What is the difference between three-dimensional space and four-dimensional space? How to understand it? Does higher-dimensional space really exist?

This question is actually very simple. Three-dimensional space has three dimensions, and four-dimensional space adds an extra dimension to three-dimensional space.

But this dimension is the spatial dimension, not the time dimension. Some friends regard four-dimensional space-time as four-dimensional space, which is wrong. Four-dimensional space-time is just three-dimensional space with one-dimensional time axis added, which still belongs to three-dimensional space.

The world we live in is four-dimensional space-time

Because humans live in three-dimensional space, or we can say in four-dimensional space-time, it is easy for us to understand our own space. That is, everything we see is three-dimensional, with three dimensions of length, width and height, and the time axis runs through it with one-dimensional forwardness, which means it will not stop and will never return.

In Einstein's theory of relativity, time, space and matter are one, they are born and die at the same time, and they cannot exist separately. Because space is the container of matter, without this container there is no matter; and matter is the content of space, without this content, there is no need for space; time is the measure of the movement and change of matter in space, matter and space are constantly changing, everything is moving forward from birth to death, therefore, without time, it means that everything will stop and vanish.

But time is an imaginary value, which only exists in the changes of things. It can only be understood, not expressed in words, but it does exist objectively. If there are other civilizations in this world, the way of measuring time may be different. For example, humans divide time into hours, minutes, seconds, days, months, and years. If there are other civilizations, they will not divide time in this way. This is the subjective nature of time. However, the decay process of all matter and atomic particles in the world, as well as the laws of nature are the same, which is the objectivity of time.

Three-dimensional space, or four-dimensional space-time, is the lowest dimension of the real world in which we exist. Adding one more dimension to this dimension makes up four-dimensional space and five-dimensional space-time. No one has ever seen what this kind of space-time looks like, so humans cannot understand it only in mathematical terms.

Mathematical understanding of space

Zero dimension is a point, which has no length, width or height. It is just a virtual position and does not really exist in our space and time. It is a bit like the singularity before the Big Bang or at the center of a black hole, infinitely small and immeasurably small; one dimension is a line between two zero dimensions, which also has no volume or area, that is, no length, width or height, and cannot be seen or touched.

Two dimensions have meaning, there is a plane, that is, there are two dimensions of length and width, but no height (that is, thickness). Therefore, if you look at it from a plane, you can see this two-dimensional plane, but if you look at it from the side, it is also gone.

Therefore, some people imagine creatures in two-dimensional space. They exist on a plane, which is also a plane without thickness. As long as a circle is drawn around them, they cannot cross it even if the circle has no thickness. However, three-dimensional creatures (that is, us) can easily catch them and throw them out of the circle. Then, the two-dimensional creatures in the circle will feel that their companions have disappeared inexplicably and will worship the gods.

Therefore, three-dimensional creatures are the gods of two-dimensional creatures. In fact, two-dimensional creatures cannot see their own kind at all, because they can only see a line segment, and cannot see its side or back. In fact, if a two-dimensional creature has no thickness, even the line segment cannot be seen. Some people also imagine that two-dimensional creatures cannot have internal organs or digestive systems, that is, the intestines that are eaten and excreted, because if they do, due to the lack of thickness, this intestine will split the body in half.

Some people regard ants as two-dimensional creatures. This is totally wrong. Although ants are small, they have volume. Even bacteria have three-dimensional measurements. Therefore, as long as it is something that we know in this world, even an atom, an electron, and a photon are three-dimensional objects.

Three-dimensional space is the space we exist in. This is easy to understand. It has axes of length, width and height, which can also be called up and down (altitude), north and south (latitude), and east and west (longitude). These three pairs of directions are orthogonal to each other at right angles, and they are generally called x, y, and z coordinate axes.

The four-dimensional space is certainly not the four-dimensional space-time, but an extra spatial axis added to the three-dimensional space, usually called the w axis, which is perpendicular to the x, y, and z axes. This is hard to imagine, just like a person has two hands, where should the extra hand be added? On the back or under the crotch? The mathematical description is that this extra direction is outside the direction of the three-dimensional world we observe.

It should be pointed out that any space has a time axis, so the four-dimensional space is actually the five-dimensional space-time. Therefore, I will not go into details about the time axis later, but only explain it from the perspective of space.

The fantasy of four-dimensional space

Because we are in our three-dimensional space, we cannot truly experience what the four-dimensional space is like. We can only say that it is an illusion.

In our three-dimensional space, to reach a certain point in space, we can move forward, backward, up and down, which means that we only need three directions to reach any point in space. In a sense, three-dimensional space is made up of countless two-dimensional spaces.

Theoretically, four-dimensional space is made up of countless three-dimensional spaces. You need to move in four different directions to reach any point in this space. This kind of space is very difficult to understand. The key is that in addition to length, width and height, or in other words, in addition to height, latitude and longitude such as up and down, north and south, east and west, you also need to move along a pair of new directions. In our three-dimensional space-time, we can neither see nor imagine this new direction.

