Tate Experiment

Tate Experiment
Overview
Principal Investigator	Janet L. Tate (Stanford University)
Supervisor	Blas Cabrera
Year	1989–1990
Method	SQUID measurement of London moment in spinning Nb
Key Result	Cooper pair mass excess: δ ≈ 8.4 × 10⁻⁵ (84 ppm)
Publication	Physical Review Letters 62, 845 (1989)
Status	Experimentally confirmed · Interpretation disputed
Only experimental anomaly supporting Li-Torr gravitomagnetic theory

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The Tate experiment (1989–1990) was a precision measurement of the Cooper pair mass in a spinning niobium superconductor at Stanford University. By measuring the London moment — the magnetic field generated by a rotating superconductor — with SQUID magnetometers, Tate et al. determined the effective mass of the Cooper pairs with extraordinary precision and found a statistically significant excess of approximately 84 parts per million above the expected value of twice the electron mass.

This anomaly is the single most important experimental data point in the gravitomagnetic superconductor debate. Ning Li interpreted the excess as evidence of gravitomagnetic coupling between the lattice ions and the Cooper pairs — the key prediction of the Gravitomagnetic London Moment theory.

Background: The London Moment

When a superconductor rotates, the Cooper pairs (which carry the supercurrent) cannot rotate with the lattice. This creates a charge imbalance that generates a magnetic field aligned with the rotation axis — the London moment:

${\vec {B}}_{L}=-{\frac {2m_{e}}{e}}{\vec {\omega }}$

where $m_{e}$ is the electron mass, $e$ is the electron charge, and ${\vec {\omega }}$ is the angular velocity. The coefficient $2m_{e}/e$ is universal for any superconductor — it depends only on the electron mass and charge, not on the material.

More precisely, the London moment measures the effective mass of the Cooper pair:

${\vec {B}}_{L}=-{\frac {m^{*}}{e^{*}}}{\vec {\omega }}$

where $m^{*}=2m_{e}(1+\delta )$ is the Cooper pair mass and $e^{*}=2e$ is the Cooper pair charge. Any deviation $\delta \neq 0$ would indicate physics beyond the standard London theory.

Experimental Setup

Tate Experiment Parameters

Component	Specification
Sample	Niobium (Nb) superconducting cylinder
Temperature	~4.2 K (liquid helium)
Rotation speeds	Various (up to ~100 rad/s)
Detector	DC SQUID magnetometer (superconducting quantum interference device)
Measurement	Ratio $B_{L}/\omega$ to extract $m^{*}/e^{*}$
Shielding	Superconducting lead shield to eliminate external magnetic fields
Calibration	Earth's field, applied coils, mechanical rotation system

The experiment measured the London moment at multiple rotation speeds and extrapolated the slope $dB_{L}/d\omega$ to determine $m^{*}/e^{*}$ with high precision.

Results

Key Measurement

$m^{*}=2m_{e}\left(1+(8.4\pm 0.2)\times 10^{-5}\right)$

The measured Cooper pair mass is 84 ± 2 parts per million higher than the theoretical value of $2m_{e}$.

Tate Results Summary

Quantity	Expected	Measured	Deviation
Cooper pair mass $m^{*}$	$2m_{e}=1.82189\times 10^{-30}$ kg	$2m_{e}(1+8.4\times 10^{-5})$	+84 ppm
$B_{L}/\omega$ ratio	$-1.13460\times 10^{-11}$ T/(rad/s)	$-1.13470\times 10^{-11}$ T/(rad/s)	+84 ppm
Statistical significance	—	~42σ	Highly significant

The anomaly is statistically very robust (~42 standard deviations). This is not a measurement error.

Competing Interpretations

Interpretations of the Tate Anomaly

Interpretation	Proponent(s)	Mechanism	Implication
Gravitomagnetic coupling	Ning Li & Torr (1991)	Lattice ions contribute gravitomagnetic correction to Cooper pair effective mass	Superconductors amplify gravitomagnetic fields by ~10¹¹×
Band structure effects	Various	electron-phonon interaction modifies effective mass in Nb	No exotic physics needed
Relativistic correction	Verheijen et al. (1990)	Special relativistic mass enhancement from Fermi velocity	Accounts for ~50% of anomaly
Many-body correction	Hirsch (2014)	Electron-electron interaction within Cooper pair	Predicts material-dependent mass excess
Systematic error	Skeptics	Unknown systematic in rotation calibration	Requires explaining 42σ deviation

The Li-Torr Interpretation (Gravitomagnetic)

Ning Li argued that when a superconductor rotates, the lattice ions (which carry most of the mass) generate a gravitomagnetic field through the Gravitomagnetic London Moment. This field couples to the Cooper pairs, effectively adding a gravitomagnetic contribution to their inertial mass:

$\delta m=m^{*}-2m_{e}={\frac {2G}{c^{2}}}\cdot \rho _{\text{lattice}}\cdot V_{\text{coherence}}\cdot f({\text{coupling}})$

where $\rho _{\text{lattice}}$ is the lattice mass density and $V_{\text{coherence}}$ is the coherence volume. The 84 ppm excess, in this picture, directly measures the strength of the gravitomagnetic coupling.

The Conventional Interpretation

Mainstream condensed matter physics attributes the mass excess to:

• Band-structure (effective mass) corrections specific to niobium
• Relativistic corrections of order $(v_{F}/c)^{2}\sim 10^{-5}$
• Many-body interactions within the Cooper pair

The debate has never been conclusively resolved because:

1. The anomaly has only been measured in niobium — no systematic comparison across different superconducting materials has been published
2. The predicted gravitomagnetic effect is too small to detect by any method other than the London moment (making independent verification extremely difficult)

Connection to Gravity Probe B

Gravity Probe B also relied on the London moment of spinning niobium spheres (coated gyroscope rotors) for its readout system. GP-B calibrated its SQUID readout using the expected value of $2m_{e}/e$. The Tate anomaly implies that GPB's London moment readout carried a systematic offset of 84 ppm — small enough to be within their systematic error budget but potentially significant for ultra-precision measurements.

This creates an interesting cross-check: GP-B confirmed gravitomagnetic frame-dragging (validating GEM) while simultaneously relying on a readout mechanism that may itself be affected by gravitomagnetic coupling.

Significance for Magneto Speeder

The Tate anomaly matters for the Magneto Speeder because:

1. It is experimentally real (42σ significance, published in Phys. Rev. Lett.)
2. If the Li-Torr interpretation is correct, it directly measures the gravitomagnetic coupling strength in superconductors
3. The magnitude (84 ppm) is consistent with Li-Torr's predicted amplification factor
4. It motivates the search for stronger gravitomagnetic effects in rapidly rotating superconductors — exactly what Martin Tajmar attempted

From Tate to Magneto Speeder

Link	Connection
Tate → Li-Torr	Mass anomaly motivates gravitomagnetic coupling theory
Li-Torr → Gravitomagnetic London Moment	Theory predicts controllable gravitomagnetic field generation
London Moment → Tajmar	Tajmar attempts to detect the predicted field
Tajmar → Magneto Speeder	If confirmed, provides engineering basis for magnetogravitic drive

See Also

• Ning Li
• Gravitomagnetic London Moment
• Martin Tajmar
• Gravity Probe B
• Gravitoelectromagnetism
• Magnetogravitics
• Magneto Speeder
• Magnetogravitic Tech