In the circular hall of the Theoretical Physics Center at the String Light Research Institute, Yue'er stood alone before a blackboard that spanned an entire wall. The blackboard was densely covered with differential geometry symbols and quantum field theory equations—these winding curves and operators formed a mathematical bridge to the ultimate theory of the universe. Yet at this moment, a crack had appeared at a critical node of this bridge.
A piece of white chalk was held between the index and middle fingers of her right hand, chalk dust coating her fingertips, leaving faint traces on her deep-blue lab coat. She had maintained this posture for nearly half an hour, her gaze fixed on the lower right corner of the blackboard. There, a set of equations circled in red chalk—precisely these equations had plunged her unified field theory into an unprecedented dilemma.
"The stability condition for wormholes…" she murmured softly, her voice producing a faint echo in the empty hall.
The core of the problem lay in the fundamental contradiction between general relativity and quantum mechanics. In her unified‑field‑theory framework, gravity was described as the curvature of spacetime, obeying the Einstein field equations; the other three fundamental forces were described at the quantum level through gauge field theory. This theory exhibited astonishing self‑consistency in most cases, perfectly explaining physical phenomena from cosmic scales down to the Planck scale. However, when it came to wormholes—topological structures that might connect different regions of spacetime—the theory revealed a serious divergence.
Yue'er walked up to the blackboard and gently tapped the equation encircled in red with her chalk. This equation described the energy condition required to keep a wormhole open. According to general relativity, to prevent the throat of a wormhole from collapsing, a type of exotic matter with negative energy was needed. Such matter violated various classical energy conditions, especially the null energy condition and the weak energy condition in flat spacetime.
"The Casimir effect…" she muttered, turning toward another blackboard filled with quantum field theory formulas.
In quantum field theory, the Casimir effect indeed predicted the existence of negative energy density. When two uncharged metal plates were placed parallel to each other in a vacuum, quantum fluctuations in the region between the plates became restricted, causing the energy density in that region to become lower than that of the external vacuum. This energy difference produced a force that drew the plates closer together—an effect that had been precisely verified in experiments. In a sense, the vacuum between the plates did possess negative energy density.
Yue'er swiftly wrote the mathematical description of the Casimir effect on a blank area of the blackboard. She introduced quantum fluctuations of a scalar field under boundary conditions and calculated the difference in zero‑point energy. The results showed that, in specific configurations, the energy density in a local region could indeed be negative. But this fell far short of what was needed to support the stability of a macroscopic wormhole.
"The orders of magnitude are too far apart." She shook her head, the chalk leaving a frustrated exclamation mark on the board.
According to her calculations, the negative energy density generated by the Casimir effect was extremely tiny and decayed rapidly as the spatial scale increased. To keep open a wormhole with even a one‑centimeter radius would require negative‑energy matter equivalent to converting the entire mass of the Milky Way galaxy—something clearly physically impossible.
More seriously, the core equations of her unified field theory were fundamentally at odds with the requirement for macroscopic‑scale negative energy. In her theory, the gravitational field equations were modified to include quantum‑correction terms; these correction terms were negligible under most circumstances but became crucial in extreme spacetime structures like wormholes. The problem was that these quantum corrections always seemed to destabilize wormholes rather than sustain them.
Yue'er walked over to the computer and pulled up the latest numerical simulation results. The screen displayed the evolution of a wormhole spacetime: initially, the wormhole throat remained open, but as time passed, it began to oscillate, then rapidly collapsed into a singularity. No matter how she adjusted the parameters or changed the configuration of matter fields, the outcome was essentially the same—the wormhole was always unstable.
"Perhaps a new field needs to be introduced?" she pondered, her fingers flying across the keyboard.
She introduced a new scalar field into the theory, one that coupled to the metric tensor in a special way. At first, the simulation showed that the wormhole could remain stable, but as soon as she added tiny perturbations, the system quickly reverted to instability. It was like trying to balance a pencil on its tip: theoretically such an equilibrium point might exist, but in practice any tiny disturbance would cause it to fall.
Night had fallen; most lights in the research institute had been turned off, leaving only this hall in the Theoretical Physics Center illuminated. Yue'er was completely unaware of the passage of time—her entire world had narrowed to these few blackboards and computer screens.
"Professor Yue'er, are you still working?" A security guard peered in through the doorway, his voice tinged with concern.
Yue'er snapped back to reality, noticing that outside the window was pitch‑black. "Yes, there are still some problems to solve." She forced a smile. "I'll be heading back soon."
After the guard left, she rubbed her throbbing temples, feeling a wave of dizziness. She had not slept properly for three consecutive days; each time she closed her eyes, those equations and simulation results spun in her mind. Worse still, this problem was not merely an academic challenge—it struck at the very core of her theory. If her unified field theory could not handle spacetime structures like wormholes, then it might be incomplete in describing extreme conditions of the universe.
She walked over to the coffee machine and poured her seventh cup of the day. The bitter liquid temporarily dispelled drowsiness but could not dispel the anxiety in her heart. Returning to the blackboard, she began re‑examining every link of the problem.
