Chapter 223: The Unobservable Orbit

In an ordinary dormitory at the National Magic Academy, a young enchanter named Heisenberg frowned at a piece of parchment.

On the parchment was the atomic model proposed by the Eisenberg couple.

A dense nucleus was at the center, with electrons orbiting it in specific tracks, much like planets.

The model was simple and elegant, successfully explaining the spectral line series of the hydrogen atom.

But Heisenberg felt that something was missing from this model.

What interested him most was not which orbit the electron occupied, but what exactly happened when it “transitioned” from a high-energy orbit to a low-energy one.

Did this process happen instantaneously?

What path did the electron take through the space between the two orbits?

What internal mechanism determined the frequency and intensity of the photon emitted during the transition?

The Eisenberg couple’s model offered no explanation for any of this.

It was like a black box.

You input an initial orbit and a final orbit, and it could tell you the frequency of the emitted spectral line.

But the inner workings of the black box were a complete mystery.

Heisenberg tried to describe this transition process using classical kinematics and electrodynamics.

He assumed that during the transition, the electron would undergo some form of accelerated motion, thereby radiating electromagnetic waves.

But his calculation results were always wildly different from the observed spectral line intensities.

Classical theory seemed to fail completely here.

His research had hit a dead end.

He felt like a craftsman trying to turn a screw with a key; the tool and the problem were simply mismatched.

Just as Heisenberg was about to give up, news spread through the academy.

Professor Lia Farrien, the legendary figure who had single-handedly initiated the electrical age and ended the statistical dispute of the particle-wave war with a single prophecy, was going to hold a public lecture at the academy.

The topic of the lecture was precisely the paper that had led to the condensed state experiment, “Supplementary Notes on Quantum Statistics.”

The moment this news was announced, the entire academy was in an uproar.

The public lecture was scheduled in the academy’s largest lecture hall, but even so, the seats were snatched up within minutes of the course registration opening.

Heisenberg didn’t manage to get a seat.

But he wasn’t going to give up this opportunity.

On the day of the lecture, he arrived at the hall three hours early.

The hall was already packed, with even the aisles crowded with students auditing the class.

Using his slender frame, Heisenberg squeezed his way through the crowd to a corner near the lecturer’s platform.

He stood for a full three hours, his legs growing numb.

When Lia walked into the hall accompanied by Klein, the entire room erupted in thunderous applause.

Heisenberg craned his neck, curiously studying the legendary professor.

She looked even younger than the rumors suggested, younger even than many of the students present.

But when she stood on the platform and began to explain the profound statistical theories, her composure and confidence, which belied her age, captivated everyone.

She used no flowery language, only the most concise mathematical terms to clearly explain the indistinguishability of identical particles and the two completely different statistical laws that arose from it.

Heisenberg listened, utterly enthralled.

Professor Lia’s explanation opened up a whole new perspective for him.

For the first time, he realized that microscopic particles and macroscopic objects might follow completely different underlying logics.

After the lecture, students swarmed forward, trying to ask Lia questions.

Klein took a step forward, creating an invisible magical barrier that separated the crowd and cleared a path for Lia to leave.

Watching the departing Lia, Heisenberg felt a strong impulse.

He had to consider that this might be his only chance in this lifetime.

He summoned all his courage, squeezed out from his corner, rushed to the barrier, and shouted, “Professor Farrien, please wait!”

His voice wasn’t loud in the noisy corridor, but Klein’s brow furrowed slightly.

He stopped and looked back at this audacious young man.

Lia also stopped, looking at Heisenberg with curiosity.

“Professor,” Heisenberg looked at Lia, his palms sweating with nervousness,

“I have a question about atomic transitions. We know that electrons transition from high energy levels to low ones, but we have no idea how this process occurs. We can’t see the electron’s orbit, nor can we describe its motion…”

His voice grew softer and softer, as he realized his question sounded somewhat foolish.

Lia listened quietly without interrupting him.

Only after he had finished did she ask in return, her voice crisp and calm.

“Since you can’t see the electron’s orbit in the atom, why do you try to describe it?”

That single sentence struck Heisenberg’s mind like a thunderbolt from a clear sky.

He froze on the spot, his mind a complete blank.

‘That’s right.’

‘Since I can’t see it, why describe it?’

He had always assumed that the electron must have some kind of concrete, describable orbit within the atom.

Just like planets orbiting the sun.

But he had never considered that this premise itself might be wrong.

Seeing his contemplative expression, Lia continued to guide him, “Perhaps you should abandon the classical image of an orbit.”

“Try to build your theory using only the quantities you can directly observe, like the frequency and intensity of the spectral lines.”

“Make the things you can see the foundation of your theory, instead of building it upon an unseeable assumption.”

After speaking, Lia gave Heisenberg a slight nod and turned to leave under Klein’s escort.

Heisenberg remained standing there, motionless for a long time.

Lia’s words had pushed open a long-sealed door in his mind.

Abandon the orbit.

Use only observable quantities.

He felt the fog before his eyes being dispelled by a powerful force.

He had been trying to measure a new world with the ruler of the old one.

Now, he thought he knew what he had to do.

Not to mend the old ruler, but to forge a new one, one that belonged to the new world.

Heisenberg turned and ran back to his dormitory.

He swept all his previous calculation manuscripts into the wastebasket.

He spread out a fresh sheet of parchment, a fervent light shining in his eyes.

He no longer cared about the electron’s ethereal trajectory.

He began to try to directly link the observable physical quantities in an atom—such as energy, position, momentum—with the frequency, amplitude, and polarization of the spectral lines during a transition.

He organized all the experimental data related to the Balmer series of the hydrogen atom, including frequencies and intensities.

He arranged this data into a two-dimensional array, based on the initial and final states of the transitions.

He tried to find the hidden mathematical laws within this huge table of numbers.

This was a completely new direction, with seemingly no precedent.

He soon discovered that when he tried to process these arrays using conventional algebraic rules, everything became chaotic.

Especially multiplication.

In classical operational rules, multiplying an object’s momentum by its position and its position by its momentum yielded the exact same result.

The commutative law of multiplication was one of the most fundamental axioms of algebra.

However, when Heisenberg multiplied the array representing position with the array representing momentum, he was horrified to find that…

Multiplying A by B, and B by A, resulted in two completely different arrays.

This discovery completely overturned his understanding of mathematics.

It was as if someone had told him that one plus one did not equal two.

If even the most basic operational laws were invalid, how could he build a new mathematical edifice?

His research once again ground to a halt.

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