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      The Worldview of Relative Simultaneity         (MURAYAMA Akira)

Relativity and Four-dimensional spacetime

[The Latter half] ---- Philosophical Examination ----

6. Does Four-Dimensional Space-time exist?

   The previous sections outlined the introduction to the concept of four-dimensional space-time in physics, particularly in the theory of relativity. Four-dimensional space-time is definitely becoming an increasingly important concept in the field of physics. Now, it is time to try to get into the heart of the matter. The focal point is whether the space and time in which we actually live are four-dimensionally integrated as physics suggests or whether this just a convenient theoretical concept for solving physical problems. This section examines the issue.
   We often represent the relation of different amounts of data in the form of a graph. For example, we can express temperature changes during a day in a line graph. With respect to this occasion, nobody thinks that there is really such a line in the world. The line is just a graphical representation of obtained data. Any graphical representation of such sets of information is useful to facilitate our understanding the data, but nobody thinks that what is shaped like the graph actually exists.
   It is natural to think of four-dimensional space-time as such an imaginary graphical representation to facilitate understanding of physical theories, or to represent a certain aspect of actual space and time or perhaps just an imaginary product based on certain rules of mathematics. In fact, I thought that way in the beginning. However, as I pondered the subject, I realized that it was not so simple. I note here that the critical examinations I will present in this section are meant to be conducted at a particular level without excessive discussion. For example, from the phenomenological perspective it is not helpful to point out epistemological leaps of the concept of four-dimensional space-time as "natural-way-of-thinking-based." Here, I do not mean to focus on the validity of phenomenological thinking. If the subject of four-dimensional space-time is approached that way, three-dimensional space, the solar system, elementary particles, DNA and cerebrum, as well as four-dimensional space-time, should be discussed at the same level. This approach undermines notable points unique to four-dimensional space-time.
   In this section, I focus on the following conventional simple worldview: "Current three-dimensional things in motion exist objectively." ("Current things" are unrecognizable due to the barrier of light velocity and the hypothetical existence of those things leaves some room for refutation, but I will discuss this matter later.)
   If we think on the basis of the relativity of simultaneity this common sense-based approach leads to difficulties. Consider the following basic postulates:

(A) "I exist now."
      Even Descartes (1596-1650) could not be suspicious of this fact.

(B) "Other people exist apart from me."
      If this proportion is denied, there is no room for the establishment of science based on objectivity.

(C) "Other people sometimes travel at different speeds from mine."
      This proposition cannot be denied either.

(D) "What exists at the same time as other existent things does exist."
      If this condition is not in place, there can be no spatial expansion.

These four basic postulates and the concept of the relativity of simultaneity lead to the following conclusions.

(1-1) Another person moving toward me from a distance at the same time as I, who
exist, does exist.

(1-2) It is myself in the future that exists at the same time as another existent person (on the basis of the relativity of simultaneity).

(1-3) The future myself existing at the same time as the existent other person does exist (on the basis of the fundamental proposition D).

See Figure 1-6-1 (a) for details.

Figure 1-6-1

The following conclusions can also be drawn.

(2-1) Another person moving away from me from a distance at the same time as I, who
exist, does exist.

(2-2) It is myself in the past that exists at the same time as the other existent person (on the basis of the relativity of simultaneity).

(2-3) The past myself existing at the same time as the existent other person does exist (on the basis of the fundamental proposition D).

See Figure 1-6-1 (b) for details.

In addition, the other person existing at the same time as the existent future or past myself is also the other person in the future or past and we could say that the other person does exist. Furthermore, the future or past myself existing at the same time as the other person also does exist. This line of reasoning goes on and on.
   Additionally, the distance between the other person and me is arbitrary and the speed at which the other person moves toward or away from me can also be arbitrary. My point of time that corresponds to the same time as others differs in accordance with the distance between us and our respective velocities. Therefore, we can say that 'myself' in the arbitrary future or past does exist. All other existing things can be substituted for the "myself" described here and the past and future of all other existing things exist.
   This reasoning supports the existence of four-dimensional space-time and leaves little room for discrediting it. It shows how the relativity of simultaneity follows from the notion of four-dimensional space-time. In addition, based on the general theory of relativity, the four-dimensional space-time can be distorted in response to specific physical conditions, such as the distribution of mass and energy, and not simply as an abstract framework.
   However, four-dimensional space-time is neither visible nor imaginable. It is certainly difficult to get the real feeling of the existence of such a thing. For example, we cannot see the entire galaxy, but we can imagine a situation in which we place ourselves in such a condition. People could only imagine the spherical shape of the earth for a long time, but today an increasing number of people are able to see it with their eyes. It will not be possible for us to see four-dimensional space-time despite technological advances in the future. In essence, it cannot be an object of our sight. Indeed the phenomenon of human sight itself is established in the four-dimensional space-time and we cannot even imagine the idea of seeing it from outside. The existence of the invisible and the unimaginable is never rare in the world of physics after the 20th century. Elementary particles with particle and wave properties can neither be seen nor precisely imagined but we readily accept and approve their objective existence.
   A major reason why we have difficulty accepting the reality of four-dimensional space-time is that we cannot perceive the relativity of simultaneity as supporting its existence by our day-to-day experiences. Even if we find ourselves far apart from each other, the distance is at most between the earth and the moon. Special space vehicles have been developed to travel to Saturn and over the solar system on our behalf, but the distance is only a dot at the galactic scale. Additionally, the speed at which the space vehicle travels away from the earth, even if the latest highest-speed rocket is used, is almost static in comparison with the speed of light. Therefore, the concept of simultaneity is almost absolute for us. We share the concept of absolute simultaneity and we have the same recognition that the world is a three-dimensional object in motion.
   As noted above, the theory of relativity created the necessity of devising the concept of four-dimensional space-time. The theory's effect becomes particularly noticeable in a system of coordinates in which the relativity of simultaneity is highlighted. This relationship is still an unfamiliar matter to our daily life.
   Why are space and time quite different subjects in our awareness? Why do we have in our consciousness the idea of the continuous occurrence or flow of the world's three-dimensional "cross section"? The third chapter explores these themes. It can at least be said that our consciousness also works inside the realm of four-dimensional space-time and that our consciousness never produces four-dimensional space-time in an arbitrary way.
   Is this reasoning truly free from error? As a fundamental question, what is existence? How is this way of thinking related to quantum mechanics? What is its relation to determinism, if any? The following section examines deterministic worldviews and how they are likely to be effected by the concept of four-dimensional space-time.


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