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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

5. Time Direction

As the final subject of this chapter, I will argue about time direction in this section. Time direction can be divided into two categories: the direction to the past and the direction to the future. As long as time is considered as one-dimensional, there can be nothing but these two directions.
An important point about time direction is a case that is based on the premise that space-time from the past to the future exists, even if it is considered unconsciously. With regard to the worldview that only the present exists, it is fundamentally nonsense to think about time direction. This is thinking affected by understanding the time from the perspective of spatiality. The distinction between recalled past events and predicted future events is evident and does not involve the concept of direction at all. Even if the concept is involved, it can be established as an imaginary notion. Even if a phenomenon like running a movie in reverse occurs, it is just that such phenomenon happened and it cannot be considered that time direction has reversed.
The subject of time direction always involves the law of entropy increase, but it seems that there are some cases in which the principle is mistakenly believed to create time direction. The law is pointed out just as one of the indicators of time direction and this does not mean that time direction itself has been created on the basis of the law, just as a magnetic compass’s nature of pointing to a particular direction does not enable the north-south direction to exist. Just as the north-south direction based on the earth’s axis of rotation exists even without the nature of geomagnetism (for the current earth, its magnetic pole and the pole of its axis just happen to be almost in accord), the direction itself of the past and the future can exist without the law of entropy increase. This is a direct attribute based on the one-dimensionality of time. But you need to be an advocate of the B-series theory to insist on this. Conversely, unless an advocate of A-series theory is careful about his argument over time direction, he will he will lead to unnecessary confusion.
The subject of time direction does not at least focus on whether time has direction or not. If you recognize that one-dimensional time exists, it follows that time has direction. The subject of time direction is related to the symmetry and asymmetry of time direction. I guess that some people are confused about this point.
Phenomena in the world clearly differ in their characteristics between the case of the time direction from the past to the future and the case of the time direction from the future to the past. As the proverb about no use crying over spilt milk suggests, we are surrounded by various phenomena that are not considered to occur in the reversed direction. A cup of glass can be broken into pieces, but it is completely unthinkable that broken pieces automatically gather to form a cup of glass. Such irreversible phenomena are said to be asymmetrical in terms of time direction.
These asymmetrical (irreversible) phenomena are scientifically divided into the following three categories.

(1) Thermodynamic irreversibility (the law of entropy increase)
(3) Asymmetry of the past and the future in the cosmological structure

Based on these categories, causal relationship (interaction) and information transmission are generally considered to occur only in one direction from the past to the future (at least from a macroscopic perspective).
For the asymmetry of time, the focus is placed on the asymmetry of events in space-time and the structural asymmetry of space-time itself. The above first and second categories are approached from the former perspective, but for the third category, the latter point of view is also significant.
Probably, some people wonder what is wrong with the world, arguing that the world is actually comprised of irreversible structures and there is no problem with that. However, quite a few physicists have continued to wonder why the world is irreversible and the past and the future are asymmetrical.
The reason many physicists wondering about the common sense of the world’s irreversibility and asymmetry is that most of the basic physical laws they depend on (with the exception of a few cases(*5)) are comprised of symmetrical structures with regard to the direction to the past and the direction to the future, which allow for reversibility. The question is why the real world is asymmetrical in spite of the symmetry of many basic principles. Physicists think that there must be some reason that makes the world asymmetrical.
Generally, basic physical laws are often expressed by differential equations involving time. That is, they are represented in the relational expression of each physical quantity in minute areas and time. To solve those differential equations means to obtain functions that universally retain the relations (they are called primitive functions) and these become various functions, depending on contextual conditions (geographical and historical). In these functions, time works as a parameter and physical quantities corresponding to each clock time are obtained. Suppose that the functions are turned around in terms of time. That is, the graphs of the functions are reversed on the basis of a certain spatial axis. The functions obtained by these processes also meet their original differential equations. That is, this means that basic principles are available in the world with time reversal.
The question is if this is just a logical conclusion involving the representation of basic physical laws by using differential equations. Time-symmetric basic laws have undergone strict demonstrative physical examinations. In fact, simple processes, such as the movement of celestial bodies according to Newton’s laws of motion, are never unnatural if they are reversed. These symmetrical laws in terms of time represent physical truths and every phenomenon should be based on those principles. In accordance with this line of reasoning, we face the question: “What is the temporal asymmetry we experience based on?”
In this section, I will give brief explanations about phenomena representing the above-noted temporal asymmetry (irreversibility).

