Reply to " on Stapp's 'nonlocal Character of Quantum Theory' " *

The question raised by Shimony and Stein is examined and used to explain in more detail a key point of my proof that any theory that conforms to certain general ideas of orthodox relativistic quantum field theory must permit transfers of information over spacelike intervals. It is also explained why this result is not a problem for relativistic quantum theory, but, on the contrary, opens the door to a satisfactory realistic relativistic quantum theory based on the ideas of Tomonaga, Schwinger, and von Neumann. ∗This work is supported in part by the Director, Office of Science, Office of High Energy and Nuclear Physics, Division of High Energy Physics, of the U.S. Department of Energy under Contract DE-AC03-76SF00098 Shimony and Stein[1] have raised a question about an essential claim made in my 1997 paper[2]. I begin by explaining the claim, and the question they raised. Lines 1 through 5 of my proof[2] show that under certain explicitly stated conditions the statement L2 ⇒ [(R2 ∧ R2+) → (R12 → R1−)] (1) is true, while lines 6 through 14 of that proof show that under these same conditions the statement L1 ⇒ [(R2 ∧ R2+) → (R12 → R1−)] (2) is false. Shimony and Stein arrive at the same conclusion—namely that (1) is true and (2) is false—under similar conditions. I then claim that this fact, that (1) is true and (2) is false, entails that information must sometimes be transferred over space-like intervals. Shimony and Stein question this claim, and suggest that one must make a hidden-variable assumption, as was done in Bell’s theorems [3,4], in order to arrive at this strong conclusion. This issue is important, because all the assumptions used my proof are elements of orthodox quantum philosophy, and hence my claim, if valid, means that the precepts of orthodox quantum philosophy entail that information must sometimes be transferred over spacelike intervals. That conclusion is far stronger than what is proved by Bell’s theorem[3], and its usual generalizations[4,5], and it seems to have profound implications for development of relativistic quantum theory. To provide an adequate foundation for the discussion I need to explain the meanings of (1) and (2), the assumptions that go into my proof that (1) is true and (2) is false, and the technical differences between my assumptions and those of Shimony and Stein. The conditions under which I prove that (1) is true and (2) is false are these: