Minimal Conditions for a Ground State

Article 3 in the series: In Search of the Foundations of Reality

Disclaimer. The ideas presented in these articles are speculative and have not been experimentally confirmed. They constitute a philosophical and ontological exploration of possible underlying structures of physical reality and are not intended as a replacement for experimentally validated physics. As far as can currently be assessed, the hypotheses described here are not in conflict with the experimentally confirmed results of established theories such as quantum mechanics and relativity. The central question is not how these theories might be replaced, but whether their descriptions could conceptually emerge from a more fundamental underlying structure.

1. Why ‘Nothing’ May Not Exist

The question at the heart of the previous article — why physical reality exists at all — calls for a different approach from that usually adopted in physics. Traditional physics begins with observable phenomena and describes them through mathematical models. This approach has proved extraordinarily successful, but it is concerned primarily with how reality behaves, rather than with the conditions under which reality can exist in the first place.

The question that has occupied me for many years is simple to state: how is it possible that anything exists at all? And if we imagine that there is still ‘nothing’, how could a physical reality emerge from it? Put differently: what would that ‘nothing’ have to be in order to make physical reality possible?

For that reason, these articles adopt a different perspective. Their focus is not on the phenomena themselves, but on the minimal conditions that a ground state must satisfy in order for physical reality to become possible. What is the simplest dynamic structure capable of meeting those conditions?

The concept of ‘nothing‘ is, however, misleading. Empty space — the vacuum — is already something: it possesses structure, fields exist within it, and fluctuations occur. In the first article I suggested that ‘nothing’ might perhaps be understood as a state possessing inherent potentiality. This article refines that idea. Strictly speaking, any state endowed with potentiality is already no longer ‘nothing’ — and it is precisely at that point that the present investigation begins.

By nothing I mean something far more radical: a limiting state without space, time, matter, structure or fields — a state in which no physical quantity has any meaning whatsoever. The question is whether such a state could itself be physically meaningful.

My answer is simply: no.

A state that is completely inert, without any form of dynamics or distinction, can by definition give rise to nothing. There is nothing that can change, nothing that can differ, and nothing from which structure might emerge. An absolute ‘nothing’ is therefore physically meaningless — not because experiment excludes it, but because nothing whatsoever can, even in principle, follow from it.

My working hypothesis is therefore that a workable ground state must necessarily possess the capacity for distinction and dynamic continuation. Without the capacity for distinction and dynamic continuation, no form of physical reality could ever arise.

This conclusion is fundamental to the argument developed here. Yet it has a further implication that deserves to be made explicit. One might imagine that absolute ‘nothingness’, although incapable of producing anything, could nevertheless occur somewhere or sometime — as an empty region or an empty interval.

It cannot, and for the following subtle reason.

Somewhere presupposes space, and sometime presupposes time — and space and time are already something. A state of nothingness is therefore not a state at all. Where there is nothing, there is no where; when there is nothing, there is no when. Absolute nothingness therefore not only occurs nowhere; it cannot occur at all. It is not one possible state alongside other states, but a self-excluding limiting concept.

This also reverses the positive conclusion. Here another linguistic trap appears. In an earlier article I wrote that “minimal dynamics exists everywhere and always”. That formulation quietly smuggles space and time back into the discussion. The relationship must instead be reversed.

The ground state does not exist within space and time. If this hypothesis is correct, space and time themselves emerge from the ground state. Every where and every when already presuppose it. The ground state therefore does not fill space and time; rather, space and time are emergent descriptions of that ground state.

Its universality is therefore not like air filling a room, but like the fabric of a carpet: there is no place within the carpet that is not made of fabric, because every place in the carpet is itself nothing other than fabric.

2. Three Starting Assumptions

2.1 The Laws of Nature Do Not Precede the Ground State — They Coincide with It

The first assumption is that the laws of nature must already be inherent in the ground state itself. The ground state cannot be regarded as something that precedes physical law, because those same laws determine what is physically possible.

Some laws may perhaps later emerge as higher-level regularities, but the ground state itself can only be defined through physical regularity.

This leads to an idea that plays a central role throughout these articles: the laws of nature and the ground state may not be two different things, but two descriptions of one and the same underlying reality. The law is then not something imposed upon the structure from the outside; the law is the structure.

This formulation has an important advantage. It avoids the infinite regress that otherwise immediately arises (“and where do the laws themselves come from?”).

Only one fundamental question remains: why this structure rather than another? And that is precisely the question to which modern physics, at least for the present, has no answer.

This identification also has a methodological consequence. When attempting to describe the ground state mathematically, we may use any consistent and generally valid mathematical structure, including relations found in harmony, symmetry, crystal formation and natural growth patterns. The field in which the mathematics was originally developed is not decisive; what matters is which assumptions it carries in the present application.

The chosen formulation must not presuppose properties that the model is intended to explain. Time or frequency, space or distance, mass or energy, temperature and other emergent physical quantities may therefore not be introduced implicitly into the fundamental equations. They must follow from the organization of the ground state. At this level, mathematics describes only abstract differences, relations, orderings and proportions.

