Emergent Causality from Decoherence: A Postulated Regime with an Explicit Conjecture
Eduardo Lorca
Abstract
Emergent Causality from Decoherence: A Postulated Regime with an Explicit Conjecture
An imaginary hypothesis, not a theory.
This is the third revision. It corrects the definition of causality, changes the parameter, acknowledges the circularity of time, and states the conjecture explicitly. It is still a hypothesis, not a theory.
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Abstract
This manuscript proposes that classical causality is not fundamental but emergent, arising from the degree of decoherence of a system. We define causality as definite causal order between events. We choose a decoherence parameter that is basis-dependent and dimension-independent: the interference suppression factor relative to the pointer basis. We postulate (not derive) that definite causal order emerges when this parameter exceeds a critical value. We acknowledge the circularity of time, the lack of a full mathematical derivation, and the absence of experimental confirmation. We add an explicit conjecture connecting the parameter to the process-matrix formalism of Oreshkov, Costa and Brukner. The hypothesis is offered as a framework for critique and development.
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1. Introduction
The nature of causality remains an open problem in physics. In quantum mechanics, there are correlations, not causes in the classical sense. In classical physics, causality is absolute and local. These descriptions do not obviously fit together.
This manuscript proposes that classical causality is not a fundamental property of the universe, but a property of the level of description. It emerges from the degree of decoherence of a system, in a manner analogous to how temperature emerges from the collective behaviour of many particles.
The hypothesis is labelled "imaginary" because it lacks full mathematical formalism, experimental confirmation, and a resolution of the circularity of time. It is offered as a framework for critique, not as a completed theory.
Scope: This hypothesis addresses only the transition between the quantum regime (no definite causal order) and the classical regime (definite causal order). It does not address the relativistic regime.
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2. Defining "Causality"
In this manuscript, "causality" means definite causal order between events. That is: for any two events A and B, either A precedes B, or B precedes A. Not intervention. Not deterministic evolution. Definite order.
This definition is chosen because it is the one that can be connected to the process-matrix formalism (Oreshkov et al., 2012), and because it is the one that emerges in the classical limit. Other definitions (interventionist causation, deterministic evolution) are distinct and are not addressed here.
This is a choice. Other definitions are possible. This choice is made for definiteness.
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3. The Parameter
The central parameter is the degree of decoherence, γ. We choose a specific measure: the interference suppression factor relative to the pointer basis.
This measure is:
• Basis-dependent. It is defined relative to the pointer basis selected by the environment.
• Dimension-independent. It is a ratio (a contrast), not an absolute quantity, so it ranges from 0 to 1 regardless of the dimension of the Hilbert space.
• Explicit about the cut. It requires specifying the system, the environment, and the pointer basis.
This measure is chosen over purity because purity has three defects: it depends on dimension, it is basis-independent, and it presupposes an unspecified system-environment cut. The interference suppression factor does not have these defects.
This is a choice. Other measures are possible. This choice is made for definiteness, not because it is uniquely correct.
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4. The Postulate (Not a Derivation)
With this parameter, we postulate that classical causality emerges when γ exceeds a critical value, γ_c. Below γ_c, the system is in a quantum regime: correlations without definite causal order. Above γ_c, the system is in a classical regime: definite causal order.
This is not a derivation from first principles. It is a postulate. But it is a postulate with a defined parameter. And it is a starting point.
The intermediate regime is not derived. It is postulated as a transition. And it is acknowledged that this placement is in tension with established physics: relativistic causal structure is a property of the spacetime metric, not of partial decoherence. This hypothesis does not address the relativistic regime. It addresses only the transition between the quantum regime (no definite causal order) and the classical regime (definite causal order).
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5. Co-Emergence (and the Circularity of Time)
This hypothesis proposes that causality and the arrow of time co-emerge from decoherence. Neither is prior. Neither is the cause of the other. They emerge together.
This is a conjecture, not a derivation. And it is acknowledged that this position is in tension with the literature: Oreshkov et al. (2012) suggest that the arrow of time produces causal order, not that they co-emerge. The difference is subtle but important: if the arrow of time is prior, then time is more fundamental than causality. If they co-emerge, neither is more fundamental.
