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Join the ServerKlein switched off the crystal ball.
Samuel’s face vanished, and the study returned to its proper quiet.
Lia looked at him, waiting for him to speak.
“Do you think it’s right?”
Klein’s voice was calm. “Patching it up is meaningless.”
He walked to Lia’s side, his gaze falling on the ashes of the burned papers.
“We need to build a new house.”
“A house that will never collapse because of a single beam of light.”
Lia’s eyes reflected Klein’s figure, and she nodded.
“Exactly. And for that, we need a new foundation.”
She waved her hand, and on the other side of the study, a huge blackboard that took up almost an entire wall slid automatically in front of them.
“I believe there are only two foundational principles.”
Her voice, clear and powerful, echoed in the spacious study.
At the top of the blackboard, she wrote the first sentence in beautiful script.
“First Postulate: In all inertial frames of reference moving in a straight line at a constant velocity, all laws of physics have the same form of expression.”
Klein’s gaze froze on that sentence.
He chewed over the meaning of each word.
“Not some laws, not macroscopic laws or microscopic laws.”
“All of them.”
‘Whether it’s mechanics or electromagnetism, they must all follow the same principles, possess the same concise and beautiful form.’
‘This is an almost domineering declaration, proclaiming the inherent harmony and unity of physics.’
Lia didn’t pause, the tip of the chalk leaving a second trace on the blackboard.
“Second Postulate: In a vacuum, the speed of light is the same for all observers, regardless of the motion of the light source or the observer.”
Klein’s breath caught slightly.
‘If the first postulate is the blueprint for the new edifice, then this second one is the indisputable cornerstone.’
The constancy of the speed of light.
It was no longer a corollary of electromagnetic theory, an anomalous phenomenon that needed to be explained with various strange patches.
Lia had elevated it to the status of a postulate.
It was the underlying rule of this world.
“Madness,” Klein said in a low voice.
He wasn’t saying Lia was mad, but that the world described by these two postulates was utterly insane.
‘If the speed of light is absolute, then everything else must become relative to maintain its absoluteness.’
‘Time, space—concepts once considered absolute, uniform, and eternally unchanging—would all have to bend and deform before this iron law of light speed.’
“Yes, it’s very mad.”
Lia put down the chalk and turned to look at him. “But my intuition tells me this is the only path to the truth.”
“All those ugly and complex theories, full of correction coefficients, exist because they dare not admit this one fact.”
“They would rather believe that space contracts, that aether has viscosity, that photons get tired, than admit that their understanding of time and space was wrong from the very beginning.”
Klein was silent.
He walked to the blackboard, reached out, and his fingertips gently brushed across the two lines of text.
A cold sensation came from his fingertips.
His brain was operating at an unprecedented speed.
Countless formulas, models, and thought experiments flashed, collided, and then annihilated in his mind.
He tried to find a logical flaw, a paradox that could overthrow these two postulates.
He failed.
The two postulates were self-consistent; they merely contradicted “common sense.”
But for a mage, especially for an Eighth-Circle Archmage, common sense was the most unreliable thing.
“I think… I need to prove it,” Klein finally spoke.
His voice was a bit hoarse, but his eyes burned with a bright light.
“Let’s try. Let’s see if we can derive everything about this new world from these two postulates, using rigorous mathematics.”
“Derive how time will change, how space will change, and what will become of everything we thought we knew.”
A smile touched the corners of Lia’s lips.
She knew Klein would react this way.
For a true explorer, there was nothing more attractive than a brand-new world, full of unknowns yet logically self-consistent.
“Then let’s begin,” she said.
Klein said no more.
He seemed to have entered a state of intense focus, his entire presence changing.
He walked to the blackboard, picked up a piece of chalk, and began his deduction.
He needed a sufficiently simple model to reveal the secrets of time and space.
“A thought experiment.”
“Let’s imagine a box.”
As Klein spoke, he drew a rectangle on the blackboard.
“There’s a mirror on the top and bottom of the box. A beam of light reflects back and forth vertically between the two mirrors.”
He drew a dashed line moving up and down inside the box, representing the path of the light.
“For an observer standing inside the box, the time it takes for the light to make one round trip is very easy to calculate.”
He wrote the formula on the blackboard: Δt₀ = 2L/c.
“L is the distance between the two mirrors, c is the speed of light.”
“Now, let’s have this box move horizontally at a speed v,” Klein drew a second scenario on the blackboard.
