Imagination of spatial interface 4
Fourth level: other mathematical structures
Although the initial conditions and physical constants may be different in the first, second and third layers of the multiple universe, the basic laws governing nature are the same. Why stop here? Why not diversify these basic laws? How about a universe that only abides by the classical laws of physics and haunts quantum effects? Imagine a universe where time passes discretely like a computer, instead of a universe that passes continuously as it does now? Imagine a simple hollow dodecahedra universe? In the fourth multiverse, all these forms exist.
The ultimate classification of the parallel universe, the fourth layer. It contains all possible universes. Differences between universes may not only show physical positions, properties or quantum states, but also may be basic physical laws. They are almost impossible to observe in theory, and all we can do is think abstractly. This model solves many basic problems in physics.
Why is the above-mentioned multiple universe not nonsense? One of the reasons is that there is an inseparable relationship between abstract reasoning and actual observations. Mathematical equations, or more generally, mathematical structures such as numbers, vectors, and geometric shapes can describe our universe with incredible realization. In a famous lecture in 1959, physicist Eugene P. Wigner explained, "Why is mathematics so helpful to natural sciences?" Conversely, mathematics has a terrible sense of reality for them (natural sciences). Mathematical structure can become the main criterion based on objective facts: no matter who learns exactly the same thing. If a mathematical theorem holds, no matter a person, a computer or a dolphin with high intelligence, it also thinks it holds. Even alien civilizations will find the same mathematical structure as ours. Therefore, mathematicians have always believed that they "discovered" a mathematical structure rather than "invented" it.
There are two long-standing and completely opposite models on how to understand the relationship between mathematics and physics. The formation of the two differences can be traced back to Plato and Aristotle. Aristotle's model believes that physical reality is the origin of the world, while mathematical tools are just a useful approximation to physical reality. The Plato model believes that pure mathematical structure is the real "real", and all observers can only make an imperfect perception of it. In other words, the fundamental difference between the two models is: which is the foundation, physics or mathematics? Or the observer standing from the frog's point of view, or the physical law standing at the bird's point of view? The "Aristotle" model prefers the former, and the "Plato" model prefers the latter.
Before we were very young and even heard of the word mathematics, we all accepted the "Aristotle" model. The Plato model comes from the acquired experience. Modern theoretical physicists tend to Platonism. They doubt why mathematics can describe the universe so perfectly because the universe is born mathematical. In this way, all physics is attributed to a fundamental mathematical problem: a mathematician with infinite knowledge and resources can theoretically calculate the perspective of the frog from the bird's perspective - that is to say, calculate for any self-conscious observer what is in the universe he observes and what language it will invent. Describe everything it sees to its kind.
The mathematical structure of the universe is an abstract and eternal entity independent of space-time. If history is compared to a video, the mathematical structure is not one of the pictures, but the whole video tape. Try to imagine a three-dimensional world composed of point-like particles moving around. In four-dimensional time and space -- that is, the bird's point of view -- the world is like a pot of entangled spaghetti. If the frog observes a particle that always has a constant rate and direction, the bird will directly see its entire life cycle - a long, straight noodle. If the frog sees two particles rotating around each other, the bird sees two noodles wrapped in a double spiral structure. For frogs, the whole world operates according to Newton's laws of motion and the laws of gravity; for birds, the world is depicted as "spaghetti geometry" - a mathematical structure. Frogs themselves are just noodles - a lot of noodles that are so complex that the particles that make up them can store and process information. Our universe is much more complicated than the above example, and scientists have not found -- if any -- the mathematical structure that can correctly describe it.
The Platonic model brings a new question, why our universe is like this. For the "Aristotle" faction, this question is meaningless: because the physical origin of the universe is what we observe. But the Plato faction not only can't avoid it, but also confuses why it can't look different. If the universe is inherently mathematical, why is it only based on "that" mathematical structure? You should know that mathematical structures are diverse. There seems to be some basic injustice at the core of the truth.
As a way to solve this problem, I think the mathematical structure has complete symmetry: the universe based on any mathematical structure does exist. Every mathematical structure has a parallel universe related to it. The foundation that constitutes this universe is not within it, but outside time and space. Most parallel universes are likely to have no observers. This hypothesis can be regarded as essentially Platonicism, which asserts that there is a corresponding physical reality in the mathematical structure mentioned in Plato's field or the so-called "mindscape" of Rudy Rucker, a mathematician at San Jose State University. It is also similar to the "π in the sky" mentioned by John D. Barrow, a cosmologist at Cambridge University, or the "principle of multi-production" proposed by Robert Nozick, a philosopher at Harvard University, or what Princeton philosopher David K. Lewis calls "formal reality". Doctrine." The fourth layer finally announced the end of the multiverse at the level, because any self-compatible physical theory can be expressed as some mathematical structure.
