Chapter 603: Distortion
He woke up as if from a dream, finding that the Mythical Wizard Bruce, who had recommended him, was grabbing him and saying in a low voice:
“Focus your attention and dodge the streams of light. You were lucky this time and received a blessing.
“Attar, you are Eva’s son, so I will take care of you, but I can’t possibly keep an eye on you every single moment here either.
“You were very lucky to encounter a kind stream of consciousness. It’s impossible to guarantee that the consciousness will be benevolent every time. If there is malice, you might not come back.”
Attar nodded and said apologetically, “I will pay close attention and not hold everyone back.”
The tear-shaped light on the back of his hand flickered. His heart was incomparably tranquil and peaceful, and his attention was highly focused.
“It seems to be able to calm the mind. It’s actually a pretty good blessing.”
As long as one dodged the streams of consciousness and the mist of memories, the Sea of Consciousness actually didn’t hold much danger. Existences Level 3 and above had stable souls and did not fear the scouring of the Sea of Consciousness.
Above the center of the entire Sea of Consciousness, a “Door” stood tall. Over three hundred meters high and over a hundred meters wide, the door frame was bronze-colored, bearing the mottled marks of time. The entire door flowed with radiant colors, very intoxicating.
The wizards stood waiting on the stone platform in front of the door of light.
On the other side, inside the Central High Tower, Ace had already unrolled another magic parchment scroll and began earnestly calculating covariant equations.
“Under the two axioms of General Relativity, we need a new geometry, different from traditional plane geometry. I once wrote a dust-covered, ‘useless’ geometry book a hundred years ago, and it’s exactly applicable now.
“This is Spherical Geometry.
“The geometry we generally understand is the geometry defined in the Elements by the mortal mathematical master Pythagoras. I call it Plane Geometry.
“Pythagorean geometry has five postulates:
“First, a straight line can be drawn from any one point to any other point. Second, a finite line segment can be extended continuously. Third, a circle can be described with any center and any radius. Fourth, all right angles are equal to one another.
“Fifth, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
“The first four are easy to understand, but the fifth is actually food for thought.
“For example, the closer the sum of these two interior angles is to 180 degrees, the further away the intersection point of the other two straight lines will be.
“According to limit theory, we can completely assume that the two lines never intersect…
“Therefore, based on the above deduction, the fifth postulate cannot be proven.
“Although we cannot prove whether the fifth postulate holds, we can derive a simple axiom from it: the sum of the interior angles of a triangle equals 180 degrees.
“This is the plane geometry we study daily. I call it Pythagorean space, or flat space.
“However, non-Pythagorean spaces also exist in this world: where the sum of the angles of a triangle is less than 180 degrees, and where the sum is greater than 180 degrees.
“Here we will focus on discussing the situation where the sum of the angles of a triangle is less than 180 degrees, calling it curved space or elliptic space.
“The space-time studied by our General Relativity is curved, and elliptic space, or curved space, perfectly meets the needs of this research.
“Here we need to use calculus to first demonstrate from mathematical equations…”
Extremely complex mathematical deductions—second-order partial differential equations with sixteen independent variables. The important variables among them were the Ace Tensor, Curvature Tensor, Curvature Scalar, and Energy-Momentum Tensor.
With the completion of this equation, it was as if a spark ignited all the explosives. The Great Source of the entire world boiled for it, and the Source Power of the Great Source within the artificial demi-plane of the floating City of Academia reached its apex.
The gods all felt a palpitation, but when They saw the source of the palpitation was the Salia region, They stopped taking action.
For a hundred years, Ace, the Lord of the Magic Net and Dreams, with His near-invincible posture, had suppressed seven ordinary Main Gods. His terrifying power, approximating a Titan Main God, made the deities not dare to have the slightest complaint against the leader of this alliance.
And the High Tower Wizards were also extremely powerful. Although there were only three Immortal Legends, instances of Mythical Wizards counter-killing True Gods and capturing True Gods had occurred repeatedly. Several Elven Outer Gods were lying on the wizards’ experimental tables. Even the Kaya Gods felt a sense of dread.
