Chapter 593: Trump Card
The wizards of the Supreme Council all listened earnestly to Ace’s words. Warren even had a magic pen taking notes, preparing to go back and think carefully.
Special Relativity was a new thing for all wizards, and it also represented power. The unknown four-dimensional space and time dilation made the wizards’ heads hurt a bit.
“This theory is not very friendly.”
Laval pushed up his glasses and murmured.
On the stage, Ace continued: “We know that three-dimensional space can be represented by a perpendicular, or orthogonal, coordinate system. Time, as the fourth dimension, must inevitably be perpendicular to the other dimensions. But how can we find a plane in real life that is perpendicular to all three wall surfaces of a room’s corner?”
The wizards fell into thought, while Ace’s eyes were full of expectation. After a long silence, Blania suddenly stood up.
“Lord Ace, perhaps we can solve this matter from a mathematical perspective, it’s just that I haven’t thought of the specific solution for the moment.”
Ace nodded, saying with a hint of approval: “Indeed. Expressing space with mathematical geometry doesn’t necessarily require three dimensions. If you open an umbrella and can’t hang it on the wall, you can consider folding it up first.
“We can make the following hypothesis to imagine and understand four-dimensional space-time.
“Suppose there is a flying insect moving in a circular motion around a stone. We can view the circular motion of the flying insect as moving on a plane, thus saving one dimension. This allows us to derive the flying insect’s time-axis movement speed multiplied by time.”
With a wave of Ace’s hand, mana formed a three-dimensional holographic image: a flying insect was making a continuous circular motion around a stone.
“As time passes, the stone remains that stone. We can represent it with a cylinder, calling it a ‘world-sheet’. But the flying insect is no longer that flying insect; its ‘world-line’ is a sine wave function.
“From this point, it can be seen that the world-line of the flying insect is no longer an isolated spatial concept, but is inextricably linked with time. Each point on the line represents not only a position coordinate but also an event. In other words, this is a chain of events extending through a sequence of time.”
The wizards present fell into thought. Thoth’s Mythical Wizard projection stood up and said: “I understand. We are situated in a three-dimensional world. Before dimensional ascension, we can in no way imagine and depict a four-dimensional state.
“In other words, a three-dimensional existence cannot directly imagine and depict the fourth dimension.
“However, mathematics grants us power. We can collapse three dimensions into zero dimensions, which is a point. Then an event is a point, and the line segment connecting these two points is the fourth dimension.
“Mathematics is everything in this world, the absolute truth!”
The Lich Witte, having turned into a youth, also stood up and said:
“The saying that a person cannot step into the same river twice is actually the passage of the timeline. In three dimensions, it cannot be stepped into, but on the four-dimensional level, it is the same river, because time is also a necessary component.
“Even philosophical thinking is built upon dimensions.”
The wizards discussed heatedly. Unknowingly, they began to discuss the Time Dilation Effect and the Length Contraction Effect. When they asked Ace, Ace snapped His fingers, and a holographic image appeared.
“If we want to understand these two effects, we need to first understand light—more accurately, understand the world-line of light.
“We know the speed of light is constant. Then on a space-time diagram, it is a straight line. With the speed of light being c, and the vertical axis being the speed of light multiplied by time, then its world-line is a straight line with a slope of one, at a forty-five-degree angle.”
Ace’s holographic image displayed a two-dimensional coordinate system with a horizontal axis and a vertical axis. The world-line of the speed of light was exactly that diagonal line with a slope of one.
People began to widen their eyes. It was clearly a very simple two-dimensional plane diagram, yet it seemed to contain the mysteries and truths of the world.
Ace snapped His fingers, and a diagonal line slowly drew out on the upper left side of the light’s world-line.
“For an object in uniform linear motion, if we treat this three-dimensional object as a point with no length, width, or height, then its world-line is also a straight line.
“According to relativity, no speed can exceed the speed of light, so the slope of any line must be greater than or equal to one. Less than one is meaningless.
“An object with variable speed motion is a parabola.”
Looking at this two-dimensional coordinate system, Bayen’s eyes flickered with light. His understanding of prophetic magic changed again, or rather, deepened.
“The speed of light is the dividing line. If we take this present moment as the starting point and divide time into past, present, and future, then represented on a graph, it is a light cone.”
Bayen slowly spoke, and a two-dimensional coordinate system image emerged. He raised his hands high and said seriously: “Above, inside the light cone, is the future. Below is the past. The intersection of the coordinate system is the present. Everything else is meaningless.”
