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 ----2. The Principle of Light Speed Invariance
Albert Einstein (1879-1955) was a great alien. Obviously, I do not mean that he came from outer space, nor am I calling Einstein an extraterrestrial creature. Rather, the alien I refer to here is a universal cosmopolitan. People often regard such types of persons who think and act beyond ordinary and familiar frames of reference as aliens, but it is probable that those persons are cosmopolitans who will lead people to a larger world. In fact, Japanese people were also led into the modern world by global-minded samurais who boldly acted well beyond the interests of their domains, and currently as well, many active individuals working borderlessly for the world have an enormous impact on the world history. Einstein had Jewish, German, Swiss, Austrian, and American backgrounds, but he was a genuine universal cosmopolitan who could think beyond the wall of the earth, as well as racial and national borders. The fundamental principle underpinning his thoughts was that the entire universe is equal under the law. This way of thinking was pioneered by Isaac Newton (1642-1727), Galileo Galilei (1564-1642), and Nicolaus Copernicus (1473-1543), all great universal cosmopolitans. Giordano Bruno (1548-1600), who appeared in the century after Copernicus, presented the pioneering insight that the sun is not the center of the universe. In this sense, he was also a universal cosmopolitan with great foresight. However, Bruno was persecuted by the organized religion that could think only within the scope of its interests. Aristotle (384-322 B.C.) was not as great a cosmopolitan as Alexander the Great (356-323 B.C.) with regard to his social worldviews, but Aristotle was a great thinker who presented notable nature-views as a global cosmopolitan. However, he cannot be considered a universal cosmopolitan because his mode of thinking remained earth-centered.
Developments in the fields of physics and astronomy after early modernity can be regarded as a major break from earth-centered thinking. This new trend was based on the idea that both the movement of immediate objects and that of heavenly bodies are controlled by one consistent law ruling the entire universe. Universal principles based on this way of thinking were established through demonstrative analyses. Humankind has since elaborated enormous and precise theoretical systems on the basis of these huge accumulations of knowledge.
Through the process, humankind has also discovered that things believed to be common throughout the universe were instead specific to the earth or unique to human beings' distinctive conditions. One such discovery was the concept of the relativity of simultaneity based on the theory of relativity, the latter that can be described as the biggest epoch-making discovery not only within the history of physics, but indeed the history of human thought.
This discovery stemmed from issues concerning light velocity in the vacuum. In the 19th century, it was discovered that light was a type of electromagnetic wave. Before that discovery, people had been engaged in fervent debate as to whether light was a set of waves or particles. Newton and his followers espoused the particle theory. However, based on experimental results showing that light contained interference patterns, the wave theory postulated by Christiaan Huygens (1629-1695) and his supporters dominated public opinion. In the meantime, the theory of electromagnetism that was initially developed by Michael Faraday (1791-1867) was completed by James C. Maxwell (1831-1879) as a refined mathematical theory. This theory demonstrated that electromagnetic waves spread in the form of transverse waves and that light also was that type of wave. For now, the most important thing to note about electromagnetic theory is that the speed of light in the vacuum (electromagnetic waves) was obtained as a certain value using a basic electromagnetism equation. That value was quantified at approximately 300,000 kilometers per second.
Speed as a constant is an odd concept. As discussed above, velocity depends on a standard system of coordinates. More specifically, different values are obtained dependent upon what is considered static from a particular vehicle. For instance, when a car is moving at a speed of 50 kilometers per hour in pursuit of another car that is moving at a speed of 80 kilometers per hour, the person in the second vehicle feels that the car just ahead of him or her is traveling at a speed of 30 kilometers per hour. According to this reasoning, a significant problem occurs when determining the speed of light with the above-referenced equation: What is considered static in the system of coordinates that is a basis for this equation?
People previously believed that if light were indeed a set of waves, then there must be some medium transferring fluctuations. This entity was expressed as "ether," a word borrowed from ancient Greek philosophy. Light was thought to travel at the speed of 300,000 kilometers per second with respect to ether. The system of coordinates predicated upon ether is a special system of coordinates in space used as the basis for light velocity. How fast, then, does the earth travel with respect to ether?
The Michelson-Morley experiment is famous as a test measuring the answer to this question. Based on the earth's movement in accordance with ether, the speed of light differs between the scenario where light travels back and forth along the same direction that the earth is moving and the scenario where light travels back and forth vertically to the direction of the earth's movement. Michelson and Morley created a measurement device in order to measure this difference and calculate earth's speed relative to ether.
