Are superluminal connections necessary?

Abstract

The following theorem is proved: If the statistical predictions of quantum theory are true in general and if the macroscopic world is not radically different from what is observed, then what happens macroscopically in one space-time region must in some cases depend on variables that are controlled by experimenters in far-away, space-like-separated regions. By what happens macroscopically in one space-time region is meant specifically the occurrence or nonoccurrence of a macroscopic event, such as the detection and recording of a particle by some macroscopic device. By a variable controlled by an experimenter in a certain space-time region is meant specifically the experimental setting in that region of some macroscopic device, in which this setting is controlled by an experimenter acting within that region. The theorem pertains specifically to experimental situations in which there are two far-apart, spacelike-separated regions in each of which there is a device that can be set at either of two alternative settings by an experimenter acting within that region. There is also a long sequence of experimental results (i.e. events) in each of the two regions. The theorem asserts that, for some such cases, it is mathematically impossible, within the manifold of all conceivable results compatible with the statistical predictions of quantum theory (to within a generous limit of, for example, 1000 standard deviations), that what happens in each region be independent of the experimental setting of the device in the far-away region. In short, there are situations in which it is mathematically impossible to meet both the statistical requirements of quantum theory and also the locality requirement that what happens in each region be independent of the setting made in the far-away, spacelike separated region. This result is a sharpening of a result due to Bell. Bell's result was formulated in terms of unspecified local hidden variables, and claimed merely to rule out the notion of local hidden variables, which was believed by hardly anyone anyway. The present theorem is formulated directly in terms of specified macroscopic quantities, and within the philosophic framework of contemporary quantum theory. The aim of this work is to discuss the significance of this theorem and its possible uses.