theory of radiation, Albert Einstein postulated that light of frequency v contains quanta of energy hv which he called photons. Einstein’s version of quantization is useful in explaining photoelectric effect. Electrons are emitted from an insulated metal surface when light of sufficiently high frequency falls on the surface. This phenomenon is called the photoelectric effect. Under the wave theory of light the kinetic energy of the emitted electrons should increase with the intensity of the incident light. The photoelectric effect, also, should occur for any frequency of the incident light provided the light is intense enough. Under the wave theory, for a very feeble source, the part of the wavefront that is intercepted by an electron in the irradiated material will be so small that it will take the electron a long time lag between the incidence of the light and the electronic emission (Evwaraye, 2002:229). 30 Ephraim Essien, pp.29-36 Annales Philosophici 5 (2012) Reacting against the failure of the wave theory of light to explain the observed effects in photoelectricity, Einstein enunciated a mechanism for the phenomenon based on Planck’s quantum theory of black body radiation. Einstein postulated that light of frequency v contains quanta of energy hv which he called photons. A photon of light of frequency v carries an amount of energy E=hf, where h is Planck’s constant 6.6260755x10 -34 J.S). In Einstein explanation of the photoelectric effect, (i) The entire energy of a photon is transferred to a single electron in the metal, which gets emitted instantaneously. This immediately removes the difficulty regarding time lag. (ii) When the electron comes out of the metal surface it will have a maximum kinetic energy given by 1/2 (iii) mv2 = hv –φ This equation shows that no electron can be emitted if the frequency of the incident light is so small that hv<φ. Thus, there is threshold frequency in agreement with experimental results. The particle nature of radiation was further confirmed by the Compton effect. When x –rays were scattered by a target with loosely bound electrons, e.g. carbon, the scattered radiation was found to consist of two components. The one was having the wavelength as the incident beam (unmodified line) and the other having a slightly longer wavelength. But there should be no change in wavelength or frequency following the classical electromagnetic theory. The incident radiation was expected to set the atomic electron vibrating with the frequency of the incident radiation, and then produce radiation emitted in all directions with the same frequency (scattered radiation). Compton in 1923 provided the explanation to the observed effect by treating the incident radiation as a stream of individual photons each of which could interact with a single electron. This is the Compton Effect. The wavelength λ of the scattered x – rays is greater than the wavelength of the incident radiation. In photoelectric effect the photon ceases to exist when all the energy of the photon goes into the energy necessary to remove the electron from the surface. However, in Compton Effect, the photon continues to exist, but does not lose energy as shown by the change in the wavelength or frequency of the incident x –rays. Huygen proposed a wave theory of light. The wave theory sees light as a wave form spreading out from a light source as spherical or circular waves. (C = 3 x 108m/s). a sensation is produced as these wave fronts reach our eyes. A long way from the source, the circular waves appear as plane parallel waves. James Clerk Maxwell showed that light was an electromagnetic wave. Light consisted of electrical and magnetic vibrations. Though the electromagnetic theory’s calculation of the speed of light was approximately equal to 3 x 108m/s, the theory failed to account for certain properties of light such as emission and absorption of light and radiation of energy by heated bodies. Louis de Broglie later postulated in 1923 that since light waves could exhibit particle – like behavior, that particles of matter equally exhibit wave-like behavior. Since nature, in his reasoning, is symmetrical in many ways and our sensible universe is made of energy and matter; again, since light has a wave-particle nature, Broglie concluded that matter does also. In predicting the wavelength of a particle, Broglie stated that the wavelength of particle is given the same relation that applies to a photon. Put in other words, the wavelength of the predicted matter waves was given by the same relationship that held for light, such that 31 Annales Philosophici 5 (2012) Ephraim Essien, pp. 29-36 Λ=h/p where λ is the wavelength of a light wave and p is the momentum of the associated photons. Broglie’s wave nature of matter was confirmed few years later by Clinton J. Davison and Lester H. Germer through an electrons-diffraction experiment. The duo demonstrated that electrons exhibit wave-like properties of diffraction and interference by passing a beam of