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Frame Dragging and Pulsars

by John G. Cramer

Alternate View Column AV-207
Keywords:   general relativity. frame dragging, rotating neutron star, Lense-Thirring effect, gravito-magnetic field, precession
Published in the July-August-2020 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 03/18/2020 and is copyrighted ©2020 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

An unusual binary star system has demonstrated  frame dragging, one of the most exotic predictions of Albert Einstein's general theory or relativity.  After 105 years of calculating and testing, general relativity remains our standard model of gravitation.  Let me begin with a brief history of Einstein's two theories of relativity.

In 1900, young Albert Einstein, characterized as an undergraduate by one of his professors as a "lazy dog", received his academic diploma in physics from the Swiss Federal Polytechnic Institute in Zurich .  When he failed to find an academic job after graduation, a friend arranged for his employment as a patent examiner in the Swiss Patent Office where he worked from 1902 to 1909.  He used his spare time from this rather undemanding job in the patent office to think about and work on several major unsolved problems in physics that interested him.

The year 1905 is called Einstein's annus mirabilis (or miracle year).  In this year he brought his spare-time work in physics to a spectacular conclusion by publishing ground-breaking physics papers in four different areas.  These included his explanation of the photoelectric effect, for which he later received the Nobel Prize in Physics, and in particular his development of the special theory of relativity.  Special relativity essentially asserts that the laws of physics, including mechanics and electromagnetism, must be the same when viewed by an observer in any inertial (i.e., non-accelerated) reference frame.  Einstein demonstrated that this requirement can only be met if longitudinal length gets shorter, time slows down, and mass increases when a moving system approaches the speed of light.

  In the following decade, as his physics reputation grew exponentially, he worked on the daunting problem of including gravity in his theory.  Finally in 1915, ten years after he had published his theory of special relativity, Einstein presented to the world his new general theory of relativity, which includes the effects of gravity.  General relativity requires that uniform acceleration is indistinguishable from a uniform gravitational field, an assumption called the equivalence principle.  Einstein's formulation asserts that mass produces the effects of gravity by curving space near the massive body.

General relativity predicts a number of effects that, over the years, have been observed to verify the theory.  It predicts the angular shift in the perihelion (i.e., the closest point to the Sun) in the orbit of the planet Mercury, which has been well observed by planetary astronomers.  It predicts the deflection of light by a massive body, which has been observed during total eclipses of the Sun.  It predicts the slowing of a clock in a gravitational field, which has been observed using gamma rays and the Mössbauer effect.  And it also predicts that space itself is twisted by the rotation of a nearby massive body.  This twisting of space is called "frame dragging".

Frame dragging is the gravitational analog of the magnetic field produced by an electric current or a moving charge.  It causes precession of the rotation axis of a spinning object that is in orbit around a rotating planet, collapsed star, or black hole.

In electromagnetism, consider a spinning electrically-charged sphere near a wire carrying an electric current.  Standard electromagnetic theory tells us that the electric current will produce a non-uniform magnetic field.  The spinning sphere of charge will develop a magnetic moment like a compass needle, on which the non-uniform magnetic field will exert a torque (or twisting force).  This torque will cause the spin axis of the sphere to precess, like a gyroscope on a string, so that it points in progressively different directions.

Einstein's general relativity tells us that in the world of gravity, a similar thing happens.  A massive rotating body like the Earth produces a "gravito-magnetic" field, the gravitational analog of a magnetic field.  A massive spinning body immersed in this gravito-magnetic field will experience a torque proportional to its angular momentum and rate of spin.  This gravitational phenomenon is an aspect of frame dragging called the Lense–Thirring effect.  The Lense–Thirring effect is quite small because gravity is a very weak force.  Even a spinning body as massive as the Earth will produce only a very small precession in the rotation axis of a rotating body in low-Earth orbit.

Gravity Probe B, an Earth-orbiting experiment containing an isolated spinning sphere, was designed by a group at Stanford University to test this effect.  It was initially funded by NASA as early as 1964 and was continued for the next forty years.  Finally in 2004, Gravity Probe B was launched and successfully measured the tiny Lense–Thirring precession effect (1.1×10-5 degrees/year) produced by the frame dragging of the Earth.