2.2 Minimality: The Planck Scale as Grain, Not as a Grain Particle

The second assumption is that the search should begin with a minimal ground state. Anyone looking for the simplest physically meaningful structure is naturally led to the Planck scale (of the order of 10⁻³⁵ metres): the scale at which our current physical descriptions begin to lose their validity, and below which concepts such as distance, duration, location and motion are likely to lose their meaning.

From a philosophical perspective, this is a remarkable situation. It suggests that there exists a level below which not only our theories cease to be adequate, but at which it may no longer be meaningful to speak of physical reality in the ordinary sense of the term. Only from the Planck scale onwards does a world become conceivable in which space, time, matter and causal relationships can emerge.

One clarification is important. Within the present framework, the Planck scale should not be interpreted as the size of the fundamental elements themselves — as though the element introduced in the next article were itself a tiny building block measuring 10⁻³⁵ metres across.

If space is itself emergent, then the fundamental elements possess neither size, shape nor location. These are concepts that acquire meaning only at the emergent level. In this interpretation, the Planck length is not the diameter of a fundamental building block, but the grain of the emergent spatial description: the scale below which the very concept of length ceases to refer to anything physically meaningful.

2.3 No Ether — But What Is the Vacuum?

The third assumption arises from the historic debate between Lorentz and Einstein concerning the existence of an ether. That debate was ultimately resolved in Einstein’s favour, largely on the basis of the Michelson–Morley experiment (1887), which found no evidence whatsoever for the Earth’s motion through a light-carrying medium. The classical ether — a medium possessing a state of rest — therefore disappeared from physics, and rightly so.

Yet an important conceptual question remained. It is instructive to consider how Einstein himself addressed it. In his 1920 Leiden lecture, he argued that general relativity does indeed attribute physical properties to space, and that one may, if one wishes, refer to that structure as an ether — on one strict condition: no state of motion may be assigned to it. No state of rest, no velocity, and no possibility of being ‘at rest with respect to’ anything else.

Light exhibits unmistakable wave phenomena, including interference and diffraction. The question, therefore, is not whether a classical ether should somehow be reintroduced — that possibility has been ruled out experimentally — but whether the vacuum truly represents the absence of structure, or whether it reflects a deeper dynamical substratum.

I adopt Einstein’s condition as a strict design requirement. Whatever ground layer is proposed in these articles, it must possess no state of rest. How such a remarkable requirement might be satisfied will be the subject of the next article.

3. On the Limits of Language

Before attempting to formulate the ground state itself, a word of caution about language is appropriate. I touched upon this issue in the first article of this series, because it is precisely here that discussions about the foundations of reality almost invariably go astray.

At any ordinary level, the question “What is X?” always means: what is X made of, and how is it organised? Water consists of H₂O molecules arranged in a particular way; a proton is a bound state of a deeper underlying structure.

At the fundamental level, however, no further “made of” question is possible by definition — otherwise the level would not be fundamental. At that point the question “What is X?” changes its character. All that remains is how X, being itself the foundation, behaves and in what relationships it stands.

Ask a physicist today what the electromagnetic field is — not how it behaves, but what it actually is — and the answer will be either silence or a description of its behaviour.

That silence is not a deficiency. It reflects the present state of our knowledge at what is presently regarded as the most fundamental level of physics.

Whether the field truly constitutes the deepest level of reality, however, remains far from certain. For me, that is the challenge addressed by these articles: not to eliminate the silence — at the genuinely fundamental level it inevitably returns — but to investigate whether it currently resides one level too high.

Perhaps beneath the field there exists a simpler layer, and perhaps that is where the silence properly belongs.

For the purposes of this article, ordinary words such as state, fluctuation and counter must therefore be used for concepts they were never designed to describe. The solution is not to search for perfectly neutral words, because no such words exist. Rather, it is to define carefully how these terms are used within the present framework.

The following brief lexicon serves that purpose.

Ground state — the most elementary physically meaningful state considered in these articles. The next article explores how such a ground state might be modelled in concrete terms.

State — a point within a set of possible configurations. At the fundamental level, this is not the state of an object; the state and its relations constitute the complete description.

Fluctuation — a relational difference between neighbouring configurations. A fluctuation is not a process unfolding in a pre-existing time, but a distinction within the underlying structure itself.

Counter — a countable step within a sequence of state differences. A counter counts; it does not tick. It defines neither duration nor rate, but only order and number.

The next article proposes how a minimal dynamic unit might satisfy these definitions. That working hypothesis will be introduced under the name Nulcyclus.

4. Conclusion

This article does not claim to formulate a new physics. Its purpose has been to investigate the minimal conditions that a ground state must satisfy in order to make physical reality possible.

Its central conclusion is that a completely inert nothing cannot serve as a workable ground state. If a physical reality is possible, the ground state must at least allow for distinction, dynamics and physical regularity. What concrete form such a minimal ground state might ultimately take remains, for the time being, an open question.

The fundamental question that now presents itself is therefore this:

Can a world emerge from nothing more than relational differences — without pre-existing space and without pre-existing time — such that space, distance, duration and direction arise as emergent properties?

The articles that follow explore one possible way of answering that question. They investigate whether a minimal dynamic structure can satisfy the conditions derived here, and whether such a ground layer can also fulfil Einstein’s design requirement of possessing no state of rest.