But some people are determined to imagine what four-dimensional space would look like, and the most famous one is the "Klein bottle" principle. This imaginary bottle was proposed by the famous mathematician Felix Klein in 1882.

The structure of a Klein bottle can be described as: a bottle with a hole at the bottom, with the neck of the bottle extended, twisted into the bottle, and connected to the hole at the bottom. In this way, the bottle has no inside or outside, and no edges, and an ant can climb to any position inside or outside the bottle.

But in fact, a real Klein bottle can never be made in the three-dimensional world. After all, in the three-dimensional world, it still has an inside and outside, and only by leaving a hole in the connecting channel between the bottleneck and the bottom of the bottle can you reach the inside of the bottle. Therefore, it cannot be an object in four-dimensional space.

My understanding of the four-dimensional space is that our world is a sphere and we live inside the sphere. The four-dimensional space is an extra dimension added at a position inside or outside the sphere that we cannot know. It is like an invisible hand that can grab us out of this originally closed sphere from the three-dimensional space at any time, just like we grab creatures in the two-dimensional space and make us suddenly disappear in the sphere. In our opinion, apart from magic, only a god can do this.

In his masterpiece "The Three-Body Problem", the sci-fi master Liu Cixin described the four-dimensional space to the effect that entering the four-dimensional space is like looking at the two-dimensional world from the three-dimensional space, and you can see all the creatures there, but they themselves cannot see themselves. We in the three-dimensional space cannot see inside ourselves, but the creatures in the four-dimensional space can see everything in the three-dimensional space, front and back, left and right, inside and outside, development and change, past and future. Even the internal organs, blood flow, and cells in the body are clear, without any boundaries, and can be touched and taken out at will.

In the American science fiction film "Interstellar", astronaut Cooper falls into a five-dimensional space-time. An advanced civilization constructs a four-dimensional space-time for him composed of countless superimposed and changing cubes. In different windows of these boxes, Cooper can see his daughter on Earth from childhood to adulthood, and finally communicates with his daughter through the gravitational effect and sends her the formula to save the earth.

The amazing thing is that this kind of communication had already happened when I was still on Earth. My daughter was aware of some supernatural phenomena, but she just hadn't communicated with them yet. This shows that in the fifth-dimensional space-time, time has no order and can be intercepted at any time.

Cooper's daughter grew up to be a world-class scientist, and used the formula Cooper sent her from the fifth-dimensional world to bring back the endangered human race. However, due to the gravity of the black hole, Cooper's one hour on Miller's planet was equivalent to seven years on Earth. When he returned to Earth, his daughter was already old and in a dying state.

These are human understandings of the four-dimensional space. Is it reliable? I think not. The real four-dimensional space is unimaginable in our world, just like creatures in the two-dimensional space cannot imagine our three-dimensional space.

How many dimensions does our world have?

We are three-dimensional space and four-dimensional space-time, which has long been known to people. However, some theories believe that the universe was originally 10-dimensional, that is, 9-dimensional space and 1-dimensional time, but now 6 of these dimensions have curled up and shrunk into the space we cannot see, leaving only 3-dimensional space and 1-dimensional time.

This is the so-called string theory or its upgraded version, superstring theory. This theory holds that all subatomic particles are not small dots, but strings similar to rubber bands. These strings are very small and linear. Some have endpoints, which are called "open strings", and some are closed circles, which are called "closed strings". These strings are constantly vibrating, and different vibration modes produce different particles.

In 1926, German mathematical physicist Theodore Kaluza tried to add a spatial dimension, also called an extra dimension, to the four-dimensional space-time, making the space-time five-dimensional. Then he rewrote Einstein's field equations to unify the two fundamental forces known at the time, electromagnetic force and gravitational force, into one equation.

Later studies suggested that at least 10 dimensions, or 6 extra dimensions, are needed to establish a theoretical framework, and this framework is likely to solve the problem of the integration of the four basic forces of gravity, electromagnetism, strong force, and weak force, that is, to make Einstein's theory of relativity's gravitational theory compatible with quantum mechanics. It is the most promising theory to achieve grand unification.

In some experiments, such as the one at the Fermi National Accelerator Laboratory in the United States, where the MiniBooNE detector was used to emit a muon neutrino beam, the phenomena that emerged were completely consistent with the string theory model. Therefore, many scientists are now full of interest and expectations in string theory, hoping that in the near future there will be a new breakthrough in the understanding of the universe.

String theory is very profound and complicated. I only know the basics through study. Friends who are interested in in-depth learning can collect information and study it slowly. This is just common sense science, so I won’t go into details.

In short, it is difficult to understand the space of extra dimensions in our real world, and it is still unclear whether it exists or not. We only need to know the general idea. As a popular science, there is no need to be obsessed with it or delve into it. What do you think? Welcome to discuss, thank you for reading.

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