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The Kelly's Room Principle:
A Locality-Based Reformulation of Wavefunction Extent
A rigorous investigation into the spatial limits of quantum superposition, proposing that wavefunctions possess finite, physically effective reach rather than infinite mathematical extension.
Abstract
The Kelly's Room Principle provides an empirically grounded argument against the conventional assumption that quantum wavefunctions extend infinitely in physical space.

Drawing on reproducibility of laboratory experiments, observer locality, decoherence theory, and the absence of unexplained remote collapses, this principle asserts that wavefunctions possess a finite, physically effective spatial reach.
The foundational insight is straightforward yet profound: if an observer located in an adjacent room cannot collapse a quantum state, then its wavefunction cannot extend into that room in any operationally meaningful sense.

This whitepaper formalizes the principle, establishes its logical foundation through both theoretical analysis and empirical observation, explores far-reaching implications for quantum ontology and the measurement problem, and proposes a quantitative framework for defining the spatial extent of quantum superposition states.
We introduce two novel constructs—the Jackson Superposition Radius and the Kelly Bound—which provide measurable parameters for characterizing wavefunction spatial extent and establish testable predictions that distinguish this framework from traditional interpretations of quantum mechanics.
Introduction:
The Spatial Paradox of Quantum Mechanics
Standard quantum mechanics asserts that a particle's wavefunction mathematically extends over all space until an observation collapses it into a definite state.

This formalism leads to the widely repeated—but rarely examined—claim that quantum superposition is "spread everywhere" throughout the universe.

Textbooks present Schrödinger solutions with nonzero amplitude at arbitrarily large distances, suggesting that quantum uncertainty pervades all of physical reality until the moment of measurement.
However, the physical world provides no evidence that observers at macroscopic distances randomly or unintentionally collapse quantum states in nearby experiments.

Laboratory interference patterns form reliably despite large numbers of people, animals, photons, cosmic rays, and thermal particles within the surrounding environment.

A double-slit experiment conducted in Princeton produces identical results whether performed in an empty building at midnight or during busy daytime hours with hundreds of people in adjacent rooms and hallways.
This reproducibility is so fundamental to experimental physics that we rarely pause to consider its profound implications. If wavefunctions truly extended everywhere with physical significance, we would expect environmental observers to cause random, unpredictable collapses.

Yet experimental quantum mechanics exhibits remarkable stability and repeatability.
This mismatch between mathematical formalism and observational reality exposes a critical conceptual gap: the wavefunction cannot be both physically meaningful everywhere and simultaneously immune to collapse by nearby observers.

If collapse requires physical interaction—as all experimental evidence suggests—then the wavefunction must have a finite operational boundary beyond which it ceases to have measurable physical effects.

The Kelly's Room Principle formalizes this fundamental insight.
The Kelly's Room Principle:
Formal Statement
Primary Assertion
If an observer located in an adjacent room cannot induce collapse of a quantum system through any physically available interaction, then the wavefunction of that system does not extend into that room in any operationally meaningful sense.
Corollary
A wavefunction's physically effective extent is therefore finite and bounded by a characteristic radius beyond which collapse-inducing interactions become impossible.


This principle reframes quantum collapse not as a mystical, instantaneous global event affecting the entire universe, but rather as a function of local interaction within a limited spatial domain.

It forces a critical distinction between two fundamentally different notions of wavefunction extent:
Mathematical Extension
The idealized, infinite support of Schrödinger solutions in Hilbert space—a formal mathematical construct that may have nonzero amplitude everywhere.
Physical Extension
The actual spatial region where collapse-inducing interactions can occur and where the wavefunction exerts measurable physical influence on experimental outcomes.
The systematic absence of unexplained, remote collapses in the entire history of experimental quantum physics provides strong empirical support for the existence of a finite physical wavefunction extent, even if the mathematical formalism suggests otherwise.
The Logical Foundation
1
The Standard Assumption
Quantum mechanics textbooks often state or strongly imply that the wavefunction extends everywhere in space, collapse occurs when any observer interacts with the system, and superposition ends instantaneously upon observation regardless of distance.
2
Logical Consequence
If this were literally true in physical space, then anyone or anything within the wavefunction's infinite region would act as a potential observer capable of inducing collapse, and superposition would end unpredictably based on random environmental interactions.
3
Empirical Reality
Yet this prediction fails catastrophically.

