Modern physics has revolutionized our understanding of space and time. Experiments like Gravity Probe B and observations of binary pulsars have confirmed Einstein's predictions about frame-dragging and geodetic effects with incredible precision.

These tests push the boundaries of experimental physics, using ultra-precise gyroscopes and cosmic clocks. They provide compelling evidence for general relativity, validating our current model of gravity and spacetime curvature.

Experimental Tests of Frame-Dragging

Gravity Probe B Experiment

• Gravity Probe B launched in 2004 to measure frame-dragging and geodetic effects
• Consisted of four gyroscopes in a satellite orbiting Earth at an altitude of about 640 km
• Gyroscopes were nearly perfect spheres coated with superconducting niobium (precision of 0.5 micrometers)
• Measured the precession of the gyroscopes due to the curvature of spacetime (geodetic effect) and the dragging of spacetime by Earth's rotation (frame-dragging)
• Confirmed the predicted geodetic effect to an accuracy of 0.28% and frame-dragging to an accuracy of 19%

Frame-Dragging and the Lense-Thirring Effect

• Frame-dragging is a phenomenon predicted by general relativity where a rotating massive object "drags" spacetime along with it
• Causes nearby objects and light to be "dragged" in the direction of the rotation
• Also known as the Lense-Thirring effect, named after Austrian physicists Josef Lense and Hans Thirring who first described it in 1918
• Effect is very small and difficult to measure (precession of a gyroscope in Earth's orbit is only 0.042 arcseconds per year)
• Has been measured by Gravity Probe B and observations of pulsars in binary systems

Measuring Frame-Dragging with Pulsar Timing

• Pulsars are rapidly rotating neutron stars that emit beams of electromagnetic radiation
• Act as precise cosmic clocks due to their extremely stable rotation periods (can be measured to within a few microseconds over years)
• In a binary system with another neutron star or white dwarf, the pulsar's orbit is affected by frame-dragging
• Precise timing of the pulsar's pulses can reveal these relativistic effects
• PSR J0737-3039A/B, a double pulsar system, has provided some of the most stringent tests of general relativity and frame-dragging

Geodetic Effects and Equivalence Principle

Geodetic Effect and Spacetime Curvature

• Geodetic effect is the precession of a gyroscope's spin axis due to the curvature of spacetime
• Caused by the motion of the gyroscope through the curved spacetime around a massive object like Earth
• Predicted by general relativity and measured by Gravity Probe B to an accuracy of 0.28%
• Effect is larger than frame-dragging (precession of 6.6 arcseconds per year for a gyroscope in Earth's orbit)

Testing the Strong Equivalence Principle

• Strong equivalence principle states that the outcome of any local non-gravitational experiment should be independent of where and when it is performed
• Implies that self-gravitating objects (like planets or stars) should follow the same trajectories as test particles in a gravitational field
• Lunar laser ranging measures the distance between Earth and the Moon with centimeter precision using retroreflectors placed on the Moon by Apollo astronauts
• Has tested the strong equivalence principle to a few parts in $10^{13}$ by comparing the free-fall accelerations of the Moon and Earth towards the Sun

Very Long Baseline Interferometry (VLBI)

• VLBI is a technique that combines radio telescopes across the globe to create a virtual telescope with a size equal to the maximum separation between the telescopes
• Provides extremely precise measurements of the positions of distant astronomical objects (accuracy better than 1 milliarcsecond)
• Used to measure the geodetic effect by observing the apparent positions of quasars as the Earth moves through the curved spacetime around the Sun
• Has confirmed the predictions of general relativity to within a few parts in $10^4$

Binary Pulsar Observations

The Hulse-Taylor Binary (PSR B1913+16)

• Discovered in 1974 by Russell Hulse and Joseph Taylor, it was the first binary pulsar system found
• Consists of two neutron stars orbiting each other with a period of about 7.75 hours
• One of the neutron stars is a pulsar with a spin period of 59 milliseconds
• Observations of the pulsar's timing have revealed relativistic effects such as the decay of the orbit due to gravitational wave emission
• Provided the first indirect evidence for the existence of gravitational waves and won Hulse and Taylor the 1993 Nobel Prize in Physics

Testing General Relativity with Pulsar Timing

• Binary pulsars provide unique laboratories for testing general relativity in strong gravitational fields
• Relativistic effects cause deviations from the predicted Keplerian orbit, which can be measured through precise timing of the pulsar's pulses
• Effects include perihelion precession, time dilation, and the Shapiro delay (delay of light passing through the gravitational well of the companion star)
• The double pulsar system PSR J0737-3039A/B has allowed tests of general relativity to a precision of better than 0.05%

Frame-Dragging and the Strong Equivalence Principle in Binary Pulsars

• Binary pulsars can also be used to measure frame-dragging and test the strong equivalence principle
• Frame-dragging causes a precession of the orbit, which can be detected through long-term timing observations
• The strong equivalence principle predicts that the neutron stars' self-gravity should not affect their orbital motion
• Observations of the double pulsar system have verified the strong equivalence principle to within 0.01%, providing one of the most stringent tests to date