(1) Thermodynamic irreversibility (the law of entropy increase)

This is the second law of thermodynamics. The law is that entropy constantly increases in the direction from the past to the future (in an energetically closed system). The law declares that if you put hot water in cold water, it turns into tepid water but that conversely, tepid water should not break into cold water and hot water. This is interpreted as a statistical tendency of constituent particles. That is, there could be cases in which tepid water breaks into cold water and hot water, but such cases are usually interpreted as being quite rare with a probability of almost zero percent.
In the process of life development, entropy decreases, but the life system is an open system and emits entropy in some process of material and energy metabolism. Entropy increases from the perspective of the entire system including those processes. This is a general law, which has been thoroughly examined from a macroscopic perspective. However, if you consider a fluid that is almost in equilibrium in an adequately limited area, the fluid can naturally slip from its average state (the maximum of entropy) and become lopsided. This phenomenon is called fluctuation. In this case, a decline in entropy occurs. Therefore, the law can be considered a statistical one that can be applied to macroscopic phenomena.

This law means that if you drop a stone in a pond, wave fronts in a concentric circle can spread from the center to the bank but not vice versa, in which wave fronts rippled at the bank of the pond proceed to the center with decreasing in its size. The former is called a backward traveling wave and the latter an advancing wave.
The radiative wave equation obtained by solving Maxwell’s equation represents both waves. In practice, the solution of an advancing wave is abandoned, but in principle, an advancing wave cannot be regarded as an irrational phenomenon in terms of physics. With regard to the special theory of relativity as well, judging from the equation, the future light cone is equivalent to the past light cone. The future light cone represents the spatiotemporal structure of a backward traveling wave and the past light come expresses the spatiotemporal structure of an advancing wave. But the latter is just considered to be the imaginary spatiotemporal boundary “phase” and in fact, no waves with such form, at least in the world that we know, exist.
The question is why an advancing wave doesn’t exist. The general belief is that, in terms of the probability theory, no vibration phenomenon exists in which the scattered parts in various places corresponding to the bank of the pond create a harmonious wave moving toward the center.

