Solution to the Combination Problem

Resolving Quantum Paradoxes with Energy
Exchange and Precise Definitions

Michael Rowen

August 5, 2026

Introduction

Modern physics rests on two foundational theories, quantum mechanics and general relativity, which together describe our physical universe from the subatomic to the cosmological scale with extraordinary empirical precision, yet these theories remain mutually incompatible and jointly incomplete. Quantum mechanics in particular harbors a series of foundational ambiguities at its core as its formalism fails to provide:

A physical account of what quantum particles are between measurements.
Definitions for what constitutes a measurement, a measurement device, an observation, and an observer.
A physical mechanism to explain how measurement produces definite outcomes from the indefinite wave states the formalism describes.
Rules to define the proper scale and scope of a quantum system prior to performing quantum mechanical calculations.
Whether/where the boundary exists between the quantum and classical worlds.

The ambiguities of standard quantum theory combined with an ad hoc “collapse postulate” that lies outside its formalism leads to a myriad of paradoxes precisely because many of its terms and rules remain undefined. The Wave Energy Exchange (WEX) principle removes these ambiguities by proposing specific definitions, rules, and a physical mechanism that is grounded in the most experimentally robust fact in quantum physics – that energy is always exchanged between quantum systems in discrete quanta characteristic of each particle type – which together elevate this experimental fact to a proposed foundational principle that eliminates numerous paradoxes.

The WEX principle proposes an ontology in which elementary particles are physically real, spatially extended energy patterns that exist independent of whether they are being measured or observed, while classical particles are treated as the signatures of quantized energy-exchange events. In other words, the WEX ontology embraces the intrinsic wave nature of matter as what is physically real and fundamental, with the particle nature of matter appearing only as evidence that an energy exchange event has occurred. Quantum theory is treated as a set of tools and rules for modeling the behavior of these physically real energy patterns. Wave functions, the primary such tool, are not considered physically real objects in their own right – only the energy patterns they describe are. With this context established, let's explore the quantum scale starting with quantum physics' central mathematical tool, quantum wave functions.

Quantum Wave Functions

At the core of quantum theory lie wave equations, mathematical formulas that model the behavior of quantum systems over time. The Schrödinger equation is the primary one used in quantum mechanics but there are other variations that model quantum systems moving at or near the speed of light (e.g. Klein-Gordon, Dirac, and Weyl Equations). Quantum wave functions are specific solutions to wave equations that describe the state and information content of elementary particles, which can be mathematically combined to describe more complex multi-particle quantum systems.

Wave functions are complex vectors defined in infinite dimension Hilbert space. The infinite dimensions are not physical but rather a mathematical abstraction used to model the infinite degrees of freedom of possible properties that particles may have. Wave functions also require “normalization” of probabilities to ensure they sum to 100%, and some require more involved “renormalization” procedures to remove infinities that may arise in certain Quantum Field Theory (QFT) calculations. Given the abstract nature of wave functions as they are defined, combined with the complex manipulations required to do calculations in quantum mechanics, wave functions are best understood not as real objects that exist in nature, but as abstract mathematical representations of physically real particles that exist in nature.

The Intrinsic Wave Nature of Matter

Standard quantum physics treats particles as having definite properties while they are being measured and lacking definite properties when not being measured. Wave functions model the behavior of particles between measurements as existing in a superposition of many possible states at many possible locations with many possible properties, requiring the infinite dimensions of Hilbert space to describe the range of possible states of a single particle. Wave functions do not model particles as solid objects like microscopic billiard balls, nor do they describe any aspect of particles when they are being measured, rather they model particles as energy waves spread out over a region of space which lack properties such as dimension, position, momentum, and spin. That quantum scale matter sometimes appears as a particle and sometimes as a wave led to the term “Wave-Particle Duality.”

Since particles are modeled as spread-out energy waves that only have properties during measurement suggests the intrinsic nature of matter is wave-like as opposed to particle-like. This brings us to the first two WEX definitions:

Wave Packet: The term 'wave packet' is often used to describe elementary particles in their wave-like state, typically modeled mathematically as a superposition of basis states within Hilbert space representing a localized energy pattern. Consistent with the ontology established above, the WEX principle adds an explicit commitment regarding what this mathematics describes: the localized energy pattern itself is physically real, spatially extended, and propagates through 4D spacetime, existing whether or not it is being measured or observed. Under WEX, wave packets are the fundamental physical objects that exist at the core of reality; the Hilbert-space superposition used to model them remains a mathematical tool, not the physical object itself.