Their measurement results consistently demonstrated that the speed of light was the same in both cases. There was no question about their device's precision. The numbers remained completely the same even when the direction of the device, the time, the season of measurement, and the locations of observation were all changed. This can be explained by the assumption that the earth is static relative to ether. That is, the ether system of coordinates, the fundamental scale of the entire universe, moves in perfect sync along with the earth, which rotates while revolving around a fixed star in the galaxy. This shocking discovery suddenly challenged the earth-centered thinking at the close of the 19th century. Of course, no physical scientists initially believed this theory, and even if the theory had been given credit, it obviously contradicted many other astronomically observed facts.
George FitzGerald (1851-1901) and Hendrik Lorentz (1853-1928) tried to explain the contradiction between the results of Michelson and Morley's experiment and previous related theory, presenting their hypothesis that if objects were moving through ether, they would shrink at a minute rate depending upon the speed in the direction in which they were traveling. FitzGerald and Lorentz also argued that it was because the measurement itself contracted at the same rate that the contraction of the objects was not actually observed. It seemed strange that any substance would contract at the same rate, regardless of its materials and density, but at least this explanation was rational. In addition, Lorentz devised a coordinate transformation formula different from Galileo's simple formula, and discovered that electromagnetic laws, and therefore light velocity, remained unchanged. Furthermore, Henri Poincare (1854-1912) transformed mechanical laws on the basis of these ideas, devising several formulas similar to those that later would be incorporated into Einstein's special theory of relativity.
Indeed, although they lacked consistency and demonstrated unclear physical visions, several formulas used in the special theory of relativity were already emerging prior to Einstein's own work on and completion of the theory. However, the validity and meanings of those early complicated formulas were murky. Nonetheless, it was undeniable that plausible explanations were given for these early formulas. Prior to Einstein's work, physicists were still unable to break away from conventional viewpoints and pursue laws concerning objects or operate from a fundamental viewpoint that examined the nature of space and time itself.
Einstein made an epoch-making achievement. He developed uniform and fundamental solutions on the basis of simple principles by changing the very concept of space and time itself. He theorized mechanics and electromagnetism in a comprehensive manner on the basis of two principles:
(1) The physical rules observed by all inertial coordinate systems are equal to each other; and
(2) The speed of light is consistent regardless of the movement of its source with regard to all inertial coordinate systems.
The first principle above (1) is predicated upon the basic relativity principle that all inertial coordinate systems are physically equal, a basic physics principle that has been postulated since the age of Galileo Galilei. Notably, the theory highlighted the point that this principle should be applied to electromagnetism as well. The rule of electromagnetism often involves the concept of "speed" directly in the generation of power. This was a source of additional consideration. Speed makes sense only when a standard system of coordinates is in place. The speed in a basic law should be based on a particular standard system of coordinates. Acceleration played a regulative role in the basic equation of Newtonian dynamics. This is because acceleration (the ratio of changes in speed) shows the same values in accordance with any inertial coordinate system. (The inertial coordinate system here refers to a system of coordinates that is not involved in any acceleration movement in relation to another inertial coordinate system.) Therefore, Newtonian dynamics provided firm support for Galileo's principle of relativity. In this sense, the above-mentioned rule has reconfirmed this theory that everything is equal under the law in the universe.
The second principle set forth above (2) can be considered as an instance of the first principle (1). Because light speed is a constant obtained from the basic equation of electromagnetism, which is a common physical rule through all inertial coordinates and that basic physical constants should not be dependent upon a particular system of coordinates. However, unlike measurable constants, such as elementary charge, light velocity is a form of speed. It makes no sense to think that speed is consistently unchanged, completely independent of any system of coordinates. Essentially, a system of coordinates represents the concept that at whatever speed a vehicle in which you travel to observe an object runs, then that speed should essentially depend upon a particular system of coordinates. However, in fact, the above-referenced principle states that speed is consistent, completely independent of any system of coordinates. Although the Michelson-Morley experiment demonstrated this, the proposition remains quite difficult to understand as a concept. In this sense, although the second principle (2) is an instance of the first principle (1), it is necessary to note its striking difference from conventional ideas by addressing it as a separate principle.