Like cooking oil over a raging fire, the power of the wizards was booming day by day. Before the Titan Main Gods descended to the Prime Material Plane, the deities were powerless to stop them.
Under such a situation, some deities firmly sided with Ace, while others awaited the judgment of the Titan Main Gods. But regardless, as long as it concerned the High Tower Wizards, no god wanted to get involved.
Within the artificial demi-plane, a vast sea of various mathematical equations and symbols floated and flashed, then turned into bizarre runes one by one, only to disappear again.
Such a spectacle aroused the excitement and anticipation of the wizards throughout the floating city. This situation almost convinced them that a new theory was being born.
“Incomprehensible… these flashing runes… just looking at them from afar makes me feel like my head is going to explode.”
“Can we not mention that word? It’s taboo!”
The wizards looked up at the sky, feeling the mysteries they could not fully understand, while Ace was still writing furiously in the Central High Tower.
The dense Source Power of the Great Source surged around Him, gurgling into His body and soul, nourishing His mental imagery world. Like a cardiotonic, Ace’s power also grew stronger and stronger.
“How does space-time curve?
“We can use a two-dimensional spherical surface to understand it simply. Suppose we place a lead ball on a trampoline; the trampoline will curve.
“Similarly, if we place the sun in originally flat space-time, the massive mass of the sun will curve the entire space-time. Planets are situated in this curved space-time and continuously orbit the sun at their own initial velocities.
“Suppose we pick up a wooden ball from the water; it will inevitably create water waves, and the water surface will take a while to calm down.
“Similarly, if someone removes massive celestial bodies like the sun or the earth core, space-time will also generate similar ‘water waves.’ A gravitational field is the curvature of space-time. From the perspective of General Relativity, the reality we see is not gravity, but the curvature of space-time.
“Gravity is the manifestation of space-time curvature, and gravitational waves will also exist like water waves.
“The physical picture of universal gravitation against the background of flat space in Special Relativity becomes, in General Relativity, the physical picture of free motion not subjected to force (assuming no interactions like electromagnetism) against the background of curved space. Its dynamical equations have nothing to do with its own mass and become geodesic equations.
“At this moment, we wizards finally see the truth of the world, see the truth of four-dimensional space-time. Space-time is curved, and this curvature is related to the mass of matter.”
Ace stood up. The runes flashed, seemingly bowing to Him, congratulating Him for revealing the macroscopic mysteries of the world. A massive amount of Source Power madly surged into Ace’s body. He opened His arms, embracing the blessing of the Great Source.
Ace slowly digested the Source Power. The Ocean of Rule Runes in His mental imagery world was like going through a violent storm. Countless bizarre runes danced here; they seemed to want to condense into some kind of spell model, yet found it difficult to continue.
Perceiving carefully, Ace gradually understood.
“I must go to four-dimensional space-time. Only there, without relying on mathematical tools, can one plainly see the essence of space-time curvature, and condense a spell model based on this essence.
“All changes in gravity are changes in space-time curvature. Space-time curvature is the origin of everything.”
Ace’s figure dissipated like foam, and the various anomalies of the Great Source dissolved along with it. Like a passing thunderstorm, the clouds cleared and the rain stopped in an instant.
The wizards and deities both felt as if they had a dream. In a place they didn’t know, Ace had already appeared in four-dimensional space-time, the great Divine Secret Realm.
Even for deities, Level 6 existences could not fully understand the Four-Dimensional Secret Realm. Advancing to Level 6 made Them existences of both the fourth and third dimensions simultaneously, but Level 6 existences only knew how to use this power; it didn’t mean They understood the principles behind it.
Ace roamed in the four-dimensional space-time full of space-time curvature, like a fish rippling in the water, yet also like a fish that had climbed onto shore but hadn’t yet evolved four legs—very unaccustomed, but unable to return to the water ever again.
“There are no longer any obstacles on my path of advancement; it only requires the accumulation of time and resources. I must have either an Eleventh Ring spell model or a Supreme Law domain. Otherwise, I cannot anchor the four-dimensional particle, and thus cannot achieve the synchronous state of four dimensions and three dimensions.”