Particle Signature: The term 'particle signature' refers to the brief, localized physical manifestation of an energy exchange event, produced when a wave packet transfers a discrete quantum of energy (characteristic of its elementary particle type) to scientific equipment during measurement or observation. This transfer is what scientific equipment detects as a particle, thus represents the ‘particle’s signature’. WEX explicitly rejects wave-particle duality: only the wave aspect of elementary particles (wave packets) is considered physically real, while a particle signature is not a persisting object or a second mode of existence, but simply fleeting evidence that an energy exchange event has occurred.

The central premise of the WEX principle is that the intrinsic nature of matter is physically real wave packets propagating through 4D spacetime which exchange energy that our scientific instruments detect as particle signatures.

An analogy is to think of a particle signature as similar to a lightning bolt. One could create a wave function that describes the voltage differential between a storm cloud and the earth, modelling the potential energy contained in the storm cloud as spread out over its 3D structure which varies relative to the contours of the earth below. As the cloud drifts over the earth, both its shape and voltage differentials are influenced by molecular and energy dynamics both inside the cloud and in the environment outside of the cloud, and by changes in the contours of the earth below. The cloud’s wave function is thus evolving over time, analogous to quantum wave functions evolving over time. One could view the cloud as containing a superposition of many potential lightning bolts that could strike the earth in many locations at any given moment. At some point a voltage differential threshold is exceeded somewhere in the cloud which causes a lightning bolt to appear for a brief instant, traveling a specific and measurable path through space while transferring a specific and measurable amount of energy between the earth and cloud. The lightning bolt quickly disappears, and a new wave function must be created to model the updated voltage differentials between the cloud and earth below.

Wave packets are spread out over a region of space (like storm clouds), producing particle signatures (or lightning bolts) with measurable classical properties for brief instants during energy transfer. The WEX principle rejects the idea that elementary particles can physically exist in superposition of being in multiple places at the same time because the WEX ontology is that the intrinsic nature of matter is physically real wave packets spread out over a region of space when not being measured. WEX views superposition as an antiquated and misleading term left over from the classical physics era where particles were viewed as tiny 3D objects that have definite properties and permanent existence. Embracing the intrinsic wave nature of matter means accepting that quantum scale matter can transfer energy from any point within the region of space its wave packet is spread over, just like a lightning bolt can transfer energy from any point in the region of space the cloud is spread over. Quantum wave functions are viewed as mathematical models to predict where wave packet energy exchange events might occur, with the Born rule describing the probability distribution for energy exchange events occurring at specific points in spacetime.

Wave Function Collapse

In standard quantum physics it is the act of measurement or observation of a quantum system that physicists view as “collapsing the wave function” of the system, causing one of the many statistical possibilities to manifest into a single definite classical result. Since this collapse of wave functions is not embedded within the wave equations of quantum formalisms, it is included as a separate “Collapse Postulate” outside of quantum theory as a non-physical mechanism to bridge the gap between the quantum and classical worlds. WEX interprets the localized detection event associated with measurement as a physical energy-exchange event. The framework therefore replaces the textbook notion of collapse with a physical mechanism and subsequent state update. Under WEX the appearance of a particle signature is evidence that an energy exchange event has occurred between multiple quantum systems or between a quantum system and a measurement device.

Wave function collapse can thus be viewed as removing the uncertainty in a quantum system due to an energy exchange event. The uncertain state of the quantum system is eliminated by measurement, whereby certain properties of the system are precisely discovered at a specific point in spacetime where a particle signature appears, signifying that an energy exchange event has occurred. After measurement, wave functions “collapse in their usefulness” in describing the new current state of the quantum system because the energy extracted from the system renders the prior wave function moot. New wave functions must be created to describe the updated state and future evolution of quantum systems post measurement, using the properties discovered during the energy exchange event as an updated set of initial conditions for the new wave function.

