From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: TIME HAS INERTIA        ABIAN REPLIES TO M.S.T.  WATTS
Organization: Computer Science Department,  Stanford University.
Date: Tue, 10 Nov 1992 15:35:58 GMT

In article <1992Nov10.082114.28659@nuscc.nus.sg> matmcinn@nuscc.nus.sg (Brett McInnes) writes:
>abian@iastate.edu (Alexander Abian) writes:
>:     TIME HAS INERTIA  and some energy is lost to move Time forward  
>:   E = mcc  (Einstein)    must be replaced by    E = m(0) exp(-At) (Abian)
>
>I am sorry, there seems to be an error here.
>   E = m(0) exp(-At)  (Abian) must be replaced by
>		E = m(0) exp(-Mtt) (McInnes)

While I don't know about either formula, it just occurred to me that if
a small change is made to the part about "some energy is lost to move
Time forward" it would exactly describe the situation contemplated in
the following reference, also available as /pub/dti.{tex,dvi} from
boole.stanford.edu.  If an incremental loss of energy is identified
with an incremental gain of information (justifiable for isothermal
situations via dQ=TdS) then the necessary change is that energy is lost
(or information gained) precisely when time does NOT move forwards.

        @InProceedings(
Pr92e,  Author="Pratt, V.R.",
        Title="The Duality of Time and Information",
        Booktitle="Proc. of CONCUR'92, LNCS 630", Publisher="Springer-Verlag",
        Pages="237-253", Address="Stonybrook, New York", Month=Aug, Year=1992)

Subsequently to writing this, John Baez set me straight on the symmetry
of time (to within the question of whether it is experimentally
possible to tell whether the retarded solution to Maxwell's equation is
more real than the advanced, where I think John sides with Zeh in "The
Physical Basis of the Direction of Time" in affirming).  I am as a
result rather less sure of the potential connections with physics
claimed in the concluding speculative section of the paper.  Perhaps
the connection can be sustained by interpreting information and energy
locally, so that "gain of information" refers to gain in a
neighborhood.  This would bring space into the connection, a parameter
not contemplated in my paper.  Have to think about that some more...

Here are the first four paragraphs.  Note the appearance of phase space
in the fourth paragraph.  "Event" is used synonymously with "state
transition," a physicist may get something out of taking it to be
synonymous with "attribute" or "observable."

=========

The behavior of an automaton is to alternately wait in a {\it state}
and perform a transition or {\it event}.  We may think of the state as
bearing information representing the ``knowledge'' of the automaton
when in that state, and the event as modifying that information.  At
the same time we may think of the event as taking place at a moment in
time, and the state as modifying or whiling away time.

Thus states {\it bear} information and {\it change} time, while events
{\it bear} time and {\it change} information.

We often speak of events as ``time-stamped;'' we might similarly speak
of states as ``information-stamped.''

One way of viewing this is to think of computational behavior as motion
or flow in a space whose two dimensions are time and information, which
we will conventionally plot horizontally and vertically respectively.
Horizontal motion denotes a state, a quiescent period in which time
passes while information is held constant.  Vertical motion denotes an
event, a transient phenomenon in which information changes but time
does not.  This accounts at least for rigid local behavior or
nonbranching sequential computation; to extend it to flexible
distributed behavior we might extend the linear geometry of each of
time and space to spaces that can branch and increase in dimension, and
to permit computation to be a broad flow like a river as opposed to
motion of just a point.  In this paper we confine attention to motion
upwards (monotonically increasing information) and to the right
(monotonically increasing time), leaving open the proper algebraic
treatment of downward motion (forgetful automata and nonmonotonic
logic), and raising as an interesting philosophical question what
meaning might be attached to motion to the left, a feature of both
Feynman diagrams and time machines.

=========

In the above view, motion in phase space is rectilinear: either time or
information changes depending on whether the automaton is quiescent or
in transition respectively.  While this is the natural way for a
computer scientist to view the behavior of an automaton, when viewed
from a distance the rectilinearity may become too fine to see (cf.  my
recent post about bitmap vs. outline fonts).  In that case, at least
for motion "up and to the right," one would see time increasing
concomitantantly with information (negative energy), giving the second
half of

>:     TIME HAS INERTIA  and some energy is lost to move Time forward  

without worrying about the two directions of motion having to
alternate.

I have no clue what any of this has to do with inertia.  Anyone
understand why Abian thinks mass can be taken to be E/exp(-At)?  Is A
real, complex, an operator, Abian (as suggested by Matt?), or what?

=========

A remark on dQ=TdS.  A beginning thermodynamics student may well wonder
why not the simpler Q=TS, energy = temperature x entropy, like Ohm's
law?  Well, the components of Ohm's law are all state parameters,
whereas in dQ=TdS only T is a state parameter, Q and S are quantities
accumulating in the course of a process.  To convert the latter to
state parameters we take only increments (derivatives) of each.

The information theoretic interpretation of this identifies temperature
with noise.  Then at a given noise level the inward flow of
information, of which dS represents (the negation of) a small
increment, requires a corresponding outward flow of energy, in
proportion to the prevailing level of noise over which one must shout
for one's bit of information to be heard.
-- 
Vaughan Pratt