The circularity of time is not resolved. Decoherence presupposes time. The arrow of time is traced to a low-entropy initial condition, not to decoherence itself. The hypothesis does not resolve this circularity. It assumes it.
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6. Confrontation with the Literature
The hypothesis is placed against the established literature. We do not confront as attacks, nor attempt to surpass. We use as anchors.
• Zurek (2003), "Decoherence, einselection, and the quantum origins of the classical," Rev. Mod. Phys. 75, 715. Zurek shows that decoherence selects a small set of stable states (pointer states) and that the combination of einselection with dynamics leads to the emergence of classical phase-space structure. This hypothesis assumes, as an additional premise, that classical dynamics is causal. This premise is not derived from Zurek. It is an independent claim, and it is the weakest point in the argumentative chain. If the premise is true, then causality emerges from decoherence. If it is false, the hypothesis fails.
• Gell-Mann and Hartle (1994, 2014), "Quasiclassical Realms in a Quantum Universe" (gr-qc/9404017) and "Adaptive Coarse Graining, Environment, Strong Decoherence, and Quasiclassical Realms" (arXiv:1312.7454). These works derive classical deterministic time-correlations and the fixed-past/open-future asymmetry from coarse-graining and strong decoherence, with no observer. The present hypothesis is close to this programme. It differs in framing the result as "emergent causality" rather than "quasiclassical realms." The substance is similar.
• Oreshkov, Costa, and Brukner (2012), "Quantum correlations with no causal order," Nature Communications 3, 1092. DOI: 10.1038/ncomms2076. This work constructs correlations with no definite causal order and shows that definite order is recovered in a classical limit. The present hypothesis is consistent with this, but does not engage with the formalism. A conjecture connecting the two is offered in Section 7.
• Page and Wootters (1983), "Evolution without evolution: Dynamics described by stationary observables," Phys. Rev. D 27, 2885. This work obtains time from entanglement with an internal clock. The present hypothesis does not address this. It assumes time as a parameter.
• Joos and Zeh (1985), "The emergence of classical properties through interaction with the environment," Z. Phys. B 59, 223. Foundational work on decoherence in open quantum systems.
• Rovelli (1996), "Relational quantum mechanics," Int. J. Theor. Phys. 35, 1637. Relational quantum mechanics holds that states are relational, not absolute. The present hypothesis extends this to causality: if states are relational, perhaps causal structure is too. But the extension is not derived. It is proposed.
• Schlosshauer (2005), "Decoherence, the measurement problem, and interpretations of quantum mechanics," Rev. Mod. Phys. 76, 1267. A review of decoherence and its interpretational implications.
• Allen, Barrett, Horsman, Lee, and Spekkens (2017), "Quantum Common Causes and Quantum Causal Models," Phys. Rev. X 7, 031021. This work defines interventionist causation in quantum mechanics. The present hypothesis uses a different definition (definite causal order), but acknowledges that other definitions are possible.
The honest assessment: The hypothesis is not new in its intuition. It is new in its emphasis on causality as the emergent property, and in its attempt to frame the quantum-classical transition as a causal transition. But the emphasis is not a theory, and the transition is not derived.
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7. Conjecture: Connection with the Process-Matrix Formalism
Oreshkov, Costa and Brukner (2012) have shown that, if one does not assume a global causal order, there exist quantum correlations that violate the causal inequality. These correlations are described by process matrices that are causally non-separable. In a classical limit, causal order emerges.
This hypothesis proposes, as a conjecture, that the causally non-separable process matrix could correspond to γ = 0 (no decoherence, no definite causal order). The causally separable process matrix could correspond to γ > γ_c (sufficient decoherence, emergent causal order). The quantum-to-classical transition mentioned by Oreshkov et al. could be the transition in γ.
This is a conjecture. It is not derived. There is no formalism that supports it. It is offered as a direction for future work: if someone with the appropriate mathematical tools wishes to attempt the connection, here is the intuition. And here is the criterion for success: if the connection is derived, the hypothesis gains. If it is not, it loses. Both outcomes are valuable.
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8. The Limits (and the Doors)
The hypothesis has several limits, acknowledged here:
1. The parameter is chosen, not derived. The interference suppression factor is one measure among many. Other measures would give different results.
