On Aevum
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
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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.
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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
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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.
•˜ 4. Having thus discussed the preparatory stage of my argument, I would like to
proceed to discuss the possibility that aevity as a concept may again play an important role not only in our studies of time, but as an important element of
modern physics and philosophy. By this I mean that in our efforts to satisfy our
urge to maintain consistency within the framework of modern physics, aevity
seems to be an excellent concept. Because it is a field that will enable us to
obtain an answer from the standpoint of the theory of relativity, which observes
space-time from the outside, as well as from the standpoint of quantum mechanics,
which describes it as a system which includes the observer. Granted that human
beings are finite physical entities and are bound by time, they are in their thoughts
transcending time and it is quite appropriate for them to consider aevity as their
field of activities. Thomas Aquinas only makes fleeting remarks on this point.
Following the above mentioned argument, he mentions under the heading "Is there
only one aevity?" in clause 6 and says that the human souls (animae humane)
also exist within aevity. The entire field of activity of human existence is never
bound by time. At the same time, he is not an eternal existence. And this is
where, as an intermediate field, aevity presents a field of activity to man. What then is the nature of the field called aevity? Here we are confronted with the problem "How does the human spirit work and what is its relationship with time and aevity?". We will have to wait for further developments in philosophy, in order to obtain an insight on this problem. However, what we can say at this stage is that, as a one dimensional straight line on a surface, the physical existence of man and his activities is limited by the axis of time on which - 304- No. 5 On Aevum 35
he is. His spiritual activities take place on a surface which includes the axis of time. In the case of energy in physics which is represented by a complex plane, the observed quantities are limited on a real axis. Likewise our human existence must be described as an ordered sequence of phenomena on a time axis, as long as they are observed through sensory organs. The same situation applies to the relationship between aevity and space. Although there seems to be no mention of this fact in medieval literature, I would like to propose, as a natural analogy with the relationship between time and aevity, to consider aevity as a field which enables us to observe three dimensional space from outside. Because it not only applies to the theory of relativity and quantum mechanics, but also applies to ordinary spiritual human activities of man. If we use the above mentioned metaphor of the straight line and surface and apply it to space, it will be comparable to the relationship between three dimensional space versus four dimensional space, and if we use four dimensional Minkowski space-time as a field of physical phenomena, five dimensional space time aevity will be the field for describing the world in a consistent way, including human activities. The more detailed arguments along this line are left to further studies.
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