Moving Away from Einstein to Understand Both Special and General Relativity A Simple Way to Understand Relativity, an Easy Entry Point to Make It "Click"

Moving Away from Einstein to Understand Both Special and General Relativity A Simple Way to Understand Relativity, an Easy Entry Point to Make It "Click" Is Relativity Hard to Understand? Many people have probably tried to study relativity only to find it difficult and give up. Things can be viewed in many ways, and what seems incomprehensible can sometimes be easily understood by simply changing your entry strategy. When trying to learn special relativity, many books start with something like an explanation of Einstein's original paper. Einstein was a genius, but trying to understand relativity through an explanation from over 100 years ago can be as fruitless as trying to understand algebra and geometry by reading translated originals of Euclid's Elements, Diophantus's Arithmetica, or Archimedes's works. Therefore, to understand relativity without it being a fruitless endeavor, we should adopt a method of understanding and study that is based on the accumulation of over 100 years of science and mathematics. With that in mind, I have tried to explain the theory of relativity in a way that is easy to understand. First, Special Relativity Many people, from the general public to those who have studied physics or engineering in college, have likely studied special relativity. There are many ways to study and understand it, but here I would like to present an entry point to special relativity from one particular approach. Minkowski's Perspective It was Hermann Minkowski who, after the publication of Einstein's special theory of relativity, mathematically formulated it and gave it a new interpretation. Whether by chance or not, Minkowski was Einstein's mathematics professor during his university days. He was also a close friend of Hilbert, the father of modern mathematics. Minkowski had a perspective on special relativity that goes like this: "If you think of time and space in the same way and view them from the perspective of a four-dimensional spacetime, all things are moving at the speed of light, c." This is called four-velocity. For example, if we move through space at a speed close to that of light, our subjective experience of time doesn't change. However, from the perspective of an observer watching us, the time flowing for us appears to be slow and delayed. In relativity, it's necessary to look at time from the dual aspects of time discrepancy and changes in the speed of time, but we'll set that aside for now. This is because getting too complicated might consume memory and put an unnecessary load on the brain, making it harder to understand. You could say that time is flowing slowly, or that the speed of time is slow. Since the speed of light is constant, it is always c in space for any observer. This means that light allocates all its possible motion in spacetime to moving through space. In other words, the speed it allocates to time becomes zero. If we were to personify light, it's unclear how it would subjectively experience time, but from the perspective of an observer, light has no time. Time does not flow for light. It could be described as living in an eternal now. It's a cool, or perhaps edgy and dramatic, expression like Neo-Platonism's "eternity is an instant, and an instant is eternity," but that's what it amounts to. Conversely, when we are at rest in space, our velocity in space is zero, so our entire velocity is allocated to time. Unfortunately for us humans (or is it?), unlike light, we have mass, so we cannot allocate our entire speed c to our velocity in space. Time flows for us no matter what. If you travel through the universe at high speed and return, you will experience the Urashima effect (like the twin paradox), but you won't be the exact same age as when you left. Upon returning to Earth, the traveler will have aged a little since their departure. Our subjective experience of time doesn't change, but for an observer, our time is observed as flowing faster. We are in a state of allocating our fixed value c entirely to the flow of time. Conversely, since light cannot allocate any velocity to time, from an observer's perspective, time does not flow for light. This feels like a kind of conservation law, so perhaps some people might intuitively feel that "special relativity is a satisfying theory." Not only is it interesting, but from this perspective, many phenomena that appear as consequences of special relativity can be easily explained. An Easy Way to Approach General Relativity General relativity is a generalization of special relativity. How was it generalized? Special relativity theorized the laws of physics between systems in uniform linear motion relative to each other. It was created because classical mechanics could not explain the constancy of the speed of light. In contrast, general relativity deals with the observation problems between two systems that are in a state of acceleration relative to each other. From the perspective of overall accelerated motion, uniform linear motion and being at rest are just special cases of acceleration. Therefore, general relativity is a more general theory that includes special relativity. Commonly used phrases are "mass warps space" and "the inertial force felt in accelerated motion and gravity are the same thing." People who are good at topology might be able to form a good understanding or image, but others might feel it's not quite clear, or that it's not a good starting point for understanding why this is the case. Understanding Special and General Relativity Together The difficult part of relativity