> If you "go back in time" you are going to
> a different branch of the multiverse.
Hawking said: "...if somebody try to move on journey in past effects of
indefinites will be evoke phenomenon of large amount of irradiation.
This irradiation will be or disort space-time and not to be possible back
in time, or will be evoke end of space-time in singularity like Big Bang
or Big Crush. Fact how is tourist from future not yet visit us is best proof
how time-travel is not possible and never will be."
Since the original works by Goedel there has been a long debate over the
issue whether the laws of physics might allow for the existence of closed
time-like curves (CTCs) inside our universe. Macroscopic CTCs might be
realized as a consequence of the "quantum foam" structure of spacetime, at
Planck scales. For spacetimes with CTCs, past and future are no longer
"globally" distinct. Writes I.D. Novikov that events on CTCs should
causally influence each other along the "loops in time" in a self-adjusted,
consistent way. 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. Novikov showed that the "principle
of self-consistency" actually needs not to be imposed as an independent
assumption which is necessary in order to make sense of spacetimes with
CTCs, but instead can be seen as a direct consequence of the more
fundamental "principle of minimal action". (Does MWI, in the strongest
version, violate the principle of minimal action, or Occam's razor?).
Sean M. Carroll wrote interesting things (below) about J. Richard Gott
proposal (Phys. Rev. Lett., 4 March 1991) for a time machine.
------------
Gott showed that if you had two infinitely long, perfectly straight,
parallel cosmic strings moving at a sufficiently high relative velocity,
then you could in principle travel around the pair of strings and come back
before you left. Of course this is a very special (and unlikely) situation,
but it has the benefit of not requiring negative energy densities (as do
time machines based on wormholes and so forth). Even better, it is a very
simple situation to analyze, since there is a dramatic simplification -
since the strings are infinitely long and perfectly straight, you can
basically ignore the direction along the strings, and imagine you are
dealing with point particles in a three-dimensional spacetime.
>From this point of view, the Gott time machine was analyzed by Deser,
Jackiw and 't Hooft (1992, Phys. Rev. Lett. 68, p. 267). They considered
the "momentum" of the two-string system comprising the Gott time machine,
which (due to the gravitational interaction of the strings) is not simply
the sum of the individual momenta of the two strings. In fact, the result
is not equal to the momentum of any conceivable single string, in some ways
it resembles a tachyon (a particle moving faster than light), although
there are differences as well.
Farhi and Guth and Sean M. Carroll used that piece of information to place
limits on the ability to construct a time machine in an open universe (1992,
Phys. Rev. Lett. 68, p. 263, p. 3368). They basically showed that, in an
*open* 3-d universe, if you started with a pair of strings that were moving
too slowly to be a Gott time machine, you could never accelerate them fast
enough to make them into a time machine. (Essentially you could never fit
enough energy into the universe to have enough rocket fuel). But there is an
important difference between 3-d and 4-d, in 3-d there's an upper limit on
the mass of the universe. See also S.M. Carroll, E. Farhi, A.H. Guth and
K.D. Olum (1994), Phys. Rev. D 50, p. 6190, or at
http://xxx.lanl.gov/abs/gr-qc/9404065
In *closed* universes (in 3-d) you can fit more mass than in open universes,
and indeed you have enough energy to make particles/strings go fast enough
to be a Gott time machine. Surprisingly, though, if you try to actually loop
around the strings to meet yourself in the past, the universe collapses to a
singularity (a big crunch) before you can ever get there. This was shown by
Gerard 't Hooft (1992, Class. Quant. Grav. 9, p. 1335).
So general relativity - says Sean M. Carroll - is quite successful at
preventing you from making a time machine from scratch, at least in
3-dimensions. It would be nicer to know the situation in the real
4-dimensional world, but it's trickier there. There are some theorems that
imply you need either singularities or negative energy densities to do it,
but the situation is still murky. See for example Hawking's paper: (1992),
Phys. Rev. D 46, p. 603.
-----------
As far as I remember there's a theorem saying that if you have a closed
null geodesic, then the energy density of a region near some point
on it, gets magnified when it takes a trip along this geodesic.
If we find infinite energy densities unreal, we can say that there are
no closed null geodesics (and no time machines). The argument then becomes
whether quantum "violations" get you out of it.
- "Time Machines", by P.J. Nahin
- "Black Holes and Time Warps: Einstein's Outrageous Legacy ", by Kip Thorn
- "Bangs, crunches, whimpers and shrieks: singularities and acausalities in
relativistic space-times², by John Earman
- ³Evolution of the Universe², by D. Novikov
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