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# Evidence of Warped Spacetime

If Einstein's theory of General Relativity is an accurate description of gravity, then there are some bizarre consequences. In this section the implications of General Relativity's claim that gravity is the warping of spacetime will be explored in a prediction-observation format. A scientific theory must make testable predictions which are tested through observations and experiments.

1. Prediction: light passing close to a massive object should be noticeably bent. The amount of bending increases as the mass increases.

Observation: During a solar eclipse you see that the stars along the same line of sight as the Sun are shifted outward''. This is because the light from the star behind the Sun is bent toward the Sun and toward the Earth. The light comes from a direction that is different from where the star really is. But wouldn't Newton's law of gravity and the result from Einstein's Special Relativitytheory that E = mc2 predict light deflection too? Yes, but only half as much. General Relativity says that time is also stretched so the deflection is twice as great.

Observation: The light from quasars is observed to be bent by gravitational lenses produced by galaxies between the Earth and the quasars. It is possible to see two or more identical images of the same background quasar. In some cases the light from background quasars or galaxies can be warped to form rings. Since the amount of warping depends on the mass of the foreground galaxy, you can estimate the total mass of the foreground galaxy.

The Einstein Cross (Q2237+0305) is formed by a foreground galaxy lensing the light from a background quasar into 4 images.

 Image courtesy of Bill Keel. Galaxy nucleus produces the image. Zoomed-in image of nucleus on right. Image courtesy of the Space Telescope Science Institute

Below is a picture from the Hubble Space Telescope showing the lensing of a background galaxy by a cluster of galaxies in front. The distorted blue arcs visible around the center of the picture are the lensed background galaxy. If you select the image, an enlarged version will appear (courtesy of the Space Telescope Science Institute).

2. Prediction: time should run slower'' near a large mass. This effect is called time dilation. For example, if someone on a massive object (call her person A) sends a light signal to someone far away from any gravity source (call him person B) every second according to her clock on the massive object, person B will receive the signals in time intervals further apart than one second. According to person B, the clock on the massive object is running slow.

Observation: a) Clocks on planes high above the ground run faster than those on the ground. The effect is small since the Earth's mass is small, so atomic clocks must be used to detect the difference. b) The Global Positioning Satellite (GPS) system must compensate for General Relativity effects or the positions it gives for locations would be significantly off.

3. Prediction: light escaping from a large mass should lose energy---the wavelength must increase since the speed of light is constant. Stronger surface gravity produces a greater increase in the wavelength.

This is a consequence of time dilation. Suppose person A on the massive object decides to send light of a specific frequency f to person B all of the time. So every second, f wave crests leave person A. The same wave crests are received by person B in an interval of time interval of (1+z) seconds. He receives the waves at a frequency of f/(1+z). Remember that the speed of light c = (the frequency f) × (the wavelength l). If the frequency is reduced by (1+z) times, the wavelength must INcrease by (1+z) times: lat B = (1+z) × lat A. In the doppler effect, this lengthening of the wavelength is called a redshift. For gravity, the effect is called a gravitational redshift.

Observation: spectral lines from the top layer of white dwarfs are significantly shifted by an amount predicted for compact solar-mass objects. The white dwarf must be in a binary system with a main sequence companion so that the amount the total shift due to the ordinary doppler effect can be determined and subtracted out. Inside a black hole's event horizon, light is redshifted to an infinitely long wavelength.

4. Prediction: objects with mass should create ripples in the surrounding spacetime as they move, called gravitational waves. These waves do not travel through spacetime, but are the oscillations of spacetime itself! The spacetime ripples move at the speed of light. However, the waves are very small and extremely hard to detect. Since the objects that make significant waves are RARE, they will be on average very far apart in the universe => very far from the Earth. Therefore, the waves are very small and extremely hard to detect by the time they reach Earth.

