CPT22 — An Axiomatic Theory of Time and Emergent Spacetime
Is spacetime a fundamental structure of the Universe, or could geometry, matter and the laws of physics emerge from a more fundamental structure of time?
CPT22 is an author-proposed physical theory developing the concept of CTA (Coexisting Time Arrows). Its fundamental assumption is the primacy of time and the emergent nature of space and spacetime geometry.
The theory assumes the coexistence of two oppositely oriented temporal sectors, denoted τ⁺ and τ⁻. They are not separate Universes, but coexisting structures within a single physical reality.
CPT22 proposes both an ontological interpretation and a mathematical formalism for investigating whether Lorentzian geometry, gravitational interactions and other physical phenomena can arise from this structure.
1. Fundamental assumptions of CPT22
The theory rests on five main postulates:
- One Universe — a single shared physical reality exists, governed by the same fundamental laws.
- The primacy of time — time exists fundamentally and eternally; its existence does not require a single initial event.
- Two opposite arrows of time — two temporal sectors with opposite orientations, τ⁺ and τ⁻, coexist.
- Emergent geometry — the spacetime metric is not a primary structure, but arises from local configurations of temporal fields.
- Restricted interactions between sectors — the theory postulates gravitational interactions and possible weak couplings, with no direct electromagnetic or strong couplings between the sectors.
These are ontological and physical assumptions. Accepting them makes it possible to construct a mathematical model, but does not in itself prove that the Universe actually has this structure.
2. The central mathematical result — emergent geometry
One of CPT22’s key results is an investigation of the possibility of constructing a spacetime metric without treating it as an independent, fundamental object.
The original model used a single pair of scalar temporal fields. Mathematical analysis showed, however, that a metric tensor formed from the gradients of one such pair has rank no greater than two.
This means that one pair of temporal fields is insufficient to construct a nondegenerate four-dimensional spacetime.
In response, CPT22 introduces a multimode construction. The two fundamental temporal sectors are represented by multiple pairs of scalar fields, whose local gradients jointly determine the metric tensor.
The following results were obtained within this construction:
- At least three pairs of temporal modes are needed to reproduce a four-dimensional Lorentzian metric with signature (−+++).
- Three pairs are sufficient for an explicit construction of the Minkowski metric describing the flat spacetime of special relativity.
- The construction has a geometric interpretation as an induced metric in an auxiliary six-dimensional space with signature (3,3).
- Variation of temporal fields need not imply spacetime curvature. Curvature requires a separate analysis of the induced geometry.
This result demonstrates the mathematical possibility of obtaining flat Lorentzian geometry from temporal-field configurations without introducing the metric as an independent fundamental variable.
It does not yet prove that physical spacetime actually emerges from time. Nor does it independently derive the existence of three spatial dimensions: the four-dimensional spacetime signature is an assumption of the construction being analysed.
3. From geometry to gravity
CPT22 investigates the possibility of connecting geometry induced by temporal fields with gravitational dynamics.
To this end, it introduces an action containing an Einstein–Hilbert term and components dependent on the temporal fields.
An important feature of the model is that the metric tensor is not an independent variable. It depends on field configurations, so the equations of motion must account for that dependence.
This leads to an important distinction: the presence of an Einstein–Hilbert term in the action does not automatically imply recovery of all the equations of general relativity.
CPT22 offers a proposal for the dynamics of emergent geometry, but full agreement with general relativity remains an open mathematical and physical problem.
In particular, it is necessary to demonstrate the existence of suitable curved solutions, investigate their stability and test their agreement with gravitational observations.
4. Two temporal sectors, matter and antimatter
One of CPT22’s hypotheses concerns a connection between opposite temporal orientations and physical symmetries, particularly CPT transformations.
In this approach, matter and antimatter could be considered manifestations of deeper relationships between temporal structures.
The model also investigates the possibility of interpreting elementary particles as local oscillatory or topological configurations of temporal fields.
