General Relativity

Discussion

introduction

I will not define time, space, place and motion, as being well known to all.

Isaac Newton

Welcome to another paradigm shift.

principle of equivalence

• The absence of a gravitational field (true weightlessness) is indistinguishable from free fall acceleration in a gravitational field (apparent weightlessness).
• Accelerated motion in the absence of a gravitational field is indistinguishable from unaccelerated motion in the presence of a gravitational field. The local effects of gravity are the same as those of being in an accelerating reference frame.

Gravitational red shift.

• 1959 Harvard Tower Experiment. Pound, Rebka, and Snyder. Jefferson Physical Laboratory, Harvard.
• 1976 Scout Rocket Experiment. Smithsonian Astrophysical Observatory
• 1971 Atomic clocks on airplanes. Hafele and Keating (also tested ordinary, kinematic time dilation)

Gravitational time dilation

postulates …

1. mass-energy curves space-time — a new version of Hooke's law
2. objects trace out world lines that are geodesics (paths of least action in curved space-time) unless acted upon by a net external force — a new version of the law of inertia

Gravity isn't a force, it's the curvature of space-time caused by the presence of mass-energy

or the presence of mass, energy, and (probably) an extra something-or-other

Matter tells space how to curve. Space tells mater how to move.

John Archibald Wheeler

Embedding diagrams.

Some predictions …

• precession of closed (and open) orbits
  • In 1859 Urbain Jean Joseph Le Verrier (1811-1877) France, director of the Paris Observatory published his observations of an anomaly in mercury's orbit. The precession of mercury's perihelion (point of closest approach to the sun) had been precessing at 574 seconds of arc per century. Thinking that this was due to the effects of the other planets he calculated the precession rate using Newton's laws at 531 seconds per century, leaving 43 seconds unaccounted for. Can you say "tiny".
• gravitational bending of light
  • Confirmed by Arthur Stanley Eddington (1882–1944) England in 1919. General relativity replaces Newton's theory of universal gravitation as the most complete theory of gravitation. Newton and Eddington were English. Einstein was German. 1919 was the first year after World War I. Anti-German sentiment was still high in Europe. Eddington's confirmation of Einstein's theory showed that science was above culture and politics. Einstein became a celebrity.
  • Einstein cross
  • gravitational lensing
  • magnification of distant objects
• gravitational time dilation
  • gravitational red shift
    Confirmed in an experiment conducted in an elevator(?) shaft at Harvard University by Robert Pound and Glen Rebka in 1959. A source of gamma rays was placed at the top of the shaft and a detector at the bottom. The source produced gamma rays of a very precise frequency and the detector was designed to detect only gamma rays with that particular freqency. In the process of "falling" down the shaft, the gamma rays were blue shifted to a higher frequency. Pound and Rebka placed the source on a vibrating speaker. When the speaker moved up at the right velocity, the gravitational blue shift was cancelled by the motional red shift and the detector would detect the gamma rays. Move with any other velocity and noting is detected. Measure the speed of the source, the local gravitational field, height of detector above emitter, and the speed of light; put numbers into equation; check to see if both sides equal to within the limits of experimental error (~10%, Pound and Snider reduced this to ~1% in 1964).
  • Gravity Probe A, 1976. Fly an atomic hydrogen maser on a Scout rocket launched to a height of 10,000 km. A maser is like a laser for microwaves. It produces microwaves of a very precise frequency. Measure the doppler shift due to gravity and motion and compare to predicted values (error = 70 ppm = 0.007%). Gravity Probe B, 2004-2005 tested for frame dragging.
  • Clocks on planes experiment
    Prediction Abstract: During October 1971, four cesium beam atomic clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward, to test Einstein's theory of relativity with macroscopic clocks. From the actual flight paths of each trip, the theory predicts that the flying clocks, compared with reference clocks at the US Naval Observatory, should have lost 40 ± 23 nanoseconds during the eastward trip, and should have gained 275 ± 21 nanoseconds during the westward trip. Results Abstract: Four cesium beam clocks flown around the world on commercial jet flights during October 1971, once eastward and once westward, recorded directionally dependent time differences which are in good agreement with predictions of conventional relativity theory. Relative to the atomic time scale of the U.S. Naval Observatory, the flying clocks lost 59 ± 10 nanoseconds during the eastward trip and gained 273 ± 7 nanoseconds during the westward trip, where the errors are the corresponding standard deviations. These results provide an unambiguous empirical resolution of the famous clock "paradox" with macroscopic clocks.s.info
  • GPS
• gravitational waves (unconfirmed)
  • Taylor and Hulse, binary pulsars spiraling into one another, indirect evidence
  • suspended aluminum cylinder
  • interferometer
    • LIGO (Laser Interferometer Gravitational Wave Observatory), Advanced LIGO
      The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a facility dedicated to the detection of cosmic gravitational waves and the harnessing of these waves for scientific research. It consists of two widely separated installations within the United States — one in Hanford Washington and the other in Livingston, Louisiana — operated in unison as a single observatory
    • Virgo, Advanced Virgo
      The Virgo detector for gravitational waves consists mainly in a Michelson laser interferometer made of two orthogonal arms being each 3 kilometers long. Multiple reflections between mirrors located at the extremities of each arm extend the effective optical length of each arm up to 120 kilometers. Virgo is located within the site of EGO, European Gravitational Observatory, based at Cascina, near Pisa on the river Arno plain. The frequency range of Virgo extends from 10 to 6,000 Hz. This range as well as the very high sensitivity should allow detection of gravitational radiation produced by supernovae and coalescence of binary systems in the milky way and in outer galaxies, for instance from the Virgo cluster.
    • LISA (Laser Interferometer Space Antenna) proposed launch date 2018~2020
      LISA consists of three identical spacecraft whose positions mark the vertices of an equilateral triangle five million km on a side, in orbit around the Sun. LISA can be thought of as a giant Michelson interferometer in space. The spacecraft separation sets the range of GW frequencies LISA can observe (from 0.03 milliHertz to above 0.1 Hertz). The center of the LISA triangle traces an Earth-like orbit in the ecliptic plane, one astronomical unit from the Sun, but 20 degrees behind Earth. The plane of the triangle is inclined at 60 degrees to the ecliptic. The natural free-fall orbits of the three spacecraft around the Sun maintain this triangular formation, with the triangle appearing to rotate about its center once per year.
• astrophysics, cosmology
  • black holes
  • large scale structure of the universe
  • big bang, Georges Lemaître (1894-1966) Belgium

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