TIME-TRAVEL

After 1905, special relativity made scientific discussion of time trav el and time machines possible. The question may be posed in this way: it makes perfectly good sense to speak about travel that returns to th e same point in space. But Einstein and Minkowski tell us that space a nd time are equivalent, so after a journey can we return to our starti ng position in time? But such travelling requires velocity more than t he velocity of light (existence of the so called tachyons). There are no known tachyons, and time machines cannot be constructed with the ph ysics provided by special relativity. In Einstein's theory of general relativity due to curved space-time there can exist geometries contain ing paths along which one can travel into past with velocity less than that of light - such paths are called closed time-like curves was obt ained in 1949 by Godel and it permits construction of time machines. T he reason for current interest in time travel ideas derives from the r ecent realization that infinitely long and arbitrarily thin cosmic str ing with nonzero spin per unit length can support closed time-like cur ves. Now intrinsic spin attached to a cosmic string mag; still be deem ed unphysical, so we need not worry about closed time-like curves supp orted by the cosmic string. However, one may ask whether two or more s pinless cosmic strings, moving relative to each other and thus also ca rrying orbital angular momentum, can still support time-like curves. T his question was answered affirmatively by Gott. He Found that two spi nless cosmic strings, each moving faster than some critical but sublum inal velocity v/c > (v)cr/c = cos (4 pi Gm/(c)2) < 1 (where G - Newton constant, m - mass of string per unit length) do indeed support close d time-like curves. But there is a cath: sicne one needs a pair of mov ing strings, one may ask what is their combined energy and momentum. W hen space-time is as globally complicated as it becomes in the presenc e of strings, the addition rules for combining energy and momentum bec ome non-trivial and non-linear. The analysis shows that to have total mass of the system real we must have v/c < cos (4 pi Gm/(c)2). This is precisely opposite to Gott's criteria for the presence of closed time -like curves. So just like the special relativistic time machines, whi ch could only be constructed if tachyons exist - but they do not - so also the cosmic string time machines require tachyonic center-of-mass velocities, and cannot be produced in the absence of tachyons, that is in our world.