Quantum Entanglement

Einstein famously questioned both the validity and completeness of quantum theory his entire life. Einstein, Podolsky, and Rosen published a landmark paper in 1935 that they believed would demonstrate quantum theory to be incomplete. The paper made a complex argument to show that if quantum theory is correct, then it is possible for two elementary particles to violate the principle of local causality embedded within all classical scientific theories, originally called the EPR paradox which became known as quantum entanglement over time. In 1964 physicist John Bell developed an inequality theorem that provided a way to experimentally test the paradox, and in 1982 Alain Aspect and colleagues reported results that violated Bell’s inequality, establishing quantum entanglement as a real phenomenon. Einstein assumed this strange behavior of quantum scale matter must be explained by local hidden variables, an assumption that Bell’s theorem and the experiments that followed ruled out. The 2022 Nobel Prize in Physics was awarded to Alain Aspect, John Clauser, and Anton Zeilinger for this body of work.

Imagine a star exploding in a galaxy one billion light years from earth. The explosion causes photons to be emitted in all directions, with many pairs of "entangled" photons emitted that travel in the exact opposite directions from the exploding star. Consider one pair of these entangled photons, photon A and photon B, which form entangled wave packet AB which contains two photon quanta of energy.

Now imagine photon A hits the retina in one of your eyes after traveling across the universe for one billion years. When photon A hits your retina, the entangled connection is severed and its entangled partner (now referred to as photon B' in the illustration below) instantly adopts complementary properties to photon A. An alien quantum physicist on a distant planet that subsequently measures photon B’ will discover the complementary properties established when wave packet AB was split in half by the energy exchange with your retina.

The WEX principle views entanglement to be an aspect of the intrinsic wave nature of matter. The wave packets of photon A and photon B were produced as a single unified wave packet AB that carries two photon quanta of energy in a bi-modal wave configuration with two modes moving away from one another. When wave packet AB encounters a system that causes it to exchange energy, such as hitting your retina, a quantized particle signature is produced at the point of energy exchange. Wave packet AB loses one photon quantum to your retina, leaving the residual photon quantum of energy in photon B’. Since photon A no longer exists, the entangled connection is split and photon B’ is left with complementary properties to photon A’s particle signature due to universal conservation laws.

Conservation laws constrain the allowed correlations between the two components of the entangled state. Entanglement can best be understood by embracing the intrinsic wave nature of matter and viewing entangled wave packets as unified physically real objects extended through space, rather than as two separate wave packets that were never truly independent systems. When the entangled wave packet exchanges energy at one mode, conservation laws instantaneously constrain the properties at the other mode, not because information travels faster than light, but because the constraint is a structural property of the unified physical object itself. No usable information is transmitted between the modes, consistent with the no-signaling theorem, and no observer at either location can detect anything unusual until the results are later compared.

WEX does not restore local causality in the sense ruled out by Bell's theorem; it rejects the premise that the two photons were ever separate, locally causal systems to begin with. This reframing does not, however, resolve the underlying tension between quantum correlations and special relativity, it relocates it. Because simultaneity for spacelike-separated events is frame-dependent under special relativity, no observer-independent fact specifies which of the two measurements occur first, and therefore what 'instantaneously' means physically when conservation laws constrain the unified structure. This is not a defect unique to WEX: every realist account of quantum correlations that treats measurement outcomes as definite and mind independent. Bohmian mechanics addresses it by positing a preferred relativistic frame, yet inherits the same open problem. WEX does not resolve this tension; it shares it. From the WEX perspective, an entangled state corresponds to one non-separable physical structure whose correlations are constrained holistically, with the further question of how to reconcile that holistic constraint with relativistic simultaneity left as an acknowledged, unresolved feature of quantum foundations rather than a claim WEX makes to have settled.

The Measurement Problem

The central mystery in quantum physics revolves around the “Measurement Problem” (aka. “Observation Problem”). In standard quantum theory, observation is synonymous with measurement as both terms refer to any interaction with a quantum system that extracts precise information from the system. At its core, the measurement problem involves explaining how quantum scale matter transitions from a distribution of possible properties pre-measurement to a precise set of classical properties post-measurement. The WEX principle naturally resolves the measurement problem because the appearance of a particle signature with precise properties (i.e. precise information) is a direct consequence of a measuring device extracting a quantum of energy during a measurement.

