A PHILOSOPHY OF THE FOUR-DIMENSIONAL SPACE-TIME
The Worldview of Relative Simultaneity (MURAYAMA Akira)
CHAPTER I
Relativity and Four-dimensional spacetime
[The Latter half] ---- Philosophical Examination ----7. Deterministic Worldview
Before knowing the theory of relativity, I understood the past as the aggregation of totally determined events and the future as a world that still remained to be determined. Accordingly only present things in motion existed and the past was just a thing to be reflected upon because it was completely gone. However, if the past has already been totally determined, then the present is formed on the basis of the past and the future is envisaged in the direction of the present. Therefore, the future remains to be determined, and exists in the conceptual world merely as a form of prediction. I had lived with the world view based on this way of thinking.
However, I became suspicious of this way of thinking after having learned the concept of the relativity of simultaneity. Figure 1-7-1 (a) illustrates the world lines concerning "me" and "another person" who are approaching each other from a distance. Generally speaking, the past is the aggregation of events that have already occurred and that everyone takes for granted. At least in my system of coordinates, the past events from the standpoint of "the present myself" have already occurred and have been determined. By this line of reasoning, with regard to "another person at the same time as the present myself" approaching me from a distance, the past events before "now" must likewise have already occurred and been determined.
From the standpoint of the person at the same time as me, as his or her simultaneity is different from that of the present myself, the present myself for him or her should represent me at some time in the future. The past of the person involves myself in the present time or in the near future. The span of the future depends on the distance between the person and me and our traveling speed, but the future in this case has been determined because it represents the past, what has already occurred, for that person in the already determined situation.
By this reasoning, it follows that the past for myself in the near future has also been determined. Therefore, the past for another person, who exists still farther in the future, has also been determined. Then myself existing a little farther in the future is involved in the person's past. This leads to the conclusion that the entire universe involving myself and another person in the future has already occurred and been predetermined.
Now think about things based on the nondeterministic view of the future. See Figure 1-7-1 (b) illustrating the world line depicting "another person" and "me" traveling away from each other. The future is the aggregation of things that have not yet occurred and thus are undetermined at least in terms of common sense. First and foremost, let's recognize that all events, which exist in the future ahead of the "present myself" in my coordinate system at least, remain yet to occur and be determined. With regard to "another person at the same time as the "present myself" who moves farther away from me, the future ahead of "now" also remains to occur and be determined.
Now from the standpoint (system of coordinates) of the other person, immediately before the things are determined, as his/her simultaneity is different from that of myself, myself, which is present for him/her, represents myself at a point of time in the past for me. His/her future involves myself in the present or in the close past. The past depends on the distance between us and our traveling velocities, but the time beginning just after the past is the future for that person and remains to occur and be determined.
This way of thinking leads to the proposition that "myself" (including the present myself) existing in the future ahead of the aforementioned point of time in the past for me also remains to occur and be determined. Therefore, things of "another person existing slightly prior to the time he or she existed" are undetermined and this is also the case with "myself in the past" from the person's standpoint. This leads to the conclusion that the entire universe involving "myself" and "another person," even when indefinitely going further into the past remains to be seen and determined.
Are "myselfs" in both the present and past times undetermined? Then, what is myself in the present time? Supposing that past things have already occurred and have been determined, it follows that future things have also occurred and have been determined. By the same token, provided that future things remain to occur and be determined, past things also remain to occur and be determined. According to this reasoning, the relativity of simultaneity cannot specify the distinction between the "already occurred" (determined) situation and the "yet to occur" (not determined) situation as to the past and the future.
The concept of past and future seems significant only as a kind of physical direction on the basis of a certain point of space-time (and a certain system of coordinates). It is in the same league as the concept of "right or left" and "north or south." The concept of past and future cannot involve further attributes. That is, the attributes of existence and determination cannot be added to the concept as elements characterizing the differences between the two.
Here, I would like to step back and think about whether or not the above-noted examinations involve erroneous judgments and debate the conclusions reached. The conclusion that the future as well as the past is predetermined is based on the following assumptions:
(1) Simultaneity is relative.
(2) The present myself is determined.
(3) Past events that occurred before determined events are determined.
The conversion of (2) and (3) into the (2') and (3') shown below leads to the conclusion that the past as well as the future is undetermined.
