Completed
second draft of this book

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The structure of the universe

Central to this discussion of physics is the assumption that the structure of the universe is simple, understandable, mathematical and finite. If completed infinite totalities exist our philosophical views are false. The universe may however be unbounded and potentially infinite. Simplicity and in particular the simplicity implied by locality is not essential to the position we take but it is in the spirit that leads to that position. Quantum mechanics as it stands is consistent with a finite universe. A finite amount of information can fully characterize the state of any finite space time region.

Many physicists label assumptions like the above about locality
and simplicity as naive realism. They would
claim that as long as a theory has an elegant mathematical
formulation it is simple. Philosophical and aesthetic debates can
never be conclusive. Ultimately experiments will decide the issue
and tests of Bell's inequality are one arena where such tests are
possible. There are others. Quantum computing
takes advantage of the superposition of states to compute not a
single result but many possible results simultaneously. There are
important practical problems that quantum computing can in theory
solve that would require far too much computation for a practical
solution with conventional computers. These are not *recursively
unsolvable* problems. They just require computing power that
grows exponentially with the size of the problem on a standard
computer but not on a quantum computer.

There is significant research in this area. How far quantum computing can go depends on how accurately physical reality is described by quantum mechanics. Quantum computing will eventually fail if time and space have a discrete and not continuous structure.

Quantum cryptography comes in several forms some of which depend on quantum entanglement. In theory quantum cryptography can provide levels of security and tamper detection that are not possible with more conventional approaches. The attempt to develop practical devices in this area can run into problems if quantum entanglement results from an underlying mechanistic process that enforces the conservation laws.

The potential for economically important devices in these two areas provides an incentive to test the limits of physical theory that does not exist in tests of Bell's inequality.

Science provides simple explanations for complex systems. That has been its history. Two related aspects of quantum mechanics, irreducible probabilities and quantum entanglement, seem at odds with the historical trend. Quantum entanglement leads to space-time connections between events far more complex than the spatially separable universe of classical physics. Absolute randomness seems to be impossible to define mathematically since an absolutely random sequence would have to be recursively random but recursively random sequences cannot be truly random. They are higher up on the scale of mathematical complexity than recursive sequences.

To some quantum mechanics seems like a marvelous structure To this author it looks like a house of cards waiting for a gentle breeze to collapse it. There are too many interconnected implausible assumptions. Consistency with special relativity requires irreducible probabilities which implies no intermediate state evolution between observations. There can be no objective definition of observation although physics is dependent on experimental technique which has a well developed practical approach to objectively defining observation.

The claim is made that physicsts have come to understand the weird and wonderful way that nature is. No one can know for certain but skepticism is called for. One can always invent new philosophical principles to deal with the inexplicable. That was the standard approach before science.

Completed
second draft of this book

PDF version
of this book

**Next:** Bibliography **Up:** Relativity plus quantum
mechanics **Previous:** Exploring discretized wave
equations **Contents**

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