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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


3. What Has Now and What Does Not Have Now

Temporal consciousness scans four-dimensional space-time from the past to the future using three-dimensional cross sections, but do not things without consciousness, for example, rocks, scan four-dimensional space-time? That is, do rocks have now? In my opinion, rocks do not have now. Rocks simply exist in four-dimensional space-time. Only cognitive subjects with a sense of time can think about now. I speculate that now is a kind of phenomenon in consciousness that does not belong to any purely objective matters. This is because an absolute objective now can never exist; now should be regarded as an attribute of the cognitive subject.
   Consciousness in this context cannot be confined to high-level human awareness, such as linguistic ability. It is likely that dogs and cats have something similar to a human sense of time and that they must be aware of now. I guess that their behavior of jumping for food or running from danger is based on their ability to perceive now, although it is impossible for us to confirm whether such is true by our becoming dogs and cats.
   Apart from dogs and cats, there are living things with rudimentary systems that cannot be considered to involve consciousness and yet likely have a sense of now. It is difficult to conceive that insects, which can quickly prey on other creatures and run from danger, do not have what corresponds to a sense of now. How about paramecia? They do not have a nervous system, but they can catch and eat other living things.
   Then, how about plants? It is impossible to say that plants have awareness, but they can react to a change in light and temperature. I have the feeling that plants have a kind of sense of now in a broad sense, although their sense is not as elaborate as that of animals.
   How about the larvae of sleeping chironomid in dormancy? They inhabit semi-arid regions of Africa and can stay in a state of suspended animation in their dry physical state called eternal dormancy (cryptobiosis). Are these midges just like inanimate rocks during that period of time? Do they have now during that time? Do they perceive that period as a moment? Or is their time divided by this state of suspended animation? That is, is the period before the suspended animation a previous incarnation and is their resuscitation the beginning of new time?
   In addition, how about viruses? Viruses form high polymer structures rather than creatures and they sometimes become crystalline. Do viruses have now? Viruses are just genes (DNA) with a few protein parts rather than the object in lower level than cells, but already discovered is a circadian clock of living things incorporated into their genes. As long as creatures have circadian clocks, it is conceivable that nucleuses and active viruses have a sense of now. Certain types of genetic groups are believed to function as clocks with the cycle of approximately 24 hours by feedback regulation through the promotion and control of several protein syntheses. It is thus probable that they have a broad sense of now that can be stretched to a level of today. How about a cyclical clock functioning by chemical control of proteins, not involving genes, as has recently been discovered inside the most primitive cyanobacteria? Is this level of cyclical clocks close to mechanical clocks? Do these subjects with clocks have now?
   How about computer systems? A computer’s central processing unit (CPU) has a clock within itself and supports its action control in principle. A computer system does not usually involve any consciousness, but a computer can react to a certain type of information that has been entered. Is there now in this area? It is difficult to think that such a simple system has a concept of now, but if there is a kind of memory system that can retain the past, does now exist in that system? If it does, is it possible that a highly organized computer system has now, depending on how the system is configured?
   Where is the borderline between what has now and what does not have now? This proposition has seldom been presented before and, in all honesty, I have much difficulty in considering it. If now is objectively the only and absolute thing, it makes no sense whatever to think about such a thing. Once this assumption has collapsed, it becomes necessary to examine the matter. However, it is likely to be closely related to what consciousness is and how it emerges at a primitive level, and this is no easy subject.
   It is conceivable that now involves a time width that does not show zero (for example, it can be perceived as a moment). Existence with a time width of zero is non-existence. It makes no sense to consider now of non-existence, and everything should be examined on the basis of this premise. Consider the now with a given time width of a person moving at a speed close to the speed of light. That width looks stretched in the coordinate system of a person at rest. It is never a moment. In the meantime, now for static person is stretched in the eyes of the moving person. In this context, simultaneity is inconsistent and the time width of now is also different because of the relativistic effect. Therefore, no common now can exist in the universe.
   An extreme case is that of photons. Do photons have now? In space photons consistently move at the speed of light. Therefore, the line of simultaneity and the line of equipositionality overlap in the photon system. In the case of photons, both the spatiotemporal point where they arise and the spatiotemporal point where they disappear are at the same temporal and spatial points. Can time flow exist there? Everything occurs at the same time and at the same spatial point from the past to the future. Things moving at the speed of light are always special. Things that move a little more slowly than the speed of light can be relatively equal to all other speeds and can be changed to every speed, including a static state, by coordinate transformation. Only the speed of light is completely consistent in all systems of coordinates. In addition, in this context, neither unit time nor unit length can be clearly defined. Everything is a moment and can be the entire realm at the same time. It is quite unthinkable that now can be established in the light speed system. Here can never exist either. It is an extremely special and ultimate system of coordinates.


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