Ace smiled and said: “Correct. You have comprehended the most basic principles, Bayen.”
Bayen slowly sat down. A somewhat crazy idea flashed in his mind. In the coordinate system, exceeding the speed of light means being meaningless. But what if… what if the impossible possibility could be achieved? Could a crazy spell be created to exile an opponent to an impossible space-time?
This thought was buried in Bayen’s mind, like a newly sprouted seed.
Ace then continued: “Now, please listen carefully. Let us use relativity together to understand the Length Contraction Effect and the Time Dilation Effect.”
Faint sounds of thunder could be heard. Thoth’s projection trembled all over. Did He seem to feel the attention and expectation of the Great Source?
He looked at Ace, who was talking eloquently, His mood extremely complex for a moment.
“Let’s assume there are two frames of reference: frame a is stationary, and frame b is in uniform linear motion. According to the Blania Transformation, the coordinates of both in the same space-time diagram can be derived.
“Taking frame a as the baseline, the two coordinate axes of frame b surprisingly might not be perpendicular to each other.”
A two-dimensional coordinate graph floated into everyone’s eyes. “Actually, we have been ‘deceived’ by the space-time diagram. This situation frequently occurs; it just doesn’t conform to our thinking habits.
“For example, a normal three-dimensional coordinate system, when drawn on a flat surface, one of the coordinate axes is not perpendicular to the other two. Similarly, if frame b is taken as the baseline, then the coordinate axes of frame a are also not mutually perpendicular. Therefore, the two inertial coordinate systems are equal.
“So now let’s assume there is a stationary ruler in frame a. From the perspective of frame b, the ruler is naturally moving. In a space-time diagram, it looks like this.”
Ace snapped His fingers again. A shadow appeared in the space-time diagram coordinate system, labeled “World-sheet of the ruler.”
The Great Source’s vibration and jubilation seemed to grow stronger. Various illusions of the real and ethereal appeared. It seemed little sprites were playing music, and it seemed demons were roaring in anger.
Bizarre Level 5 runes (rule-level runes) faintly appeared one by one. It was like scratching an itch through a boot: although it could stop the itch, it couldn’t truly provide relief.
Ace ignored all this and said with bright eyes: “In this diagram, the intersection of the coordinate system is O. Oa is the length of the ruler at time t under frame a. Ob is the length of the ruler at time t under frame b.
“According to relativity, a moving ruler will shorten, meaning Ob is less than Oa. But in reality, it’s obvious that Oa is less than Ob. Why is this?”
Everyone frowned in thought. Blania stood up again, bowed, and said: “The Length Contraction Effect refers to the length of the same ruler measured in a certain inertial frame: the measured value during relative motion is shorter than during relative rest.
“Ob is the length of the ruler used to measure motion under frame b. But Oa does not represent the length of the ruler when stationary under frame b. Therefore, comparing the two does not conform to relativity. This is the space-time diagram ‘deceiving’ our habits.”
Ace couldn’t help but applaud, saying: “Your Excellency Blania, your mathematical talent is stunning. Everyone, exactly so. If we want to know the length of the ruler when stationary under frame b, we need to draw a calibration curve, which is a hyperbolic calibration curve derived using the Blania Transformation.
“Where this curve intersects with the x-axis of frame b, OB is the length to be measured. Clearly, Ob is less than OB.
“Because the status of frame a and frame b is equal, when this ruler moves along with frame b, the measured value in frame a will also be smaller than Oa.”
More and more faintly visible rule-level runes shrouded the hall, like a sea of stars. And Ace was exactly the center of this sea of stars, with runes orbiting Him.
“Seems to be brewing something. A new spell model?”
Within Ace’s mental imagery world, He seemed to sense something. He continued speaking: “Let’s look at the Time Dilation Effect again. Now assume there are two perfectly accurate clocks. Calibrate the two clocks at time t. One stays in frame a, and the other moves in frame b.”
Following Ace’s words, the space-time diagram changed again.
“From the perspective of frame a, the clock in frame b has slowed down. By the same logic, from the perspective of frame b, the clock in frame a has slowed down. Which clock actually slowed down?”
Ace’s voice was deafening. Everyone felt as if they were immersed in an infinite world of clocks. Some Legendary Wizards’ mental imagery worlds even showed signs of collapsing again.
