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= Lense–Thirring Frame Dragging =

{{Audience_Sidebar
| difficulty = Intermediate
| reading_time = 10 minutes
| prerequisites = Basic [[General_Relativity|GR]]; linearised gravity; [[Gravitoelectromagnetism|GEM]] is helpful but not strictly required.
| if_too_advanced_see = [[What_is_Frame_Dragging]]
| if_you_want_the_math_see = [[Gravitoelectromagnetism]]; [[Modified_Einstein_Equations_with_Psi]]
}}

{{Notation
| psi_convention = ψ = scalar field amplitude.
| signature = Mostly-plus (−,+,+,+).
| units = SI for observable quantities.
}}

The '''Lense–Thirring effect''' (also called '''frame-dragging''') is the prediction of General Relativity that a rotating mass drags spacetime around with itself. Discovered in 1918 by Josef Lense and Hans Thirring, the effect was confirmed experimentally in 2011 by the [[Gravity_Probe_B]] satellite mission.

Frame-dragging is the gravitational analogue of a magnetic field surrounding a moving electric current — a key prediction of [[Gravitoelectromagnetism|GEM]].

== The classical prediction ==

For a stationary, axisymmetric mass M rotating with angular momentum '''J''', the gravitomagnetic field at distance '''r''' from the centre is:

'''B'''g('''r''') = (G / c2 r3) [ 3 ('''r̂''' · '''J''')'''r̂''' − '''J''' ]

This is the gravitational analogue of a magnetic dipole field. A test gyroscope at distance r experiences a precession of its spin axis:

'''Ω'''LT = (G / c2 r3) [ 3 ('''r̂''' · '''J''')'''r̂''' − '''J''' ] · (1/2)

For Earth (J ≈ 5.86 × 1033 kg m2/s) at the orbital altitude of [[Gravity_Probe_B]] (~ 642 km), the predicted Lense–Thirring precession is approximately '''39.2 milliarcseconds per year'''.

== The physical picture ==

Imagine spacetime as a viscous fluid surrounding a spinning ball. As the ball rotates, it drags the surrounding fluid along with it. In GR the "fluid" is the inertial-reference-frame structure of spacetime itself — and a freely-falling gyroscope (which would, in flat spacetime, keep its axis fixed relative to the distant stars) is instead carried along by the rotating frame.

The effect is tiny in everyday situations (Earth's rotation drags inertial frames by less than a millionth of a degree per year) but becomes dramatic near rotating black holes, where frame-dragging is so extreme it produces the "ergosphere" — a region where ''no'' inertial observer can remain stationary relative to the distant stars.

== Experimental confirmation ==

=== Gravity Probe B (2011) ===

The dedicated [[Gravity_Probe_B]] mission flew four superconducting gyroscopes in polar orbit around Earth from 2004 to 2005, with data analysis completed in 2011. The mission measured both:

* '''Geodetic effect''' (de Sitter precession): 6601.8 ± 18.3 mas/yr (GR prediction: 6606 mas/yr — confirmed to 0.3 %).
* '''Frame-dragging (Lense–Thirring)''': 37.2 ± 7.2 mas/yr (GR prediction: 39.2 mas/yr — confirmed to ~19 %).

This is the cleanest direct measurement of frame-dragging to date. Published as ''Physical Review Letters'' 106: 221101 (2011).

=== LAGEOS satellites ===

Two passive laser-ranging satellites (LAGEOS, LAGEOS 2) have been used since 1976 to measure frame-dragging via the precession of their orbital plane. Ciufolini and collaborators (2004, 2010) report agreement with GR's frame-dragging prediction at the 10 % level.

=== LARES (2012–present) ===

The LARES satellite — designed specifically to improve frame-dragging measurements — has confirmed the LT effect to about 5 % accuracy by 2016.

== Frame-dragging near astrophysical objects ==

The effect becomes important near:

* '''Rotating black holes''' — the Kerr metric describes spacetime around a spinning black hole; frame-dragging is responsible for the ergosphere and for the Penrose process (extracting rotational energy).
* '''Neutron stars''' — typical frame-dragging frequencies ~ 10−2 Hz near the surface of a millisecond pulsar.
* '''The galactic centre''' — Sgr A* exhibits frame-dragging effects on stellar orbits at the milli-arcsecond level.

== Coupling to ψ in the present framework ==

In the [[Psionics|psionic framework]], frame-dragging is unmodified at the [[Sanity_Check_Limits|sanity-check limit 11]] where ψ → 0. The standard prediction is recovered exactly — and [[Gravity_Probe_B]] confirms it.

In regions where ψ is dynamically significant, additional gravitomagnetic source terms appear:

:<math>\mathbf{B}_g(\mathbf{r}) = \mathbf{B}_g^{\text{standard}}(\mathbf{r}) + \bigl(\text{extra }\psi\text{-contribution from }\!\int \mathbf{j}_\psi\,d^3 r'\bigr)</math>

This is the rigorous mathematical basis for the prediction that '''rotating superconductors and other strong-ψ-coupling systems should show anomalously large frame-dragging'''. The [[Gravitomagnetic_London_Moment|Tajmar 2007 anomaly]] (28 orders of magnitude larger than GR predicts in a rotating superconductor) is consistent with this picture.

== Why the factor of 4 ==

A famous puzzle in GEM: the factor of 4 in the gravitomagnetic Lorentz analog '''F''' = m('''E'''g + 4'''v''' × '''B'''g/c) compared with the EM Lorentz force '''F''' = q('''E''' + '''v''' × '''B'''). The factor comes from the spin-2 nature of gravity: a gravitational "dipole moment" sourced by a mass current couples 4× as strongly as the corresponding electromagnetic dipole would. This is not an arbitrary normalisation but a consequence of the tensor structure of GR.

== Sanity checks ==

* '''Non-rotating mass (J = 0)''' → '''B'''g = 0; no frame-dragging. ✓
* '''v → 0''' → only the Newtonian (gravitoelectric) force; the LT force vanishes. ✓
* '''ψ → 0''' → standard Kerr-like frame-dragging. ✓ ([[Sanity_Check_Limits]] §11.)
* '''Weak-field limit''' → linearised GEM equations. ✓ ([[Gravitoelectromagnetism]].)

== See Also ==

* [[What_is_Frame_Dragging]]
* [[Gravity_Probe_B]]
* [[Gravitoelectromagnetism]]
* [[Gravitomagnetic_London_Moment]]
* [[Modified_Einstein_Equations_with_Psi]]
* [[Famous_Experiments]]

== References ==

* Lense, J., Thirring, H. (1918). "Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie." ''Physikalische Zeitschrift'' 19: 156–163.
* Everitt, C. W. F., et al. (2011). "Gravity Probe B: Final Results of a Space Experiment to Test General Relativity." ''Physical Review Letters'' 106: 221101.
* Ciufolini, I., et al. (2004). "Confirmation of the General Relativistic Prediction of the Lense-Thirring Effect." ''Nature'' 431: 958–960.
* Ciufolini, I., et al. (2016). "A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model." ''European Physical Journal C'' 76: 120.

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

Lense-Thirring Frame Dragging - Revision history

JonoThora: Phase N (01b): LaTeX restoration — promote Unicode display-math to ; lint-clean per tools/wiki_latex_lint.py

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