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On Mar 7, 2012, at 1:47 PM, art wagner wrote:

http://arxiv.org/abs/gr-qc/0612021

Without taking sides about the physical possibility of chronology violations, in this paper we will show that, from a logical viewpoint, the so-called time travel paradoxes may be seen as a consequence of the fact that, in presence of chronology violations, we insist on the adoption of the usual Temporal Logic. The adoption of suitable unusual Temporal Logics allows to get rid of any mathematical inconsistency.

Indeed not only the affection of the past but even its change can be formalized by suitable consistent Temporal Logics.

A curious feature of General Relativity is that there exist solutions (M, gab) of Einstein’s equation such that

Vchronology(M, gab) 6= ∅. The so called time travel paradoxes then occur.

[Jack: not so, for example the papers of Novikov, Kip Thorne on globally self-consistent paradox-free loops. OK see "2" below.]

These paradoxes can be divided in two classes:

• consistency paradoxes involving the effects of the changes of the past (epitomized by the celebrated Grandfather Paradox in which a time-traveller goes back in the past and prevents the meeting of his grandfather and his grandmother)

[Jack: See also papers by Deutsch, Seth Lloyd.]

• bootstrap paradoxes involving the presence of loops in which the source of the production of some information disappears (as an example let us suppose that Einstein learnt Relativity Theory from [1], [2] given to him by a time-traveller gone back to 1904).

[Jack: This is not a paradox at all. Indeed, it is the back-from-the-future signal nonlocality mechanism for human creativity already glimpsed in Bem's ---> Libet's presponse data - in my opinion.]

They has been faced by the scientific community in different ways (see the fourth part ”Time Travel” of [3] as well as [4]):

1. adding to General Relativity some ad hoc axiom precluding the physical possibility of causal loops (such as the strong form of Penrose’s Cosmic Censorship Conjecture)

2. appealing to consistency conditions (such as in Novikov’s Consistency Conjecture) requiring that causal loops, though allowing causal influence on the past, don’t allow alteration of the past

3. arguing that the problem is removed at a quantum level (such as in Hawking’s Chronology Protection Conjecture

[5] stating that the classical possibilities to implement time-travels are destroyed by quantum effects)

4. arguing that the so called time-travel paradoxes are only apparent and may be bypassed in a mathematical

consistent way

As to General Relativity we think that discarding tout court non globally-hyperbolic solutions of Einstein’s equation considering them ”unphysical” is a conceptually dangerous operation:

in presence of ”unphysical” solutions of physical equations we have always to remember that our intuition is not a neutral quality but is affected by the Physics to which we are used.

Consequentially, in presence of new Physics, it is natural that it appears to us as counter-intuitive.

If Dirac had discarded as ”unphysical” the negative-energy solutions of his equation he would have never predicted the existence of anti-matter [6].

While we agree with Visser’s [4] idea that solutions with ”non-localized” chronology violating set may be seen as produced by a sort of garbage in-garbage out phenomenon (where the garbage in are perverse initial-value conditions and the garbage-out are the resulting perverse solutions) we think that solutions with ”localized” chronology violating set should be taken seriously.

Of course, depending on the precise mathematical definition that we adopt for the term ”localized”, we may arrive to different conclusions.

A minimal definition of the term ”localized” would consist in imposing that Vchronology(M, gab) 6= M.

This is sufficient to discard G¨odel’s solution, the Van Stockum - Tipler time machine, some spinning cosmic

string time machine but not Gott time machine that may be excluded only assuming a more restrictive definition of ”localized” as ”suitably bounded”.

An other argument often used in the literature consists in the refutal as ”unphysical” of any non asymptotically-flat space-time; this is (at least) curious: the fact that asymptotically flatness is a condition required in order to be able to define a black-hole (as the complement of the causal past of future null infinity B := M − J−(I+)) is not a good reason to assume as ”physicality”’s criterion one incompatible with the assumption of homogeneity and isotropy under which the Friedmann-Robertson-Walker solutions of Classical Cosmology are derived.

Finally we agree with the Headrick-Gott’s [7] refutation of the claim that the observed absence of time-travellers

[Jack: Some UFO investigators of sound mind disagree here as to what the evidence is.]

in the present and in the past would be an empirical datum supporting the physical impossibility of time-travel:

no experimental fact on M − Hchronology(M, gab) can be used as an argument in favour or against the hypothesis

that Vchronology(M, gab) 6= ∅.

When also Quantum Mechanics is taken into account we again agree with Visser’s viewpoint [4] according to which the Kay-Radzikowski-Wald singularity theorems (stating that in presence of a non-empty chronology-violating set there are points of the chronology horizon where the two-point function is not of Hadamard form [8], [9]) has to be interpreted not as a support of Hawking’s Chronology Protection Conjecture but as an evidence of the fact that in such a situation Semi-classical Quantum Gravity (defined as Quantum Field Theory on a fixed curved background augmented with the semi-classical Einstein equation Rab − 12Rgab = 8 < | ˆ Tab| > taking into account the backreaction of the quantum fields on the spacetime’s geometry [10]) is not a good approximation of Quantum Gravity.

Hence we think that the status of Hawking’s Chronology Protection Conjecture may be decided only at the Quantum Gravity level.

Since most of the phenomenology of Quantum Gravity is detectable only at the Planck scale (lengths of the

magnitude of the Planck length lPlanck ∼ 10−33 cm, energies of the magnitude of the Planck energy EPlanck ∼

1019 GeV ) that is enormously far from our present possibility of experimental investigation, the quantum status of Hawking’s Chronology-Protection Conjecture may be at present investigated only on a theoretical basis, all the rival alternative proposals (String Theory [11], [12], Loop Quantum Gravity [13], Connes’ Quantum Gravity [14], [15], Simplicial Quantum Gravity [16], Prugovecki’s Quantum Gravity [17], Finkelstein’s Quantum Gravity [18], ÅE ÅE ÅE ) being far from giving, on this issue, clear and univocal answers.

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