Chapter 289 - 268: Let the Physical Process Speak for Itself
It leads to physics.
...
Li Dong paid no mind to what else Gamov was saying in the group chat.
He didn’t even notice that Mendeleev, who had just been ruthlessly shut down, had finally managed to squeeze out a sentence after a long pause: "Your Excellency George, aren’t you speaking a bit too definitively..."
His entire being had already plunged through the door that had just materialized.
The first wall: The basis functions were fighting each other.
Expanding with three different sets of bases, each gave a phase difference of π.
From a purely mathematical perspective, this was a problem with the gauge invariance of a pathological operator under different representations.
But from a physics perspective...
This wasn’t a problem with the basis at all.
X-rays excite a dipole transition of a core electron to an unoccupied orbital.
The selection rule for a dipole transition is the parity selection rule.
For this transition, in any basis set, the sign of the matrix element is fixed firmly by parity.
There was fundamentally no such thing as "a difference of π."
The so-called π was the result of mathematicians, during a basis transformation, incorrectly placing a real number’s sign—which should be determined by parity—into a complex phase.
To put it simply...
The operators they had were physical operators.
The bases they used were mathematical bases.
When the gauges on both sides didn’t match up, π popped out.
Li Dong silently recited this in his mind.
’This first wall...’
’Can be demolished just by providing a real representation of the dipole operator.’
And the second wall was the pathological nature of the measurement operator.
The peak for the third coordination shell was always a blurry mess, impossible to extract no matter how much regularization was applied.
When mathematicians got this pile of data, they had only one word for it—pathological.
𝐟𝗿𝐞𝚎𝚠𝐞𝚋𝕟𝐨𝚟𝐞𝕝.𝕔𝕠𝚖
Gikhmanov’s entire method was, in essence, to "brute-force" a prior into the data to suppress the operator’s condition number.
But no matter what kind of regularization, it was still a mathematical prior.
A mathematical prior has no physical meaning.
What it suppresses is "what I hope the solution looks like."
What it cannot suppress is "what the solution must physically look like."
That’s why the third peak remained a blur.
But...
Li Dong closed his eyes.
’What if you don’t do the inversion?’
’What if you do it in the forward direction?’
The X-ray comes in, excites a core electron, the electron leaps out from an empty orbital, probes out into the vacuum along the branch extended by the orbital, and then tunnels onto the probe tip...
This is a complete physical process.
In this process, every atomic shell has its own unique tunneling decay constant, κ.
The more core-level the shell, the larger the κ, and the shorter the distance it probes from the atom’s surface.
The more outer-level the shell, the smaller the κ, and the longer the distance it probes from the atom’s surface.
The "signals" from different shells are not superimposed at the tunneling stage to begin with.
They are naturally separated by their spatial decay lengths.
This separation relies on the Gamov factor from the WKB approximation.
The Gamov factor!!
Li Dong’s eyes flew open.
’That’s why Gamov couldn’t hold back.’
Between these two walls, there was a door. The door had two words written on it.
"Quantum Tunneling."
And the key to this door was one that only two or three people in the entire twentieth century were most fit to hold.
The very first among them was Gamov.
Li Dong shot out of bed.
He reached for the draft paper in his drawer.
The phrase "wrong direction" that had been looping in his mind also vanished.
Li Dong sat at his desk, his pen flying across the draft paper.
Part one of the key:
Rewrite the inverse problem as a forward problem.
The variables are no longer the "coordination field tensor," but physical quantities.
The dipole transition matrix element of the core electron, the symmetry of the unoccupied orbital, the angle of the orbital’s protrusion relative to the probe tip, and the WKB decay constant κ for that stretch of vacuum tunneling.
Part two:
Bring the X-ray polarization vector openly into the picture.
The polarization vector determines which orbital is excited.
This is equivalent to pinning down the question of "which orbital are we actually measuring" to the polarization axis right at the source, instead of tossing it to a set of mathematical bases to argue over.
Part three.
The third coordination shell doesn’t need to be inverted.
It is described by its own branch of κ.
The more outer the shell, the more it exclusively occupies a piece of the tunneling current’s tail end.
Part four, part five...
...
Li Dong had no idea how long he had been writing.
He lifted his head. His throat was dry, his eyes sore.
Outside the window, the sky was still a hazy gray.
He subconsciously let out a "Huh?"
’I haven’t been thinking for that long, have I?’
He turned his head.
The lights in dorm room 404 had been turned off at some point.
