I. Physical Integrity of Eigen-Oscillations: Indivisibility
Starting from natural quantization, we recognize that eigen-oscillation modes are the natural resonant states of physical systems. These modes possess fundamental physical properties: integrity and mutual exclusivity.
Just as a violin string cannot simultaneously vibrate at its fundamental frequency and its overtones, an electron cannot simultaneously occupy two eigen-orbits. This is not a mathematical limitation, but a fundamental constraint of physical reality.
The integrity of eigenstates implies:
The electron is either fully in a given eigenstate,
or fully not in that eigenstate.
There is no intermediate state of "partially being in" an eigenstate.
This is a basic fact already known from classical physics: at any given moment, an oscillatory system can occupy only one definite vibrational mode.
II. Logical Necessity of Photon Quantization: Wholeness of Interaction
Natural quantization tells us that the interaction between charge and the electromagnetic field must occur via complete energy quanta. This means:
When an electron transitions from one eigenstate to another:
It must emit or absorb a complete quantum of energy,
The process is all-or-nothing,
There is no such thing as a "partial transition."
If an electron could "simultaneously occupy" multiple orbits, then:
It should be able to emit a photon partially,
Or emit different photons simultaneously from multiple orbits.
This contradicts the very essence of photon quantization!
The indivisibility of the photon directly negates the divisibility of the electron.
III. The Truth About the Superposition Principle: Statistical Description of an Ensemble
Then, what exactly is the ubiquitous "superposition state" in quantum mechanics? The answer is clear and simple:
The superposition state |ψ⟩ = α|1⟩ + β|2⟩ does not describe the state of a single electron, but rather the statistical distribution of a large ensemble of electrons.
|α|² is the fraction of electrons in the ensemble that are in state |1⟩,
|β|² is the fraction in state |2⟩.
For any single electron, it is either in |1⟩ or in |2⟩.
This is analogous to saying "a coin has a 50% probability of landing heads"—this does not mean the coin is simultaneously in a superposition of heads and tails!
IV. The Truth About Schrödinger’s Cat: A Paradigm of Pseudo-Paradox
The Schrödinger’s cat paradox is built upon the erroneous premise that a single particle can be in superposition:
The reality is:
A radioactive atom is either decayed or not decayed at any moment,
The cat is either dead or alive at any moment.
There is no "both dead and alive" superposition state.
Probabilistic descriptions reflect only our ignorance, not an ontological fuzziness of physical reality.
Schrödinger himself proposed this thought experiment to ridicule the absurdity of the superposition principle—tragically, later generations have turned it into an icon of quantum mysticism.
V. Reinterpreting Quantum Computing
If a single particle cannot be in superposition, how does quantum computing work?
Answer: Quantum computing exploits the parallelism of ensembles, not the superposition of individual particles.
A "qubit" is in fact:
A large collection of identically prepared quantum systems,
Each system occupying a definite eigenstate,
Computational results obtained via statistical sampling.
Quantum speedup arises from parallel processing of multiple definite states—not from the mystical superposition of a single system.
VI. Demystifying Entanglement
If single particles cannot be in superposition, how should we understand "quantum entanglement"?
Entanglement describes the correlation distribution among particle pairs in an ensemble:
Each pair is in a definite state,
But different pairs may be in different states,
Measurement correlations reflect constraints from the initial preparation.
This is analogous to two playing cards of different suits:
If one card is drawn as a heart, the other cannot be a heart.
Such correlation requires no "spooky action at a distance"—
It is simply a logical consequence of the initial condition.
VII. The Necessity of a Conceptual Revolution
Accepting that "a single particle cannot be in superposition" demands a profound shift in understanding:
Misconceptions to abandon:
The wavefunction fully describes a single particle.
Measurement causes physical collapse.
Quantum systems are inherently fuzzy.
Superposition is a fundamental principle of nature.
New understandings to embrace:
The wavefunction describes eigenfield amplitudes and, approximately, ensemble statistics.
Measurement reveals a pre-existing definite state (provided the measurement does not disturb the system).
Quantum systems are deterministic; randomness stems only from incomplete information.
Superposition is a mathematical tool, not physical reality.
VIII. Philosophical Implications: The Return of Determinism
Recognizing that a single particle cannot be in superposition leads us back to a deterministic worldview:
Every particle has a definite state at every moment.
Randomness is merely a reflection of our incomplete knowledge.
Nature possesses no true fuzziness or indeterminacy.
Einstein was right: "God does not play dice."
Apparent quantum randomness is simply our statistical description of an underlying deterministic system.
IX. Reinterpretation of Experimental Evidence
All experiments allegedly "proving" the superposition principle require reinterpretation:
Interference experiments
Demonstrate wave-like behavior, but the wave is a field—not the particle itself.
Particles follow probability distributions dictated by the field.
Rabi oscillations
Represent periodic changes in the ensemble distribution between two states,
Not "oscillation" of a single atom.
Quantum eraser experiments
Alter how information is accessed,
Do not retroactively change past physical events.
All these phenomena can be perfectly explained by deterministic single-particle dynamics combined with ensemble statistics.
X. Systemic Errors in Textbooks
Current quantum mechanics textbooks are riddled with conceptual errors:
Error 1: "Electron clouds" are described as probability distributions of a single electron.
Correction: Electron clouds represent spatial distributions of many electrons in an ensemble.Error 2: "Before measurement, the particle is in a superposition."
Correction: Before measurement, we simply do not know the particle’s definite state.Error 3: "The wavefunction provides a complete description of the quantum system."
Correction: The wavefunction is a statistical tool, not a complete physical description.
These errors have misled generations of physicists and students.
XI. Prospects for a New Physics
Based on the insight that "a single particle cannot be in superposition," we can construct a new physics:
Deterministic quantum mechanics
Seek descriptions of individual particle behavior,
Develop a complete theory beyond statistical formalism.
Eigenstate dynamics
Study how particles transition between eigenstates,
Understand the physical mechanism of quantum jumps.
Authentic quantum field theory
Distinguish between field superposition and particle definiteness,
Eliminate fictitious concepts like "virtual particles."
Conclusion: Farewell to the Superposition Myth, Return to Physical Reality
The logical necessity of natural quantization leads to an inescapable conclusion: a single electron cannot simultaneously occupy multiple orbits.
This simple physical fact dismantles the core myth of quantum mechanics—the applicability of the superposition principle to individual particles. What we call "quantum superposition" is merely a statistical description of ensembles, not the physical state of a single particle.
This realization is revolutionary:
It restores determinism: every particle has a definite state.
It dispels quantum mysticism: there are no "both-and" fuzzy states.
It clarifies the nature of measurement: measurement reveals, not creates, reality.
It unifies classical and quantum physics: quantum phenomena are statistical manifestations of deterministic systems.
Physics need not abandon reason, embrace paradox, or accept mystery.
Nature is deterministic, clear, and comprehensible. What is fuzzy is our knowledge; what is mysterious is our misunderstanding. When we recognize that a single electron cannot split itself, quantum mechanics is liberated from the fog of mysticism and returns to the path of rational science.
This is not a regression in physics—it is a return to truth. The truth is often simple: an electron is an electron. It cannot split, cannot be in two places at once. This is the plain truth of physical reality.