“The box is moving, and an observer is standing on the ground, stationary.”
“For the observer on the ground, the path the light travels is no longer a vertical line but a slanted, zigzag path.”
‘The light travels from the bottom mirror to the top one, which has moved forward.’
‘Then it reflects back, catching up to the moving bottom mirror.’
“In this process, the distance the light travels becomes longer.”
He used geometric relations to calculate rapidly on the blackboard.
He used the Pythagorean theorem to calculate the slanted distance of a single leg of the journey.
He calculated the time measured by the ground observer: Δt = 2√(L² + (vΔ t/2 )²)/c.
Having written this far, Klein stopped.
He looked at the two time formulas he had written.
Both formulas described the same process: light making one round trip between two mirrors.
But the times they yielded were different, one called Δt₀, the other Δt.
Klein’s brow furrowed tightly.
He began to perform algebraic manipulations, trying to find the relationship between Δt and Δt₀.
He substituted L = cΔt₀/2 from the first formula into the second.
After a series of simplifications, squaring, transposing terms…
His movements became faster and faster, the chalk leaving a series of rapid marks on the blackboard.
Finally, he arrived at a result.
A result he could not comprehend.
Δt = Δt₀ / √(1 – v²/c²)
He stared at this formula, repeatedly checking his derivation process.
There were no mistakes.
Every step was impeccable.
But this result…
He tried to solve for Δt from this formula.
Klein threw down the piece of chalk.
It broke in two on the floor.
“Absurd,” he said in a low voice.
According to this formula, the rate of time passing inside the moving box (with Δt₀ as one unit) appeared to have slowed down from the perspective of the stationary observer.
A moving clock runs slower.
This conclusion completely violated all the physical intuition he had built up in the past.
‘How can time be relative?’
‘Isn’t the length of every second the same for everyone in the universe?’
He felt a wave of frustration.
He began to doubt his derivation.
‘No, the derivation is correct.’
‘So the problem lies with the principle of the constancy of the speed of light?’
‘Is there a problem with the thought experiment itself?’
He tried reconstructing the model in several different ways, using two synchronized clocks, using the transmission of light signals.
But every time, he returned to the same conclusion.
In order to maintain the constancy of the speed of light c in all reference frames, time must be relative.
Klein felt his worldview being violently shaken.
Just like Laurent had when he faced “length contraction.”
Except, he was stronger than Laurent; his mental strength was sufficient to withstand this shock.
But the logic within his mind was struggling repeatedly.
“I see it now. Are you trying to use an old ruler to measure a new piece of cloth that is constantly changing?”
Lia’s voice sounded softly behind him.
She had walked to Klein’s side.
Klein turned around abruptly, a hint of confusion in his eyes.
“What do you mean?”
“Your derivation process, your thought experiment, they all rely on a hidden premise.”
Lia’s gaze was as clear as water. “You subconsciously used the coordinate transformation method of the old world.”
“When you were calculating that slanted distance, you defaulted to the idea that the vertical distance L measured by the ground observer and the observer in the box are exactly the same.”
“You defaulted to the idea that the passage of time is independent of spatial coordinates.”
“You defaulted to x’ = x – vt, and t’ = t.”
In a corner of the blackboard, Lia wrote down this set of coordinate transformation formulas, which had been considered “self-evident” since she published them.
“You are using the ruler of the old era to measure the light of the new world.”
“So you reached the conclusion that time slows down, but you cannot find a harmonious place for it within your mathematical system.”
“You think it’s a monster, a paradox.”
Klein was stunned.
He looked at the set of formulas in the corner, then back at his own derivation of time dilation.
He understood instantly.
The problem wasn’t with the conclusion.
The problem was with the entire framework upon which his thinking relied.
He had been trying to force this new part, “time dilation,” into the old machine.
The natural result was hitting a wall at every turn, full of contradictions.
What he needed was not a repair.
What he needed was to completely abandon the old machine.
He needed a brand-new set of coordinate transformation equations.
A set of equations that could perfectly integrate the two postulates and naturally derive all the strange phenomena like time dilation and space contraction.
“I understand,” Klein let out a long breath.
The frustration and confusion in his eyes were swept away.
He picked up another piece of chalk.
This time, his goal was no longer to verify a certain conclusion.
But to create a whole new set of laws for spacetime.
The adventure continues! If you loved this chapter, I Possessed the Obsessive-Captive Dominant Top is a must-read. Click here to start!
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