The process of picking up runes was not smooth. Rather than picking up runes, it was more like recording data on the curvature of surrounding space-time and deducing the patterns within. And the traces of these patterns were Level 6 runes unfolded in four dimensions one by one.
This was an extremely energy-consuming action. Even Ace only recorded a small area and picked up two precious Level 6 runes before exiting four-dimensional space-time.
In the Magic Sanctuary, the group of wizards had also just returned from four-dimensional space-time. Their level and vision were not yet sufficient to collect curvature information and condense Level 6 runes, but They still gained a lot in four-dimensional space-time.
The massive energy released by high-dimensional disintegrating dimensional reduction, and the great mysteries within the fourth dimension, intoxicated the wizards.
Just as the wizards left the Sea of Consciousness and returned to the sanctuary hall, everyone suddenly discovered that Ace’s true body was waiting here. Black top hat, decent magic robe, His gaze daunting yet His voice gentle.
“Those below Mythical Wizard, go back first. The rest stay; I have something to say.”
Hearing this, the Legendary Wizards didn’t dare to stay long, stepping onto the magic array together to return to the floating City of Academia.
Ace looked around at the crowd. The hall transformed, and divine seats appeared one by one.
“Everyone, sit!”
Once the members of the Supreme Council were seated, Ace said in a gentle voice: “You all possess the state to advance to Immortal Legend. I believe you have also understood relativity. Why haven’t you advanced?”
A period of silence. After a long while, Thales stood up, bowed slightly, and said: “Lord Ace, advancing means further solidifying our cognitive worlds. But we all feel that relativity seems to still have imperfections, and our understanding of the domains of deities is also very one-sided. So we want to advance after gaining a better understanding of the truth of this world.”
Ace nodded and said: “Your idea cannot be said to be wrong, but without advancing, it is also very difficult to observe the world more effectively. Let me show you this galactic universe, one million stars.”
While speaking, gentle yet solid mana enveloped everyone. Ace’s voice transmitted, “Do not resist. Relax.”
Out of trust in the Fire Spreader, everyone subconsciously relaxed. In an instant, they appeared not far from a star. Waves of heat rushed at them. Fortunately, the position here was not extremely close, and the mana on the wizards was enough to insulate the temperature.
“What do you see?”
Ace asked.
“A star?”
Someone said subconsciously.
“In Special Relativity, we believed the essence of the world was flat space-time. However, this is not the essence of the world. Today, I want you to feel the truth of the world, to feel General Relativity.”
Hearing Ace’s words, everyone couldn’t help but gasp. A breakthrough in foundational theory really happened?
Screens of light flashed in front of them. The relevant papers of General Relativity were displayed plainly before them. This was the truth of the world, and it was actually obtained so easily.
Bayen’s hands trembled as he slowly swiped on the light screen. He felt somewhat parched. A bit of saliva secreted in his mouth, which he swallowed dryly, making a gulping sound.
“The Equivalence Principle?
“Divided into the Weak Equivalence Principle and the Strong Equivalence Principle. The Weak Equivalence Principle posits that the dynamical effects of an inertial force field and a gravitational field are locally indistinguishable.
“The Strong Equivalence Principle elevates ‘dynamical effects’ to ‘any physical effect.’
“It must be emphasized that the Equivalence Principle is only valid for local inertial frames; it is not necessarily valid for non-local inertial frames.
“Does this mean acceleration equals gravity?”
Bayen felt as if the door to a new world had been opened in a trance. His mental imagery world began to fluctuate violently. The mental imagery world based on Special Relativity, as well as the derived sub-plane, were perfectly integrated with General Relativity. His cognition began to rapidly alter his mental imagery, which subsequently altered the sub-plane through diffraction.
On the other side, Betty also read with a trembling voice: “The Principle of General Relativity.
“The form of physical laws is invariant in all frames of reference.
“This theorem is a generalization of the Principle of Special Relativity.
“In Special Relativity, if we attempt to define an inertial frame, a dead loop appears: generally, for an object subjected to no external force, the coordinate system in which it maintains a state of rest or uniform linear motion is an inertial frame.