The measurement problem in standard quantum physics is a direct consequence of a lack of definitions for what constitutes an observation, a measurement, an observer, a measurement device, and where the boundary lies between the quantum and classical worlds, if such a boundary exists at all. It is the absence of these definitions that leads directly to the paradoxes of quantum physics such as Schrodinger’s Cat. But before we discuss cats that may be considered simultaneously alive and dead, a few more definitions are needed to fully define the WEX principle.

Additional WEX Definitions

WEX offers precise definitions for the undefined terms in standard quantum theory that lead to the paradoxes, including:

Entangling Interaction: Any physical interaction between two wave packets that correlates their subsequent behavior without either wave packet transferring a discrete, characteristic quantum of energy to the other. Consistent with the treatment of entangled photon pairs described previously, the two wave packets are now treated as a single, unified, spatially extended wave packet. Because no discrete quantum of energy is exchanged in forming this correlation, the entangling interaction does not produce a particle signature. The unified wave packet persists until a measurement occurs anywhere within its spatial extent that extracts a quantum of energy, which produces a particle signature at that location while irreversibly producing complementary properties in the remainder of the structure through conservation laws.
Measurement: The ‘active extraction’ of a quantum of energy from a quantum system, either directly from the system itself or indirectly from a probe wave packet that was first entangled with the system via an entangling interaction.
Measurement Device: Any quantum or classical system that actively initiates an interaction with a quantum system in order to extract information about it, either by directly extracting a quantum of energy that produces a particle signature at the point of contact (e.g. a photon detector), or by actively extracting the energy of an intermediate probe wave packet that was previously entangled with the system (e.g. a dispersive qubit measurement).
Observation: The ‘passive detection’ of energy that was released from a quantum system, without the observing system having initiated the interaction that caused the energy release.
Observer: Any quantum or classical system that can passively detect energy that was released from a quantum system (e.g. a human retina).
Quantum System: The wave function for a quantum system should be written from the perspective of a measurement device or observer. If the system has undergone an entangling interaction with another wave packet, the wave function must describe the full spatial extent of the resulting unified wave packet, not merely the original system in isolation, until a measurement occurs anywhere within that unified structure. Furthermore, a wave function cannot contain a measurement device or observer inside the quantum system it describes.
No Quantum Boundary: Since the intrinsic nature of matter is wave-like, there is no boundary between the quantum and classical world where quantum dynamics cease to apply.

Researchers have demonstrated quantum effects in experiments involving increasingly larger and more complex configurations of matter. Organic molecules with thousands of atoms have demonstrated the intrinsic wave nature of matter applies at the scale of complex molecules. Micro-mechanical resonators made from trillions of atoms have demonstrated collective vibrational states that illustrate the intrinsic wave nature of matter at scales that are now visible with microscopes. Quantum biology has produced evidence of quantum effects operating at the molecular and cellular scale in living organisms, including coherent energy transfer during photosynthesis and in retinal proteins that migratory birds appear to use for magnetic navigation. This evidence suggests that the assumption that quantum effects cannot occur in macroscopic structures, nor in the wet, warm, and electromagnetically noisy environments of biological organisms, is incorrect. Environmental interactions more broadly can also strongly suppress observable macroscopic coherence. Quantum effects are theoretically independent of scale under the WEX principle as a natural consequence of the intrinsic wave nature of matter.

As researchers look for quantum effects in ever larger matter structures, the challenge becomes isolating and detecting the energy exchange events occurring between the wave packets that form matter structures against the backdrop of environmental noise. The WEX principle suggests that wave energy exchange events are constantly occurring in all matter structures and at all scales independent of whether they can be detected by scientific instruments.

Schrödinger’s Cat and Nested Observer Paradoxes

This paradox involves placing a cat in a box with a radioactive atom, Geiger counter, and a vial of poison. The Geiger counter will detect if the atom decays and is set up to break the vial which releases the poison and kills the cat. It is unclear in standard quantum theory whether the cat qualifies as an observer nor whether the cat exists on the quantum or classical side of the undefined boundary between the two. Given the lack of definitions, the paradox emerges when the cat is treated as part of the quantum system with everything else inside the box, resulting in the cat being viewed as existing in a "superposition" of simultaneously alive and dead until the box is opened and the cat’s fate is observed (and hopefully still alive!).