(2') Myself in the future ahead of present time is undetermined.
(3') Events existing in the future ahead of undetermined events are undetermined.
The denial of the assumption (1) is necessary to facilitate the consistency between the former (2) and (3) and the latter (2') and (3'). That is, simultaneity must be absolute.
The flat denial of the "relativity of simultaneity" means not just a partial modification of the theory of relativity but the fundamental return to Newtonian dynamics and the total negation of Einstein's theory. Although an authoritarian negative reaction to the flat denial of the current established theory is not always desirable, it is extremely difficult to return to Newtonian dynamics based on any criticism against the theory of relativity. Since the advent of the theory of relativity, many such efforts by some people have been made again and again in various countries, but none has succeeded. The relativity of simultaneity is clearly incorporated into the Lorentz transformations. The denial of the relativity of simultaneity means that Lorentz transformations are at least a wrong form of worldview and that Galilei transformations are right. As a matter of fact, wrong Lorentz transformations have produced much success in experiments, observations and developments, whereas right Galilei transformations have caused much failure in those attempts. This suggests that it is necessary to explain why these phenomena have actually occurred on the basis of right Galileo transformations. Doing so is an exceedingly challenging task.
Here, I focus on light cones in my elaborate efforts to examine erroneous deduction. The arguments above are based on examining the past and future in accordance with simultaneity in the reference frames of another person and me. However, in fact, things we can perceive do not exist at strictly the same time. This is because no information can exceed the speed of light. What can be seen "now" is an event on the surface of a light cone in the past and a thing that can be perceived generally is an event within the light cone in the past side. The space-time "cross section" representing "present" is positioned in the future side from the past region and its inclination is indefinite due to dependence on a system of coordinates. In addition, I can never perceive events existing in this uncertain "present" if they are far away from me. It is no wonder that someone has doubts about whether such unperceivable events in principle can be judged as determined events. If only past events within the surface of a light cone in the past are determined, theories based on the relativity of simultaneity lose their grounds. The surface of the light cone is unchangeable even in a system of coordinates with different speed. (See Figure 1-7-2.)
However, this reasoning has already failed because the light cone can be the only absolute criterion only when "the present myself" is the benchmark point of space-time and there are innumerable light cones conceivable from the standpoint of many other observers existing distantly from me. As long as the worldview that the "present myself" is the center of the universe is accepted, this way of thinking is valid. The thinking model works only from the perspective of the so-called solipsism.
Judging from the above discussion, there are three conceivable worldviews concerning determination patterns accepted in the theory of relativity:
(1) Both the past and the future are completely predetermined. (Determinism)
(2) Neither the past nor the future is determined. (Many-worlds interpretation)
(3) Only the awareness of the present myself exists (self-centered way of thinking or solipsism). The past has been determined, but the future is not predetermined.
The absoluteness of simultaneity is an essential requirement for establishing the familiar idea that the past has been determined and the future is not predetermined, avoiding the self-centered, solipsistic way of thinking in (3). To achieve this, it is necessary to take the stance of discrediting the theory of relativity and of advocating the return to Newtonian physics, too much challenging position in the current world.
However, there are few ardent advocates of solipsism because taking this stance itself is problematic. If you claim to someone that the present yourself and the world that you are perceiving exist only for yourself, what does 'someone' mean? Additionally, if many people agree to this view, things become more complicated. If B agrees to A's solipsistic way of thinking, who is the only center of the universe, A or B? If both are the center, their assertions are inevitably contradictory. Therefore, people usually do not insist on such things. It would take a considerable level of strong will to persist in this stance. In this way, physics would be the science that deals with the objective pattern of awareness of myself.
Now, let's look at (2). By this line of reasoning, we cannot avoid facing the serious proposition: "Why does the past exist in a uniquely determined way in our consciousness?" Why does my recognition of past events accord with those of many other observers? Those other people are just people in my eyes. Are there others of the same kind that I do not know? Do those others know "another I" that even I myself do not know? The idea that there are innumerable spaces corresponding to every case is closely related to one stance on the problem of observation in quantum mechanics, that is, Hugh Everett's (1930-1982) "many-worlds interpretation." Despite its grotesqueness, this way of thinking seems helpful in consistently resolving difficult problems in quantum mechanics and a considerable number of people have adopted this thinking in recent years. However, its validity can neither be verified nor denied by experiments and it can be nothing more than a physical interpretation.
