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TAI and UTC are based on the SI second. The SI second is specifically defined in terms of cesium atoms at no temperature, no velocity, and no elevation (aka, on the geoid). Consequently TAI and UTC are immune from relativistic effects, by definition.

On the other hand, the physical clocks in the laboratory are not immune and that's why they have to be corrected for a dozen factors, the largest of which is usually gravitational redshift. To appreciate the complexity and precision of this correction see this NIST paper:

https://tf.nist.gov/general/pdf/2883.pdf

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> TAI and UTC are based on the SI second. The SI second is specifically defined in terms of cesium atoms at no temperature, no velocity, and no elevation (aka, on the geoid). Consequently TAI and UTC are immune from relativistic effects, by definition.

This is not quite correct. The definition of the SI second does not make any requirements or assumptions about the state of motion or location of the cesium atoms. The only requirement is that the device that measures the frequency of the cesium atom hyperfine transition is at rest relative to the atoms themselves and spatially co-located with them. That is what ensures that no relativistic effects are involved in the measurement.

The definitions of TAI and UTC are not simply based on the SI second, but on the SI second as recorded by clocks on the geoid that are at rest relative to the rotating Earth. That extra qualifier is why measurements recorded by clocks not on the geoid have to be adjusted.

I think you might be misunderstanding. Clocks must necessarily have a frame of reference. TAI's frame of reference is imaginary (geoid), and in reality we calculate it from an average.

Because TAI's frame of reference is the geoid it will experience relativistic effects based on earth's motion viewed from any other frame of reference (in OP's example, from the reference of the sun)

Clocks cannot exist without a frame of reference. Accurate timekeeping necessarily involves tracking spatial information as well.

The current SI second[0] does not make any mention of Earth. Elevation does not factor into the definition.

[0]: https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-... page 16

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