The Physics
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Opus in profectus

# General Relativity

## Discussion

### introduction

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

Isaac Newton, 1689

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)
 ƒ = ƒ0 ⎛⎝ 1 + Vg ⎞⎠ = ƒ0 ⎛⎝ 1 + Gm ⎞⎠ ≈ ƒ0 ⎛⎝ 1 + gΔh ⎞⎠ c2 rc2 c2

Gravitational time dilation

 t = t0 ⎛⎝ 1 − 2gΔh ⎞⎠ −½ c2

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

 Rμν − 1 R gμν = 8πG Tμν 2 c4 space-timecurvature = mass-energystress strain ∝ stress ut tensio, sic vis

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

 Rμν − 1 R gμν = 8πG Tμν − Λ gμν 2 c4 space-timecurvature = mass-energystress − cosmologicalconstant

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

John Archibald Wheeler, 1973

Embedding diagrams.

Some predictions…

• precession of closed (and open) orbits
• In 1859 Urbain 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 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 (1919–2010) and Glen Rebka (1931–0000) 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)
• Joseph Taylor and Russell 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