Abstract: This paper puts forward six concepts of time and space. Considering the nature of time and space, it is considered that we can't talk about the boundary conditions of the universe; It is considered that the basic equation describing the universe should be a nonlinear semi-integer differential equation. First, the essence of time and space lies in "difference". Only when there are differences can there be time and space. Absolute unity, identity, stillness, balance and symmetry cannot have time and space. In an absolutely identical world, everything is indistinguishable. There is no sense of order and direction, no distinction between dynamic and static, and no concepts of change, dispersion and movement. Come to think of it, in the absolutely same world, because there is no up and down or so. Before and after, direction, past, present, future and so on, so there will be no distance, area, volume, causality and randomness! No matter what you think, the absolutely same world can only be a "point"!
The negation or "breaking" of identity forms time and space. So negation and breakthrough are an explosion from "point" to "time and space". Why use "explosion" to describe the formation of time and space? Because there is no "time" in the process of changing from "point world" to "time and space", in other words, the process from "point" to "time and space" is an eternal process, similar to an explosion, which can be realized in an instant. This is the fundamental reason why the "big bang theory of the universe" can be established.
Second, the "N-dimensional fracture" of identity produces an N-dimensional space and an N-ary number.
The "breaking" of identity is the root of "quantity" When we perceive a one-dimensional straight line, the essence is to distinguish points by the size of the "relative distance". The existence of this "relative distance" makes every point on a straight line connected with a real number, and it can be considered that one-dimensional "breaking" is the basis for generating real numbers; Similarly, two-dimensional breaking identity produces two-dimensional plane, and the difference between points is reflected by two "relative distances". In essence, two-dimensional identity breaking is the basis of generating complex numbers. Similarly, the four-dimensional breaking of identity produces a realistic four-dimensional space-time and a "quaternion" that reflects the differences between points. But whether this quaternion is a quaternion in classical mathematics is similar, but not necessarily the same.
An N-dimensional space is described and understood by an "N-ary number", and different N-dimensional spaces have different N-ary numbers. 1/2 dimensional space and fractional dimensional space should correspond to "1/2 yuan number" and "fractional number", which is also a description tool for some identity breaking features in the physical world.
Thirdly, the law of space-time evolution is an odd solution of nonlinear differential equations.
As long as we think about the problem carefully, we can find that the two concepts of "beginning" and "end" are meaningful only if "time" exists. Only in time and space can we talk about events and understand the whole process of events. The concepts of "beginning" and "end" only apply to things other than time itself, but not to time itself. Therefore, it is meaningless to talk about the beginning and end of time.
It is also meaningless to ask BIGBANG's "before" status. In view of this, we can't talk about the "initial conditions" for the evolution of the whole universe. If the differential equation is used to describe the evolution of the universe, then the evolution law of the real world with time should be the "singular solution" (envelope) of this equation without initial conditions. However, the equation with this kind of singular solution must be nonlinear, so the evolution law of space-time in the universe should be the singular solution of nonlinear differential equation.
Fourthly, there is a relationship of "virtual reality" in time and space.
Real space-time has a basic attribute: time is one-dimensional and space is three-dimensional. So time can only have positive and negative directions, while space has infinite directions. Comparing this characteristic with quaternion in mathematics, we can correspond time to real part and space to three imaginary parts. So there is a matching relationship between time and space. It can be considered that time is real and space is virtual, which can be understood as "fuzzy" time that "divides into three dimensions".
Five, can't talk about the speed of time itself, can only say that time scaling.
Studying the speed of things is relative to the process of time, and it is the rate of change of state variables to time. As the basic process of the world, time doesn't matter to itself. We can't talk about the speed and speed of time itself, because it is meaningless.
In any case, time is the benchmark of the process. For a certain frame of reference, it is indomitable, without the concepts of pause, acceleration, return, slowness and so on. Relativity of time means that the speed of the concrete process of everything in time is related to the motion state of the reference system. For example, the clock in motion goes faster, and the biological rhythm in the motion system needs to be faster, but we can't say that time goes faster, only that the numerical value describing time has shrunk. The time interval of things is relative, which is related to the observer's motion state. Time itself has no concept of "speed", and "speed" is only meaningful to specific things, that's all.
Six, the law of nature should be a "semi-integer order" differential integral equation about time.
When describing time with real numbers, we must pay attention to the irreversibility of time. That is to say, the real world only allows time to move forward, and does not allow time to go backwards. If t represents a time variable and Δ t represents the variation of the time variable, this irreversibility means that both t and Δ t are greater than zero. Therefore, the equation describing the physical process does not allow t and δt to be negative. Once they are negative numbers, the equation loses its meaning. Let's look at this "square root of time" variable. Only when Δ t is positive, it takes a real value. If δt takes a negative value, it becomes an imaginary number, that is, an unobservable quantity, which just describes the fact that time is irreversible! Obviously, both Δ t and t represent a period of time, and their square roots should be included in the equation describing the change of physical variables with time, that is, the solution of the semi-integer differential-integral equation of things' state variables will generally include the square root factor of time, so it can describe the irreversible characteristics of time. In other words, the natural law should be a "semi-integer order" differential product equation of state variables with respect to time.