Quantum experiments succeed reliably in environments filled with people, electromagnetic radiation, air molecules, and thermal fluctuations—none of which cause premature, random collapse.
4
Necessary Conclusion
A locality constraint on collapse must exist, implying that wavefunctions do not extend physically beyond a finite, quantifiable boundary.
Empirical Contradiction:
The Evidence from Laboratory Physics
Quantum interference experiments—such as the canonical double-slit experiment, Mach-Zehnder interferometry, and quantum eraser configurations—routinely occur in environments filled with potential observers and decoherence sources.

Consider the typical experimental context:
Human Observers
People walking in nearby hallways and adjacent rooms, researchers monitoring equipment, maintenance staff, and building occupants—all containing trillions of particles in various quantum states.
Electromagnetic Environment
WiFi signals, cell phone radiation, fluorescent lighting, cosmic microwave background, and thermal photons constantly permeating the laboratory space.
Atmospheric Interactions
Approximately 10²⁵ air molecules per cubic meter continuously colliding, each carrying momentum and capable of interaction.
Mechanical Vibrations
Building vibrations from HVAC systems, footsteps, traffic, seismic activity, and acoustic noise propagating through all structures.

None of these uncontrolled environmental factors collapse the wavefunction prematurely.

A properly isolated quantum system maintains coherence and produces expected interference patterns with extraordinary reliability.

This reproducibility across laboratories worldwide, across different times of day, and in the presence of varying numbers of nearby observers provides powerful evidence for a locality constraint on quantum collapse.
If wavefunctions truly extended infinitely with physical significance, the presence of a single additional person in a building should alter experimental outcomes.

The fact that it does not implies that wavefunctions possess finite, localized extent—they simply do not reach into Kelly's room, or any other sufficiently distant location.
Mathematical
vs
Physical Extent
Mathematically, solutions to the Schrödinger Equation for many quantum systems possess nonzero amplitude at every point in space.

Free particle wavefunctions, harmonic oscillator eigenstates, and even bound state solutions technically have exponentially small but nonzero tails extending to infinity.

This reflects the formal mathematical structure of quantum theory in Hilbert space—it does not necessarily describe physical reality.
The Kelly's Room Principle asserts a crucial distinction: mathematical tails do not imply operational influence.

Only the spatial region within which collapse can actually occur through physical interaction reflects the true, meaningful extent of the quantum state.
Mathematical Extension
Represents the formal support of the wavefunction in configuration space—an idealization that may assign nonzero probability amplitude to arbitrarily distant locations.
Physical Extension
Represents the actual spatial domain where the wavefunction can participate in collapse-inducing interactions and influence experimental outcomes in measurable ways.

This distinction parallels how meteorologists treat probability distributions for hurricane trajectories.
While the conceptual probability distribution may extend broadly across an entire ocean basin, only a bounded region actually experiences measurable weather effects.

Similarly, exponentially suppressed wavefunction tails beyond a characteristic distance should not be interpreted as having physical presence or causal influence.
There must exist a quantifiable radius beyond which wavefunction amplitude, though mathematically nonzero, has no measurable physical effect on collapse dynamics or experimental outcomes.
The Jackson Superposition Radius (RJ)
To formalize the spatial limits of quantum superposition, we introduce a novel construct:

The Jackson Superposition Radius (RJ)
RJ defines the maximum distance from a quantum system's center of mass at which that system remains vulnerable to collapse by external interaction. Beyond RJ, the wavefunction has negligible physical presence and cannot participate in collapse-inducing measurement processes.