This hypothesis opens a direction of research into the origins of mass, electric charge and other particle properties.
It has not yet been demonstrated, however, that the assumed axioms imply specific Standard Model particles, their masses, charges or observed gauge symmetries.
5. Dark matter as a possible effect of the second temporal sector
CPT22 proposes an alternative interpretation of phenomena attributed to dark matter.
According to this hypothesis, some observed gravitational effects could originate from structures associated with the oppositely oriented temporal sector.
The model assumes that this sector has no direct electromagnetic coupling to observed matter, which could explain its electromagnetic invisibility.
Such an interpretation nevertheless requires a quantitative account of observed phenomena, including:
- galactic rotation curves;
- gravitational lensing;
- galaxy-cluster dynamics;
- cosmic microwave background anisotropies;
- the formation of the large-scale structure of the Universe.
CPT22 presents a hypothesis about the nature of dark matter, but does not yet constitute a quantitatively validated alternative to current cosmological models.
6. Dark energy, expansion and the beginning of the Universe
Assuming fundamental and eternal time makes it possible to consider cosmologies in which time does not begin with the Big Bang.
CPT22 examines the hypothesis that observed cosmic acceleration and some phenomena interpreted as spatial expansion could have a deeper origin in temporal geometry.
This opens the possibility of investigating cosmological models without a fundamental initial singularity and without the need to postulate an independent substance responsible for dark energy.
It does not mean, however, that standard cosmological expansion or the Big Bang model has been disproved.
For such an alternative to be physically credible, it must reproduce observed distance–redshift relations, the cosmic microwave background, the history of structure formation and other cosmological measurements.
7. Possible implications for quantum physics
CPT22 considers the possibility of a quantum description of temporal fields, including the introduction of field operators and their conjugate momenta.
One research direction is to investigate whether appropriately constructed field configurations could lead to behaviour resembling quantum phenomena and to stable structures interpreted as particles.
At present, however, neither full quantum mechanics nor the Standard Model has been derived from the CTA axioms.
Questions of quantisation, solution stability, interactions and agreement with experiments remain open.
8. Predictions and the possibility of verification
CPT22 identifies directions in which observational differences between CTA and standard theories might be sought.
These include:
- measurements of cosmological redshift drift;
- the history of cosmic structure growth;
- observations of dark matter and gravitational lensing;
- properties of gravitational waves;
- tests of fundamental symmetries and possible couplings between sectors.
Scenarios under consideration, such as zero redshift drift or a different structure-growth index, are currently conditional hypotheses rather than quantitative predictions derived from a complete solution of the CTA equations.
Developing such predictions is one of the most important next stages of research.
9. The significance of CPT22
CPT22’s most important feature is its attempt to reverse the traditional ontological order of physics.
Rather than assuming spacetime as a primary structure, the theory considers the possibility that geometry is a consequence of more fundamental temporal relationships.
The new multimode construction gives this idea a concrete mathematical form.
It has been shown that three pairs of appropriately configured temporal fields are sufficient to obtain the Minkowski metric, while a single pair is insufficient to construct a nondegenerate four-dimensional metric.
This is a result concerning a particular mathematical formalism, not a proof of the physical truth of the entire theory.
The other proposals — concerning gravity, dark matter, cosmology, matter and quantum physics — constitute a programme for further research.
10. Final conclusions
CPT22 is an axiomatic research proposal in which two oppositely oriented temporal sectors are postulated as the foundation of physical reality.
Its most important mathematical result is the construction of flat four-dimensional Lorentzian geometry from three pairs of temporal modes.
This result shows that a spacetime metric can be constructed mathematically from temporal fields, without treating it as an independent fundamental object.
It does not yet prove that such a construction describes the actual Universe.
Further development of CPT22 requires the derivation of consistent dynamics, obtaining curved solutions, connecting the model to observed particle physics and developing quantitative cosmological tests.
CPT22’s fundamental question remains open:
Does time exist in space, or is space one of the possible manifestations of the structure of time?