Computing the appearance of physical reality☆

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Abstract

The role of theoretical physics is to investigate, represent and thereby explain the nature of physical reality. We claim that this goal is unattainable using current standard mathematical models of physics, not just for practical reasons, but as a matter of logical necessity. Standard models of quantum theory and relativistic spacetime are logically equivalent to models in which the nature of classically observable motions is a form of necessary illusion. Consequently, no standard deductions as to the nature of space, time and motion can be deemed sound.

Section snippets

Manifesto

All mathematical theories of physics (even quantum theories) ultimately depend for their validation upon classical observations. This is inevitable, since no matter what form a physical apparatus may take, the observations made using that apparatus must ultimately be conveyed to and interpreted by human beings using biological sensory systems that have evolved, for better or worse, to interpret the world directly in classical terms.

Being classical, these observations all involve a physical

Motion

What can we say about the way bodies move in space and time? We will begin by considering this question in the context of inertial bodies subject to special relativistic kinematics as formalised in [1], [2], [3] by the theory SpecRel over (1 + N)-dimensional spacetime, where N > 1 (e.g. taking N = 3 corresponds to one temporal dimension and three spatial ones).

Restriction to dense subfields

As with all theories, the usefulness of SpecRel relies on the relevance of its axioms, and the most fundamental of these is AxField, the assertion that Q is an ordered Euclidean field. However, Q is primarily used to coordinatize spacetime, whereas our focus is on observations. This presents no problems to theories like SpecRel, provided we assume that observed non-geometric values, like mass, also range over Q, but in ‘real life’ not even the most accurate physical measurements can be made to

Algebraic hops

As we have noted, superpositions of Q-paths lead inexorably to the continuous motion we expect to see in theories like SpecRel. But we need to decide which hops are permissible. We are arguing that continuous motion in QN+1 is an ‘illusion’ induced by quantum superposition. But if we are happy to assert that continuous motion is illusory, what about finitary motion? In fact, we can even argue that all motion is an illusion generated by underspecification of Q.

Our starting point is the

Summary and conclusions

It follows from Theorem 4.2.1 that the equations of finitary motion can all be re-expressed in terms of algebraic hops, whence the existence of algebraic hops is itself enough to generate the appearance that particles move along continuous paths in QN+1. In particular, since it tells us that m sees herself moving continuously along her time axis, it also tells us why time appears to flow.

This is rather unexpected, because an algebraic hop that swaps α and β is essentially an extension of the

Acknowledgements

This research was funded in part by the EPSRC (HyperNet, Grant Ref. EP/E064183/1). My especial thanks go to the members of the Budapest Relativity Group (especially István, Hajnal, Judit and Gergely), who very kindly set aside several days in early 2009 to explain their logical approach to relativity theory to me.

References (4)

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    Logical Analysis of Relativity Theories

  • H. Andréka et al.

    Logic of space-time and relativity theory

There are more references available in the full text version of this article.
☆

This paper is an extended version of an informal talk presented at Physics and Computation 2010, Nile River, Egypt, 30 Aug–3 Sep 2010. It is based in part on a talk presented at PIRT (Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory), Budapest, 4–6 September 2009.

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