21st Century Series
A PHILOSOPHY OF THE FOUR-DIMENSIONAL SPACE-TIME
The Worldview of Relative Simultaneity
MURAYAMA Akira Written in Dec. 2006
Introduction
People occasionally face situations that they wish they could somehow escape from. There is one thing, however, that people cannot control, regardless of their most valiant efforts. That thing is time. A situation not bound by time’s grasp is simply unimaginable.
I do not remember when I first began to cogitate about time so consciously. In the past, I simply looked forward to as much happy time as possible, while hoping that unpleasant situations would pass by quickly. When thinking this way, I must have been enveloped within time without necessarily paying conscious attention to it. Later as I began to learn about history and science, I gained an understanding about the concept of time as measured in chronological tables or numerical lines, external methods of objectifying time. Nevertheless, people experience time as a constant movement of the “present” in their daily lives, not in tables or lines. As I considered the issue of time, I sometimes wondered about these two types of time – that which we perceive in our daily lives and the chronological table and numerical line perspectives – even though the two orientations are completely different and no “present” exists in the table and line perspectives. I satisfied my early musings about time by concluding that models of time as measured by chronological tables or numerical lines were merely convenient tools, which were devised by human beings in the ongoing effort to describe memory and laws.
Eventually I reached a point in life when I keenly felt a strange desire to examine the meaning of life and the world. As I began to delve into this material, I realized that these were philosophical subjects and that many philosophers argued about time. I was struck by the significance of time. In addition, I have observed very strange representations of time in modern natural science being demonstrated through science fiction. If my memory serves me, it was in the movie Planet of the Apes (1968) that I first witnessed a mysterious depiction of time that could only be explained with the theory of relativity. In that film, when an ultra high speed spacecraft traveled far away for well over a year before returning to earth, the spacecraft crew discovered that two full millennia had meantime passed on earth. “How can that be?” I wondered. Of course, in those days, still a primary school student, I had not yet heard the phrase, “theory of relativity,” nor was there anyone who could clearly explain the concept to me. Nevertheless, my curiosity lingered and ultimately led me to an interest in the theory of relativity.
*
There have been innumerable guidebooks published worldwide about the theory of relativity, ranging from basic explanatory writings to complex treatises. This suggests both how many people are interested in the theory and how difficult it is to understand it. It is noteworthy that the theory has attracted such attention despite its incomprehensibility. For instance, if a company manufactured a complicated computer system that was very difficult to handle, likely nobody would be interested in it except for those particular persons in charge of its system operations. Why, then, are so many people interested in the theory of relativity?
The answer may lie in the collective human experience. Despite the theory of relativity’s great complexity, it addresses the subjects of space-time, philosophical questions pondered by people throughout the ages. Surely developing a complete understanding of the theory of relativity, including general relativity, requires a considerably high level of mathematical knowledge. Such an endeavor would be tough for someone like me, one who has not mastered the technicalities of physics and mathematics. However, understanding the special theory of relativity that constitutes the basics of the entire theory of relativity merely requires rudimentary mathematical knowledge. Handling such numerical formulas is not so difficult. In fact, there are many fields that are much more complicated and difficult to understand than these theories, yet people working in complex areas of study can appropriately handle them. In my opinion, what makes the theory of relativity truly incomprehensible is not its theoretical complexity, but rather its uncertain interpretation of the world.
I was not able to gain an understanding of the special theory of relativity by simply working on numerical formulas. Even when I read explanations about how trains or light clocks worked, I still could not understand the theory. I gained some sense of understanding about the theory’s logic for the first time only when I read a commentary that used the space-and-time figure. However, as my understanding deepened, simultaneously more questions arose. I wondered about the nature of space-time. What is four-dimensional space-time? I asked if the world really existed.
The clearest distinction between the theory of relativity and Newtonian dynamics is how simultaneity is viewed. Before the theory of relativity was published, people believed that "now" was consistent in any place or at any velocity and that what occurred an hour ago simultaneously was determined in conformity with the flow of the whole universe. However, after the diffusion of the relativity theory, things dramatically changed. I noted the assumption that this relativity of simultaneity constitutes the core essence of the theory. Based on this concept, I have focused my inquiries upon the existence of four-dimensional space-time. Such is the primary concentration of this book. As a result of my examination, I have concluded that four-dimensional space-time does truly exist and that both the past and the future definitively exist as well. In accordance with this line of reasoning, we can no longer state that the models of looking at time through a chronological table or a numerical line are simply convenient observational tools. Such an approach inevitably leads us to wonder about the exact nature of the past, present, and future that we experience. Other inquiries arise. What is the flow of time? What is the “now” that is continually changing? We even encounter the question of freedom. Are we indeed free?
*
I have long been attempting to solve these riddles, and I cannot say I have gained any satisfactory answers. In fact, I have nearly given up in frustration many times over the last twenty years. In 2002, the Osaka Independent School of Philosophy’s Mr. Minoru Tabata, who has long promoted the civil philosophical movement, offered me the opportunity to participate by publishing in the 21st Century series. Mr. Tabata’s proposal triggered my decision to organize my long-elaborated ideas for publication. Such was the genesis of this book. Cogently expressing these ideas has proven difficult.
In recent years, by taking advantage of the Internet and its plethora of information, I have conducted research using several keywords regarding the theory of relativity and four-dimensional space-time. I found I was not alone in my critical thinking viewpoint on the subject. Furthermore, when I searched English keywords, I discovered many Web sites on those subjects. I paid especial attention to international conference sites regarding the ontology of spacetime. The first such conference was held in 2004, and the second one followed in June 2006. The ontology of four-dimensional space-time has since become a hot issue for philosophers and physicists worldwide.
