From: vadim@bolvan.ph.utexas.edu (Vadim S. Kaplunovsky)
Newsgroups: rec.arts.sf.science,sci.physics
Subject: Re: Feedback, Boundary Conditions, and Time Travel (long....)
Date: 4 Oct 92 08:02:40 GMT
Followup-To: rec.arts.sf.science

In article <1992Sep25.190757.3397@spss.com> markrose@spss.com (Mark  
Rosenfelder) writes:
> In article <FSy-WYC@engin.umich.edu> ingles@engin.umich.edu (Ray Ingles)  
writes:
> >I think we have a misconception here. If you posit a change in the
> >past, you require (at least) one more time axis, orthogonal to the
> >'normal' time axis. 
> 
> You're quite right that the ability to change the past requires a sort of
> hypertime in which to move.  I don't know that that's so bad.
> 
> [explaination deleted for brevity]

Hypertime may sound like a bizarre concept, but I've seen it used
(under different names) in some unusual formulations of quantum
mechanics and quantum field theory.  I'm not talking about an alternative
quantum theory here, just an alternative formulation that is believed
to be mathematically equivalent to the usual formalism.

For those familiar with basic concepts of QFT, here is the outline:
Ordinary quantum mechanics can be formulated in terms of the Feynman's
path integral over all conceivable trajectories of the classical system,
including those that violate the classical equation of motions (i.e.,
Newton laws).  This formulation works even better for the quantum field
theory, where the integral is taken over all conceivable configurations
of the classical fields.  For example, in QED, one integrates over
all V(x,y,z,t) and A(x,y,z,t), including the configurations that violate
Maxwell's equations.  To properly define the path integral, the Minkowski
space-time is often analytically continued to a four-dimensional Euclidean
space in which time is indistinguishible from the ordinary space coordinates
x,y,z.

In Euclideanized space-time, the path integral is mathematically identical
to a partition function of a classical field theory in four dimensions
of space in which the classical action plays the role of energy and the
Plank constant plays the role of temperature.  Other field-theoretical
concepts also have their statistical-mechanics analogues, and the connection
has proven extremely useful for investigating the behavior of strongly
interacting quantum field theories such as QCD.  Note, however, that only some
aspects of Statistical Mechanics have their QFT analogues.  In particular,
QFT is believed to be equivalent to the *equilibrium* StatMech of a
four-dimensional classical field theory at finite (hyper)temperature.
A non-equilibrium StatMech would require a hyper-time in which to evolve,
and there is no analogue to such hyper-time in conventional QFT.

The QFT-StatMech connection I tried to outline above was worked out in late
'60s and early '70s and by now is taken for granted by most theoretical
physicists, although some odd details still need to be worked out before
we can be sure that StatMech-like formulation of QFT is indeed equivalent
to the older formulation.  One of those `odd details' is what to do with
with Quantum Gravity --- it's Stat-Mech analogue apparently has no
equilibrium state-(.  Another `odd detail' is whether different approaches
to StatMech are equivalent to each other from the QFT point of view.

Among the unusual approaches to equilibrium StatMech is to start in some
simple but out-of-equilibrium state, and then let the system's own dynamics
drive it to equilibrium.  Mathematically, this introduces the auxiliary
time-like variable that describes the system's evolution; it's usually
called the auxiliary time or the Langevin time (after the Langevin equations
governing evolution of systems subject to external random noise).
In computer simulations of StatMech, the Langevin time is more or less
the same as the CPU time.

From the QFT poin of view, the Langevin time has nothing to do with the
usual Minkowski time or its Euclidean counterpart.  Instead, it acts
precisely like the hyper-time that Ray and Mark talk about --- the
auxiliary time-like variable that governs the evolution of one altenative
history of the ordinary space-time (and everything within) into another.

For conventional field theories that do not involve gravity and and live
in flat space-time,  the Langevin evolution eventually reaches equilibrium,
in which nothing interesting happens anymore as the hypertime goes on and on.
But what happens in space-times with wormholes connecting two different
(ordinary) times?  Nobody knows.  I can only speculate.

Speculation #1:  Wormholes do not preclude equilibrium.
In this case, the history hyper-eveolves to a configuration in which
time travel is possible, but everything you do in the past is already
part of your own history.  That is, if you own history includes a grandfather
who was shot, you can go back in time and become the person who shot him.
If he wasn't shot before you plunge down the wormhole, you are doomed to
miss.

Speculation #2:  Once gravity is included into dynamics,  wormholes become
unstable under Langevin evolution.
In this case, any attempt to use a wormhole to travel into the past and
change it would set up a cascade of destabilizing change that ends up
in a state of no wormholes and no time travel.

Speculation #3:  Langevin dynamics of field theories that include gravity
is semi-chaotic and produces long-lived metastable equilibrium-like states
that eventually destabilise and evolve into something else.
This would support the Anderson's picture of time-line disturbances:
Most (hyper)times, the history would readjust itself with minimal changes,
but once in a while, you would trigger an avalanche of disruption.

Speculation #4:  There is no consistent way to describe Quantum Gravity
using Langevin equations.
In this case, hyper-time is a pure SF concept without a counterpart
in real physics:-(.

Speculation #5:  None of the above!

My personal opinion is that #5 is more likely than not.


---
Vadim S. Kaplunovsky               | vadim@bolvan.ph.utexas.edu (internet)
Assistant Professor of Physics,    | VADIM AT UTAPHY (bitnet)
University of Texas at Austin.     | UTSPAN::UTAPHY::VADIM (SPAN/HEPnet Decnet)