As some science fiction has adopted the idea of many-worlds interpretation, in which histories realizing multiple possibilities exist in parallel, it has given a romantic impression. For example, there are histories of the assassination of Oda Nobunaga (1534-1582), a famous Japanese samurai lord who conquered the entire nation in the 16th century, at Honnôji Temple and his successful escape from the attempt. When there are countable numbers of histories, we may consider them as romantic. However, in this kind of many-worlds interpretation, we have to consider that there are all possible histories and variations of those histories, for example, the innumerable possible cases flamed arrows shot at Honnôji Temple. Our brain capacity is not large enough to perceive this process as romantic. Apart from this kind of subject, even if I can successfully solve problems of observation in quantum mechanics with a focus only on logical consistency, the question of why the universe I know is as it is and as it tries to be like will remain totally unsolved as a metaphysical subject. In terms of many-worlds interpretation, other people I know just happen to be other people for me and I have the impression that many-worlds interpretation can be termed "multi-solipsism." Perhaps an individual and specific world exists subjectively only in my eyes and that the objective world is dispersed in an abstract space with infinite possibilities. This seems to be an influential way of thinking about the problem of observation in modern quantum mechanics. It is impossible in principle to verify the validity of this idea because we cannot experience and compare multiple spaces, but this impossibility of verification does not mean that the stance is theoretically wrong because the impossibility of verification is derived from this stance. However, it is clearly wrong to opportunistically support this stance. To advocate the idea, it is necessary to be consistent with it at every moment in every place.
With regard to its relationship with the interpretation of quantum mechanics, solipsism (category 3) may correspond to the most genuine and radical attitude of the mainstream Copenhagen school. That is, my consciousness (observation) creates the world. Perhaps, this radical interpretation does not make up the essence of the school. Most physicists seem to cleverly avoid making judgments about the problem of observation. A majority of physicists do not have enough time and resources to resolve those intractable metaphysical problems. Instead, many physicists tend to obtain significant results and develop theories by discovering some rules correlated to practical achievements for some operations. From the quantum mechanical perspective, it is not specific observational values but quantum conditions corresponding to probability that can be concluded by determinism. But in actuality, we can handle only specific observational values. With respect to the interpretation of these observational values, contemporary physicists are split over which stance they should take, subjective idealism, many-worlds interpretation or pragmatism.
Categories (2) and (3) are quite incompatible with our day-to-day senses, and seem somewhat compatible with the logic of quantum mechanics. In sharp contrast, the category (1) appears completely contradictory to quantum mechanics. Quantum mechanics is considered to have overturned deterministic worldviews, but the category (1) is obviously based on determinism.
However, the category (1) is the easiest to accept in approaching the space-time diagram of the theory of relativity without considering quantum mechanics. Unless you take the stance of the category (1), the development of the mechanical content in theory of relativity will be annoyingly complicated. Therefore, I will further examine category (1) in the sections below, considering the likelihood of facing unexpected twists. The following section will explore again the problems in quantum mechanics.
Now, I think about things from the perspective of category (1) of determinism. In this context, we face the problem: "Why doesn't the future sometimes seem predetermined in our consciousness?" This problem can be explained as follows: Information transference occurs only in a one-way direction from the past to the future in the real four-dimensional space-time and it is impossible to know what the future will be like in our awareness. This is related to the direction of time. I will discuss this subject in detail on another occasion. In any case, information can only travel more slowly than the speed of light from the past to the future. That is, information transference can occur only in the inside of the surface of a future light cone. Therefore, the real four-dimensional space-time is structured in such a way that information can never travel from future events (including events in the space-like region that can be the future in a different system of coordinates with different speed by switching from a system of coordinates where the event exists in the past and the present.) At least in modern physics, there have been no cases observed that are contradictory to this principle. (In quantum mechanics, a speed faster than light velocity is sometimes argued in a non-local relationship, but even in such case, the idea that information transference can occur faster than the speed of light is not established.) Accordingly we cannot know the future in a direct manner; we can only predict what the future will be like on the basis of past information and rule-based knowledge obtained from the accumulation of experiences. In addition, we do not have any guarantee that the prediction is completely trustworthy.