Applying the WEX definitions to this paradox leads to the radioactive atom being the only relevant quantum system that needs to be described by a wave function to model the state of the cat. The Geiger counter acts as the observer that passively detects whether the atom has released energy. Neither the Geiger counter, vial, or cat should be included within the wave function. The Geiger counter is excluded because the WEX definition of a quantum system explicitly excludes the observer from the system it observes. The vial and cat are excluded because they neither actively extract energy from the atom nor passively detect energy released by it. The relevant boundary to define the wave function of the system is the atom alone. WEX treats the cat as always possessing a definite physical state, while the radioactive atom is the quantum system whose decay probability determines the statistics of that state.

More complex versions of the Schrödinger’s Cat paradox involving multiple nested observers (e.g. Wigner’s Friend and Frauchiger-Renner paradoxes) are similarly resolved by recognizing the WEX principle explicitly excludes observers inside quantum systems. The Frauchiger-Renner paradox leads to the claim that one of the following three core assumptions in the foundations of quantum physics must be incorrect:

Universality: Quantum theory can be applied to everything, including observers and measurement devices.
Consistency: Two physicists performing the same calculations on a quantum system will agree on the resulting statistical predictions of the system.
Single Outcomes: Two physicists observing the same measurement of a quantum system will agree on the result.

Adopting the WEX definition of a quantum system narrows the scope of the “Universality” definition above by “explicitly excluding” observers and measurement devices rather than “explicitly including” them. This dissolves the Frauchiger-Renner paradox at its source rather than requiring revision to the other core assumptions.

Double Slit Experiment

The double slit experiment is the most well-known quantum experiment because it directly illustrates the wave nature of matter. A photon wave packet emitted from a light source will spread out over the region of space between the source and a barrier with two slits. The wave packet will pass through both slits then begin spreading out as a bi-modal wave packet emerging from the two slits on the other side of the barrier. As this bi-modal wave packet approaches the screen it will begin to interfere with itself, and when it hits the screen, it transfers its energy to the screen, appearing as a particle signature somewhere on the screen.

Successive photon wave packets produce a series of particle signature impacts that are distributed on the screen according to the statistics of a single self-interfering wave packet, resulting in the classic double slit interference pattern on the screen which directly illustrates the wave nature of matter. This description is consistent with the WEX principle as the wave packets travel through both slits in their intrinsic wave state and appears as particle signatures when they transfer a quantum of energy to the screen.

An alien quantum physicist on a distant planet that subsequently measures photon B will discover these complementary properties, confirming the entangled correlation established when wave packet AB was bifurcated by the energy exchange with your retina.

The WEX principle considers entanglement to be a natural aspect of the intrinsic wave nature of matter. The wave packets of photon A and photon B were produced as a unified wave packet AB that carries two photon quanta of energy. The wave function of AB describes a bi-modal wave packet with two nodes moving away from one another with significantly higher probability of energy exchange occurring in the nodes. When wave packet AB encounters a system that causes it to exchange energy, such as hitting your retina, a quantized particle signature is produced at the point of energy exchange, causing wave packet AB to bifurcate into two independent photons with complementary properties due to universal conservation laws. Conservation laws constrain the allowed correlations between the two components of the entangled state. WEX asserts that the observed correlations arise from the holistic structure of the unified state rather than from a signal transmitted between spatially separated particles.

Entanglement can best be understood by embracing the intrinsic wave nature of matter and viewing entangled wave packets as unified physically real objects extended through space, rather than as two separate wave packets that were never truly independent systems. When the entangled wave packet exchanges energy at one node, conservation laws instantaneously constrain the properties at the other node — not because information travels faster than light, but because the constraint is a structural property of the unified physical object itself. No usable information is transmitted between the nodes, consistent with the no-signaling theorem, and no observer at either location can detect anything unusual until the results are later compared. WEX does not restore local causality in the sense ruled out by Bell's theorem, it rejects the premise that the two photons were ever separate, locally causal systems to begin with. From the WEX perspective, an entangled state corresponds to one non-separable physical structure whose correlations are constrained holistically.

