1. Relativity ds 2 = ( 1 - ) dt 2 – (1 + ) dr 2 – r 2 d  2 – r 2 sin 2  d 2 “ 2GM R R Twinkle, twinkle little star How I wonder where you are “1.75 seconds of arc from where I seem to be For Source Unknown

2. Relativity Frame of Reference - A set of coordinate axes in terms of which position or movement may be specified or with reference to which physical laws may be mathematically stated. Also called reference frame. Relativity – the study of the laws of physics in reference frames which are moving with respect to one another.

3. Relativity Relativity – the study of the laws of physics in reference frames which are moving with respect to one another. Two cases: Case 1 (special case): reference frames move at a constant velocity with respect to each other. Case 2 (general case): reference frames accelerate with respect to each other.

4. Special Relativity Introduced in 1905 by A. Einstein Special Relativity – the study of the laws of physics in the special case of reference frames moving at a constant velocity with respect to each other. Inertial Reference Frame – a reference frame that moves at a constant velocity.

5. Special Relativity The Postulates of Special Relativity First postulate Observation of physical phenomena by more than one inertial observer must result in agreement between the observers as to the nature of reality. Or, the nature of the universe must not change for an observer if their inertial state changes. Every physical theory should look the same mathematically to every inertial observer. To state that simply, no property of the universe will change if the observer is in motion. The laws of the universe are the same regardless of inertial frame of reference. Second postulate (invariance of c) The speed of light in vacuum, commonly denoted c, is the same to all inertial observers, is the same in all directions, and does not depend on the velocity of the object emitting the light. When combined with the First Postulate, this Second Postulate is equivalent to stating that light does not require any medium (such as "aether") in which to propagate.

6. Special Relativity The Postulates of Special Relativity As a result of the second postulate, once the distance to a celestial object is know, one can determine how far in the past the event occurred. Given the speed of light and the distance to the Large Magellanic Cloud, Supernova 1987a actually occurred 160,000 years before the observation, in about 158,000 BC !!

7. General Relativity Introduced in 1916 by A. Einstein General Relativity – the study of the laws of physics in the general case of reference frames accelerating with respect to each other. Non-Inertial Reference Frame – a reference frame that accelertes.

8. General Relativity Thought experiment g = 9.8 m/sec 2 Scale reads 170 lb a = 9.8 m/sec 2 Scale reads 170 lb

9. General Relativity Principle of Equivalency - Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a = intensity of gravity field.

10. General Relativity Implication of the Principle of Equivalency – photons should experience a gravitational force just like all other particles. The deflection is not observed under “normal” (ie, earth) gravitational fields because the photons move to fast. In order to observe the deflection of a photon, a large gravitational field is required. Because of the Principle of Equivalency, General Relativity is often referred to as the study of gravity

11. General Relativity Experimental test – Einstein proposed that the deflection of light from a star could be measured during a solar eclipse for a star near the edge of the sun during an eclipse. Einstein wrong Einstein right True Position Apparent Position

12. General Relativity It is common wisdom now that the determination of the defelction of light from a star during the solar eclipse in 1919 by Arthur Eddington and his group was the second observational confirmation of General Relativity and the basis of Einstein's huge popularity starting in the 1920s. (The first one had been the explanation of Mercury's perihelion shift.) Recently, the value predicted by Einstein was confirmed to an accuracy better than 0.02% [104]. The position of the star was off by 1.75 seconds of arc

13. Relativity ds 2 = ( 1 - ) dt 2 – (1 + ) dr 2 – r 2 d  2 – r 2 sin 2  d 2 “ 2GM R R Twinkle, twinkle little star How I wonder where you are “1.75 seconds of arc from where I seem to be For Source Unknown