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How to reconcile modal interpretations of quantum mechanics with relativity

Joseph Berkovitz, Meir Hemmo

Published Jan 1, 2003• 2 citations
OpenAlex

Abstract

Modal interpretations 4 are hidden-variable, no-collapse (typically) indeterministic interpretations of quantum mechanics that were designed to solve the measurement problem and to reconcile quantum mechanics with relativity. But, as recent no-go theorems by Dickson and Clifton (1998), Arntzenius

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Modal interpretations are hidden-variable, no-collapse interpretations of quantum mechanics that were designed to solve the measurement problem and reconcile this theory with relativity. Yet, as no-go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonstrate, current modal interpretations are incompatible with relativity. In the mainstream modal interpretations, properties of composite systems are generally unrelated to the properties of their subsystems. We propose holistic and relational interpretations of properties to explain this failure of property composition. Based on these interpretations, we consider strategies for circumventing Myrvold's theorem, which are also effective against the other two theorems.

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The interpretation of measurements in quantum mechanics is still under discussion (Healey [84], Bell [9], Redhead [136]). Besides the Copenhagen interpretation we have the many-worlds interpretations (Everett interpretations), the modal interpretations, the decoherence interpretations, the interpretations in terms of (nonlocal) hidden variables, the quantum logical interpretations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
A number of arguments have been given to show that the modal interpretation of ordinary nonrelativistic quantum mechanics cannot be consistently extended to the relativistic setting. We find these arguments inconclusive. However, there is a prima facie reason to think that a tension exists between the modal interpretation and relativistic invariance; namely, the best candidate for a modal interpretation adapted to relativistic quantum field theory, a prescription due to Rob Clifton (2000), comes out trivial when applied to a number of systems of physical interest. However, it is far from clear whether this difficulty for the modal interpretation is traceable to relativistic invariance per se or to the infinite number of degrees of freedom involved. In any case, the proponents of the modal interpretation have work to do.
Modal interpretations are hidden-variable, no-collapse interpretations of quantum mechanics that were designed to solve the measurement problem and reconcile this theory with relativity. Yet, as no-go theorems by Dickson and Clifton (1998), Arntzenius (1998) and Myrvold (2002) demonstrate, current modal interpretations are incompatible with relativity. In the mainstream modal interpretations, properties of composite systems are generally unrelated to the properties of their subsystems. We propose holistic and relational interpretations of properties to explain this failure of property composition. Based on these interpretations, we consider strategies for circumventing Myrvold's theorem, which are also effective against the other two theorems.