The Relativity of Objectivity

Incompatible Universes, Empty Space, and the Virtual

Proposed insertion: arxe_1_core_theory_V3_en.md, as Section 12.6
Builds on: Section 12.1 (Undecidability as foundation), Section 3.5 (Phase ordering principle)
Date: March 2026
Note: This section requires careful reading. It is easy to confuse it with Platonism or spiritualism. The distinction is explicit and fundamental.

The starting point: objectivity is not absolute

The phase ordering principle establishes that the universe updates choices with a probabilistic distribution — without preferring any. For the case of time (T⁻¹, unconditioned binary choice), the distribution is 50/50: “acting as one” 50% of the time and “acting as the other” the remaining 50%.

That same choice, expressed as simultaneity, divides space in two.

The consequence is precise: objectivity is always relative to a specific axiomatic history. What is true here — what this T³ registers as fact — is true because this axiomatic history includes it. Not because it is true in an absolute sense.

There exists an axiomatic history perfectly inverse to this one: where what is true here is false there, and vice versa. That history is not “wrong” — it is coherent with itself. It is real to itself.

What this is NOT

Before developing the idea, it is necessary to point out two confusions that this concept naturally generates and that ArXe explicitly rejects.

It is not Platonism

Platonism proposes an ideal realm where all forms exist perfectly, and the physical world is an imperfect copy of that realm. The implication is that there is a reality that is “more real” — more true, more perfect — than physical reality.

ArXe says the opposite: there is no realm where all realities coexist. The absolute universe is not a container where each relative reality is a room. The absolute universe is simply the probabilistic distribution of all possible choices — none of which has absolute existence. They only have relative existence, within their own axiomatic history. There is no hierarchy among them.

It is not spiritualism

Spiritualism proposes that there is “another dimension,” “another plane,” “another time” that is more real, more true, or more fundamental than this one. It implies possible access or communication between those planes.

ArXe says: there is no ontological hierarchy between relative realities. This time is the only real time for this universe. An incompatible axiomatic history would be equally real for the universe that actualizes it — without superiority, without inferiority, and with no possible communication between them. They are incompatible, not complementary. There is no access between them because access requires both to be axiomatically compatible — which is precisely what they are not.

The precise formulation

The “absolute” universe actualizes all possible choices with their probabilistic distribution. But for each relative universe — each specific axiomatic history — the other relative universes do not exist.

It is not that they exist elsewhere. It is that the category “to exist” only makes sense within an axiomatic history. “To exist” in ArXe means: to be registrable by T³. And the T³ of this universe can only register what is compatible with its own axiomatic history. The incompatible does not fail to exist here — the question itself has no answer from here.

This relative universe:
  Axiomatic history H
  T³ registers everything compatible with H
  "Exists" = registrable by this T³

Inverse axiomatic history H':
  Real to itself — coherent, complete
  Not registrable by the T³ of H
  → From H, H' simply does not exist
  → It is not elsewhere — the question "where is H'?" has no answer from H

The cleanest formulation:

True time is unique: it is this one. Another time exists for another, not for this one. Another time does not exist in this one.

Empty space as relations that exclude us

There is a consequence of this structure that illuminates one of the most elusive concepts in physics: empty space.

The “void” between objects is not an absence of content. It is the presence of relations axiomatically incompatible with our history.

A wavelength cannot be seen “from the side” — it can only be detected if you are in its path. The space that separates us from a wave is not empty: it is full of the relation between that wave and the points along its trajectory. We are not part of that relation — we are axiomatically excluded from it.

Empty space between A and B:
  Is not T² without content
  Is T² with relations that are real for the systems on that trajectory
  but axiomatically incompatible with the system observing "from outside"

The observer does not see the void because it is empty.
They see it as empty because the relations that fill it exclude them.