electrons through a crystalline solid. Thus there is a wave-particle duality in matter. That is to say that matter behaves in some circumstances like a particle and in other circumstances like a wave. The wave-particle duality of light and matter bequeathed to Erwin Schrodinger made possible the coinage of the concept, wavicle. Schrodinger observed electrons as patterns of standing waves. Those standing waves are quantized as particles in a discrete pattern. Based on his observation, Schrodinger gave a formular which the electron wave shape would obey if the electron was part of the hydrogen atom. By using his equation to deduce the light spectrum of hydrogen, the idea that electrons are waves was confirmed. Yet the motion of particles as well as waves is relative motion. Schrodinger observed electrons as standing waves. What was waving was not certain, but that something was waving was sure. He designated this was a wave-function. There was an indeterminate conception of what was waving, but a determinism that something was waving. Max Born considered Broglie’s and Schrodinger’s standing wave as the wave of matter and not of particle as unsatisfactory. For Max Born, the latter’s interpretation of wavefunction is an indicator of the probability of finding an electron at some point in space. This wave-function probabilistic interpretation ushered in indeterminism in quantum mechanics. Niels Bohr’s scientific interests lay at the junction of physics and philosophy, in the sphere of analysis of conceptual apparatus of physical theories. Bohr put forward the principle of complementarity, a method of description that was applied to various fields of knowledge in the analysis of alternative, contradictory situations . In point of fact, Bohr’s principle of complementarity as a method of description was suggested to interpret quantum mechanics. Here is the thesis of this principle: “To reproduced the wholeness of a phenomenon at a certain ‘intermediate’ period of its cognition, use must be made of mutually exclusive ‘complementary’ and mutually limiting classes of concepts which can be used separately, depending on specific conditions, but only taken together cover all definable information”. Bohr advocated the admission of the contradictory positions in quantum theory via complementarity. Thus the principle of complementarity helped to bring out the dual, wavecorpuscular nature of light. This principle submitted the equivalence of two classes of concepts describing contradictory situations. Bohr’s principle seems to contain elements of dialectical thinking. The uncertainty principle is one of the principles of quantum mechanics put forward by Werner Heisenberg in 1927. Simply expressed, there is a basic uncertainty in our knowledge of particles. It was observed by Heisenberg that the very act of measuring physical parameters like position and velocity of an electron disturbed the electron because of interaction between the apparatus and the electron. This invariably introduced uncertainties in the precision of measurement. On an atomic scale, Heisenberg established, that it is in principle impossible to obtain an exact measurement of both the position (x) and the velocity (v) of a particle. We are unable to specify precisely the position (x) and the velocity (v) of a particle, but the likelihood of its being located at a certain point. There is always an 32 Ephraim Essien, pp.29-36 Annales Philosophici 5 (2012) uncertainty (Δx) in the position of the particle and an uncertainty (Δv) in the velocity of the particle (Δx.Δv), according to Heisenberg, must be greater than the Planck constant (h) divided by the mass of the particle. The uncertainties concern the nature of matter and not related to errors introduced by the limited precision of the measuring device. Hence, Δx.Δv> h/m, since m.Δv =Δp, the uncertainty in momentum p, then Δp.Δx> h also ΔE.Δt > h where ΔE is the uncertainty in the energy of the particle and Δt is the uncertainty in the time measurement . Due to the contradictory, corpuscular – wave nature of micro-objects, uncertainty principle posits the impossibility of simultaneously determining their exact coordinates and impulse. Commenting on the principle, Alozie remarks that the uncertainty principle of quantum mechanics is difficult to swallow in the light of the reality of the macro-world . We have discussed Schrödinger and Bohr and their contributions to quantum physics. Their contributions were deepened by first, Schrödinger’s thought experiment and, secondly, by Bohr’s dominant Copenhagen interpretation of quantum mechanics. To analysis of these we turn. II. Copenhagen interpretation of quantum mechanics Quantum mechanics has been variedly interpreted. Among this is the Copenhagen Interpretation. The term “Copenhagen Interpretation” reflects the dominant influence of Niels Bohr (from Copenhagen) and his school of thought. For sake of clarity and analytic coherence, we shall reiterate Bohr’s complementarity principle, the