Four-dimensional space is different from four-dimensional space-time, which refers to standard Euclidean space, which can be extended to n-dimensional; Four-dimensional space-time refers to a misunderstanding of Minkowski's concept of space. As three-dimensional objects, human beings can know four-dimensional space-time, but they cannot know four-dimensional space, because human beings cannot know the fourth dimension of space.

The fourth dimension of four-dimensional space refers to the space dimension of the same property as x, y, and z.

In physics, the parameter that must change to describe a changing event is called dimension. A few parameters are just a few dimensions. For example, the position of a "door" is described only by angles, so it is one-dimensional rather than two-dimensional.

To put it simply, zero-dimensionality is a point, with no length, height, or quantity. A one-dimensional line is a line made up of countless points, with only length, no width or height. A two-dimensional is a surface made up of countless lines, with length, width, and height. A three-dimensional body is a body composed of countless faces, including length, height, and quantity.

Because the human eye can only see three dimensions, it is difficult to interpret more than four dimensions. Just as a person with normal intelligence and only one eye and one ear is born, even if he does not have the binocular effect, the binaural effect, it is difficult for him to understand distance, and he is likely to think that the world is two-dimensional.

To put it simply, the N-dimension is the space formed by two or more N-minus one-dimensional objects perpendicular.

Because humans can only understand three dimensions, the later dimensions can be constructed through mathematical theories, but it is difficult to understand them carefully. In quantum mechanics, string theory, which is still being established, holds that the world is eleven-dimensional. That is, 10 dimensions of space plus 1 dimension of time.

First of all, the wrong way to say that "four-dimensional space is defined as three-dimensional space plus a time axis", and "three-dimensional space plus time dimension" is another way of saying it. The former is not a four-dimensional space-time, and the four-dimensional space-time itself is a pseudo-concept.

Quite simply, the concept that time only appeared because of the motion of particles and the expansion of the universe, why does it become the fourth dimension?

In addition, there is a difference between the concepts of space-time and four-dimensional space, and the statement that four-dimensional space is defined as three-dimensional space + timeline is a misunderstanding of the concept of Minkowski space, and why is this misunderstanding so widespread?

Quite simply, countless so-called science fiction novels and even popular science books deliberately apply such a thing, causing a wide range of readers. This involves a set of four-dimensional vector fields, that is, four-dimensional vectors are distinguished according to the positive and negative signs of their inner product, and there are several classifications, such as time-like, empty-like, zero or light-like.

However, there is a useful result about zero vectors: "If two zero vectors are orthogonal, i.e., zero inner products, they must be proportional." ”

The above zero-based temporal direction selection, as well as the concept of time-like vectors, make many people mistakenly think that "space and time form another space", when in fact it only describes the synergy of time and space, which is the origin of the previous statement.

In fact, the time dimension is an alternative statement, not that the fourth dimension is time, which is not the same thing as the previous statement, and the fourth dimension has continuity in the mainstream statement.

In the famous mathematical model of the Klein bottle, the fourth dimension passes through the three-dimensional polyhedron of the essence, but the essence of the four-dimensional space is still space.

And why this dimension is defined as the time dimension is because there is a certain school of thought that the extended "time" has a spatial nature, so an alternative way of saying it appears, you can actually call it anything, it is a nomenclature that arises under a unified and definite definition concept according to the autonomous concepts of different schools.

Some children's shoes are a little entangled in the term "space-time", in fact, there is another reason for the statement that there is no four-dimensional space-time, that is, the concept of space-time in modern physics is originally four-dimensional, so there will be no five-dimensional space-time, and there is no zài space-time specifically described as four-dimensional.

A certain school of modern physics believes that time and space are mutable and their variables exist in each other, and the wide area they correspond to under certain conditions is called space-time.

The earliest people did equate space-time with space plus time, and now they are more evading this original definition.

Space-time can be distorted or dented by the influence of matter and energy, and its smallest units are Planck time and Planck length. This is where the concept comes from, but many people use space-time and four-dimensional space interchangeably, and the two are related, but they cannot be mixed.

It is not necessarily a description of real phenomena, geometric space and natural space cannot be completely equated, and the development of pure conceptual geometry is a milestone in the field of mathematics. The development from zero-dimensional space to three-dimensional space, especially from three-dimensional space to four-dimensional space, is a revolution in geometry.

For Einstein's four-dimensional space, it is generally believed that space is axisymmetric, or centrally symmetrical.

For example, if a person in 3D space enters 4D space and "rotates" it in an appropriate way and then returns to 3D dimension, then he will be 'axisymmetric'. This is of course not possible in a three-dimensional space, unless a three-dimensional version of the Mebius strip is used.

Of course, since no one has entered the four-dimensional space, this is only an analogy from the two-dimensional space, and it cannot be verified, but the view of the timeline and the phenomenon of the moment of space-time confusion are consistent with this.

A figure from a two-dimensional space cannot be symmetrical in two-dimensional space, but when it enters three-dimensional space, it can be flipped back to two-dimensional space, and symmetry can be achieved, because it cannot be flipped in two-dimensional space, only rotated or translated.

Therefore, we can speculate that the three-dimensional object enters the four-dimensional space, and then returns to the three-dimensional space, and the object may be "axisymmetric".

Space is measured in length, which can be regarded as the regions contained by three mutually perpendicular axes, but physical space is not limited to these regions, but there are also energy fields, gravitational fields, microscopic particles, and other areas that cannot be measured by length in space.

In other words, space has three-dimensional properties in terms of length, but at the same time there are other properties that length cannot describe.

In addition, the four-dimensional space in the mathematical sense is meaningless in the physical model, because according to the definition of N-dimensional coordinates, the fourth dimension should also be an axis in length, and this axis should be perpendicular to other three-dimensional, and the axis in length can be perceived by everyone.

If zài is saved, we can definitely observe it, but we all know that this kind of situation cannot be found in reality, so in reality, there is only a three-dimensional space in mathematical sense.

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