The Ordering of Interactions

It's often noted that our experience consists entirely of 
interactions, rather than isolated objects (e.g., one hand 
clapping), but that nevertheless we persist in encoding and 
visualizing our experience in the form of a space of usually-
isolated objects that occassionally interact.  This fictitious 
way of conceptualizing our expereince certainly seems to be 
efficient in most ordinary circumstances, but it may contribute 
to the difficulties we encounter when trying to make sense 
of elementary physical operations.

As an example, consider the notion of causality and the "ordering" 
of events.  In terms of our fictitious image of isolated objects 
we consider that each individual object induces a partitions of 
spacetime into three distinct regions, past, "now", and future, 
bounded by null cones as shown below

        \     t|Future/
         \     |     /
          \    |    /
           \   |   /
            \  |  /
        Now  \ | /
     _________\|/_________x
              /|\
             / | \
            /  |  \
           / Past  \

In contrast, if we take fundamental quantum interactions (rather 
than particles) as the primitive elements of our model, then each 
interaction induces a partition of spacetime into SIX distinct 
regions.  Letting P, N and F denote Past, Now, and Future 
respectively, the six regions are

     PP   NP   FP   NN   FN   FF

where, for example, FP signifies the Future of one end of the 
interaction and the Past of the other end.  Of course the two 
"ends" of a typical fundamental interaction are very close together, 
both spatially and temporally, so the "mixed" regions NP, FP, and 
FN are usually vanishingly small.  Thus when dealing with most 
common macroscopic events it makes sense to just focus on the three 
pure regions PP, NN, and FF.  This allows us to treat the causal 
orderings of interactions as if they have same general 3-part 
structure as the ordering of our fictitious isolated objects.

Observe that, if we restrict our attention to just the pure 
regions PP or FF we encounter no surprises relating to causality, 
correlations, etc. in quantum mechanics.  By this I mean that if 
two interactions are located entirely within each others future/past 
respectively, then there are no ambiguities about the "flow" of 
events, and quantum mechanics does not predict anything outside 
the ordinary expectations of causality. When dealing with elemental 
interactions (i.e., interactions that cannot be broken down into 
sub-interactions) we find counter-intuitive results only when the 
interactions are not well-ordered, in the sense of each interaction 
being wholly within the future or the past of the other.  

If we focus on the possible relations between just two interactions, 
there are 20 distinct ways in which they could be causally "ordered" 
(in contrast to just 3 ways for two discrete *particles*).  These 20 
"orderings" correspond to the ways in which the two ends of one 
interaction can be placed in the six regions induced by the other:

     [PP,PP]    NP,NP    FP,FP   [NN,NN]   FN,FN   [FF,FF]
      PP,NP     NP,FP    FP,FN    NN,FN    FN,FF
      PP,NN     NP,NN    FP,FF    NN,FF
      PP,FP     NP,FN
      PP,FN     NP,FF
      PP,FF

All of our ordinary macroscopic experience is with sets of 
interactions that are of the three types shown in square brackets.  
In fact, due to the large value of the speed of light, our
experience is almost all with the "well-ordered" relations [PP,PP] 
and [FF,FF].  We know what to expect in those cases, and quantum 
mechanics agrees with our expectations.  The surprising and 
seemingly "paradoxical" results of QM involve interactions that 
relate to each other in one of the 17 "mixed orderings" or the 
[NN,NN] ordering, where our experience with well-ordered 
interactions is not applicable.

In my view, when people talk about locality being violated by QM, 
they are applying a notion of "locality" based on fictitious 
isolated objects, whereas our experience actually consists of 
irreducible (quantum) interactions which have a more complicated 
set of possible orderings and causal relations.  

