Vacuum Birefringence and Neutron Stars
by John G. Cramer
Polarization and birefringence are two of those quasi-obscure technical words derived from physical optics. Quantum physics tells us that a beam of light is a stream of photons, but at the same time it is a travelling wave made of oscillating electric and magnetic fields vibrating at right angles to the direction of wave motion and to each other. The light is said to be linearly polarized if the electric field always vibrates in the same plane, and we call that its plane of polarization. (Light can also be circularly polarized, elliptically polarized, or unpolarized, but we will ignore those complications for the present discussion.)
Birefringence refers to a special property of some transparent crystals within which the speed of a light beam passing through depends on the direction of polarization and on the direction of motion with respect to the axes of the crystal structure. Solid materials have atoms in their interiors containing lots of positive and negative electric charges. Because of all the possible electrical interactions, such materials should, in principle, stop a light beam dead in its tracks. However, some insulating solid materials like glass and crystals are transparent to light because the electrons they contain are bound (not free to move around and conduct electricity). As light passes by, these bound electrons are pushed-on by the passing electric field and vibrate like tiny masses-on-springs in time with the wave frequency. The coherent motion of these electrons, all vibrating together, captures and then re-emits the light energy, forming a sort of bucket-brigade transmission of the light through the material. In this process the speed of light is slowed to less than c (its velocity in vacuum), but the light is passed through the material without significant absorption. In glass this slowing of light makes possible refractive devices like lenses and prisms.
Crystals have an organized structure made of repeating arrangements of atoms. Polarized light passing through such crystals in one direction may encounter more tightly bound electrons (with different vibration properties) from the electrons more loosely bound in a perpendicular direction. This situation, which is called birefringence, has the result that polarized light travels faster in one crystal axis direction than in another. With another polarization direction of the light, this speed-difference effect may be changed because the electric driving force on the bound electrons is in its plane of polarization, the direction of the light’s electric field. Thus, light interacting with crystals produces complicated, interesting, and useful behavior. The crystal may split an incoming light beam into two different beams that travel with different speeds in different directions.
The best-known example of birefringence is the polarized double images that are seen when a printed page is viewed through a transparent crystal of calcite. In the optics laboratory birefringence is very useful, because it can be used to split a light beam into two separate beams with complementary polarizations. It can also be used to rotate the plane of polarization of a light beam or to change linear polarization to and from circular polarization.
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However, birefringence is not confined completely to the domain of crystals. Under extreme conditions it can become a property of the vacuum itself. In 1936, quantum mechanics pioneer Werner Heisenberg and his colleague Hans Euler reported their investigation of the influence of strong electric and magnetic fields on light. In this work, they used the then-emerging theory now known as quantum electrodynamics (QED). The QED theory depicts the quantum vacuum as full of virtual electrons and positrons, charged particles of somewhat indefinite mass that spontaneously appear, briefly interact with their environment, and then vanish. Heisenberg and Euler reasoned that the behavior of these virtual particles would have to be modified by a sufficiently strong magnetic field, changing the properties of the vacuum. They showed that when a region of “empty” space contains a magnetic field of greater than the critical value of 4.41 × 1013 gauss (or 4.41 billion tesla), the familiar linearity of the Maxwell theory of light moving in vacuum gives way to a quite unfamiliar nonlinear behavior. Later theorists showed that, in particular, the magnetically perturbed quantum vacuum becomes birefringent, so that light rays with planes of polarization parallel and perpendicular to a large external magnetic field will move with differing speeds. These speeds can both be significantly less than c, the standard vacuum velocity of light.
By ordinary standards, the magnitude of the magnetic field at which this vacuum birefringence phenomenon occurs is very large. Until fairly recently, the vacuum birefringence prediction of high-field QED was considered to be merely an interesting but completely untestable curiosity of the theory, because the required magnetic field strength was many millions of times larger than any conceivable magnetic field that might be created in a physics laboratory.
However, there is a domain in which the requirement of a 1013 gauss field does not look so formidable. That domain is the astrophysics of neutron stars. When a star of about ten times the mass of our Sun undergoes a supernova and collapses to a neutron star, the parent star’s preexisting magnetic field is trapped in the collapsing medium by circulating currents that become superconducting. The existing magnetic field is compressed to occupy a much smaller space, a spherical volume having a diameter of about 20 km or less. The magnetic field lines are squeezed together within this volume, and the field strength becomes very much larger. The result of this compression is that the surface magnetic field of an average neutron star is estimated to be about 1012 gauss or more. There is also a particularly x-ray-active class of neutron stars called magnetars that includes stars with even more intense magnetic fields, ranging of up to about 1015 gauss. Thus, the large magnetic fields provided by neutron stars would be expected to provide fertile testing ground for investigating the QED predictions of vacuum birefringence.
