Article 4 — In Search of the Foundations of Reality
Disclaimer.
The ideas presented in this series of articles are speculative and have not been experimentally confirmed. They constitute a philosophical and ontological exploration of possible underlying structures of physical reality rather than a replacement for experimentally established physics. As far as can presently be determined, the hypotheses developed here do not conflict with the experimentally confirmed results of theories such as quantum mechanics and relativity. The central question is therefore not how these theories might be replaced, but whether their descriptions could conceptually emerge from a more fundamental underlying structure.
1. Introduction
In the previous article, we concluded that a completely inert state cannot give rise to physical reality. Since reality exists, the most fundamental ground state must therefore possess at least a minimal form of dynamics.
This immediately raises a new question: what might such a minimal dynamic ground state look like? What kind of dynamics would it involve, and between what would this dynamics take place?
This is not primarily an experimental question but a design question. Just as an engineer first establishes the requirements that a successful design must satisfy, I begin by deriving the minimal properties that any candidate for a fundamental ground state should possess. The concepts used throughout this article—state, fluctuation, and counter—are employed in exactly the sense established in the previous article.
2. The Design Requirements
Three fundamental design principles emerge from the previous article.
First, the laws of physics and the ground state cannot meaningfully be regarded as separate. The ground state cannot be conceived as something preceding the laws of nature, because those very laws determine what is physically possible. It may ultimately prove that the laws of nature and the ground state are simply two different descriptions of the same underlying principle.
Second, we seek the simplest physically meaningful structure conceivable. The obvious place to begin is the boundary region associated in modern physics with the Planck scale—the scale at which our familiar notions of space, time, distance and motion are generally believed to lose their classical meaning. The Nulcyclus, however, is not regarded as a tiny particle of Planck-length dimensions. If space itself emerges only at a later stage, then the ground state cannot yet possess size, shape or location.
Third, the ground state must not introduce an absolute state of rest or any preferred frame of reference. This is not merely desirable but a fundamental design constraint, following directly from Einstein’s discussion in his 1920 Leiden Address: no physical ground layer may be assigned a state of motion—neither rest nor velocity nor “standing still relative to”. The ground state must therefore be formulated in such a way that rest and motion are themselves not yet meaningful concepts, thereby remaining compatible with Lorentz invariance.
The design problem can now be formulated precisely: Can one conceive of the simplest possible dynamic structure that simultaneously satisfies all three conditions?
The Nulcyclus is proposed here as a candidate. I shall argue that the third requirement—the absence of any possible state of rest—turns out to determine surprisingly much of its eventual form.
3. Neutral — Yet Dynamic
The structure we seek must not yet presuppose space, time, particles, fields, mass, charge or matter. These are precisely the phenomena that should ultimately emerge from the ground state. We therefore seek not the smallest possible object, but the simplest possible dynamic relationship.
Two requirements immediately present themselves, and they appear to be in tension. On the one hand, the ground state must possess no permanent preference. Were it permanently “positive”, “left-handed” or “forward”, reality would already contain an intrinsic asymmetry at its deepest level. Taken as a whole, the ground state must therefore remain completely neutral.
On the other hand, neutrality alone is insufficient. A perfectly static equilibrium would once again be entirely inert—and it was precisely complete inertia that the previous article ruled out. The desired ground state must therefore be simultaneously neutral and permanently dynamic.
The central question of this article is therefore straightforward: Does there exist a structure capable of satisfying these two requirements simultaneously, rather than sequentially?
4. Complementarity — and Why Not a Continuous Phase?
The simplest way of combining neutrality and dynamics appears to be a structure consisting of complementary states that continuously transform into one another. The word continuously should be understood here exactly as defined in the previous article: it does not denote evolution in an already existing time, but rather an ordering—a point to which I shall return in Section 6.
One may think—purely as illustrations—of positive and negative, or phase and counter-phase. At the fundamental level these examples do not yet possess their familiar physical meaning. What matters is their logical form: distinct states that together introduce no lasting preference and that do not coexist statically but continually transform into one another. In this way, uninterrupted change exists without any permanent net difference.
At this point an obvious objection arises, one that should not be avoided because it touches the heart of the proposal. Physics already possesses a structure that is both neutral and permanently dynamic without consisting of two discrete states: phase. A quantity of the form e−iωt rotates continuously, remains neutral over a complete cycle, and lies at the very heart of quantum mechanics.
Why, then, postulate a discrete complementarity of two poles instead of adopting a continuous phase rotation, which appears both simpler and already ubiquitous throughout physics?