What is the speed of light is an essentialist question. Let us suppose that light is an undulation; its wave front speed has a set point independent from the speed of its source, dependent on medium. That is, light's wave front speed is always a certain numerical value in a particular system of coordinates where the medium, the ether, can be considered static. If an object moves at a certain speed with respect to the ether, the object experiences the undulation's speed change. For instance, if a surfer travels at the same speed as a sea wave, he or she will experience that wave moving at a speed of zero. This is a common sense example about wave speed. However, the theory of relativity holds that if any object moves with respect to a system of coordinates that is static with a medium of light, then the speed of light is consistent. This leaves no room for surfing on the wave of light. More specifically, however fast we may chase a wave of light, it can never be caught. Another way of describing this is to say that the speed gap can never be narrowed.
Next, let us suppose that light is a set of particles, and the light source emits these light particles at a speed of 300,000 kilometers per second. If someone travels at a speed of 300,000 kilometers per second in the direction opposite to the direction that light is moving, that person will definitely feel that the light particles are moving at a speed of 600,000 kilometers per second. Further, if anyone travels in the same direction as the light particles at a speed of 300,000 kilometers per second, that person will feel that those particles are static. Regardless, this principle of light speed invariance maintains that light always travels at a speed of 300,000 kilometers per second.
In 1905, when Einstein announced his special theory of relativity, he also presented theories of Brownian motion and of a light quantum hypothesis on the photoelectric effect. The former laid the foundation for statistical mechanics, and the latter played a significant role in establishing quantum mechanics. As Einstein's focus on the light quantum hypothesis suggests, he did not treat light merely as a set of simple waves. Instead, Einstein recognized two properties about light: (1) that it is a mass of substances with discrete energy values; and (2) that it also behaves as a set of particles. This does not mean, however, that Einstein denied light wave behavior. Nevertheless, at that time, quantum mechanics was in its infancy.
The focal point is whether light can be considered a set of waves or a set of particles. As discussed above, it is illogical to theorize that the speed of light is consistent in any inertial coordinate system. Speed depends upon a particular system of coordinates, which means that speed differs in different systems of coordinates. Naturally, these reference points about the theory of relativity gave a big jolt to scientists in the physical world. Indeed, some people remain confused about the concept and have great difficulty understanding it even now, a century later.
What is certain is that Einstein himself must have recognized the contradictory implications of his theory. He must not have had the oversimplified idea of establishing the principle of light speed invariance simply because observed facts and electromagnetic conclusions provided valid supporting data with the proposition. Einstein did not intend to jump to conclusions based upon perfunctory logic without gaining a clear grasp of the heart of the matter. It is definitely reasonable to think that Einstein could establish the principle of light speed invariance through a thorough critical examination of the concept of the speed of light. This contextual critical examination of the concept of speed constituted the germination of the principle of light speed invariance. Einstein's strenuous methodology included employing basic fundamental critical examination as he explored scientific principles. Therefore, it was not Einstein's intent to devise a plausible explanation for the results of the Michelson-Morley experiment. Those experimental results had no impact upon Einstein's motivation for developing a new theory.
One anecdote about a young Einstein tells the story that he often imagined a world where light is always static. He then theorized, "If I could run toward ether at the speed of light with a mirror in my hand, the light emitted from my face would never reach the mirror and my reflection would never be projected on the mirror forever." He could not then understand the idea that a certain point exists where light is static somewhere (on a system of coordinates) in the universe. Einstein strongly believed that light travels at a constant speed everywhere, regardless of the speed that the observer is traveling. However, this way of thinking creates contradictions if speed is to be defined as the moving distance of an object per unit of time. Taking this into consideration, Einstein decided to reconsider the definition of speed itself.
Einstein simulated his fundamental reference bases in space, independent even from the earth and the sun. Using this frame of reference, he had no tools to make an accurate measurement of distance and time in a wide area. In fact, he could not even determine whether he himself was static or traveling toward something at a particular speed. The only scale Einstein used was the speed of light, a term that always remained a specific numerical value. This single criterion enabled Einstein to define speed by focusing on what rate he traveled relative to the speed of light and without depending on distance and time measurements. In this way, the speed of light worked as a standard for the more general concept of speed.