The hypothesis of the fourth layer of multiple universes makes verifiable predictions. At the second level, it contains all possibilities (all mathematical structures) and selection effects. Mathematicians continue to categorize these mathematical structures, and they should eventually find that the mathematical structure used to describe our world will be the simplest of all structures that meet our observations. Similarly, our future observations will be the simplest and consistent with past observations; and past observations should also be the simplest and consistent with our existence.
It is a severe test to quantify this "simplicity", and the related research has just begun. But the most shocking and encouraging thing is that the simplicity and neatness of symmetrical and constant mathematical structures are also what our universe shows. Mathematical structures tend to be as simple as possible, and those complex additional axioms undoubtedly destroy simplicity.
Okam said: The above is the parallel universe theory we are discussing, which is divided into four levels from low to high, and the differences between the universe we are familiar with are getting bigger and bigger with the different levels. These differences can come from different initial conditions (first layer); different physical constants, particle types and space-time dimensions (second layer); different physical laws (fourth layer). Interestingly, the third layer is the hottest thing to study in recent decades, because it essentially does not add any new cosmic types.
In the next decade, the rapid measurement of cosmic microwave* and large-scale material distribution in space will further determine the accurate curvature and topology of space, and the results will directly support or refute the hypothesis of the first layer of multiple universes. These measurements will also verify the theory of disorderly continuous expansion, thus indirectly detecting the second layer of multiple universes. At the same time, great advances in the fields of astrophysics and high-energy physics will further clarify which physical constants of our universe have been "regulated" to strengthen or weaken the credibility of the second layer of multiple universes.
If the current efforts to develop quantum computers are successful, it will provide more far-reaching evidence for the third parallel universe. Moreover, the work of quantum computers is to essentially take advantage of the parallelism of the third layer of multiple universes. A large number of experiments are also looking for evidence that violates unity -- ultimately determines whether a quantum parallel universe exists or not. Success and failure in the most important challenge facing modern physics - unifying general relativity and quantum field theory - will change the view of the fourth layer of the multiple universe: eventually find the mathematical structure that describes our universe, or stop due to the limitations of mathematics and finally give up the fourth level.
Should you believe in the parallel universe? The main debate focuses on: they are wasteful and strange. The most important argument is that the parallel universe does not seem to follow the "Occam's Razor" principle, because it assumes that there are other universes that can never be observed. Why is God so wasteful and intoxicated with these endless different worlds? The debate is full of every level of the parallel universe. Why is nature so wasteful? Space, matter or atoms - there is no doubt that the first layer of multiple universe alone already contains infinite things. Who cares how much it wastes? The key is to make the theory explicitly simple. Speakers are worried about the amount of information needed to describe all the invisible worlds.
However, an overall collection is often much simpler than a single element in a collection. This principle is commonly used when describing algorithms. We know that a very short computer program can output an unusually large amount of information. For example, examine the integer set. Which is simpler, the integer set or one of the specific integers? You may naively think that a single integer is simpler, but in fact, the whole set of integers can be expressed by very simple rules, and only a few lines of computer programs can produce them; on the contrary, a single integer may be incredibly large. Therefore, what is really simple is the whole collection.
Similarly, Einstein's whole set of gravitational field equations is simpler than one of them. The former requires only a few equations to describe, while the latter requires specifying a large amount of initial data in some hyperplanes. From this, we learn that when we focus on a small part of the whole element, the complexity will greatly increase, and the symmetry and simplicity that the whole system should have been lost.
In this sense, a higher-level multiple universe means simpler. In order to move from the universe we live in to the entire first layer of multiple universe, we need to specify many initial conditions to eliminate each other's differences; if we upgrade to the second layer, we need to specify some physical constants; in the fourth layer, we don't need to specify anything at all. The superfluous complexity comes entirely from the observer's subjective point of view - that is, the frog's point of view. From the perspective of birds, the multiple universes are much simpler.
People who complain that the theory is too strange mostly start from aesthetics rather than science. However, this view only makes sense in the Aristotle. What are we looking forward to? When we ask such a far-reaching question as "what is the origin of reality", do we only expect an answer that sounds less strange? Evolution gives us intuition about physical phenomena in daily life, but it is only useful for our ancient ancestors. Now, when we travel far beyond everyday physics, we should foresee that they may be strange.
The common feature of the four-layer multiverse is that the simplest and elegant theory naturally includes the parallel universe. To deny their existence, you must complicate your theory and add processes and special assumptions that are not supported by observations: infinite space, wave function collapse and natural asymmetry. So, which one is real waste and indecent, many universes or many rules? Perhaps we will gradually get used to the wonder of the universe and eventually find that this incredible wonder is part of its charm.