The Measurement Problem

The central mystery in quantum physics revolves around the “Measurement Problem” (aka. “Observation Problem”). In standard quantum theory, observation is synonymous with measurement as both terms refer to any interaction with a quantum system that extracts precise information from the system. At its core, the measurement problem involves explaining how quantum scale matter transitions from a distribution of possible properties pre-measurement to a precise set of classical properties post-measurement. The WEX principle naturally resolves the measurement problem because the appearance of a particle signature with precise properties (i.e. precise information) is a direct consequence of a measuring device extracting a quantum of energy during a measurement.

The measurement problem in standard quantum physics is a direct consequence of a lack of definitions for what constitutes an observation, a measurement, an observer, a measurement device, and where the boundary lies between the quantum and classical worlds, if such a boundary exists at all. It is the absence of these definitions that leads directly to the paradoxes of quantum physics such as Schrodinger’s Cat. But before we discuss cats that may be considered simultaneously alive and dead, a few more definitions are needed to fully define the WEX principle.

Additional WEX Definitions

WEX offers precise definitions for the undefined terms in standard quantum theory that lead to the paradoxes, including:

Entangling Interaction: Any physical interaction between two wave packets that correlates their subsequent behavior without either wave packet transferring a discrete, characteristic quantum of energy to the other. Consistent with the treatment of entangled photon pairs described previously, the two wave packets are now treated as a single, unified, spatially extended wave packet. Because no discrete quantum is exchanged in forming this correlation, the entangling interaction does not produce a particle signature. The unified wave packet persists until a measurement occurs anywhere within its spatial extent that extracts a quantum of energy, which produces a particle signature at that location while irreversibly producing complementary properties in the remainder of the structure through conservation laws.
Measurement: The ‘active extraction’ of a quantum of energy from a quantum system, either directly from the system itself or indirectly from a probe wave packet that was first entangled with the system via an entangling interaction.
Measurement Device: Any quantum or classical system that actively initiates an interaction with a quantum system in order to extract information about it, either by directly extracting a quantum of energy that produces a particle signature at the point of contact (e.g. a photon detector), or by actively extracting the energy of an intermediate probe wave packet that was previously entangled with the system (e.g. a dispersive qubit measurement).
Observation: The ‘passive detection’ of energy that was released from a quantum system, without the observing system having initiated the interaction that caused the energy release.
Observer: Any quantum or classical system that can passively detect energy that was released from a quantum system (e.g. a human retina).
Quantum System: The wave function for a quantum system should be written from the perspective of a measurement device or observer. If the system has undergone an entangling interaction with another wave packet, the wave function must describe the full spatial extent of the resulting unified wave packet, not merely the original system in isolation, until a measurement occurs anywhere within that unified structure. Furthermore, a wave function cannot contain a measurement device or observer inside the quantum system it describes.
Scale Independence: There is no boundary between the quantum and classical worlds because the intrinsic nature of matter is wave-like, hence there is no assumed fundamental size boundary at which quantum dynamics cease to apply, although environmental interactions can strongly suppress observable macroscopic coherence.

Researchers have demonstrated quantum effects in experiments involving increasingly larger and more complex configurations of matter. Organic molecules with thousands of atoms have demonstrated the intrinsic wave nature of matter applies at the scale of complex molecules. Micro-mechanical resonators made from trillions of atoms have demonstrated collective vibrational states that illustrate the intrinsic wave nature of matter at scales that are now visible with microscopes. Quantum biology has produced evidence of quantum effects operating at the molecular and cellular scale in living organisms, including coherent energy transfer during photosynthesis and in retinal proteins that migratory birds appear to use for magnetic navigation. This evidence suggests that the assumption that quantum effects cannot occur in macroscopic structures, nor in the wet, warm, and electromagnetically noisy environments of biological organisms, is incorrect. Quantum effects are scale independent under the WEX principle as a natural consequence of the intrinsic wave nature of matter.

As researchers look for quantum effects in ever larger matter structures, the challenge becomes isolating and detecting the energy exchange events occurring between the wave packets that form matter structures to illustrate quantum effects. The WEX principle suggests that wave energy exchange events are constantly occurring in all matter structures and at all scales independent of whether they can be detected by scientific instruments.

Schrödinger’s Cat and Nested Observer Paradoxes

This paradox involves placing a cat in a box with a radioactive atom, Geiger counter, and a vial of poison. The Geiger counter will detect if the atom decays and is set up to break the vial which releases the poison and kills the cat. It is unclear in standard quantum theory whether the cat qualifies as an observer nor whether the cat exists on the quantum or classical side of the undefined boundary between the two. Given the lack of definitions, the paradox emerges when the cat is treated as part of the quantum system with everything else inside the box, resulting in the cat being viewed as existing in a "superposition" of simultaneously alive and dead until the box is opened and the cat’s fate is observed (and hopefully still alive!).