(3) Asymmetry of the past and the future in the cosmological structure

Strictly speaking, the big bang theory should be considered to be a hypothesis, but there are so many theories and observed facts demonstrating the truth of the theory that physicists and astronomers no longer seem to doubt the theory.
The belief is that space was born in a state of ultra-high density and high temperature 13.7 billion(*6) years ago. With respect to the critical moment, the simple application of the general theory of relativity results in a gravitational singularity, which makes calculations impossible, and also requires the integrated theories between the quantum theory and the general theory of relativity. Currently, physicists are seeking a variety of models. Now, we face the simple question: How was space before the big bang? In this context, the birth of the universe refers to the birth of space and time themselves and essentially speaking, the question itself makes no sense. In the eyes of physicists studying the cosmology, space and time are (attributes of) the universe itself and they never consider the abstract concept of space and time as a container in which the universe is trapped. When physicists argue about the cosmology, their way of thinking usually seems to be based on the block universe theory, regardless of whether or not they intentionally take that stance.
Based on the assumption that the universe originated from a highly-compressed point in the past, people also think about how the universe will be in the future. Will it shrink in the future due to the arrival of a big crunch, continue to expand or accelerate the degree of its expansion?
In addition, some say that a considerable amount of unknown mass and energy called dark matter and dark energy exist. In my opinion, humankind has yet to reach a level at which it can easily find something close to the final conclusion. We can consider various models at least on the basis of hypothetical assumptions.
Suppose that the universe reaches the big crunch and begins to shrink, will time direction (time arrow) reverse? If it does, will entropy decrease and will advancing waves be the norm? In this scenario, will the flow of consciousness also reverse? That is, will the consciousness of the human-like entity, who may exist far in the future, move from the future far away from the big crunch to the future close to the big crunch? In accordance with this reasoning, does the reverse consciousness recognize an increase in entropy just like our consciousness and perceive the world as the process of only backward traveling waves being seen? These are the themes of discussions. Does the consciousness that has passed the center of the universe recognize the world as the process of entropy decreasing or if the consciousness goes beyond the center of the universe, will its flow also reverse? In this case, it is conceivable that there is some reason why the flow of consciousness (its direction of scanning space-time) accords with the direction of an increase in entropy. Or is it fundamentally impossible for consciousness to travel through the middle point of space in a state of heat death?
We also have the subject of the uniformity of the universe as a big mystery of the universe in its initial phase. Heavenly bodies and gases currently observed in the universe are distributed in a largely uniform manner. This uniformity should be based on the uniformed distribution of materials and energy in the universe in its initial phase. But in the world in which gravity is predominant, such state of uniform distribution is quite unnatural and mysterious. In such state, things should be usually divided into big chunks and minute chunks. Therefore, in the current studies of the universe, it is more natural to think that the universe is comprised in an unbalanced way, ranging from ultra-giant black hole to dusts and gases. However, the universe is almost uniform. This is unthinkable as an accident because its probability is too small. It would be inappropriate to attribute this uniformity to God’s stroke or God’s intention. Still, this is a mystery, but we can also say that this uniformity determines the way the universe is now. In addition, some suspect that the tendency of an increase in entropy was caused by a state of low entropy at the early stages of the universe. That is, the point is to focus on why the past direction of the universe involves lower entropy, not why entropy increases.
Stephen Hawking avoids singularity issues on the basis of the imaginary time hypothesis at the birth of the universe and also explains its lower entropy at the beginning of the universe. If you define time as an imaginary number at the beginning of the universe, that space can be regarded as something spherical, not a geometrically infinitesimal point. It is possible to find a justification for the existence of well-ordered world of the universe in its initial phase.
In one of his books, Time’s Arrow and Archimedes' Point (*7), Hue Price argues about these issues on time direction by examining various views on the basis of profound physical knowledge. His argument is clearly based on the block universe theory and in this sense, his way of thinking is close to the stance of this book. Or rather, he may be much more radical than I am. He claims that the issues should be approached from the non-temporal perspective as view not from any point of time. Just as Archimedes focused on the leverage and fulcrum to move the earth from a viewpoint away from the earth, Price argues that the core essence of the issues concerning time can be discovered by examining them from a perspective apart from flowing time. To put this another way, he highlights the perspective of considering four-dimensional space-time with a bird's eye view. In this sense, his thinking pattern overlaps with that of this study.
In addition, Price emphasizes the symmetry of time represented by fundamental physical laws. Based on this stance, he doubts the common idea of absolutizing the causal direction, in which the past determines the future. He points out that many people are trapped in an erroneous double standard in the sense that they unconsciously recognize only the discussion in one direction of time and do not consider it in the reverse direction of time in an equal manner. In his opinion, this attitude toward time is problematic because people do not approach basic physical laws in an honest way. But his focus of attention does not seem to involve macroscopic phenomena. He focuses on a principle called microscopic innocence principle(μInnocence). That is, he is skeptical about the thinking that interactive systems do not have correlations until they interact in the micro-particle system. Every form of science, including physics, is usually based on the major assumption that past events control future events but not vice versa. However, he is skeptical about the absoluteness of this principle. He also notes an idea called Advanced Action. That is, he argues that the phenomenon of future interactions predetermining their prior state can occur at least in microscopic events.
Apart from abstract philosophical arguments, a specific issue of discussion is the interactions between photons and the polarizing lens, which are related to the EPR issues in quantum mechanics and Bell’s principle (Refer to Section 8 in Chapter 1). There is an observation, in which the interactions between the device to detect photons and the detected photons represent the statistical behavior as if photons had predicted the directional setting of the polarizing lens in advance. A great majority of physicists, including John Stewart Bell (1928-1990), interpret this fact as an example of non-local correlations as a result of information transmission at the ultrahigh speed. Price argues that the interpretation based on reverse causal relationships could facilitate more simple ways of thinking in the sense that it can avoid the contradiction with the special theory of relativity concerning exceeding light velocity.
Essentially speaking, what are casual relationships? Originally, casual relationships create a conceptual device implanted in human thought, which is also the religious origin. This paradigm has been naturally employed by natural science and has been recognized as a basic form of objective nature. But given the existence of four-dimensional space-time, it is undeniable that the worldview that objectively existing laws comprise the constantly creating world was just a conceptual phenomenon. The world exists from the past to the future and our consciousness perceives it as the process of movement and creation. In accordance with this reasoning, laws should be regarded as a conceptual device formed within our consciousness by our consciousness from our experience. Laws consistent with events in existing four-dimensional space-time are retained as something correct and if they contradict those events, they are improved and reformed to be more adaptable. From this perspective, our experiences are almost macroscopic phenomena and causal relationships have been established on the basis of the assumption. As long as this is the case, the causal model that the past determines the future has just not ever been betrayed. Therefore, if the reverse causal model can be applied with regard to microscopic phenomena that exceed the limit, it will involve no room for skepticism. At least at a macro level, the fact that the distribution structure of events that can be explained by the causal model from the past to the future exists cannot be an attribute of human consciousness. I could not extract adequate ideas about how to develop from a microscopic to a macroscopic from Price’s book. The book written by Price presents several issues of discussion and the field is beyond my level of proposal and evaluation.
One notable point is that time direction concerning photon world lines is more special in comparison with other types of world lines. Photons exist in the system of light velocity and which side of their world lines is the past or the future can be judged only by the coordinate system of surrounding existences other than photons, that is, the coordinate system of non-light velocity. In the light velocity system of photons themselves, all events occur at the same spatial point and the same temporal point and the concept of past and future itself cannot be applied to the system. But I have no idea whether this can be linked with the impossibility of μInnocence or not.

