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.