Chapter 586 Klein Bottle

It has to be said that this view is very reasonable. In the absence of direct experimental evidence, people are willing to believe that the real universe is like this, and the real two-dimensional space and four-dimensional space are like this.

In fact, this concept of space dimension was not known to you at this time. It appeared as early as the Earth era. It was just that when the experiment started, scientists were focused on the detection of the entire space, and no one mentioned it.

Of course, there is no actual data for this concept of dimensional space, but it has a rigorous mathematical deduction process. Although mathematicians do not need to consider the feelings of physicists, mathematical rigor may not be ironclad in the real physical world, but it always makes people feel convincing.

Therefore, after this concept of dimensional space was pulled out of history again, it was immediately recognized by many scientists. At that time, on the research ship, there were many physicists with MAX mathematical ability who directly discussed its correctness from a mathematical perspective.

In the absence of any progress in the search for the existence of hyperspace, physicists had to seriously consider the possibility of this concept of space dimension.

So in this context, many scientists began to change their ways and devote their energy to the exploration of three-dimensional distorted space. What form the three-dimensional distorted space takes naturally becomes something that the next few scientific research teams need to consider.

Speaking of which, humans have a good understanding of space distortion. After discussing this issue, scientists can easily think of a space structure, namely the Klein bottle.

In the field of mathematics, the Klein bottle refers to a non-directional plane. In topology, it is an unorientable topological space.

Its structure can usually be described as a hole at the bottom of a bottle, extending the neck of the bottle and twisting it into the bottle, and then connecting with the hole at the bottom.

Scientists who insist that this space is not a hyperspace have always had the idea that all or part of this space is composed of Klein bottles or similar distorted space structures, which are combined or arranged together to form the boundary of the entire space.

The experimental spacecraft's unconscious change of direction can be explained as a natural result of its progress along the Klein bottle distorted space. Obviously, the experimental spacecraft itself must not be aware of the so-called change in spatial direction, because for it, the direction has indeed not changed.

Based on the theoretical basis of Klein bottle, scientists have reason to believe that the phenomenon of the test spacecraft changing direction for no reason is one of the examples of space distortion.

But there is one thing that confuses scientists, because in their concept, the spatial structure of Klein bottle does have a reasonable explanation for its existence, but if this structure wants to exist, it must be possible in four-dimensional space, because there is no such situation in three-dimensional space where the bottleneck part extends into the bottle.

Just like the Möbius strip cannot exist in a space with only two dimensions, it must have a process of flipping to the third spatial dimension. Of course, it is still a two-dimensional structure.

After all, humans are creatures that live in three-dimensional space and four-dimensional space-time. It is indeed easier to use the analogy of the Möbius strip than to directly imagine the flip structure of the Klein bottle with your brain.

Imagine a strip of paper. If you want to connect it head to head according to the structural style of the Möbius strip, it will inevitably have a flip and twist in the region. It is through this flip and twist that the paper will become a belt with only one side.

The so-called twist flip is actually the paper passing through the third empty dimension. Imagine that you flip a piece of paper and connect it head to tail, and then flatten the paper. At this time, you will find that part of the paper is overlapped, and the thickness of the overlapping part of the paper is increased. There is no concept of thickness in two-dimensional space, let alone increased thickness.

So the Möbius strip cannot be expressed in two-dimensional space, it can only be expressed in three-dimensional space. Similarly, the Klein bottle is a surface that can only be truly expressed in four-dimensional space.

For this reason, scientists who insist that this space is a distortion of three-dimensional space or exists in the form of Klein bottle space are confused, because as long as they prove that the Klein bottle space structure can be expressed in this space, it is equivalent to proving the existence of four-dimensional space in this space.

In other words, this time the scientists who insist on the hyperspace viewpoint have won. Of course, it doesn't matter who wins or loses. What matters is that hyperspace will make all three-dimensional things lose the physical laws that support it, which is very contradictory.

In order to solve the unavoidable contradiction, some scientists even proposed that this space is a Möbius strip space structure, but this statement faces the same contradiction as the Klein bottle, that is, three-dimensional things will be hit by dimensionality reduction when entering two-dimensional space, but the experimental spacecraft is fine.

Moreover, how could a spaceship in three-dimensional space go to two-dimensional space to flip itself and then return to three-dimensional space again?

Therefore, for the scientific research team, whether it is the Klein bottle structure or the Möbius strip structure, there are contradictions that must be faced.

Faced with various contradictions, some scientists said: Is it possible that the awakener used some technological means unknown to humans to hide the structure of the Klein bottle that moves towards the fourth spatial dimension or the four-dimensional space riveting point, so that humans cannot find it.

Of course there is such a possibility. It is like a creature in a two-dimensional world swimming in a Möbius strip structure, but he cannot know why humans can create such a structure in his world.

But facing the unknown, using a greater unknown to explain, sometimes is not another contradiction? Of course, if this is true, it can be explained, that is: a creature living on a Möbius strip walks around the Möbius strip, he completes the left-right flip, but he will never realize that he has been in two-dimensional space and walked towards the third dimension that does not exist for him.

The reason why he did not die because of the space dimension upgrade is that it flipped to the third space dimension along with the two-dimensional space. The two-dimensional space did not change its physical laws because of the flip to the three-dimensional space. The two-dimensional space is still two-dimensional space, and he is bound to the space he is in.

The same is true for human spacecraft moving on the wall of the Klein bottle structure without inside and outside, so it can be explained as a problem of the Klein bottle structure of this space. However, this view also has loopholes, that is, it must be guaranteed that the awakener has such a powerful means.

Of course, humans cannot guarantee that the awakener has or does not have this ability.