From: carlip@landau.ucdavis.edu (Steve Carlip)
Newsgroups: alt.sci.physics.new-theories
Subject: Hawking on time travel
Summary: Summary of Hawking's paper "The Chronology Protection Conjecture"
Date: 13 Dec 92 20:31:35 GMT
Organization: Physics, UC Davis

About a week ago I posted a brief summary of Hawking's paper, ``The 
Chronology Protection Conjecture'' (Phys. Rev. D46 (1992) p.603).  
Unfortunately, my posting seems to have gotten eaten somewhere
between here and the rest of the world, so here is a new version.  
My apologies if this is redundant.

Hawking asks whether it is possible to create a time machine (technically
a region of closed timelike curves) in a finite region of space, without
singularities or pathological behavior at infinity (technically, with a
compactly generated Cauchy horizon).  This question can be asked in
two contexts --- in classical (nonquantum) general relativity, and in
quantum theory, ideally including quantum gravity.  The first context
is easier, and Hawking starts there.

Hawking shows that such a time machine cannot be created without violating
the ``weak energy condition,'' that is, without requiring negative energy
in some frame of reference.  The proof is quite general; it uses general 
relativity to connect spacetime geometry to energy, but makes no detailed 
assumptions about the form of matter present or the nature of the ``time 
machine.''  In classical physics, energy is never negative, so Hawking's 
argument is essentially a proof that a timemachine cannot be built --- at 
least, not without creating either singularities or bizarre behavior of 
spacetime extending over infinite distances.

In quantum mechanics, on the other hand, the weak energy condition can 
be violated.  In the Casimir effect, for instance, two parallel metal 
plates feel a (measurable) attraction because the energy density of the 
vacuum between them is negative.  Hawking argues that even so, time 
machines are still forbidden, because near a time machine quantum 
fluctuations in the energy density will be so large that they will 
disrupt the spacetime geometry, again preventing time travel.

This last conclusion is subject to a good deal of controversy, and so 
far there is no general consensus among people working in the field.  
There is no argument about the fact that fluctuations in energy density 
will occur.  The question is whether quantum _gravity_ will be important 
at the relevant scales.  If it is, this provides a possible loophole in 
the no-time-machine proofs, since we simply don't know how quantum 
gravity works.  

Hawking argues that the fluctuations in the energy density of matter near 
a putative time machine are already very large at scales where quantum 
gravity is still unimportant; others, like Kip Thorne, are not convinced.  
(The argument is not really about the scales at which the matter 
fluctuations are large --- this can be computed --- but rather about 
the scale at which quantum gravity is significant.  Hawking believes 
quantum gravity becomes important only at a much smaller scales than 
Thorne proposes.)

This last question is the subject of active research at the moment, and
I expect much more will be understood in another year or two, although
I wouldn't expect a completely solid answer until we know much more
about quantum gravity than we do now.

Steve Carlip
carlip@dirac.ucdavis.
Newsgroups: alt.sci.physics.new-theories,sci.energy