Factors Influencing RJ
The Jackson Superposition Radius is not a universal constant but rather depends on the specific physical characteristics of the quantum system and its environment:
Particle Mass
Heavier particles undergo more rapid decoherence due to stronger environmental coupling, resulting in smaller RJ.

Electrons maintain coherence over larger distances than molecules.
Momentum and Energy
Higher momentum particles have shorter de Broglie wavelengths and more localized wavefunctions, potentially reducing RJ through increased interaction cross-sections.
Environmental Temperature
Thermal photons and molecular collisions induce decoherence.

Cryogenic systems maintain quantum coherence over vastly larger distances than room-temperature systems.
Decoherence Rate
Systems with strong environmental coupling (electromagnetic, gravitational) experience rapid coherence loss, directly limiting the spatial extent of maintainable superposition.
Coupling Strength
Charged particles interact more strongly with the electromagnetic environment, leading to faster decoherence and more constrained spatial extent than neutral particles.
Isolation Quality
Sophisticated isolation techniques—vacuum chambers, electromagnetic shielding, vibration isolation—can substantially increase RJ by reducing environmental interaction.


These factors suggest that RJ varies dramatically across different quantum systems: from nanometers for warm macromolecules to potentially kilometers for carefully isolated ultra-cold atoms in deep space.

The principle remains invariant—somewhere, a finite boundary exists beyond which the wavefunction ceases to have operational meaning.
Relationship to Decoherence Theory
Decoherence Theory
Decoherence Theory, developed extensively in the 1970s through present day, explains how quickly environmental interactions destroy quantum superposition by entangling the system with environmental degrees of freedom.

It describes temporal dynamics—the characteristic timescale over which off-diagonal density matrix elements decay toward classical statistics.
Decoherence successfully explains why macroscopic objects behave classically, why Schrödinger's cat paradoxes do not occur in practice, and why quantum computers require such extraordinary isolation.

It is fundamentally a dynamical theory describing rates of coherence loss.
The Jackson Radius
The Jackson Superposition Radius addresses a complementary question: where can superposition exist in the first place?

It defines the spatial boundary beyond which decoherence-inducing interactions cannot occur because the wavefunction has no physical presence.
RJ is fundamentally a geometric theory describing spatial extent—the region within which quantum effects remain operationally meaningful.

It transforms decoherence from a purely temporal phenomenon into a spatiotemporal framework.

These two frameworks are complementary rather than competing.

Decoherence Theory describes the rate at which environmental monitoring destroys coherence within RJ.

The Jackson Radius establishes the spatial arena within which decoherence dynamics operate.

Together, they provide a complete spatiotemporal picture: quantum superposition exists within a finite spatial volume (RJ) and persists for a finite duration (decoherence time).

Both boundaries arise from the same fundamental physics—the system's interaction with its environment.
The Kelly Bound (RK)
To capture the empirical upper limit of collapse influence and provide an experimentally accessible constraint, we define a second fundamental quantity:

The Kelly Bound (RK)
RK represents the largest radius at which an external observer could theoretically induce wavefunction collapse through any physically available interaction mechanism. It provides an experimentally determinable upper bound on the Jackson Superposition Radius.

The Kelly Bound is defined operationally through experimental observation.

If an observer named Kelly, located in a separate room at distance d from a quantum experiment, can perform no action whatsoever that induces collapse or affects the interference pattern, then we conclude that RK < d.

The wavefunction does not extend into Kelly's room in any physically meaningful sense.

1
Experimental Setup
Prepare quantum system in superposition state in laboratory room A.
2
Observer Placement
Place observer 'Kelly' in adjacent room B at distance d, with various measurement apparatus available.
3
Interaction Attempts
Kelly performs various detection attempts: photon emission, magnetic field generation, gravitational influence, etc.
4
Outcome Measurement
Measure whether interference pattern or superposition state is affected by Kelly's presence or actions.
5
Boundary Determination
If no effect observed, conclude RK < d, establishing upper bound on wavefunction extent.


The Kelly Bound provides an experimental constraint that the Jackson Superposition Radius must satisfy: RJ ≤ RK.