Determinism based on the relativity of simultaneity provides only a small amount of resources to prediction possibility. Based on the assumption that the past and the future cannot be separated at certain points of space-time as different attributes of determination or non-determination (already occurred or not yet occurred), this kind of determinism leads to the conclusion that the past has been determined and the future has also been determined. It just maintains that the future is predetermined and does not mention at all how the future is determined. This point is hugely different from those of conventional models of determinism.
Conventional models of determinism originate from the atomic theories postulated by Leukippos (BC440-AD about 430), Dēmokritos (BC460-BC370), Epikouros (BC341-BC270) and Lucretius (BC94-BC51), and their typical pattern is seen in the worldview envisaged by Pierre-Simon marquis de Laplace (1749-1827), one of Newton's followers. The worldview was consistently in line with the principle of Newtonian dynamics and it followed that if the mass and movement of all substances in the world could be precisely grasped at a certain point of time as initial values, the future must be completely predicted. However, practically speaking, the complete prediction of mutual gravitational effects in a dynamic system of just three celestial bodies has not yet been resolved. The reason was interpreted as the technological immaturity of humankind who persisted in believing that everything is ruled by Newtonian dynamics. With regard to this theme, determination and predictability are inseparable from each other and the determination of the world is entirely explained on the basis of cause and effect.
I call this form of classical determinism "causal determinism" and call the determinism model based on the relativity of simultaneity "space-time determinism." The model based on Minkowski's space-time theories is occasionally called "relativistic determinism." (This pattern may also be described as "four-dimensional determinism" or "block-universe determinism.") Space-time-oriented determinism was presented only after the advent of the space-time interpretations of the theory of relativity. Many forms of conventional determinism virtually constituted the core of causal determinism. Otherwise, many of them would have been described as theological determinism based on God's will beyond physical causal relationships.
For example, Aurelius Augustinus (354-430) argues about his idea of time in his book, "Confessions." His sharp insight into time representation (and other subjects) has had an enormous influence on philosophical history. He expresses God's time as "eternal present" and looks upon human time on the earth as a succession of time that is in a constant process of passage. In addition, he regards human free will as powerless and asserts that human will is controlled by God's will ruling the eternal present. He also insists on asceticism and pious religious belief (probably on the basis of his own soul-searching examination of youthful behaviors.)
Moreover, some thoughts of the religious reform movement led by John Calvin (1509-1564) and Martin Luther (1483-1546) were also predicated on the worldview of theological determinism. The worldview at that time was compatible with the predestination that everything, ranging from the past to the future, was completely predetermined by God's will. Then, people emphasized returning of their mindset to Augustinus's way of thinking as part of criticism of Catholicism. In this context, human will and religious belief were considered to be under the control of God. By this line of reasoning, it followed that voluptuous, lazy and impious people should be considered to be ineligible for God's blessing. Consequently, this deterministic worldview induced people to make efforts to avoid being stigmatized as such indecent persons and inspired them to be devout, stoic and diligent. This predestination has shown as a historical example that determinism does not always lead to pessimism.
In addition, Baruch de Spinoza's (1632-1677) worldview can also be introduced as a form of pantheistic determinism. This should be regarded as "logical determinism" rather than theological determinism. (Can it be said that Spinoza's concept of substantia, that is "the absolute infinite substance being God," may be close to the idea of four-dimensional space-time? Or can it be said that Spinoza's substantia should be looked upon as being close to the infinite cases of many-worlds interpretation eliminating every prescription? These arguments are essentially likely to be meaningless. Einstein, as a pantheist, is believed to have been interested in Spinoza's ideas.)
Theological determinism is seemingly close to space-time determinism except that it is based on religious belief in God. Everything is predetermined in this framework, although strictly speaking, it is unclear how everything is determined. Only God knows it or four-dimensional space-time knows it. (Although in this case, the personified expression of "know" is not correct.) If you think that God created four-dimensional space-time and left it as it was or that four-dimensional space-time is actually God himself/herself, then it is pantheism. In fact, specific four-dimensional space-time is infinitely profound and no wonder that someone finds divinity in it. If you think that such a concept of God is unnecessary and that the concept itself has been formed within human consciousness in their daily lives, it is materialism. If you claim that this concept of God and people with materialistic ways of thinking is a form of God's creation or that they are one aspect of the universe, which is God himself/herself, the question is if this is meta-pantheism. I have the feeling that this stretch of thinking is theoretically complete with the exception of divine salvation and love of God. I am a type of person who has no idea of God and neither wish nor can expand my frame of reference any further.
