Abstract
We outline an argument that a singleparticle 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 longheld distinction is also to some extent illusory.
Similar content being viewed by others
Notes
Following Earman and Norton Earman and Norton (1987), we consider the accompanying stressenergy 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 spacetime—is to describe at least part of spacetime. By contrast, to give the manifold without the metric is not to give a spacetime, or part of a spacetime, 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:

Singleparticle universe
References
Andréka, H., Madarász, J.X., & Németi, I. (2004). Logical analysis of relativity theories’. In: Hendricks et al. (Eds.), FirstOrder Logic Revisited (pp. 1–30). Berlin: LogosVerlag.
Andréka, H., Madarász, J. X., Németi, I., & Székely, G. (2008). Axiomatizing relativistic dynamics without conservation postulates. Studia Logica, 89(2), 163–186.
Andréka, H., Madarász, J. X., Németi, I., & Székely, G. (2012). A logic road from special relativity to general relativity. Synthese, 186(3), 633–649.
Bachelard, G. (1968). The philosophy of no: A philosophy of the new scientific mind. London: Orion Press.
Bilaniuk, O. M. P., Deshpande, V. K., & Sudarshan, E. C. G. (1962). Meta relativity. American Journal of Physics, 30, 718–723.
Bojowald, M. (2012). Quantum gravity, spacetime structure, and cosmology. Journal of Physics: Conference Series, 405(1), 012001.
Doplicher, S., Fredenhagen, K., & Roberts, J. (1995). The quantum structure of spacetime at the Planck scale and quantum fields. Communications in Mathematical Physics, 172(1), 187–220.
Dowker, F. (2005), Causal sets and the eep structure of spacetime. In: A. Ashetkar (Ed.), 100 Years of relativity: Spacetime structure: Einstein and Beyond. Singapore: World Scientific. arXiv:grqc/0508109v1.
Dowker, F., Henson, J., & Sorkin, R. D. (2004). Quantum gravity phenomenology, Lorentz invariance and discreteness. Modern Physics Letters, A19, 1829–1840.
Earman, J. & Norton, J. (1987). What price substantivalism? The hole story. The British Journal for the Philosophy of Science 38, 515–525.
Einstein, A. (1920). Relativity: The special and general theory. New York: Henry Holt.
Feynman, R. P. (1949). The theory of positrons. Physical Review, 76, 749–759.
Feynman, R. P., & Hibbs, A. R. (1965). Quantum mechanics and path integrals. New York: McGraw Hill.
Glymour, C. (1972). Topology, cosmology, and convention. Synthese, 24, 195–218.
Hoefer, C. (1996). The metaphysics of spacetime substantivalism. The Journal of Philosophy, 93(1), 5–27.
Huggett, N. & Hoefer, C. (2009). Absolute and relational theories of space and motion. In: E. N. Zalta (Ed.), The stanford encyclopedia of philosophy. Stanford, Stanford University, fall 2009 edition.
Kuhn, T. S. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.
Madarász, J. X., Németi, I., & Székely, G. (2007). Firstorder logic foundation of relativity theories. In: D. Gabbay, S. Goncharov, and M. Zakharyaschev (Eds.), Mathematical problems from applied logic. Logics for the 21st Century, No. 2 in International Mathematical Series (Vol. 5), Mathematical problems from applied logic. Springer.
Madarász, J. X., Székely, G., & Stannett, M. (2014). Why do the relativistic masses and momenta of fasterthanlight particles decrease as their speeds increase?. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 10(005). 21.
Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. San Francisco: Freeman.
Németi, I. & Andréka, H. (2006). Can general relativistic computers break the Turing barrier?. In: A. Beckmann, U. Berger, B. Löwe, and J. V. Tucker (Eds.), Proceedings of Logical approaches to computational barriers, second conference on Computability in Europe, CiE 2006, Swansea, July 2006, (Vol. 3988) of Lecture Notes in Computer Science(pp. 398–412). Berlin Heidelberg: Springer.
Rynasiewicz, R. (1996). Absolute vs. relational spacetime: an outmoded debate? The Journal of Philosophy, 93(6), 279–306.
Smolin, L. (2006). The case for background independence. In D. Rickles, S. French, & J. Saatsi (Eds.), The structural foundations of quantum gravity (pp. 196–239). Oxford: Oxford University Press.
Stannett, M. (2009a). Modelling quantum theoretical trajectories within geometric relativistic theories. In: Mathematics, physics and philosophy in the interpretations of relativity theory, Budapest 4–6 September 2009. arXiv:0909.1061 [grqc].
Stannett, M. (2009b). The computational status of physics. Natural Computing, 8(3), 517–538.
Stannett, M. (2012). Computing the appearance of physical reality. Applied Mathematics and Computation, 219(1), 54–62.
Stückelberg, E. C. G. (1941). Un nouveau modèle de l’électron ponctuel en théorie classique. Helvetica Physica Acta, 14, 51–80.
Sudarshan, E. C. G. (1970). The theory of particles traveling faster than light I. In: A. Ramakrishnan (Ed.), Symposia on theoretical physics and mathematics 10 (pp. 129–151). New York, Plenum Press.
Székely, G. (2009). Firstorder logic investigation of relativity theory with an emphasis on accelerated observers. Ph.D. thesis, Eötvös Loránd University, Institute of Mathematics.
Wüthrich, C. (2012). The Structure of Causal Sets. Journal for General Philosophy of Science, 43(2), 223–241.
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to István Németi on the occasion of his 70th birthday.
Rights and permissions
About this article
Cite this article
Stannett, M. Motion and observation in a singleparticle universe. Synthese 192, 2261–2271 (2015). https://doi.org/10.1007/s112290140489z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s112290140489z