Applying the WEX definitions to this paradox leads to the radioactive atom being the only relevant quantum system that needs to be described by a wave function to model the state of the cat. The Geiger counter acts as the observer that passively detects whether the atom has released energy. Neither the Geiger counter, vial, or cat should be included within the wave function. The Geiger counter is excluded because the WEX definition of a quantum system explicitly excludes the observer from the system it observes. The vial and cat are excluded because they neither actively extract energy from the atom nor passively detect energy released by it. The relevant boundary to define the wave function of the system is the atom alone. WEX treats the cat as always possessing a definite physical state, while the radioactive atom is the quantum system whose decay probability determines the statistics of that state.

More complex versions of the Schrödinger’s Cat paradox involving multiple nested observers (e.g. Wigner’s Friend and Frauchiger-Renner paradoxes) are similarly resolved by recognizing the WEX principle explicitly excludes observers inside quantum systems. The Frauchiger-Renner paradox leads to the claim that one of the following three core assumptions in the foundations of quantum physics must be incorrect:

Universality: Quantum theory can be applied to everything, including observers and measurement devices.
Consistency: Two physicists performing the same calculations on a quantum system will agree on the resulting statistical predictions of the system.
Single Outcomes: Two physicists observing the same measurement of a quantum system will agree on the result.

Adopting the WEX definition of a quantum system narrows the scope of the “Universality” definition above by “explicitly excluding” observers and measurement devices rather than “explicitly including” them. This dissolves the Frauchiger-Renner paradox at its source rather than requiring revision to the other core assumptions.

Double Slit Experiment

The double slit experiment is the most well-known quantum experiment because it directly illustrates the wave nature of matter. A photon wave packet emitted from a light source will spread out over the region of space between the source and a barrier with two slits. The wave packet will pass through both slits then begin spreading out as a bi-modal wave packet emerging from the two slits on the other side of the barrier. As this bi-modal wave packet approaches the screen it will begin to interfere with itself, and when it hits the screen, it transfers its energy to the screen, appearing as a classical particle somewhere on the screen.

Successive photon wave packets produce a series of particle signature impacts that are distributed on the screen according to the statistics of a single self-interfering wave packet, resulting in the classic double slit interference pattern on the screen which directly illustrates the wave nature of matter. This description is consistent with the WEX principle as the wave packets travel through both slits in their intrinsic wave state and appears as particle signatures when they transfer a quantum of energy to the screen.

If photon detectors are placed at the slits to detect which slit each photon passes through, the detectors will always find a photon at one of the slits and no interference pattern appears on the screen. This is traditionally seen as illustrating the particle nature of matter which the WEX principle views as evidence that an energy exchange event has occurred. When detectors are used to identify which slit a photon is passing through, the photon wave packet always passes through both slits as a single spatially extended wave, never through one slit alone. The wave packet has some probability of undergoing an energy exchange event at either detector, determined by the amplitude of the wave at each slit. When an energy exchange occurs at one detector, a photon quantum of energy is exchanged between the wave packet and detector, producing a particle signature with a photon quantum of energy. Since the wave packet carried exactly one photon quantum of energy, nothing remains of the wave packet to exchange energy with the detector at the other slit or with the screen.

Delayed Choice Double Slit Experiment

The delayed choice double slit experiment is a more complex version of the standard double slit experiment. The mystery in this experiment is that a decision made 'after' the photon has already passed through both slits but ‘before’ it reaches the screen, appears to determine which of the two double-slit outcomes results. If no attempt is made to detect which slit the photon passed through, the standard interference pattern appears, exactly as in the ordinary double-slit experiment. If the decision is instead to detect which slit the photon passed through, the interference pattern disappears entirely, exactly as when detectors are placed directly at the slits. The puzzle is how a decision made after the photon's wave has already passed the barrier can seemingly determine, after the fact, which of these two well-established behaviors will be observed.

