On Aevum - between time and eternity- M. M. YANASE Sophia University, Tokyo •˜ 1. Modern physics, which made a new start early in this century, is based on two pillars, namely, the theory of relativity and quantum mechanics. Starting from an entirely different basis, the two theories have, unto this day, endeavored to coordinate. Quantum electrodynamics of today is considered as a comparatively perfected coordination of these two theories. It is constructed in such a way that laws of quantum mechanics satisfy the requirements of the theory of relativity, i.e. they are invariant under the Lorentz transformation. As a result, the role of time and space in quantum electrodynamics is arranged in a manner that is satisfactory both to the requirements of quantum mechanics as well as the theory of relativity. A more detailed study of the theory reveals to us, however, that although interpretation of time and space denies Newtonian absolute time and space as its framework, the theory itself is based, as mentioned, on the supposition that it is invariant under the Lorentz transformation. It means that time amd space are still playing their role as a framework. On the other hand, time in this theory is a parameter to determine the order of sequence of operators, by which various fields (particles) are represented. The physical state itself, on which these operators operate, is independent of time. This way of description is called Heisenberg representation. Although there are variations among Heisenberg representation, it reveals a state function that bears no relation to time. In Fock representation, for example, the state function is designated by the number of particles, built up from a state of vacuum. In non-relativistic quantum mechanics, however, Schrodinger representation is most commonly used, where its state function is described as changing with time. Consequently, the physical state itself is of chronological order, but operators which represent physical quantities are independent of time. Needless to say that both representations are physically equivalent, i.e. both describe the physical world which changes in the framework of time. Still, because of the time independent character of the state function by Heisenberg representa tion in the quantum theory of field, physical literature reveals to us in the words of Spinoza that the state as "sub species aeternitatis". On the other hand, as long as time within the framework of the theory of -301- 32 M.M. YANASE Vol. 4 relativity is considered as one of the four dimensional coordinate axes of Mink owski space, and as long as the world line which represents physical phenomena does not include time, the expression that it is viewed as something eternal is generally acceptable to us. Yet, to the question whether it is possible to convert time into space and observe it from outside is essentially equivalent to observing it "under an eternal phase", the answer should be in the negative. Because eternity as a concept does not mean mere conversion of time into space and observing it from the outside, but is rather a transcendental concept embracing all conceivable cognizant actions. On the other hand, to convert time into space and observe it from the outside is not only indispensable for the theory of relativity, but is necessary when questioning the consistency of quantum mechanics as a system, especially when discussing problems concerning measurement. Granted that the basis of preserving the consistency of present day quantum mechanics is to have the observer on the outside of that which is measured, we will be faced with the necessity of describing the observer from the outside as well. If the person who describes from the outside is in the same stream of time, we will be in need of someone who would describe to us from the outside and, as a result, fall into regresses ad infinitum. Consequently, if we attempt to cut off regressesad infinitum at a certain point, we will again be compelled to place our selves in a position which will enable us to describe phenomena from the outside of one dimensional flow of time. And here, againt, the problem of eternal phase will confront us. However, as in the case of the problem confronting the theory of relativity, the concept of eternal phase will be overly transcendental to be con sidered as accurate. This is the reason why I would like to propose the possibility of establishing a third field between time and eternity. •˜ 2. Early in its state of development, modern natural science, or rather the formative period of Newtonian classical mechanics, there was a stage of con frontation between the Newtonian concept of absolute time and that of the chain of events by Leibnitz. When traced to its source, this kind of confrontation had existed far back as in the days of Greek philosophy during which this problem was subject to debate. Plato's philosophy, for instance, is a typical example. In his Timaeus, Plato is dealing with the problem of the creation of universe. However, being some what vague in his description, Plato's followers found themselves in disagreement as to whether the universe was created in tempore, or cum tempore. As a result, opinions concerning the question of in tempore or cum tempore were not only found within the scope of natural science, but were also treated as basic problems related to the real nature of entities. -302- No. 5 On Aevum 33 Whatever the means of creation, once the world has been created and physical entities came into existence, their sequential relationship is established in tempore. Consequently, the existing entities are considered as having duratio in tempore. The question is, however, that eternity is the attribute of God. Granted that God alone is the only independent external existence and the fact that all created entities without exception have at most mere participation of eternity, when we cast our eyes upon each and every entity that is not necessarily a physical entity, we are confronted with the problem of defining where to place the spiritual existence. •˜ 3. It is at this point in medieval philosophy that the field between time and eternity or aevity (aevum) as a field of existence for pure spirits (angels) became an object of discussion. Aevity (aevum) in Greek is ƒ¿ƒÇƒÖƒË, which also means eternity. Efforts to clarify the difference between these two words within the system of Christian religion were first started by Boetius. In discussing the attributes of God in his Summa Theologica, Thomas Aquinas is expanding his theory on "the difference between aevity and time". (S. Th. Q. 10. art. 5). He defines it as an intermediate stage between time and eternity, a stage which belongs to neither. He then proceeds to describe the various theories related to this difference and gives us his own opinion of the problem. He begins by saying that some people are of the opinion that "Eternity neither has a beginning nor an end, whereas time has a beginning and an end." Thomas Aquinas himself, however, states that "these differences are but secondary." There are also opinions that the difference lies in the fact that eternity has no before or after. Time, however, not only has before and after, but also has innovation (innovatio) and aging (verteratio). On the other hand, although aevity has before and after, it has no innovation or aging. Thomas Aquinas indicates that even these definitons are contradictory. It would obviously be contradictory, if both innovation and aging are applied for a scale. The situation would be the same, should innovation and aging be considered as a means of describing that which is measurable. Because, following Aristotle's argument in his "Physica", temporal entities will age because they are changing entities, while it is the very changefulness of that which is measured that is used as a basis for establishing a scale for before and after. After this reasoning, Thomas Aquinas cites angels and heavenly bodies as an example of things that are measurable by aevity. The existence of angles and heavenly bodies . is changeful either actually or potentially. As far as their essential characteristics are concerned, angles, for instance, have changefulness in their selectivity concerning their intellectual activities or passions, while heavenly bodies are changeful in location of their own sense. This is the very reason that they are situated between eternity and time and are measurable by - 303- 34 M.M. YANASE Vol. 4 aevity. In other words, while time has before and after, aevity itself has neither before nor after. Though, depending on the situation, it has the potential to be conjoined to before and after. On the other hand, eternity not only lacks before and after, but even does not allow them to coexist. As Thomas Aquinas makes it clear to us in the above mentioned theory, if we deem it possible to free ourselves from the throes of one dimensional time with its before and after, we will inevtiably find ourselves in need of a field that is between eternity and time, i.e. aevity. Not only Thomas Aquinas, but Suarez in Section 5 of his Disputatio L. in Disputationes metaphysicae, or Joannes a St. Thoma in his writings on time (Q. 18), is discussing this question. However, aevity, as a concept, has been completely forgotten and is not to be found in the philosophies of modern times. It goes without saying that if we retrace our steps to Greek philosophy, aevity is comprised in ƒ¿ƒÇƒÖƒË, which is a term that is equivalent to eternity, as mentioned above. Thus, in our efforts to find an answer in the past heritage of philosophy, it is only natural that we will fail to come across aevity, if we disregard medieval philosophy.