Dear Tim and scerir,
I am VERY interested in this discussion! ;-) It seems to me that fact
that the amplitudes of observables in QM are complex valued and thus do not
obey trichotomy may be at the root of the difficulty. When we attempt to
make sense of situations such as those we obtain in EPR we have to be very
careful that we take into account the configuration of the experiment
itself. This implies that the lattice of relations or poset aspect of
causality is a posteriori and not a priori to the specifics of the
experiment. This implies, at least to me, that it is a mistake to assume the
a priori existence of a space-time (with a unique light cone structure).
One possible solution is to consider space-times strictly from an a
posteriori point of view. You had mentioned Greg Egan's novels and the "All
Topologies model" (for instance in the novel Distress) in previous posts. Do
you think that the ideas of the character Mosala could be used to "make
sense" of this?
----- Original Message -----
From: "Tim May" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Tuesday, September 03, 2002 9:30 PM
Subject: Re: Time as a Lattice of Partially-Ordered Causal Events or Moments
> On Tuesday, September 3, 2002, at 02:21 PM, scerir wrote:
> > Tim May:
> > I don't have a comprehensive theory of time,
> > but I am very fond of "causal time."
> > Sometimes we read papers saying there is now
> > experimental evidence that quantum phenomena
> > are "a-causal" or "non-causal" or "out-of-time".
> > See, in example, these recent papers
> > http://arxiv.org/abs/quant-ph/0110124
> > http://arxiv.org/abs/quant-ph/0201036
> > Now, can lattices capture also those important
> > features?
> I haven't read the papers, just the abstracts. I could wait to comment
> for a few days or weeks until I've had a chance to absorb the papers,
> if ever, or comment now.
> First, it looks like these events are the usual "entangled states,"
> which can be spacelike (the usual example of particles separated by
> light years).
> Second, for such spacelike intervals, they are outside each others'
> light cones in the extreme cases, so it would not be expected for any
> partial ordering to exist.
> Third, my own idiosyncratic view is to look at entangled particles as a
> single system, regardless of separation.
> Fourth, as to the mechanics of lattices: the essence of a
> partially-ordered set (poset) is that it does not require trichotomy,
> where either a is less than b, a is greater than b, or a is equal to b.
> In a chain, a linear form of a lattice, trichotomy holds. So, the
> integers obey trichotomy, as one integer is either less than, greater
> than, or equal to any other integer. Orders which obey trichotomy are
> said to be well-ordered.
> But not all sets are well-ordered. If the ordering relation is set
> inclusion, then a series of sets need not obey trichotomy. Some sets
> may be disjoint, with one neither including the other, being included
> by the other, or equal.
> In terms of causality, not even getting involved with speed of light
> issues and light cones, it is quite possible to say "event A neither
> caused event B nor was caused by event B nor is the same as event B."
> That is, the events A and B are incommensurate, or disjoint...they fail
> trichotomy. Clearly, most events all around us are such examples of
> incommensurate. They form posets.
> What a lattice does is to formalize the notions of order and to say
> there is only one edge between two events, and nothing in between (no
> other nodes in between). If two events are separated by many instants
> of time, many other events, then the lattice is made up of the smallest
> identifiable events. The events look like a lattice. (As I said, the
> Web has many nice pictures. No point in my spending 20 minutes drawing
> an ASCII lattice here, having it reproduced poorly, when entering
> "lattice poset" into Google will turn up nice pictures.)
> So, I would say from reading the abstracts that the Bell example just
> fits the ecample of a poset, where two events, which may or may not be
> entangled, are spacelike to each other. (This is the essence of the
> usual "instantaneous action" of EPR/delayed choice experiments.)