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In particular, we would like to determine if the visible light emitted by neutron stars shows any indication of linear polarization. However, that is not as easy as it sounds. Many neutron stars are pulsars, producing a tight beam of radio waves, light, and x-rays that is briefly visible to astronomers on Earth when the beam sweeps by as the neutron star rotates on its spin axis. The beam-sweep appears as a pulse of radiation, with a very precise interval between successive pulses that ranges from milliseconds to seconds,. The pulsar’s visible light is not of interest for vacuum birefringence tests because it is emitted along the direction of the magnetic field, where QED predicts that no birefringence polarization effects should be observed.
Instead, we are interested in the non-pulsed ambient light from neutron stars, preferably emitted in a direction perpendicular to the magnetic field. The problem with observing such light is that neutron stars are very dim except when pulsing. While they are often surrounded by highly visible supernova remnants, neutron stars on their own emit very little non-pulsed visible light. This means that measuring the polarization of the non-pulsed visible light coming from a neutron star is very difficult. Fortunately, there are a few neutron stars within our immediate galactic neighborhood that happen to be close enough to the Earth to be visible with the most powerful telescope complexes presently available.
One of those powerful telescope complexes is the Very Large Telescope (VLT) of the Paranal Observatory operated by the European Southern Observatory (ESO) in Northern Chile. The VLT is located atop a mountain that is 8,645 ft in altitude and is called Cerro Paranal. In terms of total light-collecting area, the VLT is the largest optical-infrared observatory in the Southern Hemisphere and in the world overall ranks second only to the Mauna Kea Observatory in Hawaii. The VLT is composed of four separate 320 inch (8.2 meter) telescopes. These are used together, combining their light-gathering capacity into one large effective telescope.
Recently, a team of astronomers led by Roberto Mignani of the INAF Milan and Poland’s Zielona Gora University used the VLT to observe the weak (magnitude 25.5) visible light from the neutron star RX J1856.5-3754, which is located about 400 light years from Earth. Assuming that the neutron star has a dipole magnetic field with magnetic north and south poles, the surface light from the star’s equator passing through this field will tend to be linearly polarized along the star’s magnetic field lines by vacuum birefringence. Indeed, Mignani’s group report observations made at a wavelength of 555.0 nanometers that showed a linear polarization of 16.4±5.3%. As a control, they applied the same measurements to light from 42 nearby (normal) stars and found that all were consistent with zero linear polarization. Their work constitutes the faintest star ever measured for its optical polarization,
This result, when compared with various QED theoretical models, can be considered only as indirect observational evidence suggesting the presence of vacuum birefringence. By itself, it is not definitive proof of the existence of the phenomenon, because there are a few unlikely scenarios that could account for the observed polarization.. The work will need to be followed up with more observations of RX J1856.5-3754 involving longer observation durations and measurements at more wavelengths of visible light.
In addition, the work suggests a test of vacuum birefringence with more energetic photons. Magnetars, which are exotic high-field neutron stars that are strong sources of x-rays, should be studied. Magnetars are expected to have magnetic fields that are one to two orders of magnitude larger than the field of RX J1856.5-3754. Magnetic fields of such strength would be expected to produce dramatic vacuum birefringence polarization effects on light at both visible and x-ray wavelengths.
Several space missions presently in the planning stages are designed to provide polarization-sensitive x-ray images of astronomical objects. For example, the Imaging X-ray Polarimetry Explorer, to be launched in 2021, has three identical telescopes designed to measure the polarization in the photon energy range of 2 to 8 keV x-rays. With these, more definitive demonstrations of the presence of the vacuum birefringence effect can be expected, along with accurate determinations of magnetic field strength in this extreme region and improved modeling of neutron stars. Watch this column for further results.
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John G. Cramer’s 2016 nonfiction book 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.
SF Novels by John Cramer: eBook editions of hard SF novels Twistor and Einstein’s Bridge are available from the Book View Café co-op at: http://bookviewcafe.com/bookstore/?s=Cramer.
Alternate View Columns Online: Electronic reprints of over 180 “The Alternate View” columns by John G. Cramer, previously published in Analog, are available online at: http://www.npl.washington.edu/av.
Vacuum Birefringence: “Consequences of Dirac Theory of the Positron,” W. Heisenberg and H. Euler, Z. Phys. 98, 714-732, (1936); (English translation arXiv: 0605.038 [physics.hist-ph]).
“Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels,” Koichi Hattori and Kazunori Itakura, Annals of Physics 330, 23-54, (March 2013), arXiv:1209.2663 [hep-ph].
“Evidence of vacuum birefringence from the polarisation of the optical emission from an Isolated Neutron Star,” R. P. Mignani, V. Testa, D. Gonzalez Caniulef, R. Taverna, R. Turolla, S. Zane, K. Wu, and G. Lo Curto, arXiv:1710.08709 [astro-ph.HE].
Copyright © 2018 John G. Cramer