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A PHILOSOPHY OF THE FOUR-DIMENSIONAL SPACE-TIME
      The Worldview of Relative Simultaneity         (MURAYAMA Akira)

CHAPTER III   The Problems of Time Representation


1. Reflective Examination of Time

(2) Objective Time (Pursuit of a Universal Time Unit)

First and foremost, this paper focuses on how humankind obtained the objective concept of time.
   The concept of time can be divided into clock time and time interval. Clock times are symbols corresponding to various incidents, such as someone’s birth, someone’s death and the sun coming up from the horizon. As these symbols must represent the temporal order of each incident, they are often expressed in numerical values or something like that. Two particular points of time show that two events occurred with one before or after the other or with both at the same time. In general, the occurrence of an accident is usually not momentary and its clock time is expressed by the representative point of time relating the accident, such as the time when it began or when it ended.
   By time interval we mean the length between one clock time and another. Therefore, it is expressed in numerical values. There are such relationships between two types of time (that is, one time is longer or shorter than the other or that they are the same in length). Longer time means an incident that is considered to take a fixed length of time can be realized more frequently. Thus, the comparison of time length should be based on a basic unit of time. The establishment of such a unit is essential to using numerical values.
   Once this time unit is established, it is possible to express any clock time by calculating how many units of time are repeated or what rate it marks from a starting point, which is a particular clock time set for a benchmark event. The method of expressing the time unit includes the scales of notation, such as the decimal system and the sexagesimal system. (The sexagesimal system originated from ancient Babylonia.)
   Historically, the starting point of a clock time depended on the intentions of power. In the twenty-first century, the most internationally common benchmark is a starting point of the Christian era (the Gregorian calendar), that is, a particular clock time in the year when Jesus Christ was believed to have been born. In fact, it has been determined that Jesus Christ was not born in that year, but the point is that a particular common starting point should be established and it does not make any difference what event occurred at the starting point. Behind the global dissemination of this calendar were tragic historical events in non-European areas. However, with this type of calendar, the starting point was not frequently replaced with another in accordance with power change and it is of notable prominence that it can identify particular clock time for all incidents from the past to the future in a consistent way. In this respect, the Hijrah calendar used in Islamic areas is also diachronic and significant, but it is based on the lunar calendar. The solar calendar, which has been employed in Western countries since ancient Rome introduced it from Egypt, is more reasonable and useful in that it is compatible with the seasonal cycle and suitable for the management of agriculture. The lunar calendar is based on the waxing and waning of the moon and is more appealing to the human senses. In contrast, the adoption of the solar calendar is predicated on the technological development of solar orbit observation. The solar calendar, however, is easy to manage because diachronic continuity is secured on the basis of seasonal repetitions and leap years are easily accounted for. My one complaint about this calendar is that, because the model is based on the scale of notation established by people who evaded the concept of zero, its starting point is not zero and is incompatible with common numerical concepts. In addition, the Mayan calendar, which divides a year into thirteen months, was based on high-level technology for heavenly body observation and is believed to have been at the level of high precision equal to that of the Gregorian calendar. The Maya did not have the essential military strength to win a de facto standard status and so its calendar was largely overlooked by history. (The Maya are believed have used several types of calendars with their cycles based on different days.) However none of these calendars are reasonable for people who would live apart from the earth and the solar system in the future.
   Aristotle viewed time as the numbering scheme of movement. In this context, the movement is required to be universal. Otherwise, it would be of no use as a unit. A real number-fold value of the movement phenomenon representing a universal unit time is a long-established objective concept of time interval for human beings.
   The point here is how to determine the time unit. It is desirable to focus on a cyclical phenomenon repeating at an equal interval. For example, your pulse is a useful criterion for establishing a time unit, but the exact pulse rate differs from person to person and also differs for the same person, depending on the situation, so pulse rate cannot be considered to be universal. However, from a purely theoretical perspective, time criterion can be established on the basis of any standard for a time unit. If I define my pulse as being continuously consistent, theoretically, I can interpret that delays occur in the progress of the entire universe, including my consciousness, not that my pulse beats faster when I am running or when I am tense. This thinking about the universe based on my pulse is exceedingly inconvenient even if I do not live with other people. Therefore, it is inevitable that this thinking will be abandoned. It is appropriate to interpret that my pulse beats faster, not that the universe progresses more slowly. In accordance with this reasoning, it is necessary to seek another form of universal time unit commonly available for any person.
   Historically, the movements of the heavenly bodies, particularly those of the sun and the moon, have been employed as a constant cyclical motion since ancient times and used as the world’s standard for time up until quite recently. (The average solar day is based on the earth’s rotation on its axis and the average solar year is based on the earth’s orbit around the sun.) Coupled with these forms, phenomena consistently taking a fixed length of time (that is, the time during which a particular amount of sand or water drops from a particular opening and the cycle of the swinging pendulum whose equal time intervals were discovered by Galileo) were utilized as clocks based on a standard time unit.
   Japanese people regarded sunrise and sunset as the division between day and night until the Edo period (1603–1867) and divided each day and night into small segments. In this system, the length of a two-hour period (ittoki in Japanese in those days) was different depending on day, night and seasons, but people did not find any major problem stemming from this difference in their daily lives. However, in subsequent years industrial development and dynamic international trade made precise time management necessary and those time gaps could no longer be overlooked. People found that a clock ticking at a mechanically accurate and equal interval was indispensable in their daily lives. They learned to act according to the time a clock showed, not to solar motion.
   In addition, scientific studies revealed that the earth’s rotation on its axis and its yearly orbit had not been completely consistent over time. As in the previous discussion, it is possible to define the earth’s yearly orbit as being universally consistent, but this means that you should interpret that heavenly bodies except for the earth and other micro cyclical phenomena changed in a single uniform way. In accordance with this reasoning, it is necessary to break away from the idea of regarding the earth’s yearly orbit as the ultimate time unit.
   Since 1967, the accepted universal time scale has depended on atoms. In the international system of units, one second is defined as a period of time equal to 9,192,631,770-fold of the radiative cycle corresponding to the transition between the two hyperfine levels in the ground state of cesium-133 (133Cs) atoms (under the condition of zero magnetic field and absolute zero). The choice of cesium instead of common atoms such as hydrogen, which have existed in the universe since ancient times, was based on humankind’s technological convenience of using cesium for atomic clocks. (Hydrogen atomic clocks are highly accurate, but they are not suitable for practical use as hydrogen atoms are short-lived.) Japan’s standard time is set according to the mean value of ten atomic clocks, whose accuracy is such that only one second per 100,000 years is lost, with this value also being adjusted twice a day by using another highly accurate atomic clock (one of only seven such atomic clocks of this type in the world) that loses just one second in 5 million years. (As of 2005, the world’s highest-accuracy atomic clock became imprecise at a level of one second per 30 million years.) An article published on the asahi.com website on May 19, 2005, reports the following:

A research team led by Associate Professor Hidetoshi Katori at the University of Tokyo produced an atomic arrangement called ‘optical lattice,’ in which strontium atoms cooled close to absolute zero are confined in a micro-space of approximately two-100,000ths millimeters using laser. By applying light to the atom arrangement and counting the oscillation frequency of light that the atoms absorbed, they confirmed that the structure could work as a clock.

   The project represents a significant step forward for achieving a hyper-accurate clock that would lose just 0.4 second per 13.7 billion years. Currently, length is defined by using time and the speed of light as a physical constant (on the basis of the theory of relativity), which means that the accuracy of length has also been increased.
   These high-accuracy clocks have been developed amidst the growing technological necessity of high-precision processing and super-high-speed control, as well as out of necessity in scientific research, such as for precise observation and measurement of celestial bodies and micro-particles. Currently, the measurable time width is less than a femtosecond (one-quadrillionth of one second) and has reached an attosecond, one-thousandth of a femtosecond. One attosecond represents a period of time during which light travels only three 10-millionths of a millimeter. Handling such micro-level time means that effects based on the theory of relativity cannot be ignored.
   In the era of Newtonian dynamics, space and time were considered a kind of framework or container that existed independently from the multiple processes of real substances. In that context, time corresponds to a number line with purely equal intervals and space is an absolute and ideal condition under which Euclidean geometry can be established. Based on this assumption, mathematical representations of physical laws (expression of functions including implicitly or explicitly space and time parameters) were also improved. From these representations, Immanuel Kant established space and time as a transcendental form of senses in a systematic manner. That is, it was interpreted as a universal form of human senses that existed prior to experiences concerning all materials.
   However, after the theory of relativity had been presented, people learned to recognize that neither space nor time could be approached separately from the existence of individual substances. There became no other choice but to consider the length of time in relation to the processes of specific substances. Therefore, the universality of the time unit can be sought only in the universality existing in the material world, not in a metaphysical or transcendental way. Today, we seek that kind of universality in the vibration processes of atoms and photons. Based on this criterion, the temporal length of all processes (including our awareness and thoughts) is determined. It is considered that if these universal processes are delayed, then all material processes are synchronously also delayed. Indeed, observed facts demonstrate that such is the case. No absolute scale is independent from material processes. This is the common objective understanding of time today.
   These descriptions explain only the quantitative aspect of objective time. The following section examines the qualitative aspect of time. Probably, there are many discussions about how to understand the qualitative aspect of time. In this context, the focus is on the aspect of change in things. As long as this study examines the qualitative aspect of time in an objective way, the things referred to here exist inside space and time. Each kind of change involves spatial and temporal changes. (If you consider just temporal changes, you look at only one aspect of change. Time is just one of four directions of change.) What will change and how things will change depend on natural hierarchical structures. In general, the point is that we can recognize change as change confronts non-change. What lies beneath this non-change does support the quantitative aspect of space and time (indifferent to their qualitative aspect). That is, change, or the qualitative aspect of time, can be considered only in relation to its quantitative aspect, not independently from other factors. The reason physical time forms the foundations for qualitative changes in every hierarchy is that it can represent non-change, which is the conflicting concept of change, involving uniform repetition. The history of what to choose as the basic unit of physical processes involves the pursuit of something that properly represents them. This pursuit is indifferent to the qualitative aspect of time and focuses primarily on temporal accuracy. To put this another way, quantitative time forms a common parameter that remains invariant across all hierarchical levels except for the necessary precision.


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