But this conclusion depends greatly on traditional assumptions about the nature of space and of particles. And it turns out that for the kinds of models I have discussed here it in general no longer holds.

And the basic reason for this is that if the universe is a network then it can in a sense easily contain threads that continue to connect particles even when the particles get far apart in terms of ordinary space.

The picture that emerges is then of a background containing a very large number of connections that maintain an approximation to three-dimensional space, together with a few threads that in effect go outside of that space to make direct connections between particles.

If two particles get created together, it is reasonable to expect that the tangles that represent their cores will tend to have a few connections in common—and indeed this for example happens for lumps of non-planarity of the kind we discussed on page 527. But until there are interactions that change the structure of the cores, these common connections will then remain—and will continue to define a thread that goes directly from one particle to the other.

But there is immediately a slight subtlety here. For earlier in this chapter I discussed measuring distance on a network just by counting the minimum number of successive individual connections that one has to follow in order to get from one point to another. Yet if one uses this measure of distance then the distance between two particles will always tend to remain fixed as the number of connections in the thread.

But the point is that this measure of distance is in reality just a simple idealization of what is relevant in practice. For the only way we end up actually being able to measure physical distances is in effect by looking at the propagation of photons or other particles. Yet such particles always involve many nodes. And while they can get from one point to another through the large number of connections that define the background space, they cannot in a sense fit through a small number of connections in a thread. So this means that distance as we normally experience it is typically not affected by threads.

But it does not mean that threads can have no effect at all. And indeed what I suspect is that it is precisely the presence of threads that leads to the correlations that are seen in measurements on particles.

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From Stephen Wolfram: A New Kind of Science [citation]