Quantum behavior is the outcome of structural emergence not inherently tied to probability, amplitudes, or algebraically entangled.
This attempts to pull apart the complexity behind wavefunctions.
wavefunction = state + weights + dependency + collapse input
| # | Concept | Structural Role |
|---|---|---|
| 1 | State Definition | How entities are defined, encoded, or emitted |
| 2 | Field Context | The environment in which states interact (space, potential, structure) |
| 3 | Measurement | Collapse mechanism—what triggers resolution |
| 4 | Superposition | Multiplicity of unresolved states |
| 5 | Entanglement | Shared constraints between separate states |
| 6 | Collapse | Selection of outcome from constraints, not randomness |
| 7 | Coherence / Decoherence | Conditions for trace continuity or loss |
| 8 | Amplitude / Probability | How resolution strength is computed or assigned |
| 9 | Interference | Path compatibility—how constraints amplify or cancel |
| 10 | Computation | Reversibility, gate logic, and field transitions |
| 11 | Nonlocality | Constraint propagation across separated regions |
| 12 | Interpretation | Structural logic behind what counts as "real" or "observable" |
Standard boilerplate, modular, and single purpose
state_definition()- normalized qubit statefield_context()- time evolution via unitary operatormeasurement()- projection postulate and born rulesuperposition()- linear combination of basis statesentanglement()- bell state constructioncollapse()- stochastic projectioncoherence()- simplified amplitude dampingamplitude_probability()- squared modulus of amplitudesinterference()- double-slit phase interferencecomputation()- application of quantum gatesnonlocality()- chsh test on bell stateinterpretation()- returns wavefunction + probabilities
import numpy as np
def state_definition(alpha, beta):
# Qubit: |psi> = alpha|0> + beta|1>, must normalize
norm = np.sqrt(abs(alpha)**2 + abs(beta)**2)
return np.array([alpha, beta]) / norm
def field_context(H, psi, t):
# Time evolution: psi(t) = exp(-iHt/hbar) * psi(0)
hbar = 1
U = scipy.linalg.expm(-1j * H * t / hbar)
return U @ psi
def measurement(psi, observable):
# Projective measurement: returns probabilities for each eigenstate
eigvals, eigvecs = np.linalg.eigh(observable)
probs = np.abs(eigvecs.T @ psi)**2
return dict(zip(eigvals, probs))
def superposition(states, coeffs):
# Linear combination of states
psi = sum(c * s for c, s in zip(coeffs, states))
return psi / np.linalg.norm(psi)
def entanglement():
# Bell state (maximally entangled): |00> + |11>
psi = np.zeros(4, dtype=complex)
psi[0] = 1/np.sqrt(2)
psi[3] = 1/np.sqrt(2)
return psi
def collapse(psi, observable):
# Collapse to one eigenstate randomly
eigvals, eigvecs = np.linalg.eigh(observable)
probs = np.abs(eigvecs.T @ psi)**2
idx = np.random.choice(len(eigvals), p=probs)
return eigvecs[:, idx]
def coherence(psi, decoherence_factor):
# Amplitude damping (simple decoherence model)
gamma = decoherence_factor
psi_new = np.array([psi[0], np.sqrt(1 - gamma) * psi[1]])
return psi_new / np.linalg.norm(psi_new)
def amplitude_probability(psi):
# Probability amplitudes for |0> and |1>
return np.abs(psi)**2
def interference(phase):
# Two-path interference: |psi> = |A> + exp(i*phase)|B>
psi = np.array([1, np.exp(1j * phase)])
return np.abs(np.sum(psi) / np.sqrt(2))**2
def computation(U, psi):
# Apply a quantum gate/unitary
return U @ psi
def nonlocality():
# Bell test: returns CHSH value for maximally entangled state
a = np.array([[0,1],[1,0]])
b = np.array([[0, -1j],[1j, 0]])
psi = entanglement()
AB = np.kron(a, b)
value = np.real(psi.conj().T @ AB @ psi)
return value
def interpretation(psi):
# Return full wavefunction (ontic) and probabilities (epistemic)
return {'wavefunction': psi, 'probabilities': np.abs(psi)**2}Each of these functions independently represents a constraint-encoded quantum behavior. Together, they reconstruct a structural logic that aligns closely with known features of quantum theory—without relying on its mathematical substrate.
Base Interface
class SymbolicSystem:
def emit(self, S, delta):
raise NotImplementedError
def is_valid(self, S, emission_pair):
raise NotImplementedError
def score(self, S, emission_pair):
return 1.0
def entangled(self, S1, S2):
raise NotImplementedErrorSymbolic behavior:
This is an abstract class defining the contract for any symbolic field system. It encodes emission (state generation), validation (collapse rule), fidelity (field stability), and entanglement (shared field interaction).
Quantum correspondence:
Analogous to the definition of a quantum system's Hilbert space and measurement rules. Emission aligns with possible state transitions; validation corresponds to observable constraints; score resembles measurement probability amplitude; entanglement defines correlation logic.
Structural match:
Faithfully encodes the grammar of quantum systems as structural contracts—discrete symbolic fields instead of continuous vector spaces.
Limitation:
No linearity, no operator algebra, no superposition principle. Purely rule-driven.
Readiness:
Ready to serve as a modular framework. Can be extended to model field-specific behavior across collapse types or system classes.
