Abstract
The distinction between a theory’s kinematics and its dynamics, that is, between the space of physical states it posits and its law of evolution, is central to the conceptual framework of many physicists. A change to the kinematics of a theory, however, can be compensated by a change to its dynamics without empirical consequence, which strongly suggests that these features of the theory, considered separately, cannot have physical significance. It must therefore be concluded (with apologies to Minkowski) that henceforth kinematics by itself, and dynamics by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. The notion of causal structure seems to provide a good characterization of this union.
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Notes
- 1.
It is analogous to the fact that one can simulate indeterministic dynamics on a system by deterministic dynamics which couples the system to an additional degree of freedom that is probabilistically distributed.
- 2.
A collapse theorist will no doubt reject this explanation on the grounds that one cannot solve the quantum measurement problem while maintaining unitarity. Nonetheless, our argument shows that someone who does not share their views on the quantum measurement problem need not be persuaded of a failure of unitarity.
- 3.
The assumption has also been called separability [19].
- 4.
Upon learning this terminology, a former student, Chris Granade, proposed that the defining feature of these types of model—that the ontic state encodes the quantum state—should be called “\(\psi \)-ontology”. I and other critics of \(\psi \)-ontic approaches have since taken every opportunity to score cheap rhetorical points against the \(\psi \)-ontologists.
- 5.
Norsen has proposed a slightly more credible model but only as a proof of principle that kinematical locality can indeed be achieved [20].
- 6.
This analysis also suggests that the concepts of space and time, which are primitive within the paradigm of kinematics and dynamics, ought to be considered as secondary concepts that are ultimately defined in terms of cause-effect relations. Whereas in the old paradigm, one would consider it to be part of the definition of a cause-effect relation that the cause should be temporally prior to the effect, in the new paradigm, what it means for one event to be temporally prior to another is that the first could be a cause of the second.
- 7.
There is a subtlety here: it follows from the form of the causal graph in the Newtonian model that \(Q_{1}\) and \(Q_{4}\) are conditionally independent given \(Q_{2}\) and \(Q_{3}\), but in the Hamiltonian case, this fact must be inferred from the causal-statistical parameters.
References
F. Dowker. Causal sets and the deep structure of spacetime, ed. by A. Ashtekar. 100 Years of Relativity, Space-Time Structure: Einstein and Beyond, pp. 445–464 (2005).
C. Rovelli. Loop quantum gravity. Living Rev. Relativ. 11 (2008).
D. Bohm, A suggested interpretation of the quantum theory in terms of “hidden” variables I. Phys. Rev. 85(2), 166 (1952).
S. Goldstein. Bohmian mechanics. The Stanford Encyclopedia of Philosophy (Fall 2012 edn.).
J.S. Bell, Beables for quantum field theory. Phys. Rep. 137, 49–54 (1986).
H. Everett, III., “Relative state” formulation of quantum mechanics. Rev. Mod. Phys. 29(3), 454 (1957).
G.C. Ghirardi, A. Rimini, T. Weber, Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D 34(2), 470 (1986).
G.C. Ghirardi, P. Pearle, A. Rimini, Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles. Phys. Rev. A 42(1), 78 (1990).
S. Weinberg, Testing quantum mechanics. Ann. Phys. 194(2), 336–386 (1989).
N. Gisin, Weinberg’s non-linear quantum mechanics and supraluminal communications. Phys. Lett. A 143(1), 1–2 (1990).
A. Peres, Nonlinear variants of Schrödinger’s equation violate the second law of thermodynamics. Phys. Rev. Lett. 63(10), 1114 (1989).
W.F. Stinespring, Positive functions on C*-algebras. Proceedings of the American Mathematical Society 6, 211–216 (1955).
D. Bohm, R. Schiller, J. Tiomno, A causal interpretation of the Pauli equation (A). Il Nuovo Cimento 1, 48–66 (1955).
J.S. Bell, On the impossible pilot wave. Found. Phys. 12(10), 989–999 (1982).
D. Bohm, A suggested interpretation of the quantum theory in terms of “hidden” variables II. Phys. Rev. 85(2), 180 (1952).
S. Colin, A deterministic Bell model. Phys. Lett. A 317(5), 349–358 (2003).
W. Struyve, H. Westman, A minimalist pilot-wave model for quantum electrodynamics. Proc. R. Soc. A: Math. Phys. Eng. Sci. 463, 3115–3129 (2007).
R.W. Spekkens, Contextuality for preparations, transformations, and unsharp measurements. Phys. Rev. A 71(5), 052108 (2005).
N. Harrigan, R.W. Spekkens, Einstein, incompleteness, and the epistemic view of quantum states. Found. Phys. 40(2), 125–157 (2010).
T. Norsen, The theory of (exclusively) local beables. Found. Phys. 40(12), 1858–1884 (2010).
P. Spirtes, C.N. Glymour, R. Scheines, Causation, Prediction, and Search, 2nd edn. (The MIT Press, 2001).
J. Pearl, Causality: Models, Reasoning, and Inference, 2nd edn. (Cambridge University Press, 2009).
J.S. Bell, The theory of local beables. Epistemo. Lett. 9, 11–24 (1976).
J.S. Bell, Bertlmann’s socks and the nature of reality. Le J. de Phys. Colloq. 42(C2), 41–61 (1981).
M.S. Leifer, Quantum dynamics as an analog of conditional probability. Phys. Rev. A 74(4), (2006).
M.S. Leifer, R.W. Spekkens, Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference. Phys. Rev. A 88(5), 052130 (2013).
Acknowledgments
My thanks to Howard Wiseman and Travis Norsen for valuable discussions, especially those on the subject of kinematical locality. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
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Spekkens, R.W. (2015). The Paradigm of Kinematics and Dynamics Must Yield to Causal Structure. In: Aguirre, A., Foster, B., Merali, Z. (eds) Questioning the Foundations of Physics. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-13045-3_2
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