"Cause and effect" is also a Buddhistic concept. However, the concept is different from reductionistic, logically analytical and operationalism-based approaches in natural science and focuses on linking overall universe (mandala). The Buddhistic concept represents the view of universe that everything is determined by pratitya-samutpāda (doctrine of dependent origination) and dharma (law, or the constituent factors of human experience), whereas the concept is often highlighted as an admonition against excessive personal attachment to self-consciousness through insights into inseparable interconnectedness from the past to the future. The concept of cause and effect has different purposes depending on the rule (control) of nature or the achievement of supreme enlightenment (nirvana).
The Buddhist concepts of "nothingness" and "emptiness" do not literally mean that there is nothing at all. My understanding is that the concepts represent warnings against the state of mind to easily add substance, hold to beliefs while ignoring changes, disappearance and creation of matter in time, and lose true Atman (connection with universe) due to obsession with sensuous desire. The idea of four-dimensional space-time is not one of nothingness but one of absolute existence. The two concepts seem quite the opposite, but they cannot be simplified like that. That is because the worldview based on absolute existence can potentially overlap with the concepts of nothingness and emptiness.
With regard to causal determinism in natural science, the idea of mechanically reducing determinism to Newtonian dynamics turned out to be problematic in the initial phase. Causal logic should be closely examined in accordance with complicated natural hierarchical structures. Natural laws, despite being based on their fundamental laws depending on various hierarchies, are uniquely structured in a way that they cannot be reduced to the lower categories. Close natural study, theory and prediction based on qualitative probable and conditional factors can rarely be perfect. Despite their imperfection, such attempts can sometimes produce practical, effective results and as such can be useful for industrial production activities, enhancing our daily lives and having played an important role in shaping humankind history.
Causal determinism has been developed over a long period of time in human history and is in a constant process of change. It always involves uncertainty. In addition, causal determinism also faces free will issues in terms of higher layers of nature like human society, which increases uncertainty. That is why this type of determinism can either be "hard" or "soft," depending on the worldview preference of its holders.
The development of scientific theories in recent years seems to have left no room for hard causal determinism. This is due largely to the advent of quantum mechanics and chaos theory. Quantum mechanics is a theoretical system that facilitates only probability-based conclusions at the intersection with our perceived facts. In addition chaos theory has exposed the natural state in which seemingly inessential and accidental differentials, which might otherwise be ignored, are in fact significant. Currently, it would appear that the validity of the paradigm that "nature is generated by the laws," which has been established by modern science, should be reconsidered from a more profound vantage point.
As a matter of fact a completely different form of determinism, space-time determinism has developed. This new determinism is absolute, neither hard nor soft. Suppose that an attribute value, largely determined, is given to a certain space-time point of the future. In the case of soft determinism the past will also be roughly determined in accordance with the relativity of simultaneity. But the past has been determined completely in our consciousness and we have the problem noted above (category 2). Therefore I think it is simpler and clearer that we consider the space-time determinism as completely hard determinism.
However space-time determinism does not specify anything about content. It just suggests that something must be determined but does not mention how it is determined. Suppose a street fortune-teller tells you, "Your destiny has been totally predetermined, but I have no idea of how it has been determined." Is this fortune-teller determinism-oriented? This kind of thinking pattern should probably be termed neither determinism nor necessarianism (fatalism) but a form of worldview. Although this is abstract, it will definitely be considered hard determinism.
Some say that quantum mechanics overturned determinism and this refers to causal determinism. The following section examines the relationship between space-time determinism and quantum mechanics with a focus on the quantum theory.
If you strictly define determinism as the thinking pattern, in which an event farther into the future is determined by an event farther into the past, only the causal determinism described in this study corresponds to determinism, and other forms of determinism will be called necessarianism (fatalism) or teleology. In addition, the distinction between determinism and necessarianism (fatalism) can also depend on whether human will is regarded as a deterministic factor. However, in this paper determinism is understood to mean the idea that the future is predetermined.