A PHILOSOPHY OF THE FOUR-DIMENSIONAL SPACE-TIME
The Worldview of Relative Simultaneity
CHAPTER III The Problems of Time Representation
2. The World model of Spatio-temporal Scanning
In recent years, John McTaggart Ellis McTaggart (1866–1925) has attracted much public attention as a key thinker on time theories, especially in the field of analytic philosophy. He has demonstrated that time does not exist. Inevitably, many people will doubt his idea, arguing that everyone in the world cares about time in their daily lives, but McTaggart presented the paradoxical conclusion by highly theoretical examinations. Just as no one thinks seriously that in Zeno’s paradox Achilles cannot overtake the tortoise, probably, nobody, including McTaggart himself, believes that time does not at all exist. To consider the paradox and seek a solution will reveal problems that time involves and lead to a profound and essential understanding of time.
John McTaggart Ellis McTaggart was one of the last disciples of Hegelianism, the Neo-Hegelian movement, in Britain and a contemporary of Bertrand Russell (1872–1970) and George Edward Moore (1873–1958), who belonged to the school of Cambridge analysts. McTaggart pointed out two major ways to grasp time. The first is to focus on time transition from the future to the present to the past. McTaggart called this A-series. The second is to focus on linear temporal points on the basis of a certain point of time. Physical and historical descriptions just follow this method. In this context, there never exists “now.” In this system, there are just events and objects that are positioned according to the clock time parameter and no change and transition exist. McTaggart called this B-series. (These names are too simplified for describing basic important concepts, but I have no choice other than to follow the terms.) The idea behind the concept of four-dimensional space-time in the theory of relativity (block universe theory) is a typical example of B-series.
In Japan, time theories have been attracting much attention in recent years and McTaggart is often mentioned as a time theorist. As a brief example of McTaggart’s theory on the non-existence of time, the book, The Construction of Time Theory, by Osaka University's Yasuo Nakayama(*2) summarizes time theory as follows:
(1) Time descriptions are largely divided into A-series (past, present and future) and B-series (prior to and after).
I am not so interested in how to critically examine McTaggart’s logic to construct a consistent system of time theories. Doing so is not the subject of this study. The primary focus of this study is how to consider spatiotemporal views presented by the relativity of simultaneity. My mentioning McTaggart’s A-series and B-series concepts is intended to provide one point of view to evaluate those spatiotemporal views.
(2) Without change, time would not exist.
(3) Without A-series, no change would occur.
(4) Descriptions using A-series involve contradictions.
(5) A-series does not really exist (according to the fourth explanation above).
(6) Time does not exist at all (according to the second, third and fifth explanations above).
The spatiotemporal views presented by the relativity of simultaneity are B-series theories. Fundamentally, physical theories are based on B-series because the temporal modality of the present is not induced from them. In addition, because the theory of relativity postulates the existence of all events and objects from the past to the future and denies the existence of absolute now, B-series theories are more strongly supported. Our presentational changes and movements disappear from the perspective of four-dimensional space-time.
McTaggart argues that A-series comprises the core essence of time. Certainly, it is possible to logically induce B-series from A-series, but it seems extremely difficult to do the opposite.
Why is it difficult to induce A-series from B-series? One factor is the absoluteness and uniqueness of now. For time as understood in physics, that is, B-series time, all points of time are treated equally and now, which is a special point of time, does not exist. However, this issue of discussion no longer matters according to the spatiotemporal views presented by the relativity of simultaneity because now is not the only and absolute parameter in that context.
In the meantime, however, in our consciousness, the A-series temporal modality authoritatively exists in which what used to be considered the future becomes the present over time and subsequently becomes the past. How you interpret this fact matters. With regard to this focal point, it is logical to think that our consciousness scans four-dimensional space-time from the past to the future at three-dimensional space-time cross sections. At every point of time, independent forms of now co-exist, scanning four-dimensional space-time in parallel. However, physically, there are no means of interactive communication among the different forms of consciousness of now. (One could construe that communication from now in terms of the past to now in terms of the future occurs through diaries and other written records, but not vice versa.) Therefore, in each awareness of now each of us perceives our own now and this is the only form of now.
In addition, each awareness of now cannot sense the four-dimensional nature of the world. This can be explained by Minkowski’s geometrical structure of space-time as noted in chapter two.
The biggest mystery remains unsolved: Why does our three-dimensional awareness of now scan four-dimensional space-time in a particular direction? This is the reason the world shows presentation of changing, moving, arising and disappearing in our consciousness. But why does the scanning occur?
What type of answer can be presented with respect to this point? The form of the answer itself is difficult. It is hugely different in nature from challenging problems that are extremely complicated and cannot be adequately examined by the shortage of available information. The form of the answer itself is unclear.
