Section 37 (first conceived 2.04.2021)
Uncertainty, Self-Determination, and the Abstractive Set
The uncertainty principle provides a physical analogue for the ontological notion of self-determination. According to the principle of uncertainty, the more precisely the position of a particle is determined, the less precisely its momentum can be known, and vice versa. This reciprocal limitation suggests that the determination of an end simultaneously limits the process by which that end is achieved.
When the final aim of an activity is conceived, this conception reaches the limiting condition of that activity. In Whitehead’s terms, this may be understood as the formation of an abstractive set, whereby a continuum of potential relations is terminated by a definite conceptual focus.¹ The continuity of the end point bears no duration other than the possible determination involved in setting the aim itself.
The reason that a precisely determined position excludes precise knowledge of momentum is that momentum is itself the determining principle of position. Conversely, when momentum is determined, position becomes indeterminate because it is in the process of being set. Put simply: “When I am here—now what?” The prediction of the motion of an object becomes itself an object of thought—an abstractive set—which serves as the determinative structure toward which activity is directed.
Thought operates in this same manner. When an ideal is conceived, it functions as a position: the ideal becomes the activity of actualization. During the process of actualizing the idea—which is fundamentally the thinking-through of its logic—the ideal becomes its own answer, that is, another idea. Thought is therefore not merely abstract in content but abstract in function, insofar as it enables consciousness to derive the logical structures inherent in physical relations.
On the Use of the Term “Consciousness”
The term consciousness is used here in a precise ontological sense. Consciousness refers to the alive, active, and determining principle in nature. This ontology does not assume that consciousness emerges from nature as a secondary effect—i.e., it is not the case that nature exists first and consciousness follows as a consequence. Rather, nature is alive because of consciousness, or more precisely, because of the element of consciousness intrinsic to nature itself.
In this sense, consciousness is a universal principle of self-determination and self-generation. As Peirce suggests, the activity of mind is not passive reception but a form of compulsion into thought, whereby relations are forced into intelligibility.² Consciousness derives ideas for the mind through its capacity to abstract from the physical composition of objects their logical structure.
Consciousness functions as a locus of focus. It can operate with a high degree of concentration, directly deriving particular relations. Sensation is one such degree of consciousness: it directly derives ideas from particular physical relations. Beyond sensation, there are higher degrees of consciousness that derive more general and universal forms of foundational physical relations.
The term abstract should not mislead the reader. There is no such thing as a non-physical rational principle. The distinction between physical and rational principles is itself an abstraction generated by understanding and reified by negative reason. The physical principle of consciousness is purely abstract in the sense that it is void of quantity. This absence of quantity enables consciousness to move beyond sensation and derive universally valid principles.
Consciousness may be described metaphorically as a spherical entity capable of conforming exactly to the physical compositions of phenomena. It does so in order to illuminate, for thought, the content of its own logical activity.
The Sphere as Universal Form
It is often stated that the form of the universe is spherical. Taken merely as a quantitative claim, however, this reduces the universe to a static object. A more precise claim is that the sphere is the universal form. In this formulation, the sphere is not a fixed geometry but a dynamic logic.
The sphere, insofar as it is dynamic, expresses simultaneous expansion outward and contraction inward while maintaining a constant relation to a central locus. A circle may vary in magnitude while remaining formally identical. Consciousness exhibits this same physical logic: it is a spherical void whose function is to maintain focus while permitting variation in scale.
Consciousness expands outward to disclose certain physical interactions and communicates these to the mind, from which thinking activity is instigated. This dynamic corresponds to what is described in quantum mechanics as a quantum leap: “an abrupt transition of a system described by quantum mechanics from one discrete state to another, such as the transition of an electron to a lower energy orbit.”³
This transition appears abrupt because we observe the phenomenon abstracted from the mental act that functions as its final cause. What appears in nature as a discontinuous jump reflects a leap of void—of nothing—from consciousness onto the object when it exceeds the limits of sensation. This is why quantum transitions are discontinuous: they involve a change in state that cannot be described through continuous motion.