epicenter of Bohr’s thought. Niels Bohr’s scientific interests lay at the junction of physics and philosophy, in the sphere of analysis of conceptual apparatus of physical theories. In physics, complementarity is a basic principle of quantum theory closely identified with the Copenhagen Interpretation, which says that quantum theory is about correlations in our experience about what will be observed under specified conditions (Zukav, 1979:62) . Bohr developed complementarity at Copenhagen with Heisenberg, as a philosophical adjunct to the recently and developed mathematics of quantum mechanics in particular the Heisenberg uncertainty principle. It states that a single quantum mechanical entity can either behave as a particle or as a wave, but never simultaneously as both. A profound aspect of complementarity is that it not only applies to measurability or knowability of some property of a physical entity, but more importantly, it applies to the limitations of that physical entity’s very manifestation of the property in the physical world. All properties of physical entities exist only in pairs, which Bohr described as complementary. Physical reality is determined and defined by manifestations of properties which are limited by trade-offs between these complementary pairs. The emergence of complementarity in a system occurs when one considers the circumstances under which one attempts to measure its properties. As Bohr noted, complementarity implies the impossibility of any sharp separation between the behavior of atomic objects which serve to define the conditions under which the phenomena appear”. By ‘complementary’, Bohr submits that “any given application of classical concepts precludes the simultaneous use of other classical concepts which in a 33 Annales Philosophici 5 (2012) Ephraim Essien, pp. 29-36 different connection are equally necessary for the elucidation of the phenomena” (Bohr, 1934:10). According to Heisenberg, “by the term ‘complementary’, Bohr intended to characterize the fact that the same phenomenon can sometimes be described by very different, possibly even contradictory picture, which are complementary in the sense that both pictures are necessary if the ‘quantum character of the phenomenon shall be made visible. The contradictions disappear when the limitation in the concepts are taken properly into account”(Heisenberg,1977:6). The method of complementarity, according to Heisenberg, i represented as a tendency in the methods of modern biological research which, on the one hand, makes full use of all the method’s and results of physics and chemistry and, on the other hand, based on concepts referring to those features of organic nature that not contained in physics or chemistry, like the concept of life itself (Heisenberg,1968:94). Bohr had observed an impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear. The ultimate philosophical question in quantum mechanics is “what is that quantum mechanics describes?” Quantum mechanics describes or predicts the behavior of what? These were some of the questions which bothered physicists who gathered in Brussels, Belgium in 1927, for the fifth Solvay congress. Planck, Lorentz, Einstein, Dirac, Compton, de Broglie, Born, Bohr, Ehrenfest, Schrodinger, Pauli, Heisenberg were among those who attended this congress (Hoffmann, 1973:187) . Ironically what the physicists decided there in Brussels become what is known as the Copenhagen interpretation of quantum mechanics. This was unlike the Vienna circle named after the city of Vienna. The Copenhagen Interpretation was as so named because of the dominant influence of Bohr (from Copenhagen) and his thought. The Copenhagen Interpretation says that quantum theory is about what will be observed under specified conditions. The truth is not there until we observe it. Or, we do not know the truth until we make our observations? The thing is not there until we observe or perceive. Here, we can see a correlation of Copenhagen ontology with the subjectivism and idealism of a Berkeleyan tradition, which ordained “esse est percipi” (to be is to be perceived). The Copenhagen Interpretation of Quantum Mechanics maintains that it does not matter what quantum mechanics is about. The important thing is that it works in all possible experimental situations (Zukav, 62). Zukav says that the scientific idea of truth had traditional been anchored in an absolute truth somewhere “out there”, that is, an absolute truth with an independent existence, but that the Copenhagen Interpretation does away with this idea of a one-to-one correspondence between reality and theory. Again, truth is not determined by how closely something corresponds to the absolute truth, but how consistent is it with our experience; with us. Copenhagen ontology thus becomes an observer-created ontology; an observer-created reality. How relevant then is this ontology to Schrödinger’s cat experiment? III. The Cat-In-The-Box and Copenhagen Analysis In a bid to reinforce