Registered: Dec 2003
Posts: 179

Special Relativity describes a static 4D universe:

http://www.cosmik-debris.net/?p=39

NKS, on the otherhand, describes complex systems as a set of simple rules applied to initial conditions for a dynamic system.

Are NKS and SR fundamentally incompatible?

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Registered: Jul 2005
Posts: 4

A big question. My little guess is: not if the nodes are gooey enough so they don't break approaching c.

Or if each observer has his own network. I prefer gooey nodes though.

:)

PS "Static" is very subjective.

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Registered: Dec 2003
Posts: 179

> PS "Static" is very subjective.

Why do you say that?

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Registered: Oct 2003
Posts: 103

Oyvind Tafjord gave a talk at the NKS 2004 conference in Boston which showed in detail how to get Special Relativity from Stephen Wolfram's causal networks.

http://www.wolframscience.com/confe...yvindtafjord.nb

You might also be interested in Tafjord's materials from his summer school lectures.

http://www.wolframscience.com/summerschool/materials/

It is an interesting question of how far the limit v->c can go in any discrete theory. In particular, a finite number of points in a truncated light cone necessarily show the shifting corresponding to Lorentz transformations.

It's also worth keeping in mind that traditional continuum theories are meant to be approximations. There is always some scale in which they lose their validity, and that applies also to SR as v approachs c.

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Registered: Jul 2005
Posts: 4

Really nice application of SR on the causal network. Thanks for the links, and thanks for Mathematica too. So much easier to see whats going on.

This did inspire a question and since I'm away from my Mathematica at the moment I thought I would ask it.

The man in the lighthouse lets say he is running rule 110. The man in the very fast boat going 3/5ths light speed gets the SR skewed output of 110 after arbitrary t. He uses this as his input and applies rule 110 for arbitrary t. What does the boatmans output look like from his reference point?

SR encoding and decoding on causal networks?

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Registered: Jul 2005
Posts: 4

"The causal invariance is important because it ensures that all different slices corresponds to an actual evolution.

We see that in such a universe, the order in which the rules are applied depends on your point of view!"

Makes sense now.

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Registered: Jun 2006
Posts: 1

Sorry to be re-opening an old thread:

I'm not sure that Tafjord's presention explains how NKS deals with special relativity, though it does illustrate some properties of SR in "conventional" science. Einstein himself formulated SR by considering the relationships between "events", as Tafjord has done - there are three possible configurations for a pair of events A and B in special relativity:

1. A occurs before B in all reference frames; A has causal influence on B.
2. A occurs after B in all reference frames; B has causal influence on A.
3. A and B occur sufficiently far apart in all reference frames that neither can influence the other. For some observers, A is before B; for others, A is after B; and for others they are simultaneous.

A pair of events is always in the same category for all observers, so causality is conserved. Tafjord's statement that "the order in which the rules are applied depends on your point of view" is also a good description of conventional Einsteinian special relativity; some people say that star A exploded before star B, and others say that star B exploded before star A - but this doesn't matter, since this implies that the explosions are too far apart to influence one another.

So how does all this relate to NKS? I'm not sure. I must confess that I haven't read the NKS book in its entirety, so I may be misunderstanding something. On page 3 of the presentation, Tafjord says, "Rather than starting with rigid cells with synchronized updates, we instead focus on causal events built from an asynchronous underlying evolution". So in his model the cells themselves are the EVENTS in the universe, not part of the space-time structure in which the events occur. This implies that the existence of the "cells" (events) is determined dynamically by other cells, which seems to be a departure from NKS (?). Also, the updates are also not synchronized in any way (it would be impossible to synchronize them in every reference frame, unless we impose a discrete structure for the events and Lorentz transformations).

Also - I disagree with Todd Rowland's comment that special relativity "loses its validity" as v approaches c (that's what Newtonian physics does - which is why we need SR at high velocities). Conventional special relativity claims that the laws of physics are identical for observers at ANY speed less than c relative to ourselves. If you are saying that NKS must cease to comply with SR at some fixed speed v_max less than c, this is a fundamental (and testable, if you can quantify v_max) contradiction of Einstein. Worse still, v_max itself will be different for different observers: e.g. if I launch a rocket from the earth towards the sun at c/2, and this rocket launches another rocket forward at c/2, an Earth-bound observer will see the second rocket moving at 0.89c. If v_max were fixed at 0.7c (for example), this would mean that the second rocket "violates physics" when viewed from the earth, but not when viewed from the first rocket. This problem (and also the notion of "gooey nodes"!) would hint back to the 19th Century idea that physics has a preferred frame of reference - an idea completely at odds with SR.

Last edited by Matthew Ford on 06-21-2006 at 06:39 AM

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Registered: Feb 2006
Posts: 3

Actually, there was an article about compatibility of conventional physics with preferred frames of reference in Scientific American, Dec. 2005, "An ECHO of black holes":

http://www.sciam.com/article.cfm?ch...62A83414B7F0000

Worth a read!

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