Liu Qiang, Chen Nan, and Wang Hao were asleep in their beds, their breathing even.
Li Dong couldn’t help but wonder.
’Why are these animals sleeping so early today?’
Just then...
A sharp pain shot through his head.
Immediately after, his stomach started to rumble.
"Fuck..."
Li Dong rubbed his temples, his vision blurring.
It took him a long moment to remember to check the time.
He looked at his phone.
06:42.
Li Dong blinked again.
Not 18:42.
It was 06:42.
...
So it wasn’t that his roommates went to bed early today.
It was that he hadn’t even noticed when they went to bed yesterday.
The moment he sat down, he had been thinking for an entire night.
And he himself...
...was completely unaware of the passage of time.
He glanced down at his desk.
A thick stack of draft paper was piled up, stretching from the top right corner to the bottom left.
The top few sheets had drawings of walls and doors, with messy labels next to them like "Outside M’s door/Outside MD’s door/Inside G’s door." He couldn’t help but laugh looking at it.
In a corner of the draft paper, he had, at some point, viciously scribbled a blob of red ink.
Next to that red blob were five words.
"Let the atoms speak for themselves."
Li Dong looked at those five words and smiled with satisfaction.
Then, he unsteadily pushed himself up, gripping the corner of the desk. The world spun, and his head buzzed.
He stumbled into the bathroom and furiously splashed his face with water from the faucet.
The shock of the cold water brought a bit of his soul back.
He lifted his head and leaned on the sink, looking at the mirror.
Even though his face was pale and his lips were bloodless, it couldn’t hide the handsome face of Daniel Wu in the reflection.
He gave a self-deprecating smile. ’This is the price of science.’
Li Dong didn’t go back to catch up on sleep.
He had to go to Professor Wu Kai’s place today; the project team had officially started work.
Although the breakthrough in his mind was blindingly bright...
...it was just a breakthrough.
Not a complete path.
He still needed to verify it.
To verify if the dipole matrix elements could truly converge under the three basis sets, and if the κ from the WKB section could separate the three shells as expected...
To verify... etc.
He couldn’t just calculate all of this out of thin air in his dorm room.
"I’ll head to the group first and see."
...
「North Chemical Building, Second Basement Level.」
Wu Kai’s research group laboratory.
When Li Dong pushed the door open, almost everyone was already there.
Su Yanqing was unboxing a new piece of equipment, still wrapped in protective film, with Cheng Duo and Lu Heng.
Shen Ying and Guo Han were at a desk by the innermost metal door, drawing wiring diagrams on a computer.
Professor Wu Kai wasn’t there.
From what Shen Ying had mentioned earlier, the professor had gone to the School of Chemistry for a regular meeting and probably wouldn’t be back until ten.
Li Dong first nodded to his senior lab mates.
They all smiled and nodded back.
Despite his "wrong direction" comment yesterday, no one’s attitude seemed to have changed today. No one was teasing him about it.
Li Dong silently made a mental note about them.
’The atmosphere in this group is really good.’
He had just put his bag down when a voice called out.
"East God."
Zhang Yan waved at him.
"You’re with me today."
Li Dong nodded.
As he walked over, he remembered what Zhang Yan had whispered in his ear yesterday.
"Actually, I also feel like something’s not quite right."
Li Dong walked up to her and asked in a low voice.
"Sister Yan."
"Yesterday when you said the direction was wrong... did you have some thoughts on it?"
Zhang Yan turned and gave a helpless smile.
"Sigh..."
"How could I be as certain as you?"
"It was just a feeling."
"There’s no basis for it."
"You can just take it as a joke."
Zhang Yan said it very casually.
As she spoke, she was already pulling things out of a drawer.
Li Dong said, "Oh."
But his mind started churning.
The reason Li Dong himself dared to be so certain was because he knew deep down...
His intuition never came out of nowhere.
His intuition was the combined output of his Basic Attributes: Logic, Memory, and Concentration, all stacked together.
It wasn’t a guess.
And Zhang Yan...
He couldn’t see Zhang Yan’s attribute panel, but he could sense that Sister Yan’s intuition was definitely not something a person with low attributes could casually come up with.
Among the dozen or so top research groups in the country, no one had stepped up to say the two words "wrong direction."
But Zhang Yan had just nonchalantly said it.
"..."
Li Dong silently, in his mind, moved Zhang Yan up a notch from the "PhD student" category.
He moved her to the "genius" category.