Has quantum nonlocality been experimentally verified?

Bell's theorem tells us that if we wish to preserve the results of quantum theory, then we cannot supplement the theory by any sort of locally determined hidden variables. The Aspect experiments tell us that the results of quantum theory, in certain relevant circumstances, are correct. Thus, some type of information about the result of an experiment must travel to other points of space. If we take a reasonable, simple, model of how a measurement actually produces a result, namely, the GRW collapse model, then the experiments that have so far been done, do not distinguish between instantaneous communication, which is required in the orthodox theory, and communication at the speed of light. We discuss how models which incorporate such communication might be constructed, and urge the need for experimental tests. Likely values of the relevant parameters suggest that these are possible. Finally, we note that, contrary to what is generally claimed, nonlocal collapse models which agree in all circumstances with quantum theory do permit instantaneous signals to be sent over arbitrarily large distances.Text of a talk given at the 1991 Cesena conference,Bell's Theorem and the Foundations of Modern Physics.