12 General Theory Of Relativity Grey

Topics

Theories of Relativity

‰Relativity principle ‰Equivalence principle ‰Light path as absolute ‰Consequences

(General Theory of Relativity) How does relativity treat accelerated frames of reference?

Albert Einstein 2

Postulates of the General Theory of Relativity

General relativity principle

‰General principle of relativity ‰Equivalence principle* ‰Principle of general covariance ‰Others:

The laws of physics must be the same for two observers that are moving “smoothly” together (accelerated or not).

Electromagnetics Optics Mechanics Statistical Physics Thermodynamics …all the same!

Inertial motion is geodesic motion z Local Lorentz invariance z Space-time can be curved z Stress-energy creates curved space-time z

* Not fundamental; Beginning of development. 3

Equivalence principle*

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Equivalence principle

Inertial and gravitational masses are identical. – Isaac Newton [There is a] complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system. – Albert Einstein (1907)

*Turns out to be rather a consequence of more fundamental principles. 5

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Light path as absolute

Light path as absolute

The path of light will appear to be bent when the frame of reference is accelerated. The same light should be bent by gravitational field. 7

Light path as absolute

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Consequences of the General Theory of Relativity ‰EM waves (light) are bent by gravity ‰Gravitational time dilation ‰Gravitational redshift ‰Shapiro effect (signal travel delay) ‰Blackholes ‰Orbital effects ‰Expansion of space-time and “big bang”

The path of light determines the “geometry” of space-time.

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Consequence of the General Theory of Relativity

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Consequence of the General Theory of Relativity

Gravity bends light

Gravitational lensing 11

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Consequence of the General Theory of Relativity

Consequences of the General Theory of Relativity ‰Gravitational time dilation

Einstein’s rings Simulation showing zoom in to an area with intense gravity field.

Time slows down in regions with high gravitational fields.

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Consequences of the General Theory of Relativity

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Consequences of the General Theory of Relativity

‰Gravitational time dilation experiment Time slows down in regions with high gravitational fields.

Science 177 p 168-170 (1972) (from two articles)

Science 177 p 168-170 (1972) 15

Consequences of the General Theory of Relativity

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Consequences of the General Theory of Relativity ‰Gravitational redshift

Experiment was done again, 25 years later in UK Results: • The combined flight times of 14 hours and mean height in excess of 10 km resulted in a predicted clock gain of 53 ns. This followed the principle that a clock in a weaker gravitational field (higher altitude) will run faster. • The effect of the aircraft's speed relative to the Earth's surface resulted in a predicted clock loss of 16.1 ns. This followed the principle that a moving clock runs slow.

redshift from a neutron star (schematic representation)

The wavelength of EM waves becomes longer as it propagates towards lower gravitational fields.

Experiment: 39.0ns±2.0ns Predicted: 39.8ns

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Consequences of the General Theory of Relativity

Consequences of the General Theory of Relativity

‰Gravitational redshift

‰Shapiro effect (signal travel delay)

Pound-Rebka experiment (1959-1960) Pound-Snider (1964) Signal path with sun is longer. Signal path without sun

Confirmed GR predictions within 1% accuracy. 19

Consequences of the General Theory of Relativity

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Consequences of the General Theory of Relativity

‰Blackholes XTE J1118+480

XTE J1118+480

Orbital path of black-hole microquasar XTE J1118+480, over the past 230 million years.

Good info: http://hubblesite.org/discoveries/black_holes/modules.html 21

Consequences of the General Theory of Relativity

http://www.nrao.edu/pr/2001/blackhole/highvbh.graphics.html

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Consequences of the General Theory of Relativity

‰Orbital effects

‰Solar objects with precession anomaly

Observed precession: 5600 arc-seconds per century Newton’s predictions 2-body: 5025 arc-seconds per century N-body: 5557 arc-seconds Anomaly: 43 arc-seconds per century 23

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Consequences of the General Theory of Relativity

Consequences of the General Theory of Relativity

‰Expansion of the space-time (“big bang”)

‰Proof of expansion of the space-time

The entire space-time is expanding.

The universe is expanding.

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Consequences of the General Theory of Relativity

Consequences of the General Theory of Relativity

‰Proof of expansion of the space-time

Hubble, E., A relation between distance and radial velocity among extra-galactic nebulae, Proc. Nat. Acad. Sci. USA 15:168–173, 1929

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‰Proof of expansion of the space-time

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Mould, J.R. et al., The velocity field of clusters of galaxies within 100 megaparsecs. I. Southern clusters, Astrophysical J. 383:467–486, 1991

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map.gsfc.nasa.gov

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Consequences of the General Theory of Relativity

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Extra-terrestrial planets

‰Cosmic Microwave Background (CMB)

‰Next meeting

cooler warmer http://map.gsfc.nasa.gov/

polarization direction 33

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Quiz (1/4 pc of paper) 1. State the general principle of relativity. 2. & 3. Give two of the many possible consequences of the general theory of relativity.

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