When is a Statistical Theory Causal?

Balázs Gyenis, Miklós Rédei

Qiren Zhang

We show that the quantum world with non-local states and original statistics is statistically separable. According to relativistic dynamics, the super-luminal signal transmission is impossible. The present quantum theory is therefore consistent with the relativity and the causality.

Michael J. W. Hall

M. D. Srinivas

Relativistic quantum theory is formulated as a theory of successive local observations, consistent with all the fundamental requirements of relativistic invariance. Based on the causal structure of the space–time of special relativity, it is argued that the nonrelativistic notion of a ’’time-ordered sequence of instantaneous observations’’should be replaced in a relativistic theory by the notion of a ’’causally ordered sequence of local observations.’’ The fundamental statistical law of relativistic quantum theory is then formulated such that it provides an unambigous prescription for the statistical correlations between the outcomes of any causally ordered sequence of local observations. It is also shown that the fundamental statistical law of the theory is consistent with the so-called ’’principle of local causes’’ which essentially states that the probability connections between a set of local events do not depend on local observations carried out in space–time regions which lie outside of their causal past. Finally, an equivalent formulation of the theory in terms of a relativistically covariant generalization of the collapse postulate is presented.

H. S. Perlman

It is shown that quantum mechanics is, like thermodynamics, a phenomenological theory i.e., not a causal theory, ( not because it is a statistical theory - statistical theories with caused probability distributions can be regarded as causal) but because pure states, i.e., probability distributions of measurement values, cannot inhere in elementary particles and therefore cannot change when their world tubes intersect and hence they cannot be regarded as interacting causally. By a causal theory is meant a theory that specifies the changes in time of the states of causally interacting entities in its domain. The areas in quantum mechanics in which causal interactions are relevant include, though not explicitly, measurement and therefore the Born rule, and, explicitly, the unitary Schrodinger time development of states. The Born rule probabilities are shown to to refer not to conjoint superpositions of eigenstates but to classical mixtures of mutually exclusive eigenvalues and the Schrodinger time development of states is shown to refer to the time development of the states of non-causally interacting elementary particles and hence cannot be regarded as as a causal time development equation, appearances to the contrary notwithstanding. The recognition that quantum mechanics is not a causal theory but a phenomenological theory like thermodynamics does not affect the way it is employed to calculate an predict and hence preserves its empirical success but it does allow a typically simple phenomenological theory explanation of entanglement and other apparently non-local phenomena.

O. Costa de Beauregard