View source for Cooper Pair Mass Anomaly

= Cooper Pair Mass Anomaly =

{{Audience_Sidebar
| difficulty   = Intermediate
| reading_time = 10 minutes
| prerequisites = Superconductivity basics ([[BCS_Theory|BCS]]; Cooper pairs); some QM.
| if_too_advanced_see = [[Famous_Experiments]]
| if_you_want_the_math_see = [[Tate_Experiment]]; [[Modified_Einstein_Equations_with_Psi]]
}}

{{Notation
| psi_convention   = ψ = scalar field amplitude (NB: not the BCS condensate wavefunction, which has a different ψ in the condensed-matter literature — see "Notation" below).
| signature        = Mostly-plus.
| units            = SI for the experimental observables; ℏ = c = 1 in the field-theoretic expressions.
}}

The '''Cooper-pair mass anomaly''' is a 1989 high-precision measurement at Stanford that found the effective mass of a Cooper pair in a rotating niobium superconductor to be ''heavier'' than the [[BCS_Theory|BCS]] theoretical prediction by approximately '''84 parts per million''' — a deviation many standard-deviations outside the experimental error budget.

The anomaly has stood unreplicated since 1989. Within the [[Psionics|psionic framework]] it is one of the cleanest empirical hints of a ψ-field-mediated correction to a fundamental quantum-mechanical mass measurement.

== The measurement ==

The experiment was performed by '''James Tate, Blas Cabrera, Susan B. Felch, and James T. Anderson''' at Stanford in 1989 and published in ''Physical Review Letters'' (62: 845–848). They used the magnetic-flux-quantisation property of a rotating superconducting ring (the "London moment" effect) to determine the effective Cooper-pair mass to high precision.

The setup:

* A niobium superconducting ring is cooled below T<sub>c</sub> ≈ 9.25 K.
* The ring is rotated about its axis at angular velocity ω.
* The London moment produces a magnetic field inside the ring proportional to ω and to the Cooper-pair mass m*.
* Precise SQUID magnetometry measures this field.

From the London formula '''B''' = −(2m*<sub>e</sub>/e) '''ω''' the Cooper-pair mass m*<sub>e</sub> can be extracted with high precision (here m*<sub>e</sub> ≡ Cooper-pair effective mass per electron).

== The result ==

The standard BCS prediction (with electromagnetic corrections) for the Cooper-pair effective mass is:

  m*<sub>e</sub><sup>BCS</sup>(theory) = 2 m<sub>e</sub> · (1 + small corrections of order 10<sup>−6</sup>)

Tate et al. measured:

  m*<sub>e</sub>(experiment) = 2 m<sub>e</sub> · (1 + 8.4 × 10<sup>−5</sup>)

— a deviation of '''84 ppm''', or ~ 14 standard deviations above the theoretical value when systematics are properly accounted.

The 84 ppm excess is far above any electromagnetic correction Tate could think of. In their paper they catalogue every standard-physics correction they could devise and find that none accounts for more than a fraction of the excess.

== Replication status ==

'''Unreplicated''' to date. No group has repeated the experiment with the same or better precision in the 35+ years since publication. The original result stands; no one has confirmed or refuted it.

Why hasn't it been replicated?

# The experiment is hard and expensive (SQUID magnetometry on rotating cryogenic systems).
# The condensed-matter community largely did not consider the result theoretically important (it is small and consistent enough with BCS that the question is not pressing within the mainstream framework).
# The parapsychology / fringe-physics community lacks the resources for high-precision condensed-matter measurements.

A modern repeat (with improved SQUID arrays, modern cryogenics, multiple superconductor materials) would either confirm the anomaly — making it one of the most important measurements in physics — or eliminate it. It is one of the highest-priority experiments in the [[Open_Questions_in_Psionics|open-questions]] list.

== Interpretations ==

=== Mainstream interpretation: hidden systematic ===

The default mainstream interpretation is that some unidentified systematic effect inflated the apparent mass by 84 ppm. Candidates:

* Magnetic-field penetration through the ring's surface.
* Pinned vortex contributions.
* Imperfect rotation symmetry / stray torques.
* Calibration errors in the SQUID magnetometers.

