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At the start of this chapter we observed that the continuous real line that we see is a creation of our brain and nervous system. Everything we see and touch is made up of fundamental particles. These particles cannot be subdivided into smaller units although they can transform into different particles. The universe of objects is discrete not continuous. This is equally true of wave phenomena such as light which is made up of particles called photons. We see something only when particles of light interact with photo receptors in our eye.

Although objects in space-time are all discrete space-time itself remains continuous in special and general relativity. Those theories are so dependent on the classical continuum that Einstein recognized any fully discrete theory would imply relativity was only approximately true and would make false predictions at the scale of space-time discreteness (see Section 5.1).

Space-time is very strange in quantum mechanics. It remains continuous but it has a peculiar connectivity because of quantum entanglement. In classical physics and relativity space is separable. You can fully describe what happens in any localized region over a brief time interval without taking into account distant events. This is not possible in quantum mechanics.

The nonrelativistic version of quantum mechanics exist not in
physical space but in an abstract higher dimensional structure
known as configuration space where there is a
single time dimension and a separate set of spatial dimensions for
every particle. See Figure 6.1. The connection between
configuration space and physical space is through a probability
distribution which gives the probability that a
given *configuration* of particles will be observed.

In physical space we do not have anything like the classical real line. What exactly we do have is not clear since the actualization of probabilities in configuration space to events in physical space is not part of any existing scientific theory.

A mathematical model from a scientific theory may have little to do with how nature is structured. Obviously it must provide an accurate approximation in its experimental predictions. Classical mechanics is very accurate for a wide range of experiments but quantum mechanics has shown that the structure of physical reality must differ radically, Some physicists argue that it is naive realism to expect a correspondence between nature and our mathematical models. While one must admit that anything is possible and there are many aspects of existing theory that make it seem difficult to construct such a correspondence we suspect that those are problems in the existing theories and our understanding of nature. Mathematics can model what nature does to extraordinarily accuracy and this leads us to suspect that nature at its core has a mathematical structure.

Quantum entanglement is at the core of the strangeness in contemporary physics. The evidence that distant events influence each other in ways that can never be explained by a local mechanism is dramatic and compelling but not totally conclusive (see Section 6.6). Experiments as always will decide the issue but what we make of experiments and how decisive they need to be is and always will remain a matter of judgment. One of the factors that goes into such judgments is our sense of what alternative possibilities exist. Fully discrete models would be radically different than anything we have previously investigated. They hold the possibility of the more complete theory Einstein sought. There may be an experimental path that leads to such a theory. All of these issues fall under the problem of integrating relativity and quantum mechanics which is the subject of the next chapter.

Completed
second draft of this book

PDF version
of this book

**Next:** Relativity plus quantum mechanics **Up:**
Digital
physics **Previous:** Quantum Entanglement
**Contents**

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