SPECIAL RELATIVITY PROHIBITS SPACELIKE CAUSATION

Thomas D. Angelidis
Centre for Mathematical Physics
19 Cheval Place, Suite 5014
London SW7 1EW, United Kingdom
E-mail: tdangelidis@ctr-math-phys.ac.uk

We refer to the rather inconclusive discussions for and against the claim that the theory of special relativity Th(SR) “does not prohibit spacelike (faster-than-light) causation”. Despite an extensive search we have not found in the literature (not even in Weyl’s monumental work) a formal demonstration either for or against this claim. A first such formal demonstration against this claim is given here. Adding to Th(SR) the assumption A of “a causal connection between spacelike events” leads to a contradiction. Since Th(SR) Ù A is inconsistent, whence, Th(SR) Ã ØA, and ØA is a theorem of Th(SR). The formal demonstration of the theorem Th(SR) Ã ØA assumes no topology (adding topology strengthens the result) and no dynamics, it is frame independent and coordinate-free. Consequently, Th(SR) demonstrably asserts that there is no causal connection between spacelike events. Spacelike events are causally disconnected with respect to the apex of the light-cone assigned to every event in Minkowski space-time. In other words, Th(SR) prohibits spacelike causation and therefore prohibits spacelike signalling (as causation is a weaker notion than signalling). Since spacelike causation is ruled out by the theorem Th(SR) Ã ØA, if an instance of spacelike causation were shown to exist, even if it could not be used for spacelike (faster-than-light) signalling, then the existence of an instance of spacelike causation would refute Th(SR) which asserts the truth of ØA. It is claimed that quantum theory apparently exhibits at the level of individual events instances of spacelike causation (which do not amount to spacelike signalling according to the claim) in the shape of causal connections - referred to as “nonlocal interactions” - between pairs of spacelike events. In the presence of the theorem Th(SR) Ã ØA, if such instances of spacelike causation (“nonlocal interactions”) were shown to exist, or were even presumed to exist, then quantum theory and special relativity would be incompatible. The theorem Th(SR) Ã ØA leads to an impasse. And the question it raises is: Can this impasse be resolved ?