A PHILOSOPHY OF THE FOUR-DIMENSIONAL SPACE-TIME
The Worldview of Relative Simultaneity (MURAYAMA Akira)
CHAPTER I
Relativity and Four-dimensional spacetime
[The First half] ---- Outlining the Theory of Relativity ----This chapter focuses on physical subjects, especially the theory of relativity, which introduced the concept of four-dimensional space-time. I will provide a rudimentary explanation of four-dimensional space-time as well as theory of relativity basics. The first half of this chapter (Sections 1 to 5) examines these subjects, and I include a focus on the theory from a scientific historical context. Further, these sections specifically highlight Minkowski's concept of four-dimensional space-time. I emphasize that this space-time diagram is very useful in developing a clear understanding of the theory of relativity's basic factors, such as the relativity of simultaneity, time dilation, and length contraction. I also note that the space-time diagram is helpful in intuitively deriving the most fundamental formula of Lorentz transformations.
The latter half of this chapter (Sections 6 to 8) examines philosophical issues. First and foremost, I make an argument for the existence of four-dimensional space-time. My thinking on this topic is the crux of this paper, and the relativity of simultaneity is perhaps its most important key concept. Next, I offer critical thinking about whether this recognition will lead to deterministic worldviews or not. With respect to this topic, I also arrive at a positive conclusion. This study is largely predicated upon recognizing the existence of four-dimensional space-time and an awareness of deterministic worldviews. It is this recognition that launches this paper's discussion.
Section 8 specifically takes on quantum theory. I merely sketch out quantum theory herein because I am not an expert in that topic. However, quantum theory is germane here, the primary reason being that not only is quantum theory the centerpiece of modern physics, but it also may be closely related to the subject of four-dimensional space-time. Thus, the problem of observation is particularly important.
[The First half] ---- Outlining the Theory of Relativity ----
1. The Relativity of the Equipositionality and the Relativity of Simultaneity
Tourists at a historic site often encounter a plaque stating something like the following: "A fierce battle was waged here." However, when reading such plaques, someone says to me, "A fierce battle was waged here." I am tempted to respond, "No, it was not here!" Journalists are commonly filmed saying something like this: "Last night, a bombing occurred here. I'm reporting live from the site." Similarly, I again want to protest, "No, that's not always true."
In reality, both the battle and bomb sites were completely different, years or even mere minutes later, because these sites have moved far away into space. This is because the earth moves around the sun (at an average speed of 107,280 kilometers per hour) while rotating at another dazzling speed (of 1,674 kilometers per hour around the equator). The solar system also moves in the galaxy at a speed of approximately 220 kilometers per second. Both the historic battle and bomb sites actually no longer exist on earth, even though they did exist here at the very moment when the original events occurred. However, those locations have since moved far into space, along with our globe.
We can accurately state that an incident occurred in a specific place only when describing the situation based on a highly specialized coordinate axis, from a cosmic viewpoint, that regards the earth's rotating ground surface as static, although the earth is a planet in orbit around a star in the galaxy as one of the innumerable nebulas in space.
Identifying a location as the same place has meaning only when a particular system of coordinates exists. A coordinate system is a standard scale of space (and time) that is incorporated in a vehicle that can be regarded as static. Unless people are traveling aboard a vehicle, they usually identify a particular place using a system of coordinates that is static on the surface of the earth. However, people take for granted that a coordinate system on the earth is not the single absolute scale of space and time.
This way of thinking did not become commonplace until modern times. People long believed that the earth was the center of space; they thought that the earth was static and that celestial bodies were moving. In accordance with this line of reasoning, "the same place" can be unconditionally specified, while speed is also absolute. Something that is truly static is static only relative to the earth's surface. The speed relative to the earth represents a true speed.
The intellectual development of humankind has often been based on the movement from non-perceived assumptions to perceived assumptions. For instance, the major movement of public opinion from the Ptolemaic theory to the Copernican theory shows that the unconscious assumption that the earth is immobile was eventually overturned. This particular and dramatic change in conventional wisdom caused people at the time to gain recognition that there is no absolute scale of movement (nor is there absolute stillness) and that the motion and/or inactivity of an object should instead be determined by a certain system of coordinates. The dawn of modern physics began with Galileo Galilei's (1564-1642) discovery of the law of inertia. This law theorized that the earth did not exist in an absolute scale of stillness, and Galileo also championed the Copernican theory. In fact, Galileo presented this principle as a major counterargument against those criticizing the Copernican theory, who claimed that it was illogical for an object to fall straight if the earth was moving. He demonstrated how the principle worked by dropping an object from the mast of a moving ship.
It is necessary to factor in the movement of a vehicle when considering whether or not an object remains in the same spot with the passage of time as well as to determine how fast the object is moving. Today, the law of inertia, that is, the relativity of equipositionality, is a given.
However, when considering how time works, gaps remain between scientific recognition and general understanding. The logic behind the relativity of equipositionality, that is, dependence upon a standard system of coordinates determining whether two objects existing on a different time scale are spatially in the same location or not, is well understood. This logic is, in fact, also true of time. More specifically, time depends upon a standard system of coordinates whether or not two objects existing in different places are measured on the same scale of time. This concept is known as the relativity of simultaneity. This theory is quite familiar to physicists and students specializing in physics in the early twenty-first century, but it has not yet become common knowledge among those outside the field. (See Figure 1-1-1.)
The following scenario illustrates the relativity of simultaneity in layman's terms. Begin by imagining a situation in which a wealthy man dies on earth. His wife has predeceased him, and the man also has two sons. The younger son lives on earth, but the older son is traveling on a spacecraft, returning from outer space. This older son, who is married, dies during his return trip to earth. If the father (the inheritee) dies after his older son, that son is ineligible for the inheritance, leaving the older son's wife ineligible to inherit her father-in-law's assets, and the younger son will now inherit everything. However, if the father dies before his older son, that son can inherit half of the assets, which means that three-fourths of the inherited assets will go to his wife.
Contemporary civil law (along with 21st century common sense) identifies the before and after relation of the father's and son's times of death as an absolute factor. It does not matter which death comes first (probably). However, this is not the case when thinking scientifically. That is, the older son dies before his father when measured by the system of coordinates used by the younger son, who lives on earth. However, from the older son's vantage point (the system of coordinates), he dies aboard the space vessel after his father's death. Therefore, this inheritance depends upon a particular system of coordinates.
Simultaneity, therefore, a before and after relation, creates differences between two people who live far away from each other and move at different speeds. Whether these two people exist on the same time scale or not depends relatively on a particular system of coordinates, the vehicle.
I am not making the claim here that any existing civil law incompatible with modern science should be revised. Indeed, there are many other more pressing issues that should be tackled immediately such as the appropriate use of taxes.
It is critical to understanding modern science to note that time does not travel according to a particular absolute and uniform rule throughout the universe. Nor should simultaneity be approached without any preconditions. This can be demonstrated in the case where two objects, each dozens of light years away from the other, move at a rapid speed comparable to the speed of light. Obviously, earthly humans have never experienced situations where they wait for their parents to come home at a speed of 200,000 kilometers per second from an office in the 4.3 light-year Alpha Centaur or where a loved one departs earth traveling at a speed of 150,000 kilometers per second. Instead, we mere mortals have the daily sense that time travels in an almost absolute and consistent manner, just in the same way that we believe our earthly system of coordinates is the only absolute static scale of space and time. This way of thinking is likely to remain unchanged for some time to come.
However, philosophy explores the essentialism, at least for now. Philosophers do not hesitate to pursue the heart of the matter because it has no direct effect upon our daily lives. In addition, the physical concept of time does not always refer to a completely different form of time from that time we perceive in our daily lives. The scale and precision levels within the physical concept of time are simply incomparable to the time we perceive in our daily lives. In fact, requiring time precision levels within the physical concept of time can be critical at certain production sites. For example, the Global Positioning System (GPS) used for car navigation systems requires high precision. In the 21st century, the relativity of simultaneity has ceased to be a lofty subject left only for scientists to discuss; instead, the relativity of simultaneity is increasingly becoming a matter that can truly affect our daily lives.
This study seeks to examine philosophical subjects related to time, viewed from the vantage point of the relativity of simultaneity.
The theory of relativity has generated this offshoot subject of the relativity of simultaneity. In the following sections, we will first explore how the concept of the relativity of simultaneity was derived. However, this paper does not aim to comment on the theory of relativity itself. Rather, this paper outlines the theory with a focus on the basic concepts of the relativity of simultaneity and four-dimensional space-time, both of which need to be understood as minimum basic points in approaching the text.