Determining Metric of Space-Time (H.P. Robertson 1949)

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Discussion Overview

The discussion centers on H.P. Robertson's 1949 paper analyzing the implications of several key experiments in the context of special relativity and the metric of space-time. Participants explore the meaning of "im kleinen" in Robertson's work, the limitations of the experiments he referenced, and the potential for space-time to deviate from the Minkowski metric on larger scales.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the meaning of "im kleinen" and its implications for the applicability of the Minkowski metric on larger scales.
  • Another participant interprets "im kleinen" as indicating that space-time is locally Minkowskian, suggesting that global deviations may occur due to general relativistic effects.
  • A different participant notes that the experiments cited by Robertson were only accurate to second order, which limited their ability to address larger scale effects.
  • Further reading by a participant leads to insights about spherical wave transformations of Maxwell's equations, which suggest that while locally the waves behave as if in a Minkowski space-time, they may not be globally Minkowskian.
  • The discussion touches on the relationship between special relativity and general relativity, with one participant asserting that Robertson's remarks reflect the understanding of special relativity as the local limit of general relativity.

Areas of Agreement / Disagreement

Participants express differing interpretations of Robertson's conclusions and the implications of the experiments he analyzed. There is no consensus on whether Robertson believed space-time could deviate from the Minkowski metric on larger scales, and the discussion remains unresolved regarding the extent to which this question has been experimentally addressed since his paper.

Contextual Notes

Limitations include the accuracy of the experiments discussed, which were only second order, and the potential for higher order effects to influence the understanding of space-time metrics on larger scales.

ConformalGrpOp
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In a paper published in Reviews of Modern Physics in 1949, http://journals.aps.org/rmp/pdf/10.1103/RevModPhys.21.378 , H.P. Robertson provided an analysis of the physical implications of the Michelson/Morley, Kennedy and Thorndike, and Ives and Stilwell experiments which seems definitive with respect to the points he sought to address. But, in his conclusion, he wrote something that, to some degree, is puzzling, or in some sense, seems unexpectedly incomplete. He writes:

[T]he three second-order optical experiments of Michelson and Morley, of Kennedy and Thorndike, and of Ives and Stilwell, furnished empirical evidence which, within the limits of the inductive method, enables us to conclude that the three parameters (g0, g1, g2), may be taken as independent of the motion of the observer. The kinematics im kleinen of physical space-time is thus found to be governed by the Minkowski metric, whose motions are the Lorentz transformations, the background upon which the special theory of relativity and its later extension to the general theory are based.

My first question is, what exactly did he intend to mean when he used the term "im kleinen" (trans: "in the small", or "in small scale"), and why did he stop there and not demonstrate that the Minkowski metric governs the kinematics, "im grossen" of space-time?

Second, setting aside general relativistic and other "field" effects, does it mean that Robertson conceived that it was possible that space-time on a large scale might not be governed by the Minkowski metric? Why would/wouldnt he have been able to resolve the question at that time? To what extent has this question been addressed or resolved experimentally since Robertson's paper?
 
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Read "im kleinen" as "locally" and he's saying that spacetime is locally Minkowskian everywhere. It's not globally Minkowskian because of general relativistic effects.
 
ConformalGrpOp said:
Why would/wouldnt he have been able to resolve the question at that time
The experiments he was using were accurate to second order only. So they couldn't resolve the question on scales large enough for third or higher order effects to matter.
 
Thank you Nugatory and DaleSpam.

I have since done some further reading on tests of SR, e.g.:

http://relativity.livingreviews.org/Articles/lrr-2005-5/download/lrr-2005-5Color.pdf
http://arxiv.org/pdf/hep-ph/9703240v3.pdf
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Domain_of_Applicability

which, together with your comments, answer the points of inquiry I had with respect to Robertson's remarks.

I came across a paper about, and have been researching the subject of spherical wave transformations of Maxwell's equations which result in velocity independent redshifts, i.e, light propagating with wave numbers that evolve as a function of distance/time. The transformations are not Poincare invariant, but preserve causality. Locally the waves appear to propagate in a space-time governed by the Minkowski metric. In fact, since the transformations are conformal, a local observer is not able to distinguish the fact that the radiation is propagating in a space-time that is non-Minkowskian (except by a rather "large" scale experiment). But, I think it is clear from the literature that Nugatory's reply to my inquiry is correct, that Robertson's remark relates to the fact that SR has been understood as the "local" limit of GR, and not to the fact that the second order optical experiments discussed in his paper were "local" lab experiments, per se.
 
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