It is a form of answer to declare that it is consciousness that scans space-time. Then, the question becomes what other conceivable forms of the answer are.
Can the reason for consciousness scanning space-time be explained from the
perspective of cerebral (nerve) physiology? Various functions and phenomena in the nervous system, such as the secretion of transmitters by synapses and the transmission of electric signals, are also aggregations of events distributed and lying in four-dimensional space-time. However profoundly you seek scientific knowledge from this perspective, you will just enrich theories developed in B-series time. It is difficult to imagine a situation in which A-series time can be induced from such examination.
You should be careful about the thinking pattern of reducing consciousness to elements concerning the cerebral (nerve) physiology in the dual sense. First, much of the specific content in awareness is usually provided by human group activities and cannot be explained by reducing the content of activities within the individual human nervous system. People have often pointed this out. Second, it is significant to note that prescription of consciousness should be examined more fundamentally, for example, with a focus on what space-time is all about, and that the hierarchy of the nervous system’s function is just one stratum positioned between consciousness and space-time. Just as the information and communication system is established on the basis of multilayered protocols from the hierarchy of physical structures to hierarchies closely connected to applicable business, the system realizing phenomenon of consciousness must be based on comprehensive collaboration and networks of functions through multiple hierarchies. The cerebral nervous system is just one hierarchy of those series of systematic architectures, although it plays a crucial role. The higher level hierarchical function of consciousness cannot be reduced to the nervous system and the space-time structure supporting phenomena in the consciousness at a more profound level can be considered to comprise the basal layer of consciousness.
Now, let me return to the question of why human consciousness scans space-time. In general, two major forms of answers to questions involving why are expected. The first form is to reduce everything to laws in principle and construct systematic deductive explanations (proof). The second is to identify historical conditions and explain everything on the basis of causal relationships. It makes no sense to try to answer the question (why does consciousness scan space-time?) according to the second method because the state of human consciousness did not change from not scanning space-time to a state in which it scanned space-time for any particular reason. Then, the question becomes using the first form. I suspect that the method will just end up creating aggregations of tautological propositions.
Fundamentally, science cannot provide clear and satisfactory answers to questions of why in any ultimate way. In response to the question, “Why is the solar system just the way it is?” it is possible to establish a logic to explain it from a more universal viewpoint or based on older reasons by specifying historically how the solar system was established and clarifying physical laws of movement. The inevitable is that additional questions will arise such as “Why can such laws be established?” and “Why did events causing such circumstances occur?” You can deepen the forms and specifics of questions, but you cannot ultimately give complete answers to such questions. For the subject, it just boils down to the idea of giving up resolving questions by not asking more questions but just accepting things as they are to eliminate questions. Therefore, accepted wisdom is that science does not seek to answers to questions of why but just continues to explore how.
Nonetheless, human consciousness scans four-dimensional space-time from the past to the future. Probably, this is the most plausible world model that achieves a balance between the recognition of existing four-dimensional space-time and undeniable facts about the time presentations of the future to come and the past that has gone. Otherwise, you could not avoid thinking about some form of solipsism.
The scanning of space-time by human consciousness exists in innumerable numbers continuously from the past to the future. Each form of consciousness represents now. Now exists in innumerable numbers and, as with the case of here, it is impossible to objectively declare which is genuine. However, with regard to a particular form of consciousness, the now in the eyes of that consciousness is the only one worthy of consideration. Among such forms of consciousness that look upon simultaneity as absolute, only the scanned cross section shared by them is the one and only now in the world.
There are two conceivable types of scanning three-dimensional cross sections of space-time. One is the cross section of simultaneity in the coordinate system in which the cognitive subject is placing itself. It is a set of events that constructs an objective form of now from the perspective of the cognitive subject, but those events cannot be perceived at that point of time. This is because information needs to be transferred at a pace faster than the speed of light, but that is impossible. Accordingly, the scanned cross section in this case is just one in theory and not a direct object of perception. The other type of space-time cross section is the visible one of the cognitive subject. This corresponds to the phase of the past light cone. The events existing in this cone is a set of events that the cognitive subject can see now, and the farther the events are, the closer to the past they are. When you are gazing at the night sky, it means that you are looking at this vast phase of the past light cone. That is, you are looking at the stars tens of thousands of years ago and millions of years ago at the same time as the buildings a few microseconds ago (one-millionth of one second) and the people a few nanoseconds ago (one-billionth of one second). Events existing in the future direction to this space-time cross section cannot be recognized at that point of time. The space-time cross section is peculiar to the cognitive subject positioned at a particular spatiotemporal point and cannot be shared with others far away in distance and time. In contrast, the cross section of simultaneity can be shared among static subjects with the same speed even if they are far away from one another. This sharing of the cross section represents the simultaneous existence of subjects in their coordinate system.
