Abstract Quantum Systems and the Possibilities for Paradox-Free Backwards-in-Time Causality

Abstract

In previous work, the authors have shown that spacelike causal connections can be made relativistically consistent within the quantum formalism by the introduction of symmetric spacetime intervals. Since spacelike causal connections permit both Faster-Than-Light (FTL) signaling and Backwards-in-Time Causality (BTC), the specter of temporal paradox must be dealt with. Closed timelike loops in spacetime can be either paradoxical or indeterminate, so a censor mechanism must prevent the construction of all closed timelike loops, or at least the paradoxical ones. In the latter case, a new problem emerges: causeless information can occur in indeterminate closed timelike loops. This paper introduces Abstract Quantum Systems (AQS) as a way to study systems involving these phenomena. The most thoroughly studied AQS is Quantum Tic-Tac-Toe. An AQS can be constructed from any classical system by adding three types of rules: Rules of Superposition, Rules of Entanglement, and Rules of Collapse. Such quantum systems can be placed into a one-to-one correspondence with a simultaneous set of classical systems called the classical ensemble. While superficially similar to the Many Worlds interpretation of quantum mechanics, the classical ensemble idea is significantly different. This paper shows that the classical ensemble supports a censor mechanism that prevents BTC from generating temporal paradoxes while allowing indeterminate closed timelike loops. This censor mechanism works by pruning from the classical ensemble any classical reality that has become contradictory due to superposition and entanglement. In other words, temporal paradox does what it was always feared it would do; it breaks the universe. However, it only breaks classical ones. As long as it does not break all the classical realities in the ensemble, the quantum reality persists. When a collapse occurs, one of the classical realities remaining in the ensemble is randomly chosen. In this way, the persisting realities left in the classical ensemble represent the weighted indeterminacy of states. Therefore, in addition to avoiding temporal paradox, the classical ensemble also explains the causeless appearance of information in indeterminate closed timelike loops. The information is simply “concentrated” from realities that “no longer exist.” This is formally similar to quantum computing, but now in spacetime, rather than just in space. The conclusion is that physical quantum systems may support both FTL and BTC without paradox, implying the possibility of a technology that amounts to a limited analog of time travel.