This same logic underlies quantum entanglement, defined as the phenomenon in which particles interact such that their quantum states cannot be described independently, even when separated by large distances.⁴ The system must be described as a whole, reflecting the same non-local, non-quantitative structure characteristic of consciousness itself.
Footnotes
- A. N. Whitehead, Process and Reality, esp. Part IV, on abstractive hierarchies and the termination of extensive continua.
- C. S. Peirce, Collected Papers, esp. on the compulsive character of thought and the logical force of signs.
- W. Heisenberg, Physics and Philosophy, on quantum transitions and discontinuity.
- A. Einstein, B. Podolsky, and N. Rosen (1935); later formalized in quantum mechanics as entanglement.
1. Wave Packets and the Uncertainty Principle
A wave packet exists because of the uncertainty principle. The two are not separate ideas; they are mathematically equivalent statements about localization.
1.1 Localization Requires Uncertainty
To localize a particle in space, its quantum state must include many wavelengths (momenta). This follows from Fourier analysis:
- A sharply localized packet → wide spread in momentum
- A sharply defined momentum → delocalized wave
This yields the uncertainty relation:
[
\Delta x , \Delta p \ge \frac{\hbar}{2}
]
A wave packet is the concrete realization of this inequality. It is uncertainty structured into form.
2. Why Wave Packets Spread (Irreversibility)
2.1 Packet Spreading Is Not Optional
For most particles (e.g., free electrons), different momentum components evolve at different rates. Over time:
- High-momentum components move faster
- Low-momentum components lag behind
- The packet spreads
Mathematically, the position uncertainty grows:
[\Delta x(t) > \Delta x(0)]
This happens even in perfectly empty space.
2.2 Irreversibility from Reversibility
The Schrödinger equation is time-reversible.
Wave packet spreading is not due to dissipation or friction.
Irreversibility arises because:
- Reconstructing the original packet requires perfect phase alignment
- Any interaction (even minimal) destroys that alignment
- The environment acts as an information sink
Thus, irreversibility is informational, not energetic.
This aligns with your earlier point:
- Irreversibility = quantitative increase of uncertainty
- Uncertainty = qualitative structure of irreversibility
Once phase information is lost, the packet cannot re-localize naturally.
3. Measurement, Decoherence, and Irreversibility
When a wave packet interacts with a measuring apparatus:
- The system becomes entangled with many environmental degrees of freedom
- Interference between packet components is suppressed
- The packet behaves as if it has “collapsed”
This process—decoherence—is effectively irreversible because:
- Information is dispersed into uncontrollable correlations
- Reversing it would require controlling the entire environment
Thus:
- Measurement irreversibility is not fundamental collapse
- It is the practical impossibility of reassembling coherence
4. Uncertainty as the Source of Temporal Direction
Wave packet spreading defines a natural arrow of time:
- Localization → delocalization
- Order → dispersion
- Certainty → uncertainty
Time asymmetry enters physics not through fundamental laws, but through:
- Initial conditions
- Growth of entanglement
- Loss of phase information
This mirrors thermodynamic irreversibility but at the quantum level.
5. How Wave Packets Change in Quantum Field Theory
5.1 Particles Are Not Primary in Quantum Field Theory
In nonrelativistic quantum mechanics:
- Wave packets describe particles
In quantum field theory:
- Fields are fundamental
- “Particles” are excitations of fields
A wave packet in QFT is therefore:
a localized excitation of a quantum field, not an object moving through space.
6. Energy Packets
In Quantum Field Theory:
- Energy is carried by field excitations
- A packet is a superposition of field modes
Key differences:
- Packets can be created and destroyed
- Particle number is not conserved
- Localization is limited by relativity
You cannot localize a packet arbitrarily without:
- Creating particle–antiparticle pairs
- Violating causality bounds
Thus, Quantum Field Theory places absolute limits on localization.
