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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

A possible realization of Einstein’s causal theory underlying quantum mechanics

M. Yussouf

Published Nov 1, 1979• 4 citations
Publisher
DOI
10.1007/bf02908224

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According to the theory of relativity and causality, a special type of correlation beyond quantum mechanics is possible in principle under the name of a non-local box . The concept has been introduced from the principle of non-locality, which satisfies relativistic causality. In this paper, we show that a correlation leading to the non-local box can be derived consistently if we release one of major axioms in quantum mechanics, Born’s rule . This allows us to obtain a theory that in one end of the spectrum agrees with the classical probability and in the other end agrees with the theory of non-local causality. At the same time, we argue that the correlation lies in a space with special mathematical constraints such that a physical realization of the correlation through a probability measure is not possible in one direction of its limit, but is possible in the other limit.

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I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics. 1. Introduction 2. Newcomb’s Probleme 3. Causal Decision Theory 3.1 Regions of causal influence 3.2 Evidential and effective probabilities 4. The parallel with Bell’s theorem 4.1 Consequences of the analogy 4.1.1 The marble boxes game 4.1.2 Mechanism underlying the marble boxes game 4.1.3 The causalist’s decision 4.1.4 The Bell game 5. Communicated versus Non-communicated Predictions 6. Summary and Conclusion
We propose Stratified Causal Actualization (SCA), a generative framework in which physical reality is not presupposed as spacetime populated by matter, nor as probabilistic outcomes governed by dynamical laws, but as the irreversible actualization of causally constrained possibility. Beginning from primitive events and a causality relation devoid of geometry, time, or metric structure, we construct an ordinally stratified latent causal space encoding structured potentiality. We show that physics cannot be written directly on this space: realization requires an epistemic projection that discards internal causal structure while preserving distinguishability, yielding a realizability domain Ω. On Ω we derive admissibility, filtration, valuation, and variational actualization, closing the schema (Ω,A,⪯,ρ,TA,W,Φ,JA,D) governing consistent realization. A central result is the identification of a universal causal saturation invariant: the ratio of actual to maximal admissible causal restructuring. This invariant underlies the observed invariance of light propagation without presupposing spacetime geometry or kinematic postulates, and generates causal horizons as structural, rather than geometric, phenomena. Within this framework, time emerges as restriction depth, distance as constraint-mediated reachability, matter as stable restriction cores, and physical law as the fixed-point structure of permissible actualization. General relativity and quantum mechanics arise as complementary representational regimes encoding different projections of the same underlying causal stratification. SCA does not modify existing physical theories; it identifies the landscape from which their core structures necessarily arise.
According to the theory of relativity and causality, a special type of correlation beyond quantum mechanics is possible in principle under the name of a non-local box . The concept has been introduced from the principle of non-locality, which satisfies relativistic causality. In this paper, we show that a correlation leading to the non-local box can be derived consistently if we release one of major axioms in quantum mechanics, Born’s rule . This allows us to obtain a theory that in one end of the spectrum agrees with the classical probability and in the other end agrees with the theory of non-local causality. At the same time, we argue that the correlation lies in a space with special mathematical constraints such that a physical realization of the correlation through a probability measure is not possible in one direction of its limit, but is possible in the other limit.