ie-Physics

Experiment II-11

warping space and lensing star light

Isaac Newton (1642-1727) in 1687 in his Principia described the properties of the force needed to cause heavenly bodies to move in ellipses in accord with Kepler's laws.  Newton's analysis of gravitational forces unified the physics of the heavens with that of projectiles and falling objects on earth.  Newton's three laws of motion and his fluxions procedure (now call calculus) established the foundation for understanding all other forces in the universe.

• The first paper analyzed the energy of electrons ejected from reactive metals struck with light (called the photoelectric effect) finding that the equation which fits measurements of others implied that light must be considered as being packaged in quanta determined by the frequency of the light waves.
• The Einsteins were bothered by Maxwell's equations which required electrical charges to create magnetic fields when moving but not when stationary.  They realized this required a paradox where an observer moving by a stationary charge could detected magnetic field while stationary observers could not.  The proposed solution required the speed of light must be identical for all observers and that time and distance must be different for the moving observer according to special relativity.
• The third paper analyzed the erratic, random motion of small particles in smoke and sols (called Brownian motion), providing the mathematical analysis which convinced many skeptics that the atoms and molecules of chemists must be real particles of matter.

Newtonian physics involves mass, a property of the universe which seems to have several unrelated functions.  In Newtons dynamics, F = ma, mass provides the inertia that resists acceleration.  But in Newton's law for gravity, F = Gm₁m₂/d², mass is the cause of the force.  The missing logical connection between inertial mass and gravitational mass has caused some physicists to further ponder the nature of mass and gravity.  In 1915 Einstein announced his general theory of relativity replacing Newtonian gravity with curved space.  Einstein proposed that mass deforms space so that the shortest distance between two locations would be curved by the attraction of a mass near the pathway.  For nearly all situations Einstein's theory made identical predictions to Newton's theory.  But Einstein calculated that gravity of the Sun could deflect light from a star nearly behind the Sun by up to 1.75 seconds of arc, less that 1/1000 of a degree, but twice as large as the deflection according to Newton physics.

In 1919 Arthur Eddington journeyed to the island of Principe off the coast of West Africa to photograph on May 29 a total solar eclipse where the moon would block for an extraordinarily long 7 minutes the overpowering sunlight which normally during daytime would obscure the distant stars of the Hyades constellation.  It rained every day for the nineteen days prior to the eclipse, but the sky cleared just long enough during the eclipse for Eddington to make one useful photograph of the stars.  Compared the eclipse photo with nighttime images of the Hyades showed that the sun had caused a deflection of roughly 1.61 seconds of arc for the stars closest the sun, a result confirming Einstein's theory of general relativity.  Eddington's expedition and results made Einstein famous.  (Read more about Einstein and a chemical element named for him.)

Experiment

In this experiment we shall look for the effect of space curvature caused by mass.  Light diverging from a star or galaxy behind a large mass which is nearer to us can be bent inwards towards that closer mass resulting in the light falsely appearing to originate from several locations just to the sides of the nearer mass.  Often the distance object appears to be warped into an arc centering on the mass causing the bending.

As noted in the previous experiment, light from more distant objects had greater red shift.  This allows an observer to determine which objects are closer and which are further away.

Procedure

1. Inspect the photograph of a tiny section of the sky captured by the Hubble telescope orbiting the earth in space above the earth's atmosphere which otherwise distorts and blurs images viewed from the earth's surface.  Look for patches of light which are arcs or shaped like portions of rings.  Stars and globular clusters of stars are nearly spherical while galaxies generally approximate ellipses in shape.  But strong areas of gravity between a distant light source and us can warp the light so it appears as an arc or portions of a circular ring.
2. Estimate the locations of mass (center of the curvature of the arc) apparently bending the light.
3. By locating arc shaped images equal distant from the central mass, determine which images are likely multiple images of the same object.

4. Inspect the color photograph of the same Abell 2218 cluster.  Estimate relative distance from the red shifting.  Assuming the galaxies were originally the same color, blue ones likely are closer and red further away.
5. Locate the faint deep red arcs near the 10 o'clock position to the central mass, above the blue galaxy, and the red dot near the bottom of the photograph.

The color of the lensed galaxies is a function of their distances and types.  The distance of any particular galaxy can be determined from the amount of red shift,  (See procedure in previous experiment.)  The orange arc is an elliptical galaxy at moderate red shift (z=0.7).  The blue arcs are star-forming galaxies at red shifts with z=1 to 2.5.  The encircled deep red arcs (and dot) is the star-forming galaxy at about red shift 7 discovered February 2004.  The magnification of the natural cosmic gravitational lens amplified the brightness about 25 times.  Located an estimated 13 billion light-years from earth, light from this galaxy originated only 750 million years after the big bang, when the universe was barely 5 percent of its current age.  The primeval galaxy was identified by combining the visibility of NASA's Hubble Space Telescope and red shift information from the Keck Telescopes on Mauna Kea, Hawaii.

The lensed galaxies in these photographs are particularly numerous because they are between two mass clumps, in a saddle region which causes quite large magnification.

6. Summarize the kinds of evidence available in these photographs that support the validity of Einstein's theory of general relativity.

References

• monochrome photograph credit: W. Couch, University of New South Wales, R. Ellis, Caltech, and NASA
• color photograph: NASA; the Caltech team reporting on the discovery: Jean-Paul Kneib, Richard S. Ellis, Michael R. Santos & Johan Richard.  Kneib and Richard also serve the Observatoire Midi-Pyrenees of Toulouse, France.  Santos also represents the Institute of Astronomy, Cambridge, UK.
• J J O'Connor & E F Robertson,, School of Mathematics and Statistics University of St Andrews, Scotland, Arthur Stanley Eddington
• The author attended and received partial financial support from the QuarkMatter 2004 conference and 2004 AAAS Annual Meeting (which also included sessions on cosmology).  Information from those conferences led to the development of this experiment.