Re: Time as a Lattice of Partially-Ordered Causal Events or Moments

From: Tim May <tcmay.domain.name.hidden>
Date: Wed, 4 Sep 2002 09:24:32 -0700

On Wednesday, September 4, 2002, at 07:47 AM, Stephen Paul King wrote:

> 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).

I agree that imposing a space-time structure for quantum events is a
problem. In fact, this is one of the motivations of quantum gravity
work, to get rid of the "events on a background of space and time"
which most QM has been using.

However, assuming a space-time and with local light cones seems very
reasonable to me. We have no particular evidence that the light cone
formalism isn't still applicable to quantum kinds of events (whatever
EPR "spooky action at a distance" may be, there is certainly no
evidence that faster than light travel of particles or photons is
involved, so there's no reason to throw out the speed of light as a
maximum speed).

You may be interested in Smolin's "Three Roads to Quantum Gravity." He
argues for the _relational_ view of space-time as being more suitable
than the absolute space-time coordinates in Newtonian and (ironically)
most quantum theories. Relativity of course uses the less absolute
scheme.

However--and this is very important!--there are no theories given
experimental support today which show real violations of causality. (We
could debate for a few days whether delayed-choice experiments,
Aharonov-Bohm experiments, etc. show violations of causality. While
entangled states show behaviors not found in the macroscopic,
classical, human-scale world, they don't violate causality.)

This argues for the emphasis placed on causal sets and causal
relations. And hence on posets and lattices. (In my opinion, following
the lead of the several authors I've mentioned a few times here.)

> 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?

Well, I try not to get too many of my theories out of science fiction!

Not to sound flip or dismissive, but Egan's novels and short stories
are best seen as romps through a landscape of strange and stimulating
ideas. I like his stuff a lot because he's one of the few writers today
able to (or interested in) keep up with modern physics and modern math.
There was a time when SF writers were engineers or scientists (Asimov,
Heinlein, Clarke, Hal Clement, even Larry Niven, who was at Caltech for
a while). Their editors were also science-oriented people, like Hugo
Gernsback and John Campbell, who wanted hard science in the science
ficiton they bought.

In their day, these authors wrote stories and novels involving the
then-weird ideas of hypercubes, Mobius bands, planets with extremely
high gravity, time travel, neutron stars, and black holes. (Larry Niven
was the Greg Egan of his day. Niven still writes, but his recent novels
are less compelling and certainly no longer are exploring cutting-edge
stuff.)

As SF spread in popularity to the Baby Boom generation, more and more
non-scientists and non-engineers started writing. So we got more
"sociological" SF (some of it very good, like Ursula LeGuin's stuff).
And more of the "palace intrigue" kind of novels ("The planet Cthwox
has been ruled by the Klanring for 2000 years. A spaceship from the
Vegan Federation has arrived..."). And then there is fantasy...dragons,
magic, etc.

A few writers have stuck to hard science themes. Vernor Vinge is a good
example. And some of the "cyberpunk" themes have been more or less
based on plausible science, including Gibson, Walter Jon Williams,
Bruce Sterling, Dan Simmons, etc. (I also like a less popular author,
David Zindell, and his quartet of novels set on the planet "Neverness."
Mathematics plays an unusual role.)

Steven Baxter also writes Stapletonian novels about the distant future
and the end of time, though his themes are often depressing (to me at
least).

Greg Egan is one of the few writers today actually _using_ the latest
developments in physics and even math to explore ideas about the nature
of our reality, the anthropic principle, and the colonization of
cyberspaces.

It also turns out that Egan has been doing some Java and Mathematica
programming for some of the spin foam papers by Baez and others. This
doesn't mean that any particular idea he explores, whether in
"Distress" or "Diaspora" or "Schild's Ladder," is "right," just that
Egan is obvious technically competent to write about these ideas.

What fired me up about "Distress" in particular was the several-page
synopsis of the "All Topologies Model." For some reason, this got my
juices flowing. (The rest of the novel just sort of plodded along to a
fairly predictable conclusion.)

I hope this explains why I don't look to Egan's fictional character for
actual theories, just stimulation.

--Tim May
Received on Wed Sep 04 2002 - 09:25:16 PDT