Quantum time machine

Abstract

The continuation of Misner space into the Euclidean region is seen to imply the topological restriction that the period of the closed spatial direction becomes time-dependent. This restriction results in a modified Lorentzian Misner space in which the renormalized stress-energy tensor for quantized complex massless scalar fields becomes regular everywhere, even on the chronology horizon. A quantum-mechanically stable time machine with just the sub-microscopic size may then be constructed out of the modified Misner space, for which the semiclassical Hawking's chronology protection conjecture is no longer an obstruction. PACS number(s): 04.20. Gz, 04.62.+v

Warp drive space-time

“…On the other hand, Hiscock has computed [18] for the two-dimensional Alcubierre warp drive the stress-energy tensor of a conformally invariant field and shown that it diverges on the event horizon appearing when the apparent velocity exceeds the speed of light, so rendering the warp drive instable. A similar calculation performed in this paper for the case where the interior spacetime of the spaceship bubble is multiply connected yields a vanishing stress-energy tensor even on the event horizon which becomes then a (Cauchy) chronology horizon, both for the self consistent Li-Gott vacuum [19] and when one uses a modified three-dimensional Misner space [20] as the embedding of the two-dimensional warp drive spacetime. It is worth noticing that if the astronaut inside the spaceship is allowed to travel into the past, then most of the Alcubierre's warp drive problems derived from the fact that an observer at the center of the warp bubble is causally separated from the bubble exterior [21] can be circumvented in such a way that the observer might now contribute the creation of the warp bubble and control one once it has been created, by taking advantage of the causality violation induced by the CTC's.…”

“…Rotating back to the Lorentzian section we see that time θ becomes again no longer periodic, but x 1 keeps still a periodic character with period b = 2πθ 2 . If we adhere to ansatz (4.13), this would mean that the Misner space itself should be modified in such a way that its spatial volume would vanish as time θ approaches zero [20]. When calculating then the regularized Hadamard function, one should use a method of images which ought also to be modified accordingly with the fact that the period of the closed spatial direction is time dependent.…”

“…If we use a most general automorphic field and impose constancy for the frequency of the general solution of the wave equation [20], one is led [20] to a time quantization that unavoidably implies an also strictly zero value for the renormalized stress-energy tensor, everywhere in the whole two-dimensional, superluminal Alcubierre space. The price to be paid [20] for this quantum stability is that the CTC's developing inside the warp bubble and actually the warp bubble itself should never exceed a submicroscopic size near the Planck scale, so avoiding not just the unwanted Hiscock instability, but also any violation of negative energy-time Ford like [15,16] inequality and hence any unphysical nature of the warp drive. A possible remaining question is whether the CTC's within the bubble might produce new divergences, at least if Hawking's chronology protection conjecture [28] is correct.…”

Achronal Cosmic Future

“…Even though MorrisThorne wormholes and other topological extensions from Misner space [10] appear to be stable at scales of the order the Planck length [18], macroscopic holes have been claimed to be unstable to quantum vacuum fluctuations [5]. We shall argue nevertheless that wormholes grown up by accreting phantom energy would keep their essential quantum nature, and hence their submicroscopic stability, and should be regarded as quantum spacetime constructs without classical analog.…”

Thermal properties of time machines

“…However, it was later shown by Li and Gott [6] that there exists a self-consistent conformal vacuum where all time machines become stable so violating Hawking's conjecture. Also somehow contravening that conjecture was some work [7] showing that all space-time time-machine constructs become quantum-mechanically stable at the Planck scale, so allowing the quantum vacuum spacetime foam to exist.…”