Are Superluminal Connections Necessary? (')(-)

Summary. — 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 d.etection 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 speci6cally 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 (4.e. events) in each of the two regions. The theorem asserts that, for some such cases, it is mathematically impossible, within the manifold
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