By systematically varying the distance d and the sensitivity of collapse detection, experiments can bracket the true value of both quantities with increasing precision.

This transforms the Kelly's Room Principle from a philosophical assertion into a quantitatively testable framework.
Implications for Quantum Foundations
Against the "Everywhere Wavefunction" Interpretation
The Kelly's Room Principle directly refutes the literal interpretation of universal wavefunction extension that appears in many textbooks and popular accounts.

If wavefunctions truly extended everywhere with physical significance, Kelly's observation from her room would affect laboratory experiments—but it does not.

Collapse must be local, not global.

This has profound implications for many-worlds interpretations and the nature of the quantum-classical transition.
Support for Physical Ontology
If spatial reach matters—if there exist locations where the wavefunction genuinely is not present—then the wavefunction cannot be merely a mathematical tool for calculating probabilities.

It must represent a physical distribution of potential states in real space.

The wavefunction must be ontologically real, not epistemological.

This supports realist interpretations over purely instrumentalist views.|
Locality Constraints on Measurement
The measurement problem takes on new character when wavefunctions have finite extent.

Collapse becomes a fundamentally local process constrained by RJ, eliminating nonlocal instantaneous collapse across arbitrary distances.

This may help reconcile quantum mechanics with relativistic causality.
Compatibility with Decoherence Theory
The Kelly's Room Principle does not conflict with decoherence theory—it strengthens and completes it by adding explicit spatial boundaries to decoherence's temporal dynamics.

Together they form a spatiotemporal framework for quantum-to-classical transition.
Implications for Nonlocality and Entanglement
Entangled particles exhibit correlations that violate Bell inequalities, suggesting nonlocal connections.

However, the Kelly's Room Principle implies that each particle's wavefunction has finite extent even in entangled states.

This demands careful reconsideration of what "nonlocality" means when wavefunctions themselves are spatially bounded.
Experimental Pathways
&
Testable Predictions
The Kelly's Room Principle is not merely philosophical speculation—it generates concrete, testable predictions that distinguish it from conventional quantum mechanical interpretations.

