Can a message sent back in time really happen, and what would stop it?

"would have an important bearing on whether or not the"

"spacetime looping back on itself, allowing a particle to"

"employing path-integral approaches in an effort to avoid contradictions [5,4]"

"As a consequence, there is a prima facie argument exploiting entanglement that CTC"

"we construct a “barrier” B such that each CTC in time-rolled"

"and he suggested imposing a self-consistency condition on the density matrix of a CTC qubit in order to avoid grandfather-like paradoxes."

"D-CTCs don’t provide any systematic explanation of why we fail."

"The idea of the proof is that any proper extension of M− has to fill in a point"

"Hawking, S.W. (1992) Chronology protection conjecture, Physical Review D 56 , 4745–4755."

"Gott, J.R. (1991) Closed timelike curves produced by pairs of moving cosmic strings: exact solutions, Physical Review Letters 66 , 1126–1129."

"Morris, M., Thorne, K.S. and Yurtsever, U. (1988) Wormholes, time machines and the weak energy condition, Physical Review Letters 61 , 1446–1449."

"Echeverria, F.G., Klinkhammer, G., and Thorne, K.S. (1991) Billiard balls in wormhole spacetimes with closed timelike curves, Physical Review D 44 , 1077–1099."

"Alcubierre, M. (1994) The warp drive: hyper-fast travel within general relativity, Classical Quantum Gravity 11 , L73–L77."

"Generalized quantum mechanics is used to examine a simple two-particle scattering experiment in which there is a bounded region of closed timelike curves (CTCs) in the experiment’s future. The transitional probability is shown to depend on the existence and distribution of the CTCs. The effect is therefore acausal, since the CTCs are in the experiment’s causal future."

"The effect is due to the non-unitary evolution of the pre- and post-scatteringparticlesastheypassthroughtheregionofCTCs."

"For a identified region 1 meter from the scattering center with L = 1m and T = 1s, the deviation is 1 part in 1015."

"We will use this result as a upper bound on the sensitivity of total cross-section measurements. Therefore, the deviation we have calculated in the total-cross section dueto a Politzer time machine in our futureis negligible compared to the experimental error associated with the measurement."

"Therefore, Hartle’s prescription predicts an infinitedeviation in the total cross section in this case, which is clearly absurd, so such spacetimes are ruled out."

"This extremely disturbing state of affairs has lead Hawking to promulgate his chronology protection conjecture."

"If the geodetic interval from x to itself, cr 7 (x,x), becomes negative then a closed timelike curve (a fortiori — a time machine) has formed."

"It is this unfortunate happenstance that Hawking's chronology protection conjecture is hoped to prevent."

"The recent interest in "time machines" has been largely fueled by the apparent ease with which such systems may be formed in general relativity, given relatively benign initial conditions such as the existence of traversable wormholes or of infinite cosmic strings."

"Less restrictively the Hawking Chronology Protection Conjecture allows the existence of wormholes but forbids the existence of time travel |T],0]: "Suffer not closed non-spacelike curves to exist"."

"Both the experimental evidence (the nonappearance of hordes of tourists from the future) and the theoretical computations now support this conjecture."

"It is generally believed that any attempt to introduce closed timelike curves (CTCs) into the universe will fall foul of the chronology protection conjecture 0, which states that the laws of Physics somehow conspire to prevent one from manufacturing time machines."

"Early calculations supporting this conjecture concentrated on the behaviour of the renor- malised energy-momentum tensor (T^), which was shown to diverge at the Cauchy horizon in a number of causality violating spacetimes. A possible mechanism for enforcement of chronology protection was therefore proposed as the back reaction of this divergent energy- momentum on the spacetime geometry via the se"

"Boulware ||] and Tanaka and Hiscock || both found that for sufficiently massive fields in Gott space and Grant space respectively, (T^) could remain regular at the Cauchy horizon."

"There is a critical boost at which the spacetime will develop CTCs (when a = (3/r), but the amount of boost momentum that is needed to achieve this is once again infinite and the entropy diverges to minus infinity at this critical value. In this case, therefore, there are no quantum states available for these causality violating field configurations."

"The possibility that the laws of physics might allow for the existence of closed time-like curves (CTCs) inside our universe has been a long time conjecture [1], which has been more recently revived by a series of papers [2–15]."

"Wormhole simulations revealed that stability is highly dependent on negative energy densities, aligning with theoretical predictions but constrained by the absence of observable exotic matter."

"One of the main ideas being studied is the “closed timelike curve,” a theoretical loop in spacetime predicted by Albert Einstein’s theory of relativity. According to scientists, such loops could potentially allow information to return to an earlier point in time without violating known physical laws."

"Provided the matter density in some regions of our universe satisfies certain properties (i.e. it violates the so-called ‘averaged weak energy conditions,’ see, e.g., Refs. [3–6]), these 4-d Lorentzian wormhole geometries could, in principle, exist (at least they can be exact solutions of the Einstein equations)."

"In some studies, photons appeared to exchange information in ways that seemed retroactive, though researchers emphasised that no actual human or object travelled through time."

"It states that the only solutions to the laws of physics that can occur in spacetimes containing closed timelike curves are those that are globally self-consistent"

"if the wormhole is traversed from mouth to mouth, it acts as a ‘time machine’ allowing one to travel into the past or into the future."

"and no locally initiated event can create a contradiction."

"This requirement has been explicitly formulated as the ‘Principle of self-consistency,’ according to which the only solutions to the laws of physics that can occur locally in the real universe are those which are globally self-consistent [7, 9, 13–15]."

"the only possible trajectories (for a particle with fixed initial and final positions and which traverses the wormhole once) minimizing the classical action are those which are globally self-consistent, and that the ‘Principle of self-consistency’ (originally introduced by Novikov) is thus a natural consequence of the ‘Principle of minimal action.’"

"The canonical example: a traveller acquires a document at time t₂, travels to t₁ < t₂, and delivers that document to an agent who publishes it, so that the traveller can read it at t₂."

"Crucially, Novikov and colleagues observe that self-consistent solutions to such loops arise naturally from the imposition of fixed-point boundary conditions [1]."