Chapter 91: Matrix and Subspace Navigation

The journey through the universe is a long one.

Ever since their initial communication, Yan Xia and Xin have been in almost constant contact.

The process of acquiring new knowledge is always fascinating, and Xin has been absorbing the knowledge of advanced civilizations from Yan Xia, while Yan Xia has also been learning from the achievements of lower civilizations in the Light Wing civilization.

These achievements, being of a lower level, have lower thresholds and are not as high as the science of the current Civilized Federation, making them easier for Yan Xia to understand.

"Wow, the human civilization in your Civilized Federation actually has such a powerful mathematical tool as the matrix?"

Yan Xia opened up her library to Xin.

She wasn't worried about Xin stealing this knowledge.

Firstly, Xin was completely under her control, and secondly, this knowledge was beyond what ordinary life forms could comprehend. Just understanding a single book here would take dozens of years, let alone the entire library, which contained 165,285 books.

Steal and learn?

They wouldn't even be able to understand it.

Sometimes, understanding a simple formula could take dozens of years, or even a lifetime for a scholar in that field.

Matrix theory is one such example. It is a mathematical tool, a linear equation, and can also be understood as a table used for calculations.

Linear equations have been applied in human civilization for a long time. Later, Arthur Cayley studied Gaussian elimination and used block multiplication to simplify Gaussian elimination. Finally, in his 1858 paper "A Theory of Matrices," he named these blocks and called them matrices.

Matrices, as a mathematical tool, are widely used in circuit theory, mechanics, optics, and quantum physics, making them a "universal tool."

Xin was fascinated and quickly immersed herself in the study of matrices.

"The convenience of matrices in mathematics is almost perfect. Our civilization is accustomed to using complex methods for calculations."

"We believe that complex calculations can ensure accuracy, and by understanding the process, we can locate errors when they occur. We have never used such a simple tool before."

"We were wrong. Simplified tools can greatly improve efficiency. If we had matrices, I think our civilization would not have remained at Level 1.3."

Xin was like a child with a new toy, eagerly applying matrices to perform a series of calculations.

To Yan Xia's surprise, Xin quickly extended her calculations to the subspace.

In mathematics, the subspace is also known as a linear subspace or a vector space. Its main purpose is to study objects with linear space properties and simplify them using matrices.

The linear subspace is not a physical space but a mathematical equation.

In simple terms, objects with linear space properties, whether a pen, a cat, or a dog, are simplified to the same level for analysis. For example, both pens and cats are composed of atoms.

Linear subspaces are one of the contents of matrix theory and are a form of simplification.

If we delve into human science, it seems that we have always been trying to simplify complex things to their most basic structures, like simplifying the equation 11 + 11 = 22 to 11 x (1 + 1 = 2).

When Yan Xia thought about subspaces, she immediately associated it with physical subspaces.

This subspace can also be called a hyperspace, which is the boundary between antimatter space and matter space.

The concept of antimatter space originates from relativity theory.

This theory suggests that there is an antimatter space opposite to our universe, where antimatter exists. This antimatter space has different physical rules from our matter space and may even be opposite.

If the speed of light has an upper limit in matter space, then in antimatter space, the speed of light has no limit.

Time in antimatter space can be stationary or flow backward, and it can be a four-dimensional space. (A four-dimensional space does not refer to four-dimensional spacetime and does not include time. The four dimensions here do not represent a four-dimensional spatial space but another three-dimensional space.)

Matter space is infinitely large, while antimatter space is infinitely small.

These characteristics are highly research-worthy and were once a direction Ella explored when studying tachyons.

If we want to find tachyons, do we need to discover antimatter space?

However, the tachyons Ella studied were not in antimatter space but in the Calabi-Yau space, or in their own spacetime.

So, Ella is currently researching whether antimatter space, like the Calabi-Yau space, is curled up at the Planck scale.

There may be commonalities between the Calabi-Yau space and antimatter space, or perhaps the Calabi-Yau space contains antimatter space.

Ella has not yet found evidence of the existence of antimatter space. Although they have utilized antimatter, this antimatter was produced through particle collisions and not collected from antimatter space.

All of this remains unknown.

If we can explore this, we will make further progress in the field of tachyon communication.

Moreover, if the existence of matter and antimatter spaces is confirmed, we can use matter-antimatter spaces to develop another technology.

When matter and antimatter collide, they create spacetime curvature, allowing us to enter the subspace and navigate within it.

This is also known as hyperspace navigation.

Imagine that the original space, after the collision, becomes a sphere, and the spaceship originally on the surface of the sphere can now enter the interior of the sphere.

Traveling inside the sphere is undoubtedly shorter than on its surface, and thus, superluminal speed can be achieved.

However, the development of this technology requires further proof.

If we possess this technology, the Civilized Federation can advance its technology towards a Level 3 civilization.

However, Yan Xia herself is not optimistic about this.

The energy required for hyperspace travel is enormous.

Although matter-antimatter annihilation can create spacetime curvature, the total energy released by the largest matter-antimatter annihilation cannon currently produced by the Civilized Federation can only move 1 gram of matter forward by 1 zhang in calculations.

In fact, the energy required to create such spacetime curvature is not much; perhaps 100 kg of antimatter would be sufficient.

However, creating and maintaining are two different concepts. Just as micro black holes can be created in particle collisions, maintaining these black holes requires energy multiplied by trillions and trillions of the original base amount.

Maintaining a spaceship's navigation in hyperspace and creating the required space curvature, the greater the curvature, the faster the speed.

The energy required to maintain this curvature is the same as that of the spaceship, and it can only be achieved by converting all the energy in the universe into reserves.

Yan Xia dared not think further.

At this moment, Ella suddenly appeared before Yan Xia.

"Yan Xia, through research and development, the Tiangong spacecraft has achieved the Rupert's Tear energy protection technology. Its protection capability is 271 times that of our current energy shield, but the only drawback is its stability..."