is understanding the fourth dimension. Understanding anything beyond four dimensions requires some ingenuity. General relativity is also tricky because spacetime itself is warped. There are several ways to approach it. Think of space not as three-dimensional, but as two-dimensional (or in some cases, one-dimensional). Use the analogy of a river's flow. Imagine pasting rulers or numbers of different scales onto spacetime or space. Represent the warping using something like shades of color. Think of spacetime as a fluid, and that matter isn't moving on its own, but is just riding the flow of spacetime. There are many others, but I will explain these briefly. This is a commonly used method. If you reduce space to two dimensions, the area near a mass becomes like a hole, with the mass at the bottom. The flow of a river can be seen as an analogy for the flow of time. A river might be imagined as a huge, calm body of water with a flat, horizontal surface and uniform speed, but if the riverbed is complex, the speed of the flow and the height of the water surface might differ locally. We can build an image of relativity from such a river. This is a good idea and might be good for visualization, but it seems tedious to do it yourself. It might be a good idea to use a computer or AI. Visualizing the warping with shades of color might also be a valid image. This is the main focus here. The image is of spacetime as a fluid, with the fluid of spacetime flowing into places where there is mass. Since there are relativistic effects, it's different from fluid dynamics, but in special cases, the analogy of fluid dynamics can be used locally. A mass is like a suction hole, and the larger the mass, the more water it sucks in and the faster the flow. A faster flow results in relativistic effects, so the progression of time becomes slower. If you want to represent this, you can use shades of color to show where the flow is fast. An object, setting aside the fact that it has mass itself, is something that is carried along in the flow. Riding the flow is the shortest path. If something prevents it from riding the flow, the object feels a force. That is inertial force, and it is equal to gravity. We who live on Earth think it's normal to be on the ground, not moving, or moving slowly on the surface and feeling gravity. But perhaps that's a special case, and the natural state is to flow smoothly within the fluid of spacetime. This is a possible line of thought. The Importance of the Entry Point It is often said that an exit strategy is important, but in science, an entry strategy is crucial. In technology, industry, or management, an exit strategy—that is, the result—may be important, but in science, an exit is not necessary. Rather, the entry point, the process, and the method are what matter. In basic sciences like science and mathematics, it's not even clear if there is an exit or a result at all. It's a world where one can say with sincerity that the process and effort are more important than the result. Well, there are also messy academic societies and academic politics. When studying something or making an invention or discovery, the point of view is important. Aren't there many people who find an Einstein-like explanation difficult to understand? Einstein was a genius, but I think he also had youth on his side. At the same time, many researchers were studying theories to solve the problem of the constancy of the speed of light, including mathematicians like Poincaré and Hilbert. Poincaré was undoubtedly a genius, but it is symbolic that Einstein derived special relativity using only classical mechanics, electromagnetism, and simple analogies. A genius solving a difficult problem with a simple method relying on their raw ability is similar to a genius middle school student solving one of the greatest mathematical problems using only the math taught up to middle school. In the world of mathematics, it is said that after the age of 40, you are no longer useful for research. The power of youth's abilities and brain is amazing. Even a smart older person, if they suddenly challenged a young person on the street to a 7-digit number reverse recitation contest, the young person would often win, wouldn't they? It is said that Einstein initially did not or could not understand Minkowski's mathematization of special relativity. It is also said that he incorporated Minkowski's mathematical approach when he needed mathematics to create general relativity. This contradicts the idea that younger is better, but since Einstein created general relativity more than a decade after special relativity, I suppose he was still a genius even as he got older. Or perhaps, as Newton and Gauss both said that the condition for great inventions and discoveries is to keep thinking, Einstein might have been a persistent person who could stick with a problem and keep thinking. However, it's not just in Einstein's case that an explanation summarized by later mathematicians, theoretical physicists, and others is easier to understand than an Einstein-like one. Eric Temple Bell, who was the president of the American Mathematical Society around 1900 and wrote the book Men of Mathematics, repeatedly wrote that ancient Greek mathematics reached great heights, but that it is meaningless because one can simply learn modern mathematics. The way we understand things through modern mathematics education is also easier to grasp than their understanding at the time. When studying a somewhat non-intuitive academic field, such as quantum theory or relativity in physics, I have tried to show that by just changing the angle or entry strategy a little, understanding can suddenly become much easier.