2. Only one regime is postulated. The classical regime is postulated, not derived from first principles. The relativistic regime is not addressed.
3. The circularity of time is not resolved. Decoherence presupposes time. The hypothesis assumes it.
4. The literature is confronted, but not surpassed. The hypothesis shares its intuition with Zurek, Gell-Mann and Hartle, and others. It does not add formalism.
5. No experimental prediction is made. The hypothesis does not identify a falsifiable consequence. This is a significant weakness.
6. The conjecture is not derived. The connection with the process-matrix formalism is offered as a conjecture, not as a result.
7. The weakest point is the premise that classical dynamics is causal. This premise is not derived. It is an independent claim. If it fails, the hypothesis fails.
The doors (open questions):
• Why is there an environment?
• Why is there interaction?
• Why is there time?
• Why is there something rather than nothing?
• Why is there consciousness?
• Why is there causality?
These are not resolved here. They are left open.
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9. Conclusion
This manuscript proposes that classical causality is not fundamental but emergent, arising from the degree of decoherence of a system. It defines causality as definite causal order. It chooses a parameter that is basis-dependent and dimension-independent. It postulates (not derives) that definite causal order emerges when this parameter exceeds a critical value. It acknowledges the circularity of time, the lack of full mathematics, and the absence of experimental confirmation. It offers an explicit conjecture connecting the parameter to the process-matrix formalism.
It is not a theory. It is a hypothesis. It is offered as a framework for critique and development.
The next steps would be: to derive the classical regime from the parameter more rigorously; to resolve the circularity of time; to identify a falsifiable prediction; to engage with the formalism of Oreshkov et al.; and to read the three pillars (Zurek, Gell-Mann and Hartle, Oreshkov) in depth. These steps are not taken here. They are left for future work.
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The Label (Important)
This is an imaginary hypothesis, not a theory. It is coherent with what we know, but it is not demonstrated. It lacks full mathematics, predictions, and confirmation. It does not say that time does not exist. It says that classical causality could emerge. It does not say that the relativistic regime is explained. It says that the quantum-classical transition could be a causal transition. All of this, if one takes decoherence seriously, without adding anything else. But no one has demonstrated it. That is why it is a hypothesis, not a theory. And the weakest point is the premise that classical dynamics is causal. If that premise fails, the hypothesis fails.
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A Note on the Anchor
This hypothesis does not invent its premise. It takes it from established physics: quantum mechanics already treats information as correlation, not as substance. Entanglement is pure correlation. Decoherence is entanglement with the environment. If information is always relational, then causality could be relational too. But the extension is not derived. It is proposed.
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Related Work (with authors, years, and identifiers)
• Zurek, W. H. (2003). "Decoherence, einselection, and the quantum origins of the classical." Rev. Mod. Phys. 75, 715.
• Gell-Mann, M., and Hartle, J. B. (1994). "Quasiclassical Realms in a Quantum Universe." gr-qc/9404017.
• Gell-Mann, M., and Hartle, J. B. (2014). "Adaptive Coarse Graining, Environment, Strong Decoherence, and Quasiclassical Realms." arXiv:1312.7454.
• Page, D. N., and Wootters, W. K. (1983). "Evolution without evolution: Dynamics described by stationary observables." Phys. Rev. D 27, 2885.
• Oreshkov, O., Costa, F., and Brukner, Č. (2012). "Quantum correlations with no causal order." Nature Communications 3, 1092. DOI: 10.1038/ncomms2076.
• Joos, E., and Zeh, H. D. (1985). "The emergence of classical properties through interaction with the environment." Z. Phys. B 59, 223.
• Rovelli, C. (1996). "Relational quantum mechanics." Int. J. Theor. Phys. 35, 1637.
• Schlosshauer, M. (2005). "Decoherence, the measurement problem, and interpretations of quantum mechanics." Rev. Mod. Phys. 76, 1267.
• Allen, J.-M. A., Barrett, J., Horsman, D. C., Lee, C. M., and Spekkens, R. W. (2017). "Quantum Common Causes and Quantum Causal Models." Phys. Rev. X 7, 031021.