This has consequences for quantum vacuum energy. “Vacuum fluctuations” — virtual pairs that appear and disappear — are not events occurring in the void: they are relations real to their own axiomatic histories, momentarily tangent to ours. They have measurable physical effects (Casimir corrections, zero-point energy) precisely because their axiomatic history is partially compatible with ours — not completely incompatible, but not completely compatible either.

The virtual is real for another

Virtual particles in quantum field theory have an ambiguous ontological status: they produce real physical effects (radiative corrections, Casimir effect) but cannot be directly observed without “collapsing” the calculation.

The ArXe reading: virtual particles are not “almost real” or “mathematically convenient.” They are structures with an axiomatic history partially compatible with ours.

Real particle (observable):
  Axiomatic history fully compatible with that of this T³
  T³ can register it → exists for this universe

Virtual particle:
  Axiomatic history tangent to ours — compatible in some respects
  T³ cannot register it completely without making other aspects incompatible
  → Does not fully exist here, but has effects because it is partially compatible
  → Is real for the axiomatic history that contains it completely

Antimatter particle:
  Axiomatic history compatible but with inverted ontological role (existent vs istent)
  Can interact with matter → partially compatible
  Annihilates on contact → annihilation is the moment where the two histories
  become completely incompatible and cannot coexist

Matter-antimatter annihilation is not destruction — it is the moment where two axiomatic histories that were partially compatible become completely incompatible. The result (photons, T⁻⁵) is what remains compatible with both histories simultaneously.

The non-locality of entanglement revisited

This section also illuminates quantum entanglement in a way that the previous document did not fully capture.

Two entangled particles share axiomatic history — their implications are co-present. When they are separated in space, the “space” between them is exactly the set of relations axiomatically incompatible with the shared correlation.

The correlation persists not despite the distance but independently of it: distance is a measure of incompatible relations, and incompatible relations are exactly what cannot interfere with the shared axiomatic correlation.

Physical distance between A and B:
  = set of relations axiomatically incompatible with A and B
  = what "separates" A from B in T²

Entanglement correlation between A and B:
  = shared axiomatic history in T⁻¹
  = pre-spatial → unaffected by incompatible relations in T²

Distance cannot destroy the correlation
because the correlation lives at the level that constitutes space,
and space is exactly the structure of incompatibilities.

Why relative objectivity does not lead to relativism

A natural objection: if objectivity is relative to an axiomatic history, does that not mean that “everything is relative” and there are no firm truths?

No. The relativity of objectivity in ArXe is structural, not epistemological.

Within a specific axiomatic history, truths are absolutely necessary — they are conditional implications that cannot be denied without contradiction. “If mass exists, space necessarily exists” is necessarily true within any axiomatic history that contains mass. It is neither relative nor subjective.

What is relative is which axiomatic history is actualized — and that occurs at the level of T⁰, prior to any truth. Once an axiomatic history is being actualized, the truths within it are as firm as any necessary truth.

Epistemological relativism: "Truth depends on the observer"
  → ArXe rejects this

Structural relativity of objectivity:
  "Objectivity depends on which axiomatic history is actualized"
  "Within that history, truths are necessary and unconditional"
  → This is what ArXe proposes

The difference is crucial: relativism dissolves necessity. ArXe’s structural relativity preserves it — but locates it correctly within the axiomatic history that generates it.

Summary

Concept	Incorrect formulation	ArXe formulation
Other realities	“They exist in another place/dimension”	“They are real to themselves, not registrable from here”
Empty space	“Absence of content”	“Presence of axiomatically incompatible relations”
Virtual particles	“Almost real” or “mathematical fiction”	“Real for their axiomatic history, partially compatible with ours”
Objectivity	“Absolute and observer-independent”	“Necessary within an axiomatic history, relative between histories”
Relativism	“Everything depends on the observer”	“Rejected: within a history, truths are necessary”

The central statement:

True time is unique: it is this one. Another time exists for another, not for this one. Another time does not exist in this one. And that non-existence is not a limitation of this universe — it is the condition of possibility for this universe to have a coherent axiomatic history.