7. Relativistic Constraints on Packets
In relativistic Quantum Field Theory:
- Packets cannot be sharply localized below the Compton wavelength
- Attempting to do so injects enough energy to alter the field itself
This means:
- Localization changes ontology, not just description
- The “packet” becomes a different physical situation
8. Irreversibility in Quantum Field Theory
Irreversibility in Quantum Field Theory arises through:
- Particle creation
- Field interactions
- Vacuum fluctuations
- Renormalization effects
Once energy is redistributed among field modes:
- Returning to the original packet requires undoing field excitations
- This is practically and conceptually irreversible
Thus irreversibility is deeper in Quantum Field Theory than in simple wave mechanics.
9. Comparison Table
| Aspect | Quantum Mechanics | Quantum Field Theory |
|---|---|---|
| Fundamental entity | Particle + wave | Field |
| Packet represents | Particle probability | Field excitation |
| Particle number | Fixed | Variable |
| Localization limit | Uncertainty principle | Uncertainty + relativity |
| Irreversibility | Packet spreading, decoherence | Field entanglement, creation |
| Ontological status | State of a system | Mode of a field |
10. Unified Insight
Wave packets reveal that:
- Localization is purchased at the cost of uncertainty
- Time’s arrow emerges from information loss
- Irreversibility is built into how form disperses
In quantum field theory, this insight deepens:
- What spreads is not a thing, but excitation
- What persists is structure, not substance
- What becomes irreversible is relation itself
A wave packet is uncertainty temporarily held in form; irreversibility is the release of that form back into relation.
The ontological proclamation of discrete packets of energy is entirely a physical description: it states that energy is quantized and that these laws apply to everything physical, whether directly perceivable or not. Such laws extend to all physical entities and interactions without exception. However, this quantitative description does not automatically include the qualitative dimension—namely, the question of what kind of being these energy transactions belong to, or what being underlies and unifies them.
Questions concerning the nature of energy as a universal law of physical reality are therefore not merely quantitative questions. They are fundamentally qualitative questions of Being: What is the nature of the reality in which these discrete energy states occur? What kind of being is expressed through these transitions?
From this perspective, the observer—understood ontologically rather than psychologically—is not merely witnessing external events. Rather, the observer encounters, in physical form, the very mechanisms of determination operative within mind itself. The abrupt transitions of energy states mirror the internal structures of cognition and self-determination. What appears as an external physical phenomenon is, at the same time, the objective display of the observer’s own ontological structure, extended across all species of physical beings and made available for discovery as universal law.
Natural Decoherence
There is a natural decoherence, or unpredictability, intrinsic to the observer–mind phenomenon. As part of any reaction, there is always an undisclosed element—an unpredictable and unknown variable that cannot be eliminated. This irreducible indeterminacy is the central premise of the thesis: quantum descriptions of reality articulate what we mean by discrete, abrupt, and collapsed moments and states of particles.
These moments are not merely technical features of measurement but expressions of a deeper structure in which determination always arises alongside uncertainty. What appears as a sudden transition or collapse in physical systems reflects the fact that no act of observation or determination can exhaust the totality of relations involved. An element remains undecided, and it is precisely this remainder that gives rise to decoherence and unpredictability as fundamental features of physical reality.
Consciousness, Non-locality, and the Derivation of Form
When, for example, you have the idea of Paris while sitting at home in Toronto, the idea of Paris—inasmuch as it lies beyond sensation—demonstrates consciousness’s capacity to expand beyond any particular location and derive the form of that idea. You do not merely recall sensory fragments; you apprehend Paris as a coherent form. Consciousness reaches the locus where the form of the idea is constituted, even though the body remains spatially fixed.
This is why, in the diagram referenced above, a concentrated laser beam becomes a cone emerging from a self-reflective entity such as a crystal. The magnitude of the laser beam changes to represent the nature of the medium from which it is emitted. In a spherical structure—such as a crystal—the beam takes on a conical form, polarizing itself so as to capture aspects of the whole. The system is entirely self-integrated: opposing elements are enclosed within a single coherent structure.
Every time an idea is conceived, consciousness breaches beyond any particular location and expands toward the region where the form of the idea finds its physical composition. The mind is capable of this because consciousness, insofar as it is void, bears no determinate quantity that would interfere with the quantitative structure of the physical relations it abstracts into ideas. Consciousness is not fixed to any specific place because it does not itself possess quantitative composition in the way ideas do.
This is not to say that consciousness is nowhere. Rather, it is not limited to any particular location. The mind situates consciousness relative to ideas, but consciousness itself—by virtue of its infinite magnitude—remains nonlocal. The void’s “circumference” captures relations that are otherwise spatially distinct.
If the universe is understood as having the universal form of a sphere, and if the sphere is taken as a principle of reason, then any particular relation can be disclosed within it. Consciousness, possessing the dynamic nature of a spherical void—capable of infinite expansion and contraction—can disclose rational relations without adhering to their empirical order. Thus, one can conceive water in relation to hydrogen, even though hydrogen is ontologically prior to water in physical formation.
The Cone, the Sphere, and the Inverse Square Law
The cone within the sphere represents the magnitude of consciousness. It expands from an infinitesimal focal point toward the generality of the sphere’s circumference. In physical terms, this expansion mirrors the inverse square law: as distance from the source increases, intensity diminishes proportionally to the square of that distance.¹ Likewise, consciousness disperses its focus as it expands, yet maintains formal continuity with its point of origin.
Point a, the centre of the sphere, represents the locus at which ideas are conceived.
Determination, Uncertainty, and Self-Activity
Alan Watts’s critique of causation is correct but incomplete. He rejects the notion that one event causes another in a linear temporal sequence, arguing instead that everything arises from the immediacy of the present.² There is no distinction between what is happening and what is being done; being itself is the unity of both.
However, this unity alone does not specify the content of determination. Determination cannot be reduced to efficient causation. It is inherently self-activity—the undifferentiated identity of doing and happening.
This self-activity is intrinsically contradictory. If I = I, then the “I” becomes that which cannot be grasped as an object. In Buddhism, this is often expressed through the doctrine of anattā (not-self): that which cannot be attained, yet never disappears.³ Duality contains unity; unity contains duality. The contradiction is not a flaw but the very engine of determination.
This is the basis of dialectic: self-determination proceeds through contradiction with an unattainable identity. The self is nothing—and therefore being as such—yet not that at the same time. This perpetual self-contradiction is determination.
Observation, Uncertainty, and Quantum Limits
This reframing addresses the observer problem more fundamentally. Physical interactions alone describe changes among parts, but they do not explain who observes the observer.
If observation is self-observation, in what sense is the observer distinct from the observation? If the observer is reducible to physical aggregates or conceptual contents, then the observer collapses into the observed. This leads directly to the quantum uncertainty principle: measuring one observable places the system in a definite eigenstate of that observable, but not necessarily of another incompatible observable.⁴
Bell’s theorem intensifies this problem by showing that measurements performed on one part of an entangled system produce nonlocal correlations in another.⁵ The observer can be any point on the sphere’s circumference—each point potentially containing the whole.
The observer is distinct from observation precisely because uncertainty mediates their relation. Observation is a product of uncertainty; the observer contains uncertainty as its condition. Certainty is simply the limiting case of uncertainty.
Berkeley famously asked whether objects exist when unperceived.⁶ He resolved the issue by positing God as the ultimate perceiver. Yet this does not fully explain the function of the observer. Consciousness determines observations by extracting them from the flow of uncertainty. What is not observed remains indeterminate—not nonexistent, but uncertain.
Quantum mechanics literalizes this insight: existence beyond observation is not denied, but its mode of existence remains undetermined until measured.
Motion, Identity, and Wave–Particle Ambiguity
Consider concentric circles in motion. It becomes ambiguous whether you are moving through them or they are moving toward you. Observer and observed become identical. When observer and observation coincide, motion collapses into position.
