Is the Sagnac effect a reliable measure of rotation in Kerr space-time?

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    Gravitation Inertia
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Discussion Overview

The discussion revolves around Mach's principle and its implications for inertia within the framework of General Relativity (GR), particularly in the context of Kerr space-time. Participants explore the relationship between inertia, gravity, and the influence of distant stars, raising questions about the nature of inertia in isolated systems.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants express confusion about whether inertia exists in a universe devoid of distant stars, questioning if a single particle would maintain its state of motion without external influences.
  • Others clarify that Mach's principle is not rigorously defined in GR and that inertia is also not consistently defined across literature, complicating discussions on the topic.
  • It is noted that inertial frames are influenced by both local gravitational fields and boundary conditions at spatial infinity, particularly in Kerr space-time, which may violate Mach's principle.
  • Some participants argue that in GR, acceleration and rotation can be defined without reference to distant stars, suggesting that a lone body can still exhibit acceleration and rotation independently.
  • There is a discussion about the implications of boundary conditions on the status of Mach's principle and inertia, with some participants indicating that the lack of a stress-energy tensor in an isolated system raises further questions about inertia.
  • One participant acknowledges the complexity of deriving inertia from spacetime and expresses a desire to understand the equivalence principle better.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of Mach's principle or the nature of inertia in isolated systems. Multiple competing views remain regarding the definitions and implications of these concepts in GR.

Contextual Notes

Limitations include the lack of rigorous definitions for inertia and Mach's principle, as well as unresolved questions about the implications of boundary conditions in GR. The discussion reflects a variety of interpretations and assumptions that are not universally accepted.

  • #31
A.T. said:
But in the Gravity Probe B experiment the precession was measured relative to a distant star, under the assumption that without the Earth nearby there would be no precession relative to that distant star. How is this assumption justified?

W assume our universe is an FLRW solution. There is no reason for this to be true within GR as a theory. We pick boundary specific conditions such that the solution with those conditions matches observation. Unless the theory forces those boundary conditions, it provides no explanation of what is behind them. Einstein strongly hoped GR would not need arbitrary boundary conditions, and considered it major defect that it does. It is up to some future theory to provide an explanatory framework.
 
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  • #32
A.T. said:
Is it just a coincidence that the local measurement of rotation (based on inertia, Sagnac) matches the global measurement of rotation (based on light from distant stars) ?

See post #3. To repeat, all of those fail to agree in Kerr space-time, which is a particular instance of what Bill elucidated.

We had a really long thread on this in the past, see: https://www.physicsforums.com/showthread.php?t=729416

EDIT: Also just as an aside, the Sagnac effect is not a local measure of rotation. If it was then it would always agree with the Fermi-Walker definition of rotation but it doesn't as mentioned in post #3. It is a quasi-local measure of rotation since it isn't as global as rotation with respect to spatial infinity but still not entirely local since it requires knowledge of the axial Killing field along the entire closed circuit and on the symmetry axis of the space-time.
 
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