Consider a photon wave packet that has already traveled through both slits and is at the midpoint between the barrier and the screen. Like the entangled photons discussed previously, the photon wave packet remains a unified physical object extended throughout the space it has traversed. When a detector at one of the slits extracts a photon quantum of energy from a part of the wave packet that remains at the slit, the energy exchange causes a particle signature to appear at the detector. This requires the photon's wave packet to have a coherence length comparable to or greater than the distance between the slits and the screen (which is part of the experimental design in real-world delayed-choice experiments) in order for part of the wave packet to still be physically present at the slits when a detection choice is made.

The single-photon double-slit case and the two-photon entangled case might be instances of the same underlying mechanism. In both cases, a measurement occurring anywhere within a spatially extended, non-separable wave structure extracts a quantum of energy at that location while constraining the remainder of the structure through conservation laws. What differs between the two cases is why the structure remains extended and connected prior to measurement. In the delayed-choice case, the extension is a self-coherence phenomenon where the wave packet remains present along the path it has traveled, bounded by the photon's coherence length. In the entangled case, the connection between photon pair AB is not a self-coherence phenomenon but a structural property of the unified state fixed at pair creation and enforced by conservation laws at the moment either mode is measured, consistent with the evidence of entangled correlations surviving over distances far exceeding any realistic photon coherence length.

In the double-slit case, as the single photon wave packet advances toward the screen interfering with itself, it is also extended back through both slits as a single coherent bimodal wave packet in space. This allows a detector at either slit to extract a photon quantum of energy, leaving no residual wave energy that can be transferred to the screen or a detector at the other slit. This is structurally similar to entangled photon pair AB as another example of a single coherent bimodal wave packet extended in space. In this scenario, a measurement device can extract a single photon quantum of energy from either mode, splitting the entangled connection, leaving a residual photon quantum of energy at the other mode with complementary properties to the extracted photon.

The difference in outcome (no residual energy in the double-slit case but a residual quantum of energy in the entangled case) reflects a difference in the total initial energy of the extended wave packets, not a difference in the underlying principle. The double-slit wave packet carries exactly one photon quantum, so extraction at either slit depletes all its energy. The entangled wave packet AB carries two photon quanta, concentrated in the modes of its bimodal structure. An energy exchange event triggered in either mode will extract a single photon quantum of energy from that mode, the minimum amount that can be extracted from wave packet AB, splitting the entangled connection and leaving a residual single photon quantum of energy in the opposite mode. In both cases the same rule governs the outcome: a single coherent, spatially extended wave packet undergoes local energy exchange that conserves its total quantum content. Standard quantum mechanics treats wave packets passing through a double-slit apparatus and entangled photon pairs as distinct phenomena, whereas WEX unifies them as rooted in the same underlying principle: physically real, spatially extended wave packets traveling coherently through 4D spacetime, with the potential for energy exchange occurring anywhere along its spatial extension.

Conclusion

The Wave Energy Exchange (WEX) principle proposes a comprehensive and precise set of definitions for the ambiguous terms in standard quantum theory, and a physical mechanism (quantized energy exchange) which together provides a unified physical description of quantum phenomena that avoids paradoxes. WEX leverages standard quantum formalisms and thus requires no new mathematics, relying instead on precise definitions and an ontological claim to support its arguments. WEX asserts that the intrinsic nature of matter is physically real localized patterns of energy that propagate through 4D spacetime, interacting by exchanging quanta of energy at every scale of the universe, and existing independent of whether they are being measured or observed.

Relevance of WEX to FMI

FMI is based on the assumption that mind is embedded in matter at all scales. Standard quantum theory models quantum scale matter as an ethereal phenomenon existing in a superposition of many states and many places at the same time. Under this view, mind embedded within quantum scale matter would also have to exist in this disembodied superposition of states, a requirement that presents significant challenges to FMI. In order to make a coherent argument for mind existing in quantum scale matter it was necessary to establish an ontology where quantum scale matter was physically real and embodied within a single coherent structure, which led to the WEX ontology and WEX principle.

Going a level deeper, standard quantum physics treats elementary particles as excitations in universal quantum fields, suggesting that quantum fields are what exists at the core of reality. Elementary particles are considered to result from the interactions of excitations in multiple quantum fields, which presents a second disembodiment challenge to FMI that will be addressed in a subsequent discussion on quantum field theory..