Shift the circles laterally and they appear as waves. Observe the wave locally and it becomes a particle. As particle, it is observer; as wave, it is observation.
Whitehead captures this limitation succinctly: “When you see, you do not touch; when you touch, you do not see.”⁷ Sensation is multiplex. Each sense compensates for the blindness of the others, constructing a more complete phenomenon.
Beyond sensation, reason maintains certainty. Plato’s Forms—circle, line, number—are more certain than any sensory object.⁸ There may be no perfect circle in nature, but the circle as a rational form is more real than any approximate instance.
Irreversibility, Negation, and the Certainty of Uncertainty
The uncertainty principle entails irreversibility. A localized wave function spreads over time; uncertainty in position increases while momentum uncertainty remains constant. The product ΔxΔp increases irreversibly.⁹
Irreversibility is the quantity of uncertainty; uncertainty is the quality of irreversibility. Once a principle becomes certain, it cannot revert to uncertainty. Yet uncertainty is the very mechanism by which certainty arises. Negation precedes affirmation, as Descartes already recognized.¹⁰
As certainty accumulates, new uncertainties emerge. This dialectical escalation underlies refinement, self-conditioning, and progress. Whitehead notes that increasing complexity accelerates process rather than slowing it.¹¹ The universe speeds up not despite complexity, but because of it.
God, Negation, and Religious Dialectics
Berkeley’s God preserves objects during perceptual absence, but this treats God merely as a perceptual placeholder. Hegel goes further: God is dialectical—the negation of negation.¹²
Islam provides a striking account of negation. God is said to be the essence of all things, yet whenever God is described, God is “not that.” The Qur’anic identification of God with nūr (light) presents light as the plane of being itself.¹³ Yet God is ultimately beyond even this.
Light, in physics, approaches the limit of solidity: maximum speed, minimal mass. It is the bare quality of matter. Yet in Islam, God negates even light—escaping every determination.
Sunni Islam radicalizes this negation, refusing all ideal forms. The only “ideal” is nothingness, symbolized by the Kaaba—an empty center circled in ritual. Shia Islam, by contrast, fills negation with ideality, much like Christianity does through Christ. Ali becomes the ideal continuation of human potential.
This philosophical difference—not merely theological—helps explain divergent historical trajectories. Where ideality is denied absolutely, ethical and cultural determination stagnates.
Footnotes
- Newtonian optics; see also classical field theory.
- Alan Watts, The Way of Zen.
- Buddhist doctrine of anattā; cf. Nāgārjuna.
- Heisenberg, Physics and Philosophy.
- J. S. Bell, “On the Einstein Podolsky Rosen Paradox” (1964).
- George Berkeley, A Treatise Concerning the Principles of Human Knowledge.
- A. N. Whitehead, Process and Reality.
- Plato, Republic VI–VII.
- Standard quantum mechanics; Gaussian wave packet evolution.
- René Descartes, Meditations on First Philosophy.
- Whitehead, Adventures of Ideas.
- G. W. F. Hegel, Science of Logic.
- Qur’an 24:35 (Ayat an-Nur).
1. Short Clarification: Observer ≠ Human Subject
It is essential to distinguish the observer in this account from the human subject as a psychological individual. The observer is not a person, an ego, or a biological organism. Rather, the observer names the ontological principle of determination by which any relation becomes definite at all. Human consciousness is one localized manifestation of this principle, but the observer itself is not confined to human awareness. Measurement, decoherence, and determination occur wherever relations are actualized, whether or not a human subject is present. Thus, when quantum theory speaks of observation, it refers not to human perception but to the structural act by which indeterminacy becomes determinate within any physical system.
2. Integration into the Section on Wave Packets and Irreversibility
Wave packets make visible the ontological role of the observer as a principle rather than a subject. A wave packet represents a temporary localization of possibility—a region in which uncertainty is constrained but never eliminated. As the packet evolves, it spreads irreversibly, not because energy dissipates, but because undisclosed relations become entangled with the environment. This spreading reflects the fact that determination always leaves a remainder: an element that cannot be fully predicted or recovered.