"Perhaps the issue lies in the formulation of the energy conditions." She reflected.
In classical general relativity, various energy conditions were imposed to guarantee the "reasonableness" of matter—for example, the positive‑energy theorem required that the energy density of matter fields be non‑negative. But these conditions were frequently violated in quantum field theory, not only by the Casimir effect but also by various energy anomalies arising from quantum entanglement.
Yue'er began deriving a modified energy condition, one that would allow macroscopic‑scale negative energy density under specific circumstances while ensuring that causality was not violated and the arrow of time remained unchanged. This required extremely delicate mathematical handling; she introduced new topological invariants to characterize the causal structure of spacetime.
Time ticked by, and the coffee cups emptied several more times. New formulas proliferated on the blackboard like vines, covering every available inch of space. Yet each time she felt she was nearing a solution, a new issue would arise—either causality might be violated, quantum states might become unstable, or unacceptable spacetime singularities would appear.
At three o'clock in the morning, she finally had to admit that she might have encountered a genuine theoretical obstacle. This was not something that could be resolved by tweaking parameters or introducing new fields; it might be a limitation of her theoretical framework itself.
She slumped into a chair, feeling a weariness she had never known before. It was not physical exhaustion but an intellectual defeat. For years, she had believed in the harmony and self‑consistency of the mathematical universe, certain that all physical phenomena could eventually be described within a unified framework. But now, for the first time, her faith wavered.
"Does the structure of spacetime permit us a passage at any cost?" she murmured to the empty hall.
This question was not merely about wormhole stability; it touched on the fundamental laws of the universe. If wormholes could not exist stably, then time travel might be forbidden by the laws of nature. Perhaps this was how the universe protected causality—through the physical laws themselves preventing the emergence of time‑travel paradoxes.
But if her theory was correct, then at the Planck scale, the topology of spacetime should be dynamic, and wormholes should be able to quantum‑generate and annihilate. So why couldn't such structures remain stable at macroscopic scales?
She rose again, walked to the blackboard, erased a section of formulas, and began attempting an entirely new line of thinking. Perhaps the issue was not with the energy conditions but with her understanding of spacetime itself. In quantum‑gravity theories, spacetime might not be fundamental but emergent from more basic quantum structures. If so, then the stability problem of wormholes might need to be considered at a more fundamental level.
This line of thought rekindled her hope. She began studying the concepts of spin networks and spacetime foam in loop quantum gravity, attempting to integrate her unified field theory with these frameworks. This required completely new mathematical tools; she introduced notions from non‑commutative geometry, where spacetime coordinates no longer commute, leading to a fuzzy spacetime structure at the Planck scale.
As dawn approached, Mozi gently pushed open the door to the hall. He saw Yue'er standing before the blackboard, her eyes bloodshot from lack of sleep yet unusually bright. The blackboard was covered with entirely new formulas—some mathematical structures he had never seen before.
"You haven't slept all night again?" Mozi walked to her side, his voice filled with concern.
Only then did Yue'er become aware of his presence, slightly startled. "I'm trying a new direction." Her voice was hoarse from long silence. "Perhaps we've been using the wrong framework all along."
Mozi looked at the formulas on the blackboard; though he couldn't fully understand them, he could sense the profound ideas they contained. "Do you need my help? Perhaps Xiuxiu's biological computing could offer some new insights?"
Yue'er shook her head, offering a weary smile. "This is a problem of foundational theory; it can only be resolved mathematically. But…" She paused, pointing to a new equation on the board. "This approach might work."
She explained her new idea to Mozi: if spacetime was fundamentally non‑commutative, then at extremely small scales, position and momentum could not be precisely determined simultaneously, leading to a new form of the Heisenberg uncertainty principle. In such a framework, the energy‑time uncertainty relation would also be modified, allowing for large energy fluctuations over extremely short intervals. These fluctuations might be just sufficient to stabilize microscopic wormholes.
"But how to transition to macroscopic scales?" she continued, almost talking to herself. "Perhaps through quantum entanglement and the holographic principle…"
Mozi listened quietly; though most of it was beyond his comprehension, he could sense the depth and breadth of Yue'er's thinking. This was not merely about solving a physics problem—it was about exploring the deepest mysteries of the universe.
When the first rays of sunlight streamed through the window into the hall, Yue'er finally stopped speaking. The blackboard was already filled with new formulas and computational processes; some previously contradictory aspects seemed to be showing signs of resolution.
"Get some rest." Mozi said softly. "The problem won't run away."
Yue'er nodded, yet her gaze remained fixed on the blackboard. There, a completely new theoretical framework was taking shape—one that might not only solve the wormhole‑stability problem but also provide deeper understanding of the nature of spacetime itself. Though challenges still lay ahead, at least she had found a path that might lead to an answer.
Before leaving the hall, she took one last look at those formulas. Illuminated by the morning light, they seemed almost alive, whispering to her the secrets of the cosmos. She knew that today's breakthrough was only a beginning; the real difficulties still lay ahead. But no matter what, she would continue forward—because that was her mission: to decipher the source code of the universe, whatever the cost.