Not daring to delay, Ace continued: “Actually, neither clock slowed down. Everything is an ‘illusion’ brought about by motion. Both relatively moving inertial frames believe the other’s time is dilating, and both believe the other’s ruler is contracting. And this is the truth of the world: under motion, everything is relative.”
Daina couldn’t help but murmur: “What should we take as the standard?”
Everyone looked bewildered. Even the very top batch among the wizards would fall into confusion. Right under Ace’s nose, several people had their mental imagery world cognition shatter and solidify. Ace could almost predict that this would inevitably bring about a massive wave of cruel bloodshed among Level 1 and Level 2 wizards.
But all this was necessary for growth; there was no more time to wait.
Ace said loudly: “The so-called standard is actually meaningless. It’s like blind men touching an elephant. Whether you think the elephant is a pillar or a palm-leaf fan has nothing to do with Me. Anyway, I insist the elephant is a pipe. As for the true appearance of the elephant, we, situated in three dimensions, can never recognize it clearly, and that is also meaningless.
“Even during a brief dimensional ascension, you can only recognize the whole picture at the moment of ascension. After dimensional reduction, you will lose the corresponding cognition.”
A massive number of Level 5 runes surged into the center of Ace’s brow. Within His mental imagery world, more and more runes related to space and time gathered. These runes were different from the runes of the Time Domain, but possessed very similar characteristics.
Everyone felt as if they had fallen into a dream. Even the True God Thoth was somewhat confused. After a long while, He was the first to wake up, only to find that Ace had already disappeared.
He stood up and said to everyone: “We might truly be blind men in a four-dimensional world. But mathematics will become the eyes for us to recognize the world. Everyone, as a True God, I once had the honor of reaching the fourth dimension. At that time, I didn’t know; I only called it the Divine Secret Realm.
“And today, we can say with certainty that we can ascend dimensions and go to four-dimensional space-time. And the future of wizards should also be in higher dimensions. We cannot achieve eternal super-dimensionality—even Level 6 existences cannot reach it. But as long as our lives do not cease, as long as the fire of research is not extinguished, one day we will rely on mathematics to achieve dimensional ascension and discover more truths.”
His figure slowly disappeared, and the wizards also dispersed.
Supported by Blania, Thales stared blankly at the starry sky, a trace of a bitter smile on his lips.
Blania comforted him: “Thales, don’t lose heart. Cognition shattering and solidifying doesn’t mean there’s no future. We will definitely find a way to recover.”
Thales looked at Blania and whispered: “It’s fine. Understood from common sense, it is indeed very difficult. But as long as we are alive, there is hope. Having just learned about four-dimensional space-time, such a wonderful and unknown world, how can we miss it just like this!”
In the boundless starry sky, on the Dream Star that Ace’s sub-plane collapsed into, the invisible Magic Net was still continuously weaving.
Ace had already returned to His sub-plane. The True God projection had already refined a small half of the World Tree leaf, and all the stars had been lit up. Within the miniature galactic universe, everything was as usual.
“Stop refining the World Tree leaf for now. Let’s try together to construct our new spell according to the Great Source’s blessing.”
Ace sank His mind into His mental imagery world. In the sea of rule runes, three spell models floated there. They were “Four-Dimensional Door,” “Construct Four-Dimensional Space-Time,” and “Space-Time Mythal.”
The newly acquired Tenth Ring spell “Space-Time Mythal” was actually a display of the Length Contraction Effect and Time Dilation Effect. This was an extremely wondrous space-time spell. It would construct a complex space-time system and space-time diagram, making the target completely lost in the complex four-dimensional space-time.
“First, we need to construct the Ninth Ring spell ‘Four-Dimensional Door.’ The essence of a Tenth Ring Legendary spell is a kind of four-dimensional scene; we cannot completely construct it on the three-dimensional level.
“And a Ninth Ring spell itself is a process going from three dimensions to four dimensions, perfectly matching the ‘Four-Dimensional Door’.”
He manifested the phantom of that spell model, connecting it with the “Door” in the Magic Sanctuary deep within the galactic center. The trembling from His soul made Ace instantly feel a bizarre state approximating four dimensions.
In just an instant, Ace seemed to “see” a certain kind of particle—a certain kind of faster-than-light particle deduced by Special Relativity.
It flashed and was gone. This state was already exited, and a brand-new spell model was also completely constructed.
“Stably constructing a Four-Dimensional Door. This will be one of the greatest trump cards for wizards amidst the storm!”
(Chapter finished)
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