Then, how is scanning done? With respect to this point, it matters how fast the cognitive subject scans four-dimensional space-time.
Speed can be interpreted in two different ways. One is an objective speed in a physical sense that is defined in principle on the basis of its ratio to the speed of light. This means the slant among the world lines of moving or static objects as an objective indicator of energy and momentum and is based on the structure of the four-dimensional world and its standard system of coordinates. Speed can also refer to the ratio of the temporal length of subject phenomena to phenomena occurring at a particular cycle based on the standard system of coordinates. The speed mentioned in the objective description of natural science and social science is based on this mechanism.
However, there is also the concept of speed in another sense. This is the speed at which consciousness, or something that corresponds to consciousness, scans four-dimensional space-time. This speed can be expressed as the length of a moment. It can be defined as the attribute of the cognitive subject, that is, how long the subject perceives a moment to last in an objectively and universally defined form of time in the coordinate system to which the cognitive subject belongs.
A moment is the length of time that the cognitive subject can perceive single-handedly. The moment corresponds to a short period during which no awareness arises for the subject to await its passage, but the period is not so short as to prevent the cognitive subject from sensing its passage at all. In our average consciousness, one minute is too long for a moment (in the coordinate system to which the cognitive subject belongs) and one microsecond is too short for a moment. In living human consciousness, the length of a moment can be considered approximately one second, that is, a period of time during which light travels by approximately 300 million meters. This is not a direct length of time but is an indicative value of the length scale. It may often be appropriate to focus on its logarithm.
If this length of a moment is short, the cognitive subject slowly scans four-dimensional space-time. Conversely, if the length is long, the scanning speed becomes quick. In comparison with that of an elephant, a rat's length of a moment seems shorter.(*3) For this reason, their sensory life expectancy may not be as different as it seems, although there are large gaps in the length of their real life based on the objective concept of time. Formula One drivers and experienced baseball players have dynamic vision that is much better than that of the general population and may be able to shorten the length of a moment. If drivers and players can do so, it is probable that they perceive things as moving more slowly than the general population. In addition, some people have said that at a certain moment during a traffic accident, they felt as if things were moving in slow motion. In this case as well, their nervous systems became more sensitive, which may have made them feel as if the length of a moment were contracting compared to usual moment. If a cognitive subject existed that could function as well as a supercomputer, recognizing one nanosecond as a moment, the subject would scan four-dimensional space-time exceedingly slowly. If there existed a cognitive subject that could perceive one year as a moment, it would scan four-dimensional space-time quite quickly and would not even perceive a distance of ten light-years as being far away.
The ratio of the distance that light travels in a moment to the distance that the cognitive subject can travel in that moment represents the scale of light speed for the cognitive subject. For us humans, this ratio is approximately 100 million. That is, humans perceive that light travels a distance of a hundred million times their body scale in a moment and they feel it as exceedingly fast speed. If a cognitive subject existed with the same level of our physical ability that could feel one nanosecond as a moment, numerical values representing light speed would become very short for the subject and the subject could feel the effect of the theory of relativity. In addition, if a cognitive subject existed whose physical activity scale even reached a level of hundreds of millions of meters in a moment (moving around at a quick pace that the eye cannot follow), light would also travel more slowly and the effect of the theory of relativity would be noticeably felt for the subject.
Physics just describes the speed of light as a constant in spacetime. Depending on the attribute of the cognitive subject, the speed of light is expressed as fast or slow. The expressed fast or slow values represent the speed at which human consciousness scans four-dimensional space-time, that is, the length of a moment.
This length of a moment for the cognitive subject can stretch or shorten depending on the coordinate system, just as time length in other physical processes can. That is why I used the expression the coordinate system to which the cognitive subject belongs in the previous sections. Two systems of coordinates moving at a relatively high speed perceive each other’s length of a moment as longer and psychological time for the other is judged to progress slowly. In addition, in gravitational fields where mass concentrates densely, the cognitive subject’s length of a moment is judged to be stretching. There are extreme cases: The length of a moment in the eyes of people about enter a black hole from around a Schwarzschild radius (the limited phase which nothing can get out of against gravity unless it moves at the pace of light velocity) is judged to be fully stretched and it seems as if their time had stopped from the standpoint of someone who is far away from the gravitational field where mass concentrates densely. The people who have already fallen into the black hole perceive the moment just as a short period of time. (This scenario is based on the obviously imaginary assumption that people can stay conscious even under extreme conditions.)
(*2) Refer to Yasuo Nakayama (2011), The Construction of Time Theory, Keiso Shobo, p. 74.
(*3) Refer to Tatsuo Motokawa (1992), Elephant's time and rat's time, Chukoshinsho, p. 4
It is written that Mammalian heart rate time is substantially proportional to the 4th root of body weight.