“But how to determine if an object is subjected to no external force?
“The answer can only be: when an object maintains a state of rest or uniform linear motion, the object is subjected to no external force.
“Obviously, a logical dead loop that is difficult to eliminate has appeared.
“This shows that people cannot give a strict definition of an inertial frame, which cannot but be said to be a serious flaw of Special Relativity.
“To solve this problem, the author directly removed the concept of the inertial frame from relativity, substituting ‘any frame of reference’ for the inertial frame in the original Principle of Special Relativity.
“If this is the case…”
The wizards gained some ideas, yet also seemed more confused. The two axioms of General Relativity were actually not hard to understand; the true difficulty lay in the geometric understanding and the construction of equations.
The relativistic equation of universal gravitation—the General Relativity equation constructed by Ace was not that friendly. Up to sixteen independent variables made this second-order partial differential equation look like a mathematical maze.
“Curved geometry? Or spherical geometry. From the bending of light, one can indeed guess that the space-time of our world might be curved. This would actually explain many bizarre phenomena in four-dimensional space-time. It’s a pity that after every dimensional reduction, we forget too much. Probably only Level 6 existences can truly understand the four-dimensional structure at all times?
“However, we have mathematics. Algebra and geometry are our most effective tools, or rather eyes, to observe the truth of the world.”
Through a link on the light screen, Blania began to study the booklet Ace had once written: Elliptic Geometry.
She also understood the unprovability of the fifth postulate. Looking at the derived curved geometry—accurately speaking, spherical geometry where the sum of the interior angles of a triangle is less than 180 degrees—her eyes flashed with strange brilliance.
Time slowly passed. Ace led everyone shuttling through the galactic universe. Sub-light-speed flight was not the most effective method; spatial magic was slowly activated.
This time, Ace activated the spatial magic very slowly. He no longer treated space as a kind of divine domain, but completely used General Relativity to understand space.
This kind of jump and blink caught the wizards’ attention. They also began to notice this change, re-examining their own spatial movement spell series. It was like a flash of lightning streaking through their minds, bringing complete clarity.
“Lord Ace, so the profound mysteries of space are hidden within this General Relativity. No, I should say that the space and even time we thought were profoundly obscure are actually all manifestations of General Relativity.
“We thought they were domains, but they were actually just a substitute when we couldn’t find their laws. When we find the laws, these kinds of domains should collapse. Let alone deities without time and space, even if there are, the moment we discover General Relativity, They too would perish!”
Bayen couldn’t help but shout loudly. His expression was extremely uplifted. Slowly perceiving Ace leading them in a spatial jump, he couldn’t resist stroking his beard.
Thales also interjected: “It’s curvature! The profound mystery of space-time is curvature. The reason we can achieve spatial jumps is because of curvature. The reason we can construct folded spaces is also because of curvature. Space-time is inherently curved, and it is exactly within this curvature that we have constructed extremely complex space-time.
“Taking Lord Ace’s sub-plane as an example: its manifestation on the inner side of the world is a star, which is actually a position where space-time is extremely twisted. But inside the Dream Star, there is a vast space-time. In this space-time, celestial bodies are twisting points. And at the extreme of twisting, there might even appear space-time twisting phenomena more powerful than ordinary celestial bodies.
“To the point that even light cannot escape.”
Ace snapped His fingers. Space-time shifted, and they had already arrived near that miniature black hole. This black hole had grown quite a bit and become even more powerful. Extremely powerful gravity twisted everything. The inconceivable material density shocked the wizards.
“Is this…? This is that kind of extremely twisted special celestial body!”
Thales couldn’t help but roar, his expression extremely agitated.
“We need to stay further away from it. This thing is an existence capable of twisting space-time. Even for us, once captured, it’s hard to escape.”
Another Mythical Wizard warned.
Ace also nodded. He was just about to lead everyone away when Blania pulled an extremely dense piece of metal from her subspace and aligned it in the direction of the black hole. That metal was instantly captured by gravity, rapidly twisted and stretched, and swept into the black hole, disappearing from sight.
(Chapter finished)
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