Tate et al. argue against all of these in their paper, but the mainstream view is that until replicated, "unknown systematic" is the most likely answer.

=== Psionic-framework interpretation: ψ-coupling correction ===

In the [[Psionics|psionic framework]], the Cooper-pair condensate is a highly-coherent quantum state of macroscopic size — exactly the kind of state expected to couple strongly to the [[Psi_Field|ψ field]] through the α F<sub>μν</sub>F<sup>μν</sup> ψ vertex. The ψ-field expectation value inside the condensate modifies the effective Cooper-pair mass via:

:<math>m^{*\,\text{effective}}_e = m^{*\,\text{BCS}}_e\,(1 + \varepsilon_\psi)</math>

with ε<sub>ψ</sub> determined by the local ψ-field amplitude inside the condensate. The framework predicts ε<sub>ψ</sub> ~ 10<sup>−4</sup>–10<sup>−5</sup> for typical condensate conditions — '''exactly the magnitude observed by Tate'''.

This is not a derivation — the framework cannot yet predict the precise value of ε<sub>ψ</sub> from first principles — but it is a striking quantitative match between the empirical anomaly and the predicted size of the leading ψ correction.

=== Related anomalies ===

If the Cooper-pair mass anomaly is ψ-coupling, then ''other'' high-coherence condensates should show analogous mass / inertia anomalies. The [[Gravitomagnetic_London_Moment|Tajmar gravitomagnetic London moment]] (2007) — measured in the same kind of rotating superconducting system — is structurally compatible with this interpretation. Two distinct measurement channels probing the same underlying phenomenon would significantly raise the empirical credibility of the framework if both are confirmed.

== What would settle the question ==

A modern, well-controlled, multi-laboratory replication of the Tate experiment. Specifically:

* Use multiple superconductor materials (Nb, Pb, YBCO, MgB<sub>2</sub>) to check material independence.
* Use multiple SQUID configurations (axial, gradient) to check field-measurement systematics.
* Vary ring geometry and rotation rate to check kinematic systematics.
* Compare in situ with high-precision atomic-mass measurements to cross-check.

A clean confirmation of the 84 ppm anomaly would be one of the most important condensed-matter measurements in modern physics — and a strong empirical hint that something beyond BCS + EM is operating in coherent quantum systems.

== Sanity checks ==

* '''Non-rotating ring''' → no London moment; no test possible. ✓
* '''Above T<sub>c</sub>''' → no condensate; standard electron transport. ✓
* '''ψ → 0''' (negligible ψ-field background) → standard BCS prediction. ✓ ([[Sanity_Check_Limits]] §7.)

== See Also ==

* [[Tate_Experiment]] — detailed methodological page.
* [[James_E_Tate]] — biographical page on the lead author.
* [[Douglas_G_Torr]] — collaborator on the gravitomagnetic-superconductor framework.
* [[Gravitomagnetic_London_Moment]] — sister anomaly in the same kind of system.
* [[Famous_Experiments]]
* [[Open_Questions_in_Psionics]]
* [[Modified_Einstein_Equations_with_Psi]]
* [[Sanity_Check_Limits]]

== References ==

* Tate, J., Cabrera, B., Felch, S. B., Anderson, J. T. (1989). "Precise determination of the Cooper-pair mass." ''Physical Review Letters'' 62: 845–848.
* Tate, J., Cabrera, B., Felch, S. B., Anderson, J. T. (1990). "Determination of the Cooper-pair mass in niobium." ''Physical Review B'' 42: 7885–7893.
* Tajmar, M., de Matos, C. J. (2003). "Gravitomagnetic field of a rotating superconductor and a rotating superfluid." ''Physica C'' 385: 551–554.
* Bardeen, J., Cooper, L. N., Schrieffer, J. R. (1957). "Theory of superconductivity." ''Physical Review'' 108: 1175–1204. (Original BCS.)

[[Category:Psionics]]
[[Category:Anomalies]]
[[Category:Experiments]]
[[Category:Gravity]]