situations—save those associated with the overall expansion of the universe—the basic rules for the network at least on average just rearrange nodes and never change their number.

In traditional physics energy and momentum are always assumed to have continuous values. But just as in the case of position there is no contradiction with sufficiently small underlying discrete elements.

As I will discuss in the last section of this chapter, quantum mechanics tends to make one think of particles with higher momenta as being somehow progressively less spread out in space. So how can this be consistent with the idea that higher momentum is associated with having more nodes? Part of the answer probably has to do with the fact that outside the piece of the network that corresponds to the particle, the network presumably matches up to yield uniform space in much the same way as without the particle. And within the piece of the network corresponding to the particle, the effective structure of space may be very different—with for example more long-range connections added to reduce the effective overall distance.

The Phenomenon of Gravity

At an opposite extreme from elementary particles one can ask how the universe behaves on the largest possible scales. And the most obvious effect on such scales is the phenomenon of gravity. So how then might this emerge from the kinds of models I have discussed here?

The standard theory of gravity for nearly a century has been general relativity—which is based on the idea of associating gravity with curvature in space, then specifying how this curvature relates to the energy and momentum of whatever matter is present.

Something like a magnetic field in general has different effects on objects made of different materials. But a key observation verified experimentally to considerable accuracy is that gravity has exactly the same effect on the motion of different objects, regardless of what those objects are made of. And it is this that allows one to think of gravity as a general feature of space—rather than for example as some type of force that acts specifically on different objects.

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