Decoherence marks the point at which this remainder becomes structurally decisive. The system’s phase relations disperse into the surrounding field, rendering re-localization practically impossible. This irreversibility is not imposed from outside but arises from the internal logic of determination itself. Observation, in this sense, is the momentary stabilization of a relation within a broader field of uncertainty. The observer is therefore not external to the process but identical with the act by which uncertainty is partially resolved and simultaneously extended.
3. One-Paragraph Axiomatic Statement (Conclusion)
Axiom of Determination and Uncertainty:
All physical actuality arises through acts of determination that are inseparable from uncertainty. Every discrete or abrupt state—whether described as a quantum jump, collapse, or energy packet—expresses a temporary stabilization within a field of indeterminate relations. The observer is not a human subject but the ontological principle by which such stabilization occurs. Irreversibility follows necessarily, since determination disperses undisclosed relations into the environment, preventing complete recovery of prior states. Thus, physical law describes the behavior of these stabilizations, while metaphysics discloses their condition of possibility: a reality in which being is constituted through the continuous interplay of certainty and indeterminacy.
Below are clean, academically styled footnotes that correspond directly to the clarification of the observer, the wave-packet/irreversibility section, and the axiomatic conclusion.
Footnotes
- Observer as Ontological Principle
This distinction follows the line developed in A. N. Whitehead, Process and Reality, where “actual occasions” are not human observers but loci of determination in nature itself. See also Niels Bohr’s insistence that observation refers to conditions of definiteness, not subjective perception. - Wave Packets and Uncertainty
For the mathematical equivalence between localization and momentum spread, see any standard treatment of Fourier analysis in quantum mechanics; e.g., J. J. Sakurai, Modern Quantum Mechanics. The uncertainty principle is not an empirical limitation but a structural feature of quantum states. - Decoherence as Structural, Not Psychological
Decoherence theory formalizes how phase relations disperse into environmental degrees of freedom, yielding effective classicality without invoking consciousness. See H. Dieter Zeh, “On the Interpretation of Measurement in Quantum Theory,” and W. H. Zurek, “Decoherence and the Transition from Quantum to Classical.” - Irreversibility and Information Loss
Although the Schrödinger equation is time-reversal invariant, irreversibility arises from the practical impossibility of reconstructing phase correlations once they are distributed across many degrees of freedom. This parallels thermodynamic irreversibility; see Ludwig Boltzmann and, in the quantum context, von Neumann’s entropy. - Quantum ‘Collapse’ as Effective Description
The language of collapse is retained for phenomenological clarity, but strictly speaking it denotes an update of the state description relative to a determinate interaction. See J. von Neumann, Mathematical Foundations of Quantum Mechanics. - Observer ≠ Human Subject
This position avoids both psychologism and naïve realism and aligns with relational interpretations of quantum mechanics, including Carlo Rovelli’s relational QM, while remaining ontologically prior to any specific interpretation. - Irreversibility and Becoming
Whitehead explicitly links irreversibility to creativity and becoming rather than entropy alone; see Adventures of Ideas, where complexity accelerates process rather than retarding it. - Determination and Negation
The claim that determination proceeds through negation follows the classical dialectical tradition: Aristotle’s privation, Hegel’s negation of negation (Science of Logic), and the Buddhist logic of śūnyatā as articulated by Nāgārjuna. - Quantum Jumps and Discreteness
Discrete energy transitions were first formalized in atomic theory by Niels Bohr and later refined through quantum mechanics. Their abruptness reflects state transitions, not physical motion through intermediate states. - Axiomatic Status of Uncertainty
The framing of uncertainty as ontologically primary rather than epistemically secondary aligns with Heisenberg’s later philosophical writings, especially Physics and Philosophy, where uncertainty is treated as a condition of physical intelligibility.
last updated 12.19.2025