It's interesting that both relativity and quantum mechanics
extended our notions of the possible order-relations between instances
of experience.  Relativity, by the finiteness of the speed of light,
expanded the classical relation "simultaneous" from an infintessimal 
slice of spacetime to the entire region of spacetime outside the 
null-cones associated with any two events.  Quantum mechanics, by
the irreducibility of fundamental quantum interactions, induces a
more complicated set of possible order-relations between the
basic constituients of experience.

The most common objection to this view is that by replacing
"particles" with "interactions of finite spatial and temporal 
extent" as the fundamental constituients of experience, we are 
basing our ontology on inherently "non-local" entities, so it no 
longer makes any sense to talk about locality at all.  However, 
it can be shown that quantum interactions actually ARE local, 
provided the measure of "nearness" is taken to be absolute spacetime
separation.  (There is really no choice about this if we want our
concept of locality to be based on a measure of nearness that is
invariant under Lorentz transformations.)  This is because quantum 
interactions act entirely on null-cones, which is obviously true 
of electromagnetic interactions, and it's also true of all other 
quantum interactions, as emphasized in, for example, Cramer's 
Transactional Interpretation.  The (relativistic) Schrodinger
wave propagates along null-cones.

Of course if you focus ONLY on the pseudometric structure of
spacetime and the implicit null paths connecting every pair of
points, it's tempting to slide down the reductionist slope into
thinking that the entire manifold degenerates trivially into
a single locus of "co-local" points.  On this basis some people
conclude that the absolute spacetime interval cannot serve
as the measure of nearness in any meaningful definition of
locality.  However, this view fails to take account of the
fact that the irreducible element of experience is not the
point particle but the quantum interaction.  Each interaction
does indeed reduce to a single co-local entity within the
pseudometric of spacetime, but distinct interactions do NOT
reduce to a single interaction.  Thus, the (highly non-trivial)
structure of experience arises jointly from the pseudometric
structure of spacetime - with its finite velocity of light - 
AND the irreduciblility of finite quantum interactions.

Unfortunately, this all begs the question of what exactly 
constitutes an "elemental" interaction.  The problem with treating 
interactions (rather than particles) as elemental is that it 
isn't obvious how to define "interaction" without first defining 
the entities that are doing the interacting.  This is really just 
another way of stating the well-known problem of separating the 
observer from the observed, and what it means for systems to be
"isolated" from each other.  I think we can't avoid a *relative* 
definition of elemental, by which I mean that an interaction 
that is elemental relative to me may be compound relative to you.

There's an interesting parallel here to the absence of absolute 
simultaniety in special relativity.  Does the lack of absolute 
"elementality" lead to logical contradictions?  As far as I can tell, 
it doesn't.  For example, relative to Schrodinger's Cat the outcome 
of the experiment is a result of compound interactions, all following 
in a sequence of small and well-ordered interactions.  However,
relative to an observer isolated from the Cat's environment the 
overall interaction is elemental.  Schematically it looks like 
this

            |-------compound interaction-----|
                        _____________
                ______B/   Cat's     \C____
               /       \ environment /     \
              /         \___________/       \
       _____A/                               \D_______
             \                               /
              \_____________________________/


            |------ elemental interaction -----|


Accordingly as "you" take the upper or lower branch, the interaction
between points A and D is compound or elemental.  The point of this
distinction is that it determines how those interations may be 
related, either causally or by correlation, to other interactions 
according to their full "order" in spacetime.  

It may seem strange that a given large-scale interaction must be 
treated as elemental for one observer but compound for another.  
Our intutition says that two events either ARE or ARE NOT connected 
by an elemental interaction, but this is similar to our intution 
that two events either are or are not simultaneous, i.e., it stems 
from a failure to recognize that elementality (like simultaniety) 
can only be properly defined operationally, and on that basis it 
need not be absolute.  This all suggests that each connected subset
of the set of all interactions can be regarded as a system, and
the elementality of every other interaction with which a system 
comes into contact is determined relative to that system.  On
that basis, the causal influences and correlations follow from 
the full spacetime ordering of those interactions.