Observation: even the most sensitive detectors have not yet directly detected the tiny stretching-shrinking of spacetime caused by a massive object moving. However, the decaying orbits of a binary pulsar system discovered in 1974 by Russell Hulse and Joseph Taylor can only be explained by gravity waves carrying away energy from the pulsars as they orbit each other. This observation provides a very strong gravity field test of General Relativity.

The two pulsars in the binary system called PSR1913+16 orbit each other very rapidly with a period of only 7.75 hours in very eccentric and small elliptical orbits that bring them as close as 766,000 kilometers and then move them rapidly to over 3.3 million kilometers apart. Because of their large masses (each greater than the Sun's mass) and rapidly changing small distances, the gravity ripples should be noticeable. Hulse and Taylor discovered that the orbit speed and separation of PSR1913+16 changes exactly in the way predicted by General Relativity. They were awarded the Nobel Prize in physics for this discovery.

The Laser Interferometer Gravitational-Wave Observatory (LIGO) is an international effort to directly detect the very small ripples in spacetime passing through the Earth. The basic LIGO set up involves two several-kilometer long arms perpendicular to each other. At either end of the arms are mirrors that bounce laser light back and forth many times and then are recombined to make an interference pattern of light and dark fringes as different parts of a wave's heights and troughs cancel out or combine with another wave's heights and troughs to varying degrees. Without any spacetime ripples, the laser light waves from the two arms will perfectly cancel each other out, so nothing will reach a photodetector. A gravity wave passing through a LIGO site, will stretch one of the arms while squeezing the other arm and then reverse the effect as the gravity waves passes by. This will make the combined light from the two arms get out of phase with each other, resulting in some of the laser light reaching the photodetector. The photodetector then measures how the light fluctuates over time. The technological challenge is to detect minute changes in the length of the arms as small as 10-18 meters (many times smaller than a proton!) in the midst of all of the terrestrial "noise" such as seismic events, sound waves, random laser fluctuations, and thermal effects of the materials used that can easily overwhelm the very weak gravity wave ripples of spacetime. A schematic for the United States version is shown below (adapted from a diagram in a slideset from Rainer Weiss).

LIGO sites are located in the United States (at Hanford, WA and Livingston, LA), in Germany (near Hannover), in Italy (near Pisa), in Japan (at the Kamioka mine), and a future site inAustralia. The initial run of operations completed in 2007 without any detection of the waves. An additional run using enhanced detectors was completed in 2010 also without any detection of the waves. These negative results were not surprising, however, as the technology innovations needed in hardware and software are still being developed along with our ability to analyze the weak waves amidst all of the noise. Advanced LIGO is now being installed at the two United States sites that will increase the sensitivity of gravity wave detection by a factor of ten times. Being able to detect gravity waves from sources ten times farther away means an increase of a thousand times the volume of space or a thousand times the number of possible sources. It is expected to begin operations in July 2013.

Physicists tested some other predictions of the General Relativity Theory with the Gravity Probe B spacecraft mission. The spacecraft was in a polar orbit (pole to pole) 400 miles above the Earth's surface. Four gyroscopes with extremely precise, perfect quartz spheres kept the spacecraft aligned with a particular guide star. Because the Earth warps spacetime around it and the Earth should also "drag" the spacetime around it as it rotates, there should be a twisting of the local spacetime. This twisting and stretching of the local spacetime should cause the gryroscopes in Gravity Probe B to get out of alignment as it orbited the Earth. The twisting and stretching of spacetime by the Earth should be very small because of the Earth's tiny mass, so the drifting of the gyroscopes on Gravity Probe B were very small and the instruments on the spacecraft had to be exquisitely precise to detect the slight twisting and stretching of the spacetime near the Earth. The spacecraft finished data collection in October 2005 and intensive analysis of the data began. In April 2007, the scientists announced that they detected the predicted shift caused by the stretching of spacetime (the "geodetic effect"). After another two and a half years of data analysis, they announced in September 2009 that they were able to extract out the much smaller effect caused by the twisting of spacetime (the "frame-dragging effect").