JonoThora: Create Tate Experiment — Cooper pair mass anomaly (84 ppm), London moment measurement, competing interpretations, Magneto Speeder connection

2026-03-14T06:00:11Z

Create Tate Experiment — Cooper pair mass anomaly (84 ppm), London moment measurement, competing interpretations, Magneto Speeder connection

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{{Infobox
| title = Tate Experiment
| image =
| caption = Precision measurement of Cooper pair mass via London moment
| header1 = Overview
| label2 = Principal Investigator
| data2 = Janet L. Tate (Stanford University)
| label3 = Supervisor
| data3 = Blas Cabrera
| label4 = Year
| data4 = 1989–1990
| label5 = Method
| data5 = SQUID measurement of London moment in spinning Nb
| label6 = Key Result
| data6 = Cooper pair mass excess: δ ≈ 8.4 × 10⁻⁵ (84 ppm)
| label7 = Publication
| data7 = Physical Review Letters 62, 845 (1989)
| label8 = Status
| data8 = Experimentally confirmed · Interpretation disputed
| below = ''Only experimental anomaly supporting [[Ning Li|Li-Torr]] gravitomagnetic theory''
}}
{| class="wikitable"
|+
| ⚡️ || [[Electrogravitics]] - [[Electrogravitic Tech]] || [[Electrokinetics]] - [[Electrokinetic Tech]]
|-
| 🧲 || [[Magnetogravitics]] - [[Magnetogravitic Tech]] || [[Magnetokinetics]] - [[Magnetokinetic Tech]]
|}

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''': <ref>London, F. (1950). ''Superfluids'', Vol. 1. Wiley, New York.</ref>

<math>\vec{B}_L = -\frac{2m_e}{e}\vec{\omega}</math>

where <math>m_e</math> is the electron mass, <math>e</math> is the electron charge, and <math>\vec{\omega}</math> is the angular velocity. The coefficient <math>2m_e/e</math> 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''':

<math>\vec{B}_L = -\frac{m^*}{e^*}\vec{\omega}</math>

where <math>m^* = 2m_e(1 + \delta)</math> is the Cooper pair mass and <math>e^* = 2e</math> is the Cooper pair charge. Any deviation <math>\delta \neq 0</math> would indicate physics beyond the standard London theory.

== Experimental Setup ==

{| class="wikitable"
|+ 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 <math>B_L/\omega</math> to extract <math>m^*/e^*</math>
|-
| 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 <math>dB_L/d\omega</math> to determine <math>m^*/e^*</math> with high precision.

== Results ==

=== Key Measurement ===

<ref>Tate, J.L., Cabrera, B., Felch, S.B. & Anderson, J.T. (1989). "Precise determination of the Cooper-pair mass." ''Physical Review Letters'' 62, 845–848. doi:10.1103/PhysRevLett.62.845</ref>

<ref>Tate, J.L., Cabrera, B., Felch, S.B. & Anderson, J.T. (1990). "Determination of the Cooper-pair mass in niobium." ''Physical Review B'' 42, 7885–7893. doi:10.1103/PhysRevB.42.7885</ref>

<math>m^* = 2m_e\left(1 + (8.4 \pm 0.2) \times 10^{-5}\right)</math>

The measured Cooper pair mass is '''84 ± 2 parts per million''' higher than the theoretical value of <math>2m_e</math>.

{| class="wikitable"
|+ Tate Results Summary
|-
! Quantity !! Expected !! Measured !! Deviation
|-
| Cooper pair mass <math>m^*</math> || <math>2m_e = 1.82189 \times 10^{-30}</math> kg || <math>2m_e(1 + 8.4 \times 10^{-5})</math> || +84 ppm
|-
| <math>B_L/\omega</math> ratio || <math>-1.13460 \times 10^{-11}</math> T/(rad/s) || <math>-1.13470 \times 10^{-11}</math> 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 ==

{| class="wikitable"
|+ 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:

<math>\delta m = m^* - 2m_e = \frac{2G}{c^2}\cdot\rho_{\text{lattice}}\cdot V_{\text{coherence}} \cdot f(\text{coupling})</math>

where <math>\rho_{\text{lattice}}</math> is the lattice mass density and <math>V_{\text{coherence}}</math> 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 <math>(v_F/c)^2 \sim 10^{-5}</math>
* Many-body interactions within the Cooper pair

The debate has never been conclusively resolved because:
# The anomaly has only been measured in '''niobium''' — no systematic comparison across different superconducting materials has been published
# 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 <math>2m_e/e</math>. 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 [[Gravitoelectromagnetism|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:

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

{| class="wikitable"
|+ From Tate to Magneto Speeder
|-
! Link !! Connection
|-
| Tate → [[Ning Li|Li-Torr]] || Mass anomaly motivates gravitomagnetic coupling theory
|-
| Li-Torr → [[Gravitomagnetic London Moment]] || Theory predicts controllable gravitomagnetic field generation
|-
| London Moment → [[Martin Tajmar|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]]

== References ==
<references />

[[Category:Physics]]
[[Category:Technology]]
[[Category:Magnetogravitic Tech]]
[[Category:Clan Tho'ra]]

Tate Experiment - Revision history

JonoThora: Create Tate Experiment — Cooper pair mass anomaly (84 ppm), London moment measurement, competing interpretations, Magneto Speeder connection