[Paper Review] Non-time-orthogonal Reference Frames in the Theory of Relativity

Robert D. Klauber|ArXiv.org|May 28, 2000

Relativity and Gravitational Theory3 citations

TL;DR

This paper resolves apparent contradictions in relativistic rotating frames by analyzing non-time-orthogonal (NTO) reference frames, showing that the speed of light appears non-isotropic and non-invariant locally in such frames due to their geometric structure. The analysis explains the persistent signal in the Brillet and Hall Michelson-Morley experiment and confirms consistency with Sagnac-type experiments and cyclotron data, all within standard relativity without requiring preferred frames or theory modification.

ABSTRACT

A simple, though rarely considered, thought experiment on relativistic rotation is described in which internal inconsistencies in the theory of relativity seem to arise. These apparent inconsistencies are resolved by appropriate insight into the nature, and unique properties, of the non-time-orthogonal rotating frame. The analysis also explains a heretofore inexplicable experimental result.

Motivation & Objective

• To resolve apparent inconsistencies in relativistic rotation where light speed appears anisotropic in rotating frames.
• To clarify the physical interpretation of the speed of light in non-time-orthogonal (NTO) reference frames.
• To explain the persistent signal in the Brillet and Hall Michelson-Morley experiment using standard relativity.
• To demonstrate that NTO frames are inherently non-Lorentzian and require reinterpretation of simultaneity and light propagation.
• To show that standard relativity remains consistent when NTO frames are properly analyzed, without invoking preferred frames or theory modification.

Proposed method

• Analyzes a thought experiment involving light pulses emitted in opposite directions on a rotating disk, comparing lab and rotating frame observations.
• Applies the standard rotating frame transformation (equation 2) to relate rotating and inertial frames, assuming invariance of the 4D line element ds.
• Distinguishes between coordinate speed (dependent on metric components) and physical speed (measured with local rods and clocks).
• Uses differential geometry to model the rotating frame as a non-time-orthogonal spacetime, where time is not orthogonal to at least one spatial dimension.
• Derives the condition for non-time-orthogonality from the metric tensor components, particularly g_tt and g_xx.
• Compares predictions of NTO analysis with experimental results, including Sagnac effect and cyclotron mass-energy increase.

Experimental results

Research questions

• RQ1 Why does the speed of light appear to differ in opposite directions in a rotating frame, contradicting the postulate of invariance?
• RQ2 How can the persistent signal in the Brillet and Hall Michelson-Morley experiment be explained within standard relativity?
• RQ3 What is the physical significance of non-time-orthogonal frames in the context of general and special relativity?
• RQ4 Why do standard Lorentz transformations fail as local approximations in rotating (NTO) frames?
• RQ5 Can the Sagnac effect and time dilation in cyclotrons be consistently explained without introducing preferred frames?

Key findings

• The speed of light in a rotating (NTO) frame is non-isotropic and non-invariant in coordinate terms, but physical speed measured locally remains c.
• The apparent contradiction in light travel times on a rotating disk arises from the non-time-orthogonal nature of the rotating frame, not from a flaw in relativity.
• The analysis explains the persistent signal in the Brillet and Hall experiment as a consequence of non-time-orthogonality, not a violation of relativity.
• Rotating frames are fundamentally non-time-orthogonal, and simultaneity is shared between rotating and inertial frames, implying no Lorentz contraction between them.
• NTO analysis correctly predicts time dilation and mass-energy increase in cyclotrons, consistent with experimental data.
• The Sagnac effect is fully explained by the NTO framework, with no need for alternative theories or preferred frames.