Abstract
We outline an argument that a single-particle universe (a universe containing precisely one pointlike particle) can be described mathematically, in which observation can be considered meaningful despite the a priori impossibility of distinguishing between an observer and the observed. Moreover, we argue, such a universe can be observationally similar to the world we see around us. It is arguably impossible, therefore, to determine by experimental observation of the physical world whether the universe we inhabit contains one particle or many—modern scientific theories cannot, therefore, be regarded as descriptions of ‘reality’, but are at best human artefacts. Our argument uses a formal model of spacetime that can be considered either relational or substantivalist depending on one’s preferred level of abstraction, and therefore suggests that this long-held distinction is also to some extent illusory.
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Notes
Following Earman and Norton Earman and Norton (1987), we consider the accompanying stress-energy tensor \(T\) to be contained within, rather than a constituent part of, spacetime; but we reject their identification of spacetime with the manifold \(M\), adopting instead Hoefer’s view that spacetime is more properly represented by the metric tensor \(g\): “To give the metric field without specifying the global topology—always possible for at least small patches of space-time—is to describe at least part of space-time. By contrast, to give the manifold without the metric is not to give a space-time, or part of a space-time, at all.” (Hoefer 1996, pp. 24–25).
“The way to protect the embedding against a loss of Lorentz invariance is by sprinkling the points randomly. Causal set theory uses a ... Poisson sprinkling [which] exhibits exact Lorentz invariance for Minkowski spacetime.” (Dowker 2005, p. 451).
Universal quantification over free variables is assumed implicitly in these axioms.
We are grateful to an anonymous referee for noting that a related construction was given by Adolphe Bühl in 1934. This construction, which potentially provides a physical meaning to the sums of certain ‘sawtooth’ hop trajectories, is described in (Bachelard 1968).
We are grateful to an anonymous referee for this suggestion.
Abbreviations
- CST:
-
Causal set theory
- FOL:
-
First order logic
- FORT:
-
First order relativity theory
- GR:
-
General relativity
- SPU:
-
Single-particle universe
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Dedicated to István Németi on the occasion of his 70th birthday.
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Stannett, M. Motion and observation in a single-particle universe. Synthese 192, 2261–2271 (2015). https://doi.org/10.1007/s11229-014-0489-z
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DOI: https://doi.org/10.1007/s11229-014-0489-z