The Spatiotemporal Theory - Based Viewpoint of Life and Death
The recognition that the direction in which human consciousness scans four-dimensional space-time is limited to one direction can be interpreted in two ways. (Of course, it is based on the block universe theory.) One way is to interpret that there must be some reason for the direction of consciousness to accord with that of an increase in entropy or that of backward traveling wave ripples, which limit the direction to one specific way. This interpretation is often presented. It is based on the associations between consciousness systems including memory and thermodynamics. Currently, I am one of those who place the utmost emphasis on this interpretation. But in pure theory and as a matter of form, I think that another interpretation is possible. It is to interpret that human consciousness scanning four-dimensional space-time exists in both directions but that communication is possible between each consciousness, which scans four-dimensional space-time in the same direction. This means that when multiple forms of consciousness scan four-dimensional space-time in the reverse direction to each other, they cannot confirm the existences with one another. That is why it is interpreted that each form of consciousness believes that consciousness in one specific direction can exist. Needless to say, this interpretation cannot be clearly demonstrated, but it is difficult to totally deny the way of thinking. Given the fact that antiparticles, such as positron, can be interpreted as normal particles moving from the future to the past, it is difficult to completely deny the aforementioned interpretation. In addition, the model involves no necessity of explaining why the scanning direction is limited to only one direction.
However, an image of the consciousness is very strange. Teleological worldviews create the core of consciousness that scans four-dimensional space-time in the reverse direction. To predict the "future" is easier than to speculate about the "past". This consciousness can predict the arrival of the age of the dinosaurs to come according to the existence of fossils. But a clear speculation of the "past" is rather difficult with the exception of something simple, such as the movement of celestial bodies. With regard to the "past", human consciousness cannot get the sense that it definitely exists unlike the "future" and has the feeling that it disappears along with time flow. Memory sometimes “increases” in accordance with the timing of oblivion, but usually “decreases” along with experience.
Of course, I do not think that such consciousness exists, but I do not know whether or not anything remains if I get rid of all things based on the experience of consciousness that scans four-dimensional space-time in the forward direction for me out of the reasons for my not thinking as above.
I consider life and death from the perspective of the possibility of scanning in both directions. In this context, life and death are defined without depending on any particular directions of spatiotemporal scanning.

Definitions
• Being born means the transfer from the non-existence of individuals to the existence of individuals.
• Death means the transfer from the existence of individuals to the non-existence of individuals.
• The existence of individuals means a state in which individuals work properly while retaining their given forms.