My answer is not that continuous phase is incorrect, but that it already assumes too much in order to serve as a genuine ground state. A continuous phase necessarily contains a frequency ω, and frequency is a rate—a number of cycles per unit time. It therefore presupposes metric time, precisely what is not yet available at this level.
Moreover, frequency is not Lorentz invariant. Assigning a fixed frequency to the ground state implicitly selects a preferred reference frame and therefore violates the third design requirement. Continuous phase is therefore not more fundamental than the Nulcyclus; it is richer. It already contains the metric time and frame structure that we seek to explain as emergent. Discrete complementarity requires less. It requires only distinction—two complementary states—and transition between them: ordering rather than rate.
I shall return to this distinction in Section 6. For the moment it is sufficient to observe that continuous phase, attractive though it may be, already assumes more structure than is appropriate at the level of the ground state.
The Nulcyclus should therefore be understood as a pre-geometric precursor from which something resembling phase might eventually emerge, rather than as a cumbersome reformulation of phase itself. The repeated appearance of complementary quantities throughout established physics—positive and negative charge, matter and antimatter, phase and counter-phase—does not prove the model. It merely suggests that complementarity itself may represent a fundamental organising principle.
5. The Nulcyclus: The Postulate
I call this minimal dynamic structure the Nulcyclus. “Nul” refers to the net neutrality of the whole. “Cyclus” refers to the closed structure of transition within which the complementary states continually transform into one another. The term does not refer to a process unfolding in ordinary time.
One clarification concerning neutrality is essential, because it answers an obvious objection. One might argue that if the state is continually changing, then it is never truly neutral but always “on its way” from one pole to the other. This objection assumes that the cycle can be divided into separate moments. It cannot.
The Nulcyclus is indivisible. There exists no “moment within it” at which it would occupy some intermediate position, because the very notion of “halfway” would already presuppose an internal time axis.
Neutrality is therefore not a property of instantaneous cross-sections—there are none—but of the cycle taken as an indivisible whole. Precisely because the Nulcyclus is indivisible, net neutrality becomes the only meaningful statement that can be made about it. The postulate may therefore be stated as follows:
The most elementary state of reality is conceived as a Nulcyclic complementarity: an indivisible unity of complementary poles and their continual mutual transition. Taken as a whole, this state remains net neutral; as dynamics, it constitutes a possible origin of further organisation. Within this model, Nulcyclic complementarity is regarded as a primitive concept and is not reduced to anything more fundamental.
The postulate deliberately contains only the minimum. It says nothing about space, time, light, matter, mass, charge or fields. It merely proposes that the simplest physically meaningful ground state is not static substance but permanent complementary dynamics without net preference.
The transition between the poles is not caused by an external law acting upon the Nulcyclus. The rule of transition belongs to the postulate itself. The existence of the Nulcyclus and its dynamics are therefore one and the same: it is not a static entity to which motion is subsequently added.
6. Order Without Rate
Throughout this article I have spoken of a continuous transition and of a cycle, while deliberately avoiding any assumption of time. This requires clarification, for it is here that the most subtle step in the entire proposal is found.
In the previous article I distinguished between two concepts that everyday language tends to conflate: a counter counts, but it does not tick. Counting establishes order and succession—a first, a second, a next—without thereby introducing duration or rate.
It is precisely this distinction that is employed here. The transition between the complementary poles establishes an ordering: pole – weakening/strengthening – opposite pole – weakening/strengthening – pole, in succession. It does not establish a frequency, because there is as yet no measure against which a “number of transitions per unit time” could be defined.
In this sense the Nulcyclus is ordinal rather than metric. This is more than a matter of terminology; it is precisely what makes the Nulcyclus compatible with the third design requirement.
A structure without rate possesses no frequency, and without frequency there is nothing that could change under a Lorentz transformation. Consequently, no preferred frame of reference can arise. Metric time—duration, rate and frequency—is therefore not an intrinsic property of the Nulcyclus itself. It belongs to a later, emergent level of organisation, where the collective ordering of many Nulcyclic units may eventually give rise to something that can meaningfully be described as temporal rate.
How that emergence occurs lies beyond the scope of the present article. The only claim made here is that the Nulcyclus itself does not already smuggle metric time into the theory.
7. A Closed Cycle Without a State of Rest
Why should the proposed structure take the form of a closed cycle rather than an open process? An open process would tend towards an end state or accumulate a lasting preference. In either case the required neutrality would be lost.
A closed structure, by contrast, keeps the transition entirely within its own complementary state space, allowing permanent dynamics and net neutrality to coexist. There is, however, a deeper and more elegant reason, one that follows directly from the third design requirement.