I could not resist taking immediate action, and I ventured to contribute an abstract paper to international publications. However because I lack any substantial academic track record, I had difficulty in drawing wide attention to my study. However, Mr. Vesselin Petkov, a member of the coordination committee, invited me to attend the conference. Petkov theorizes as to the existence of four-dimensional space-time and places a strong focus of attention on the relativity of simultaneity. Holding similar views, I felt a connection to him and was happy to meet him. Although I am not fluent in English and I had not yet traveled abroad alone, I nevertheless felt compelled to go. Thus, I departed for Montreal, Canada.
*
Common viewpoints on the ontology of spacetime can be classified into the following three categories:
(1) Only the present exists. The past has vanished and the future has yet to come. This point of view is called presentism or three-dimensionalism.
(2) The time scale from the past to the present exists, and the future is just an imaginary thing based on human expectation. This is known as the growing block theory.
(3) The whole time scale from the past to the present to the future exists. This is generally referred to as eternalism, four-dimensionalism, or the block universe theory.
Some will argue that the four-dimensional space-time theory (in fact all forms of physical theories) are nothing more than convenient conventions to justify denial of any third viewpoint about the existence of space-time. This position is referred to as conventionalism, and the argument about four-dimensionalism is in connection with epistemological discussions.
In four-dimensional space-time, a moving point is expressed as a line between the past and the future in space-time and is called a "world line". According to four-dimensionalism, we do not exist as three-dimensional moving objects, but instead are four-dimensional hypersolids in hypertube shapes, which themselves do not move at all. Mathematician Hermann Weyl once referred to this tube-shaped form as a "four-dimensional worm" in space-time. This "worm" itself does not move at all. The tip of the “past side” of the worm represents its birth, and the end of the worm’s "future side” represents its death.
Thus the question arises: if we are lying in space-time as four-dimensional worms, is our future pre-determined? Any argument regarding the ontology of four-dimensional space-time is likely to include a discussion about determinism. At the international conference on the ontology of spacetime, lively discussions about determinism took place alongside other topics of modern physics, such as cosmology and quantum mechanics.
Most who participate in these types of discussions are physicists, mathematicians, and other scientists and philosophers who specialize in related fields. Therefore, their arguments can invoke considerably technical themes within academic fields and joining these discussions requires a high level of technical knowledge. Naturally in the midst of such scholarship, I felt like the proverbial fish out of water. However, I was excited to know that many people from around the globe were engaged in such heated debate on the philosophical subjects of four-dimensional space-time. I was enlivened to be there to participate.
It is thus that I have felt compelled to write seriously on the subject and this book of philosophy is the result. I have considered these philosophical issues separately, removing myself from those technical arguments being made within the fields of science and philosophy. I cannot claim to know whether my thoughts deserve evaluation or public credit; I only know that I must bring them to the public eye. I leave any determination of merit to the assessment of my readers.
*
Professionals in the fields of science and philosophy have presented elaborate arguments about the existence of space-time, taking both physical and logical viewpoints. Although I believe that those insights developed over time are important, I am not interested in continuing that line of discussion ad infinitum. I have my own point as to the existence of four-dimensional space-time. What I now want to introduce and lead is the next stage of discussion, one that constructs a new worldview predicated upon the acknowledgment of four-dimensional space-time. I would like to explore how we should live from a four-dimensional space-time perspective.
Nevertheless, I am cognizant that I must tread carefully in pursuit of this goal. Therefore, in the first half of Chapter 1, I will outline the basics of the theory of relativity. More specifically, I will explain the minimum fundamental concepts necessary to any discussion of the existence of four-dimensional space-time. The concepts I will set forth are not partial copies of other guidebooks. Rather they are based on my close contemplation and will clearly explain the theory’s essence. In the second half of Chapter 1, I will philosophically analyze the existence of four-dimensional space-time and those issues related to determinism arising within the theory of relativity. This material is at the heart of the book and includes my formal declaration acknowledging the existence of four-dimensional space-time. Further I articulate a stance that accepts determinism. Building upon this, I will develop my argument, including observations in quantum theory.
In Chapter 2, I discuss the subjects of continuity and contradiction as viewed through the lens of four-dimensional space-time. I commence my argument by taking up the popular paradox of Achilles and the tortoise. I continue by approaching the logic of moving objects vis-à-vis space-time. (I have already posted these points on my websites.)
In Chapter 3, I touch on time representations that cannot be fully examined solely through physical arguments. That is, I focus on onetime modality as a subject—the flow from the past to the present to the future. It is not enough to just persist in championing the existence of four-dimensional space-time. We can enter the heart of philosophical time theories only when we focus on this point. I intend to present a hypothetical model of the consciousness as an infinite number of scanners existing in parallel. Additionally, I will address time travel, to the future or the past, and the direction of time.
In Chapter 4, I will speak to the subject of freedom theory. More specifically, I will explore whether a worm in four-dimensional space-time is actually free or not. On this question, I will posit in the affirmative. However, I intend to present philosophical reflections on the concept of freedom from a perspective of four-dimensionalism and materialism, and here my focus will be on the concept of power. I have long ruminated about how I should approach the subject of freedom from the viewpoint of four-dimensionalism. The solution I developed was to critically view the concept of power in terms of a four-dimensional evaluation.
In such a manner, this book approaches the subject of four-dimensional space-time from the broader perspectives of ontology, logic, epistemology, and ethics. This drastic and extensive approach is a major experimental challenge and one taken, I believe, in risk of my academic future. Although I may be criticized for my lack of strict academic consideration, I am confident that I have made the utmost effort not to disappoint my readers.
My fervent hope is that readers will consider my ideas closely. It is, of course, ultimately up to this book’s readers to evaluate my thoughts and decide for themselves.