his stance on quantum indeterminacy, Schrodinger posits a thought experiment popularly called the “Schrodinger’s Cat”. According to his story, a Cat is placed inside a box. Inside the box is a device which can release a gas, instantly killing the cat. A random event (the radioactive decay of an atom) determines whether the gas is released or not. There is no way of knowing, outside of looking into box, what happens inside 34 Ephraim Essien, pp.29-36 Annales Philosophici 5 (2012) the box. The box is sealed and the experiment is activated. A moment later, the gas either has been released or has not been released. Without looking, can we determine what has happened inside the box? For classical physics, the cat is either dead or it is not dead. The Copenhagen Interpretation of Quantum Mechanics says that the cat is in a kind of limbo represented by a wave function which contains the possibility that the cat is dead and also the possibility that the cat is alive. When we look in the box, and not before, one of these possibilities actualizes and the other vanishes. For classical physics, a cat is in the box whether we look at it or not, and for this conception, the fate of the cat was decided at the beginning of the experiment. Thus, according to classical physics, the status of the cat is determined, that is, either dead or alive. All that is required is to get to observe to confirm which is true. This view of classical physics conforms to the principle of bivalence in logic which excludes a middle way. For quantum mechanics, the middle way is demonstrated by the wave function, the element of probability. According to this new physics, the status of the cat in the box is shrouded by this probability: probability that it is alive and dead (Penrose, 2004:805), not alive or dead as in classical physics. According to quantum mechanics, something is not there until we do observe it. The fate of the cat, therefore, is not determined until we look inside the box. At the instant that we look inside the box, one of the possibilities contained in the wave function representing the cat actualizes and the other possibility vanishes. Then, the cat is either dead or alive. IV. Conclusion Classical physics assumes an external world which exists independently of us. Accordingly, we can observe, measure, and speculate about the external world without changing it. It is not like that in the new physics. In the new physics, we influence, and in some degree, create our reality. According to Zukav, since the new physics upholds that it is in the nature of things that we can know either the momentum of a particle or its position, but not both, we must choose which of these two properties we want to determine. Metaphysically, we create certain properties because we choose to measure those properties. Sequel to these assumptions of quantum mechanics, we can reliably make the following submission: that the Copenhagen ontology is an observer-created ontology. The observer of the Cat-In-The-Box determines the status of the cat. The reality bequeathed to us by quantum mechanics is the reality of the subject. John Wheeler refers to this subject as the participator. He says: “may the universe in some strange sense be ‘brought into being’ by the participation of those who participate?... the vital act is the act of participation given by quantum mechanics… “ But is reality just determined by the observer like that? “God does not play dice with the world”, said Einstein. Einstein, who defended determinism, certainty and objectivity of classical physics, rejected indeterminacy, uncertainty and subjectivism of quantum mechanics. While classical physicists claim that they are certain of certainty and uncertain of uncertainty, quantum physicists claim they are certain of uncertainty and uncertain of certainty. Both colleges of physicists are certain of something and uncertain of something. Certainty and uncertainty are two sides of the human quest for knowledge. But uncertainty tends to possess a higher degree due to our limited ability to know exactly about future events. 35 Annales Philosophici 5 (2012) Ephraim Essien, pp. 29-36 May this paper end with a call to all minds to entertain the epistemological implication of the following epistemological claims: Certainty of uncertainty; Uncertainty of certainty; Certainty of certainty; and Uncertainty of uncertainty. What relevance do these claims have in philosophy and physics? Schrodinger’s CatIn-The-Box experiment is compatible with the grand Copenhagen ontology in so far as both possess the functions of subjectivism and indeterminism, given the requirements of the compatibility principle, which holds that entities and systems are compatible if they share a common property, and can yet be compatible by ‘implicate order’ should they appear dissimilar (Essien:2008). References Alozie, Princewill (2003). Philosophy of Physics. Calabar: Clear Lines Bohr, Niels (1934). 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