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hypert[f82,jmc]		hypertime - speculation in physics

1. One idea is that the functions of space-time we observe are the end
result of a process taking place in hyper-time and leading to an
equilibrium.  There are three goals of the pre-theory:

a. To account for minimum principles as the result of processes reaching
equilibria.  This is the lesser goal.

b. To provide a framework for studying violations of causality - which
seem to be showing up in quantum mechanics.

c. To "expand consciousness" by indicating how the world might be different
from what it appears to be.


2. Steady supersonic flow past an obstacle provides an analogy that we
shall try to exploit.  If we, as is customary, take one independent
variable  x  along the streamlines and the other two (y  and  z)
transverse to the streamlines, the differential equations for the
velocity components, pressure, etc. as functions of  x, y, and z  are
hyperbolic with  x  as the time-like variable.  The appropriate
boundary conditions involve giving the quantities and their partial
derivatives with respect to  x  on a surface transverse to the
streamlines (analogous to a space-like surface).  The downstream
values of the functions are then the solutions of the hyperbolic
system of differential equations, wherein  x  behaves like time.


3. Now we make a leap of the imagination.  We suppose the differential
equations non-linear and we imagine the system "very large", whatever
that may mean, both in the  x  direction and transverse to it.  While
we're at it, we needn't suppose ourselves restricted to two transverse
dimensions.  With  x  as time, the system may evolve life, i.e. small
self-reproducing configurations, intelligence and civilization.  This
civilization may speculate on the differential equations of its physics.
Let's look at this phenomenon from both our external point of view
and from their internal point of view.  Eventually, of course, we'll
imagine that we ourselves are in an analog of their position.


4. From our external point of view the whole history of their civilization,
indeed of their universe, is open like a book for our inspection.
Since their time dimension is a space dimension for us, we can skip
around as we can reading a book.

5. Suppose we contemplate modifying their world, say by modifying the
obstacle around which the flow occurs.  The flow is perturbed, but
we suppose that equations are dissipative enough in time so that a new
equilibrium is soon established.  We suppose that this new equilibrium
also corresponds to the evolution of civilization in its time like
dimension; in fact we suppose that the perturbation has been small enough
so that there is even a correspondence between many individuals in both
histories.  They don't notice that there has been a change, because their
time is just a space dimension.  It's just that their whole history is
different from what it might have been if the change in the system hadn't
been made.


6. It is natural to ask whether they could detect that their world
corresponded to a space-like dimension of an equilibrium in a larger
world.  Might they even detect the tinkering we have done?
Because we suppose that the flow equations are dissipative, the
steady flow minimizes some "free energy".  They might then be able
to interpret minimum principles of their physics as resulting from
a process in what to them is hyper-time having gone to an equilibrium.
What about us?  Is there any way of confirming or refuting a
speculation that our world is the result of a process in hypertime
going to equilibrium?  What about the further possibility that
someone in hypertime - a god if you like - has tinkered with
our world, and our history is partially the result of this tinkering?
Can we interpret minimum principles, e.g. Fermat's least time
principle or Maupertius's least action principle, as the result of
a dissipative process in hyper-time?  Is anything thereby simplified?
That is speculation number 1.


7. Now we are interested in pursuing possibilities for violations
of causality.  Suppose that not only is there a steady supersonic
flow but also an electrostatic field and that the two interact,
because (say) the dielectric constant of the fluid and its
polarizability depend on density.  Suppose further that the flow
is into and out of a Faraday cage, i.e. a boundary through which
the fluid can flow unimpeded but which is impervious to the
electric field.  It would then seem that the appropriate boundary
conditions are to give the flow state variables and their derivatives
with respect to  x  on an upstream transverse surface and to
give the value of the electric potential on the enclosing boundary
of the region.


8. If the interaction is not too large, we suppose that life
and civilization would be observed to have evolved just as before,
but it seems that they would see a somewhat peculiar physics.
They would see the hydrodynamic aspects of their civilization
evolving in time, but the electric aspect would be determined by
both the past and the future, i.e. there would be an element of
"fate" in the changes in electric field.  They wouldn't see an
entirely causal universe.


9. The non-causal aspect of the development of their universe in
time would be somewhat exotic to them, because they would be
creatures of the hyperbolic, because only the hyperbolic aspect
of physics permits evolution in time, the evolution of intelligence,
and even of consecutive thought based on the notion of actions and
their consequences.

10. The second speculation is that our universe has non-causal aspects
that aren't easy for us to understand, because we live in its
causal aspect.  The particular model - involving an electric field superposed
on a supersonic flow - has nothing special to recommend it.  It
just seems to offer a physical picture of how such a thing may
be possible.


11. The more ambitious goal is to make a partially causal physics
that would actually account for apparent violations of causality
like the Einstein-Podolsky-Rosen gedanken experiment.


12. Whether hyper-time would be relevant to constructing the partially
causal physics isn't cleaar.  It is interesting to speculate on the
possibility that hyper-time would have observable consequences.  Here
are some of the possibilities.

a. If the equations of hyper-evolution are highly non-linear,  different
parts of space-time might bifurcate into different states, i.e. symmetries
in space would be broken by random hyper-time events.  If there were
a large number of such broken symmetries all explainable by random
hyper-events, then their distribution would provide information about
the actual processes that had taken place in hyper-time.

b. If there were gods living in hyper-time tinkering with history,
then this might be detected if the pattern of history of the universe
could best be explained by assuming that they or it had pursued some
objective.

c. Finally, it is possible to imagine the creatures in our hydrodynamic
model not only inferring facts about the "real world" but wanting to
get out and live in "real time".  This would require creating a pattern
that would induce and observer to read a state as a process description,
i.e. an intellectual computer program, and copy it into a computer
running in real time.

13. The imagination stretching part of all this is that hyper-time and
other explanations of apparent violations of causality might have
testable consequences.

14. I must confess, however, that none of the models advanced so far
seems at all plausible to me.  Maybe, if only I understood it better,
the Einstein-Podolsky-Rosen paradox would suggest a better idea.