Now the question arises: Is there an infinite speed? Infinite speed is quite a mysterious concept. Imagine a situation in which a certain object or information in a certain place travels in an infinitesimal period of time to another place that is infinitely distant. Can that object accelerate from a limited speed to an infinite speed within a limited period of time? If possible, is infinite acceleration necessary, and is infinite force necessary? Can a limited amount of energy generate infinite force?
The theory of relativity flatly denies the mysterious concept of infinite speed. In essence, physics, which deals with actual natural phenomena, is incompatible with the concept of infinity. Therefore, if infinite speed does not exist, it follows that speed does indeed have a particular limit. The speed of light can be considered the ultimate limit. This is based on the assumption that the speed of light is absolutely unchanged. As expressed later in the description of velocity-addition formula, it is possible to demonstrate that the speed of light cannot be exceeded by any means. Whether you consider the speed of light, or the very limit of speed, to be fast or slow, depends on the scale of individual thought frameworks.
The theory of relativity has redefined everything on the basis of the speed of light as the absolute scale of space and time. Speed has been redefined in its ratio to the speed of light. The conventional physical definition of speed was developed based on the ratio of moving distance to time. In contrast, the theory of relativity defines distance and time by referring to the speed of light.
Einstein devised a light clock for his new definition. He decided to measure everything on the basis of the speed of light, and he used light to measure time. More specifically, Einstein reflected light pulses in a mirror half a unit's distance away to measure the (constant-multiplied) time by the light reflected back to him, and he defined the time as a unit time. Anything could serve as a definition of the unit distance as long as cosmic universality was secured to ensure that nothing would change along with moves and directions. For example, if the unit distance is set at 300,000 kilometers (equaling 300 million units of the international prototype meter), the time until the light emitted toward a mirror 150,000 kilometers away reflects back to its origin is defined as one second of time unit. If the unit distance is set at one meter, the time until the light emitted toward a mirror 50 centimeters away reflects back to where it started is defined as one time unit (worth one 300 millionths of a second).
This light clock works well on an inertial system, that is, for anyone who is aboard any type of moving vessel at constant speed. This is because the speed of light is the invariable absolute standard for space and time with regard to every form of inertial coordinate systems. This constitutes a total rebuttal of the previously held physics concept that light travels through a medium of ether. The conventional physical concept of ether had held that a light clock will move in a completely different way according to the speed at which it is traveling relative to ether.
The above is one possible definition of time and lays a foundation for measuring distance. The ratio of time needed for light to move a distance to the unit time determines the distance in relation to the unit distance. For instance, one light year, which represents the distance light travels over a year, is based on this principle.
I have explained the basic time unit on the basis of distance, but the same explanation can be offered on the basis of time. For instance, if the time required for a certain phenomenon that can be considered universal in space (one that occurs repetitively at constant intervals) is set as a unit time, the (constant-multiplied) distance that light travels during that period of time can also be defined as a unit distance. (Currently, the International System of Units is defined in this way.) A particularly important thing to note here is that "the speed of light" operates as a conversion factor, a constant for distance and time. This is a conversion factor such as 3.28, which represents one meter as 3.28 feet. In this way, length and time are no longer separate units like length and the electric charge. It is worth noting the fact that light speed invariance underpins a type of homogeneity between space and time.
Before Einstein, authoritative physicists attempted to explain phenomena where light speed invariance could be observed by recognizing that light travels as a set of waves through a certain medium. In sharp contrast, Einstein started with the principle of light speed invariance and took on the reconstruction of worldviews about light and the most basic of physical concepts. His innovative physical approaches encompassed the concepts of space and time, as well as speed. Einstein's inspirations are said to have been influenced by the work of both David Hume (1711-1776) and Ernst Mach (1838-1916). However, Mach discredited the theory of relativity, and Einstein later criticized Machism. It is significant to note that Hume's and Mach's influence upon Einstein and the opportunity offered to break away from Newton's and Immanuel Kant's (1724-1804) fixed concept of space and time.
In fact, space and time had long been considered foundational for the world's existence, as well as fundamental to logical thinking. Space and time were not simple subjects that physics, that branch of science dealing with physical laws of motion of objects, could previously approach. Space was considered to be an expanse of cosmic vacant room where objects could move around, and time was looked upon as a background for movement spreading throughout space. These concepts left no room for physics to further explore, and they constituted an a priori assumption of everything, that is, an assumption prior to experience and observation. However, the advent of the principle of light speed invariance presented the need to modify conventional wisdom on space and time.