The coordinate-independent 2-component spinor formalism and the conventionality of simultaneity

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Abstract

In recent articles, Zangari (1994) and Karakostas (1997) observe that while an ε-extended version of the proper orthochronous Lorentz group O + (1,3) exists for values of ε not equal to zero, no similar ε-extended version of its double covering group SL(2, C) exists (where ε = 1 - 2ε R, with ε R the non-standard simultaneity parameter of Reichenbach). Thus, they maintain, since SL(2, C) is essential in describing the rotational behaviour of half-integer spin fields, and since there is empirical evidence for such behaviour, ε-coordinate transformations for any value of ε ≠ 0 are ruled out empirically. In this article, I make two observations: (a) There is an isomorphism between even-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions of such spinor fields. (b) There is a 2-1 isomorphism between odd-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions for such spinor fields up to a sign. Evidence that the components of such fields do take unique values is not decisive in favour of the realist in the debate over the conventionality of simultaneity in so far as such fields do not play a role in clock synchrony experiments in general, and determinations of the one-way speed of light in particular. I claim that these observations are made clear when one considers the coordinate-independent 2-spinor formalism. They are less evident if one restricts oneself to earlier coordinate-dependent formalisms. I end by distinguishing these conclusions from those drawn by the critique of Zangari given by Gunn and Vetharaniam (1995).

Original languageEnglish (US)
Pages (from-to)201-226
Number of pages26
JournalStudies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics
Volume31
Issue number2
StatePublished - Jun 2000

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isomorphism
tensors
formalism
coordinate transformations
clocks
integers
coverings
Conventionality
Simultaneity
Formalism
Isomorphism

Keywords

  • Conventionalism
  • Formalism
  • Simultaneity
  • Spacetime
  • Spinors

ASJC Scopus subject areas

  • History
  • Physics and Astronomy(all)

Cite this

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abstract = "In recent articles, Zangari (1994) and Karakostas (1997) observe that while an ε-extended version of the proper orthochronous Lorentz group O ↑ + (1,3) exists for values of ε not equal to zero, no similar ε-extended version of its double covering group SL(2, C) exists (where ε = 1 - 2ε R, with ε R the non-standard simultaneity parameter of Reichenbach). Thus, they maintain, since SL(2, C) is essential in describing the rotational behaviour of half-integer spin fields, and since there is empirical evidence for such behaviour, ε-coordinate transformations for any value of ε ≠ 0 are ruled out empirically. In this article, I make two observations: (a) There is an isomorphism between even-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions of such spinor fields. (b) There is a 2-1 isomorphism between odd-indexed 2-spinor fields and Minkowski world-tensors which can be exploited to obtain generally covariant expressions for such spinor fields up to a sign. Evidence that the components of such fields do take unique values is not decisive in favour of the realist in the debate over the conventionality of simultaneity in so far as such fields do not play a role in clock synchrony experiments in general, and determinations of the one-way speed of light in particular. I claim that these observations are made clear when one considers the coordinate-independent 2-spinor formalism. They are less evident if one restricts oneself to earlier coordinate-dependent formalisms. I end by distinguishing these conclusions from those drawn by the critique of Zangari given by Gunn and Vetharaniam (1995).",
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