A Clock That Cannot Be Dragged: Why the Preferred-Frame Test Does Not Bite a Cuscuton-Clock MOND Sector

A clock field defining a preferred foliation is normally in danger from the post-Newtonian preferred-frame parameters: a body moving at velocity w through the clock's rest frame sees a clock with a spatial gradient, and an order-unity coefficient in front of that tilt is excluded by roughly a factor of twelve for the solar system. An earlier action in this programme was killed on exactly this test. We show that a cuscuton-clock MOND sector with matter minimally coupled is blind to the boost at background level, for a structural rather than numerical reason. Because the background scalar depends only on the clock, its gradient is parallel to the clock's unit normal; the MOND invariant Y is by construction the part of the scalar's gradient orthogonal to that normal; and a boost tilts the normal and the gradient TOGETHER. Hence Y vanishes in the boosted frame exactly as at rest, to all orders in w, and no first-order preferred-frame coupling is generated at all. The clock rate, being a scalar, is likewise exactly invariant, with none of the second-order time dilation one would naively expect. What remains are two ordinary contributions: the sector's own boosted stress, 6e-16 of the Sun inside Saturn's orbit, and the scalar's leakage into the solar system, governed by the same double-filter screening whose length the static Cassini measurement of gamma already bounds. Solving for the screening length each measurement demands gives xi > 5.4e-4 pc for the preferred-frame bound against xi > 8.8e-4 pc for gamma: the static test is the more demanding, so the preferred-frame bound is satisfied automatically wherever it is, and the programme's floor of 0.03 pc clears the binding one by a factor of 34. The contrast with the action that died is diagnostic: there the clock was coupled to matter directly. No post-Newtonian parameter is extracted from a full metric expansion and none is claimed. AI-assisted research programme; not peer reviewed.

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Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-12
DOI
https://doi.org/10.5281/zenodo.22728788
Primary Topic
Advanced Frequency and Time Standards
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article
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article

A Clock That Cannot Be Dragged: Why the Preferred-Frame Test Does Not Bite a Cuscuton-Clock MOND Sector

Carl P. Zimmerman
Zenodo (CERN European Organization for Nuclear Research)
Advanced Frequency and Time Standards
article

A Clock That Cannot Be Dragged: Why the Preferred-Frame Test Does Not Bite a Cuscuton-Clock MOND Sector

Carl P. Zimmerman
article en

Abstract

A clock field defining a preferred foliation is normally in danger from the post-Newtonian preferred-frame parameters: a body moving at velocity w through the clock's rest frame sees a clock with a spatial gradient, and an order-unity coefficient in front of that tilt is excluded by roughly a factor of twelve for the solar system. An earlier action in this programme was killed on exactly this test. We show that a cuscuton-clock MOND sector with matter minimally coupled is blind to the boost at background level, for a structural rather than numerical reason. Because the background scalar depends only on the clock, its gradient is parallel to the clock's unit normal; the MOND invariant Y is by construction the part of the scalar's gradient orthogonal to that normal; and a boost tilts the normal and the gradient TOGETHER. Hence Y vanishes in the boosted frame exactly as at rest, to all orders in w, and no first-order preferred-frame coupling is generated at all. The clock rate, being a scalar, is likewise exactly invariant, with none of the second-order time dilation one would naively expect. What remains are two ordinary contributions: the sector's own boosted stress, 6e-16 of the Sun inside Saturn's orbit, and the scalar's leakage into the solar system, governed by the same double-filter screening whose length the static Cassini measurement of gamma already bounds. Solving for the screening length each measurement demands gives xi > 5.4e-4 pc for the preferred-frame bound against xi > 8.8e-4 pc for gamma: the static test is the more demanding, so the preferred-frame bound is satisfied automatically wherever it is, and the programme's floor of 0.03 pc clears the binding one by a factor of 34. The contrast with the action that died is diagnostic: there the clock was coupled to matter directly. No post-Newtonian parameter is extracted from a full metric expansion and none is claimed. AI-assisted research programme; not peer reviewed.

Zenodo (CERN European Organization for Nuclear Research)
Ad-Tech (United States) (US)
Openalex Percentile: Top 13%
Advanced Frequency and Time Standards
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