Harmonic emission with structural validation
class AsymmetricPrimeSystem(SymbolicSystem):
def emit(self, S, delta):
return (delta, S * delta - 2)
def is_valid(self, S, emissions):
return isprime(emissions[1])
def score(self, S, emissions):
k = emissions[0]
val = emissions[1]
amplitude = 1 / log(k + 1)
residue = S * k
non_trivial = {
i for i in range(2, int(residue ** 0.5) + 1)
if residue % i == 0 and i not in {1, k, S, residue}
and (residue // i) not in {1, k, S, residue}
}
coherence = 1 / len(non_trivial) if len(non_trivial) > 0 else 1.0
return amplitude * coherenceSymbolic behavior:
Generates candidate collapse values from the harmonic emission field C = nk - 2. Validity is confirmed by primality. The score combines emission simplicity (1/log(k)) with field coherence (few internal divisors).
Quantum correspondence:
This mimics quantized state emission: lower k (field tension) corresponds to low-energy states. Prime validation imposes a discrete spectrum. Score approximates symbolic amplitude and coherence fidelity—analogous to state stability and collapse likelihood.
Structural match:
Captures key features of eigenstate quantization, emission constraints, and symbolic energy-level fidelity.
Limitation:
Does not model amplitude interference, entanglement, or operator-based measurement. Only symbolic collapse fields.
Readiness:
Fully ready for symbolic modeling of quantized emission and discrete collapse. Extendable for multi-path or entangled collapse conditions.
Entangled field emission
class SymmetricPrimeSystem(SymbolicSystem):
def emit(self, S, delta):
return (S - delta, S + delta)
def is_valid(self, S, emissions):
return isprime(emissions[0]) and isprime(emissions[1])Symbolic behavior:
Emits dual collapse values symmetrically about the source. Collapse is valid only if both are prime—enforcing a constraint across the field surface.
Quantum correspondence:
Mirrors entanglement collapse, where measurement of one component constrains the other. The symmetric rule captures nonlocal resolution—collapse is only complete when both halves stabilize.
Structural match:
Captures bipartite constraint logic. Imposes a collapse requirement over shared field boundaries—behaviorally matching correlated state resolution.
Limitation:
Does not simulate entangled phase interference or partial resolution. Symmetry is discrete and binary.
Readiness:
Operable now as a symbolic entangled collapse field. Extendable by including shared scoring or recursive field tracing.
Symbolic emission field construction
def symbolic_superposition(system, S, delta_range):
candidates = []
for delta in delta_range:
emissions = system.emit(S, delta)
if system.is_valid(S, emissions):
score = system.score(S, emissions) if hasattr(system, 'score') else 1.0
candidates.append((delta, emissions, score))
return sorted(candidates, key=lambda x: x[2], reverse=True)Symbolic behavior:
Builds a ranked emission field from a symbolic source S. Each emission is scored and returned in fidelity order.
Quantum correspondence:
Analogous to constructing the basis set of possible measurement outcomes—like building the wavefunction in an eigenbasis. Score ranks symbolic stability rather than probability.
Structural match:
Faithfully encodes discrete state space formation. Collapse field is shaped by scoring—structural equivalent to amplitude modulation.
Limitation:
No interference or complex amplitudes. All emissions treated independently. No symbolic cancellation.
Readiness:
Complete as a symbolic superposition builder. Extendable for joint-emission effects or decoherence modeling.
Collapse resolution
def symbolic_collapse(field):
return field[0] if field else NoneSymbolic behavior:
Selects the top-ranked emission from the symbolic field. Collapse is deterministic, selecting the structurally most stable outcome.
Quantum correspondence:
Collapse to the highest-probability eigenstate. In quantum mechanics, this would be weighted sampling from a probability distribution; here, it is structural maximization.
Structural match:
Implements the selection logic of collapse without randomness. Deterministic resolution reflects system-defined constraints rather than probabilistic sampling.
Limitation:
No probabilistic sampling. No state branching. Collapse is absolute.
Readiness:
Sufficient for symbolic systems where deterministic resolution is desired. To support probabilistic fields, scoring would need normalization and sampling.
Structural overlap test
def entanglement_condition(S1, S2, system, delta_range):
for delta1 in delta_range:
e1 = system.emit(S1, delta1)
for delta2 in delta_range:
e2 = system.emit(S2, delta2)
if set(e1) & set(e2):
return True
return FalseSymbolic behavior:
Tests whether two sources emit any overlapping symbolic values—i.e., shared collapse outcomes. Entanglement is defined as emission surface intersection.
Quantum correspondence:
Models entangled correlation—if two systems produce the same observable result, they are considered coupled. Shared emissions act as symbolic entangled states.
Structural match:
Symbolic match of nonlocal constraint: fields are linked through shared emission possibility, even if evaluated independently.
Limitation:
No entanglement phase coherence. No density matrix formulation. No Bell inequality mechanics.
Readiness:
Valid as symbolic entanglement detector. Extendable with trace propagation and recursive interference logic.
Collapse path propagation
def trace_collapse(S, system, delta_range, depth=3):
trace = []
field = symbolic_superposition(system, S, delta_range)
collapse = symbolic_collapse(field)
if collapse:
trace.append(collapse)
next_S = collapse[1][1] if len(collapse[1]) > 1 else collapse[1][0]
if depth > 1:
trace.extend(trace_collapse(next_S, system, delta_range, depth - 1))
return traceSymbolic behavior:
Follows a collapse path through recursive emissions. Each new source is determined by the prior collapse result. This defines collapse memory.
Quantum correspondence:
Models symbolic analog of unitary evolution + collapse. Each emission acts as a local measurement update—structure is passed forward like a quantum walk.
Structural match:
Implements recursive collapse through discrete constraint satisfaction. Equivalent to a deterministic quantum trajectory in symbolic phase space.
Limitation:
No back-propagation or reversibility. No coherent branching.
Readiness:
Use-ready for symbolic collapse modeling. Extendable with decoherence scoring, trace length entropy, or symbolic fidelity decay.