Another experimental demonstration of frame dragging came from NASA's GRACE mission, a pair of satellites in a polar orbit, one following the other around the Earth, with their longitudinal separation of about 220 km monitored by an optical interferometer.  GRACE found that each satellite was frame-dragged by about 6 feet per year because the very fabric of space was shifted by the gravito-magnetism of our spinning planet.


Radio astronomers have recently found an unusual binary star system in the Small Magellanic Cloud, about 200,000 light years from Earth, that by a fortunate accident seems ideally configured to demonstrate the frame-dragging effect.  It shows the effects of frame dragging much more dramatically than previous observations, with a precession rate of many degrees in a few hours, as compared to the few micro-degrees per year measured by Gravity Probe B.

This binary star system, named PSR J0045-7319, contains both a rapidly rotating white dwarf star and a radio pulsar.  These objects circle each other in an eccentric short-period orbit.  This system is only one of two known white dwarf plus neutron star binaries in which the white dwarf formed first and is older than the neutron star.  This requires an unusual stellar evolution scenario in which the older massive star must collapse to form the white dwarf, and then feed the other star with enough accreted mass to cause it to explode in a supernova and form the neutron star and resulting pulsar. This progression allows the young neutron star to retain the large magnetic field needed for a pulsar and to have a spin axis that is not aligned with its orbital plane.  This misalignment makes possible the observed general-relativity-related spin-axis precession.

The white dwarf member of PSR J0045-7319 has a rotation period of around 100 seconds (for comparison, our Sun has a rotation period of 24 days) and a mass of 1.02 solar masses.  The spinning neutron star that forms the radio pulsar has a rotation period of  about 394 milliseconds, a surface magnetic field of about two hundred million tesla, and a mass of 1.27 solar masses.  The binary pair orbit each other in an orbit with an eccentricity of 0.8 and a period of 4.74 hours.

Starting in the year 2000, radio astronomers used two radio telescopes located in Australia to measure and record the behavior of the pulsar.  In particular, they used the 64-meter Parkes radio telescope located 20 kilometers north of the town of Parkes in New South Wales, Australia  and also used the UTMOST "Mills Cross" radio telescope, a giant cross structure built of two 1.6 km long cylindrical-parabola arms and situated in a flat valley to the east of Canberra. They carefully observed and analyzed the time sequence of pulsar radio bursts emitted by PSR J0045-7319.

The precession of the spin axis of the pulsar modulates the pulsar pulse time-of-arrival.  It is a difficult and complicated process to deduce the properties of such a complex binary system using only the times between successive radio bursts from a pulsar.  They were able to accomplish this by comparing to the predictions of detailed models that included Newtonian effects as well as Einstein's frame-drag effect.  This constitutes a definitive demonstration of Lense–Thirring frame-dragging as predicted by general relativity.

We note that while the frame drag effect is large in the PSR J0045-7319 system, it would be much larger in the vicinity of a fast-rotating black hole because of the larger mass and smaller radius.  Perhaps there is a science fiction opportunity here for a protagonist to have his frame dragged.


John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at:  http://www.springer.com/gp/book/9783319246406 or https://www.amazon.com/dp/3319246402.

SF Novels by John Cramer:  Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at https://www.amazon.com/Twistor-John-Cramer/dp/048680450X and https://www.amazon.com/EINSTEINS-BRIDGE-H-John-Cramer/dp/0380975106 .  His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: http://www.npl.washington.edu/av .


References:

The Planck 2018 Analysis:
"Planck 2018 Results VI.  Cosmological Parameters", Aghanim, N., et al. (The Planck Collaboration); ArXiv:1807.06209 [astro-ph.CO] (2018).

Evidence for a Closed Universe:
"Planck evidence for a closed universe and a possible crisis for cosmology”, , Alessandro Melchiorri, and Joseph Silk, Nature Astronomy (2019) doi:10.1038/s41550-019-0906-9; ArXiv:1911.02087 [astro-ph.CO] (2019).

Fine Tuning:
Cosmic Coincidences - Dark Matter, Mankind, and Anthropic Cosmology, John Gribbin and Martin Rees, ReAnimus Press, Golden, CO (2015), ISBN-13: 978-1511915816.

Early Dark Energy:
"Early Dark Energy Can Resolve the Hubble Tension", Vivian Poulin, Tristan L. Smith, Tanvi Karwal, and Marc Kamionkowski, Phys. Rev. Lett. 122, 221301 (2019).


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