Einstein’s condition was that the fundamental layer of reality must possess no state of rest. A closed cycle is precisely such a structure. By its very nature it never comes to a halt. There exists no state in which the transition ceases, no pole that permanently dominates, and therefore no state of rest relative to which motion could be defined.
Where an open process might eventually reach an endpoint—and thus a state of rest—a closed cycle excludes this possibility in principle. Its cyclic form is therefore not merely compatible with Einstein’s requirement; it represents its natural embodiment.
What appeared in the previous article as an almost paradoxical demand—a fundamental layer that neither rests nor moves—finds in the Nulcyclus a concrete conceptual expression.
8. Dimensionless: The Planck Scale as Boundary, Not Measure
The Nulcyclus should not be interpreted as the smallest unit of matter. Matter does not yet exist at this level. It is better understood as a dimensionless and matterless unit of dynamic possibility.
Concepts such as direction, perpendicularity, electric charge and magnetic field presuppose structures that acquire meaning only at higher emergent levels. The hypothesis is more subtle than that.
The Nulcyclus contains only a minimal relational dynamics from which increasingly complex physical relationships may emerge. Nor does the Nulcyclus possess an intrinsic length scale. The Planck scale (of the order of 10^{-35} metres) is therefore not interpreted as its physical size. Rather, it is regarded as the possible boundary at which the first physically meaningful spatial organisation emerges. Conceptually, the Nulcyclus precedes all such spatial descriptions.
9. Why Not Something Even Simpler?
One might ask whether the ground state could be even simpler than two complementary states. The only apparent alternative would be a single unchanging state. Yet such a state would be completely static and therefore incapable of generating dynamics. At a minimum, distinction and transition must both be possible.
The claim that two complementary states are sufficient—and that no more are required—is not presented as a proof but as a postulate. As discussed in Section 4, the apparently simpler alternative of continuous phase is, in fact, conceptually richer rather than simpler, because it already presupposes the metric time that this model seeks to derive.
Whether an even more fundamental structure satisfying the same design requirements exists remains an open question. The Nulcyclus is therefore not presented as a demonstrated final answer, but as the simplest candidate presently available within this conceptual approach.
10. Evaluation and Its Place Within the Series
Like any fundamental postulate, the Nulcyclus must ultimately be judged on three levels: its conceptual consistency; the possibility of a coherent mathematical formulation; and its physical fruitfulness.
For this reason the exact mathematical representation is intentionally left open in the present article. One must first understand what is being postulated before deciding how it should best be represented mathematically.
Future work must demonstrate whether the Nulcyclus can indeed be described in a mathematically consistent manner and whether known physical structures can emerge naturally from it at higher levels of organisation. Only then could it be regarded as a serious candidate for a fundamental ground state.
It is useful at this point to relate the Nulcyclus back to the earlier articles in the series. In the first article I introduced the notion of an ordering principle—an inherent possibility of distinction and coherence preceding matter itself. The Nulcyclus represents an attempt to give that still abstract concept a concrete physical form—not as a supernatural ordering principle, but as a single minimal dynamical structure.
In that sense this article forms the pivot of the series: the point where the philosophical questions raised in Articles 1 and 2 and the design requirements developed in Article 3 converge into one specific proposal capable of further examination.
The model is therefore methodologically naturalistic. It investigates whether the richness of physical reality may be derived from a single universal, dimensionless dynamic principle. Questions concerning the deeper origin or ultimate meaning of that principle lie beyond the scope of the present theory and remain open to philosophical or religious interpretation.
11. The Next Step
The Nulcyclus does not yet constitute space, time, light or matter. It introduces only one fundamental ingredient: permanent dynamics without net content.
The next question therefore becomes how such dynamics may organise themselves and how stable patterns, propagation and eventually physical structure might emerge from them. Without anticipating the detailed development, the direction of the investigation can already be indicated.
One may explore whether the two complementary poles can eventually be interpreted as the positive and negative amplitudes of an emergent field, whether the cyclic transition may develop into something resembling phase, and whether couplings between neighbouring Nulcyclic units could provide the first seed of propagation—and ultimately wave behaviour.
These are emphatically not presented here as results. They merely indicate the kind of conceptual bridge that the subsequent articles will attempt to construct. Whether one may ultimately conclude that Nulcycli indeed exist and couple to one another remains an open question. At the present stage, that conclusion would be premature.
The subject of the next article will therefore be the Nulveld (literally ‘zero-field’) : the dynamic ground layer from which progressively richer forms of physical organisation may emerge.
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