• The transference of state means that two states in the spatiotemporal positioning, where these states cannot exist at the same time in any coordinate system, sharing some substantial homogeneity are temporally adjacent with each other and have anteroposterior relationships in accordance with the direction of spatiotemporal scanning.
• In this context, with regard to what extent you consider the scope of given forms and work properly (heart death or brain death), there may be delicate differences in opinion (currently, this is an important issue of discussion about life and death). Nobody would regard the state in which body parts have been completely separated or have turned into ashes as a state of individual existence. Nobody would also look upon the state of ova and sperm before insemination as a state of individual existence.
Based on these clear definitions, I will consider life and death with a focus on reverse time flow in the following section.
How are human beings born? A typical explanation to this question goes as follows. Phosphorus, nitrogen and carbon dioxide floating in the air, ashes scattered in the crematory or bones buried in the grave and the urn gather in one particular place (the boiler house of the crematory). After they catch flames and the flames vanish, the coffin is brought in and the funeral begins. Then, the dead person with the many tubes attached is carried to the hospital bed, and the grid with the flat line brain waves begin to move on the screen. He starts to breathe. This is the very moment for the birth of a human being. The tubes are removed. The man leaves the hospital and begins to work. This is just one case although it is a typical example. How human beings are born vary. Some people are born on a tatami mat, not on a hospital bed, and others in the street near the station.
In addition, some people are abruptly born during the process in which a crushed car returns to its original state. Others are born during the process in which bullets come into the holes on their backs along with blood from various places and the bullets come out from their chests while their destroyed bodies recover. Others are born after pieces of flesh scattered around have gathered in one place. At the same time, something is born as the result of pieces of metal gathering in one place, flying up in the air in a missile shape and placed on the launch pad. Others are also born during the process in which the human head sitting on the ground docks with the body and the knife thrust into the chest comes off. Others are born crucified. Furthermore, others are tortured shortly after they have been born. In mankind’s history, there are many different ways people are born. There was a case in which many people, including terrorists, were born while an accumulation of rubble was shaping a high-rise building and a commercial plane was completed in flames. There was also a case in which intense light gathered in one point from far away (this is physically called advancing wave) just after a mushroom cloud had shrunk, the burned human body instantly returned to its original state and people began to have daily lives. More than 100,000 people were instantly born at that moment.
The way people are born varies, including these unsatisfactory ways of being born. In addition, creatures in general are often born after other living things had thrown them out the mouth, although such case is rare with human beings. As this shows, the digestive canal of predator animals is a source of life. In this way, there are many different ways that creatures are born, but in contrast, the way creatures die is monotonous and uniform.
Human beings weaken in ability over time and come to be unable to live without the help of their parents. In the end, they return into the womb of their mothers. Afterward, they gradually repeat cell fusions over and over again, become a fertilized egg during the process of decreasing their cells and sperms break away from it. Then, sexual intercourses between men and women (or external fertilization) are continued. After all, the egg gets into the fallopian tube. This is certainly the way human beings (mammals) die.
If you consider life in the reverse, life is death and death is life. Both show the borderline between the state in which individuals exist and the state in which individuals do not exist.
The existence of individuals is a macroscopic phenomenon. That is, it is a phenomenon at a different level from the movement of elementary particles and its representation differs with time direction. Therefore, the border between individuals called life and non-individuals and the border between individuals called death and non-individuals are clearly different, but both comprise the border between individuals and non-individuals. That is, they represent the edges of the future and past directions of four-dimensional worm. Considered from a four-dimensional perspective, life and death are, so to speak, the skin and represent the borderline between their internal and external structures in terms of time direction.
I noticed one detail while thinking this way: Is it an unbalanced way of thinking that we are usually afraid of death and lament over the end of life? Why don’t we lament over the limit of the past direction? Why don’t we lament over the fact that we have not existed since the big bang? Even if we do not think like this, I have not heard about someone lamenting that he wish he had lived since the Stone Age or if only he had lived since the Japanese Genroku period (1688–1704). I think that this is an unbalanced way of thinking and lamenting.
In addition, the limit is not concerned with only time direction. Our existence is also limited in terms of space. I do not know anyone who laments that his body is not as big as the universe. Conversely, there is an overwhelming number of people who go on a diet, thinking that their body occupies a vast expanse of space.
Many animals can move in space and it may be necessary to pay attention to some room for their free movement, but the human behavioral scope is quite limited. Spatial occupation at a certain point of time is just limited to the scope of human body size. Why don’t people lament over this spatial limit? In fact, many people lament that the border of the future direction of their four-dimensional body is quite limited.
Our existence is omni-directionally limited. How sincerely I believe in four-dimensional space-time!

(*5) Now as a few exceptions, a rare behavior of neutral kaon is recognized , but it is hard to believe that this is the basis for all the other irreversible phenomenon.

(*6) The age of the universe is considered approximately 13.8 billion years since March 2013. This book was published in 2007 in Japan.

(*7) Refer to Hue Price (1996), Time's Arrow and Archimedes' Point, translated by Takayuki Toyama, Katsumi Kushimoto(2001), Kodansya