Several experimental approaches could probe the finite extent of wavefunctions:
01
Distance-Dependent Collapse Sensitivity
Systematically vary the distance between a quantum system and potential observer, measuring whether collapse probability or interference visibility changes as a function of separation. Predict sharp dropoff beyond RJ.
02
Environmental Observer Scaling
Introduce controlled numbers of "observers" (measurement devices, thermal sources, electromagnetic emitters) at varying distances, determining the boundary distance beyond which additional observers have zero effect.
03
Mass and Temperature Scaling
Measure RJ for quantum systems of different masses and temperatures, testing predicted correlations between particle properties and coherence radius.
04
Kelly Bound Determination
Perform controlled experiments where observers at precisely known distances attempt various collapse-inducing interactions, directly measuring RK for different quantum systems.
05
Quantum Computer Implications
Test whether qubit coherence times correlate with physical isolation distance from environmental noise sources, potentially improving quantum computer design.
These experimental tests would refine our understanding of the Kelly Bound and Jackson Superposition Radius, potentially revealing new physics at the boundary between quantum and classical regimes. Success would provide quantitative parameters for wavefunction extent; failure would require substantial revision of the principle's assumptions.
Potential Objections and Responses
Objection: Mathematical Formalism
"Schrödinger solutions have infinite support. How can you claim finite extent?"
Response: We distinguish mathematical idealization from physical reality. Exponentially suppressed tails beyond RJ have no operational meaning. Physics is ultimately empirical, not purely mathematical.
Objection: Quantum Nonlocality
"Bell inequality violations prove quantum mechanics is fundamentally nonlocal. How does finite wavefunction extent reconcile with this?"
Response: Entanglement correlations are nonlocal, but individual wavefunctions can still have finite extent. The principle addresses single-system superposition boundaries, not entanglement correlations between distant systems.
Objection: Arbitrary Cutoff
"Defining RJ seems arbitrary. How do we determine the exact boundary?"
Response: RJ is operationally defined through experimental detectability of collapse-inducing interactions. Like all physical measurements, it has finite precision but is not arbitrary—it reflects actual physical boundaries.
Objection: Decoherence Suffices
"Decoherence theory already explains everything. Why do we need another principle?"
Response: Decoherence addresses temporal dynamics but not spatial boundaries. The Kelly's Room Principle complements decoherence by adding spatial constraints, forming a complete spatiotemporal framework.
Philosophical and Practical Significance
Philosophical Impact
The Kelly's Room Principle addresses longstanding puzzles in quantum foundations by grounding superposition in physical locality. It challenges the view that quantum mechanics describes a fundamentally holistic, non-separable reality, instead suggesting that quantum systems have definite spatial boundaries.
This supports a realist ontology where wavefunctions represent actual physical states distributed over finite regions, rather than mathematical abstractions encoding observer knowledge. The measurement problem becomes a question of local interaction dynamics rather than mysterious global collapse.
Furthermore, it provides a clear criterion for the quantum-classical boundary: systems become effectively classical when their characteristic size exceeds RJ, ensuring internal degrees of freedom cannot maintain coherence.
Practical Applications
Understanding wavefunction spatial extent has immediate technological relevance. Quantum computer design requires maximizing qubit coherence by minimizing environmental decoherence. Characterizing RJ for different qubit implementations enables optimal isolation strategies.
Quantum sensing and metrology devices could be optimized by understanding the spatial scales over which quantum advantages persist. Medical imaging technologies relying on quantum effects might be improved through explicit modeling of coherence boundaries.
Even fundamental physics experiments—gravitational wave detection, tests of quantum gravity, searches for dark matter—could benefit from rigorous treatment of quantum coherence spatial limits.
Conclusion: Superposition Is Real, But It Isn't Everywhere
The Kelly's Room Principle resolves a longstanding conceptual contradiction in quantum mechanics by establishing that wavefunctions do not exert physical influence arbitrarily far from their source. If someone located in an adjacent room cannot collapse a quantum state through any physically available interaction—and experimental evidence overwhelmingly confirms that they cannot—then the wavefunction is not present in that room in any operationally meaningful sense.
This principle leads naturally to two quantitative constructs: the Jackson Superposition Radius (RJ), defining the maximum spatial extent where superposition remains vulnerable to collapse, and the Kelly Bound (RK), providing an experimentally determinable upper limit. Together, these offer a rigorous framework for quantifying wavefunction extent and testing the principle's predictions.
The result is a more realistic, experimentally grounded model of quantum superposition that reconciles collapse locality with the remarkable reliability and reproducibility of laboratory results worldwide. By distinguishing mathematical formalism from physical ontology, we preserve the predictive power of quantum mechanics while eliminating the paradoxical claim of infinite wavefunction extension.
Core Insight
Quantum superposition is physically real and experimentally verified—but it exists within finite, bounded spatial regions determined by system properties and environmental coupling.
In the clearest possible terms: Superposition is real, but it isn't everywhere. If Kelly can't collapse it from her room, the wavefunction isn't there. This simple principle, grounded in reproducible experimental observations and logical consistency, may reshape our understanding of quantum reality and guide the next generation of quantum technologies.
Future work will refine the mathematical formulation of RJ, conduct systematic experimental tests of the Kelly Bound, and explore implications for quantum field theory, quantum gravity, and the fundamental nature of spacetime. The principle opens new research directions at the intersection of quantum foundations, decoherence theory, and experimental physics, promising deeper understanding of the quantum-classical transition and the true nature of quantum reality.
Jackson's Theorems, Laws, Principles, Paradigms & Sciences…
Jackson P. Hamiter

Quantum Systems Architect | Integrated Dynamics Scientist | Entropic Systems Engineer
Founder & Chief Scientist, PhotoniQ Labs

Domains: Quantum–Entropic Dynamics • Coherent Computation • Autonomous Energy Systems

PhotoniQ Labs — Applied Aggregated Sciences Meets Applied Autonomous Energy.

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