Astronomy 1143 – Spring 2014 Lecture 19: General Relativity

Framework Postulates Things assumed to be true about the Universe Example: the speed of light is the same for all observers Consequences What happens when moving quickly or in strong gravitational fields Example: time is different for observers who have relative motion

Framework Tests Observational proof Example: the bending of light in the gravitational field of the Sun Relevance When special or general relativistic equations must be used Example: Special Relativity – fast General Relativity – strong gravity

Key Ideas: Postulates: Gravitational mass=inertial mass Laws of physics are the same for all observers Consequences Matter tells spacetime how to curve. Curved spacetime tells matter how to move. Clocks run more slowly in strong gravitational fields Light leaving a gravitational field is redshifted

Key Ideas: Tests of General Relativity: Perihelion Precession of Mercury Bending of Starlight near the Sun/Galaxies Gravitational Redshift Gravity Waves Relevance General Relativity must be used for strong gravitational fields or for large accelerations General Relativity is not a quantum theory and does not work on the smallest scales

Principle of Equivalence This is just another way of stating the principle of equivalence.

Everything falling

Principle of Equivalance One of the postulates of General Relativity is that inertial mass=gravitational mass Appears in Newton as well, but Einstein elevated it to a postulate Consequences include Free fall = free float, aka zero-g or weightlessness Accelerations can mimic gravity (roller coasters and “pulling g’s” Matter can be thought of as moving together through spacetime instead of being pulled by forces

Principle of Equivalence No experiment that you can perform (in a small enough laboratory) that will tell you whether you are in zero-gravity or falling freely under the influence of gravity Only works for gravity (not for electric or magnetic forces for example) – thing that is responsible to creating force also thing that responds to force

Principle of Equivalence

Power of Equivalence Principle For thought experiments: what happens in an accelerating frame must also be true for gravity Everything falling at the same rate implies that there is one thing that is guiding the motion of all particles – curved spacetime Equivalence Principle only holds over small amounts of spacetime – smaller than the curvature of the Earth, for example

Bending of Light

Light under the influence of gravity behaves the same way as in an accelerating object A light beam in a rocket ship would appear to bend to the people in the ship. Therefore light under the influence of gravity also will appear to bend Light is not unaffected by gravity

Newton Einstein Mass & energy are very different things. Mass & energy are interchangeable: E = mc 2 Space & time are very different things. Space & time are interchangeable: part of 4-dimensional spacetime.

General Relativity New way of looking at gravity Maybe the motions of masses under gravity didn’t have anything to do with the objects themselves Curved spacetime tells matter how to move Consequences: Photons affected by curved spacetime Disagreement with Newton’s Law of Gravity Matter tells spacetime how to curve

How do objects move in curved spacetime? Newton’s 1 st Law Objects in motion will move in straight lines unless acted upon by an outside force Straight line=shortest distance between two points No forces = flat spacetime Objects move by the shortest distance Forces = curved spacetime Objects move by the shortest distance

The Shortest Path... On a flat surface: The shortest path between two points is a straight line. Parallel lines stay parallel always. On a curved surface: The shortest path is a curved line. Lines that start parallel can converge or diverge at some distance away.

Curved Spacetime Matter curves the spacetime around it: The least paths are curved lines. More mass = Greater spacetime curvature. Closer = Greater spacetime curvature. Einstein gave the equivalent of Newton’s Law of Gravity in the form of his field equations A freely falling object follows a curved path.

Curved spacetime around the Sun Curved spacetime around a Black Hole

A New Theory of Gravity General Relativity may be summarized as: Matter tells spacetime how to curve. Curved spacetime tells matter how to move. Replaces the Newtonian idea of a “force” with the curvature of spacetime as the agent of Gravity. GR has withstood all experimental tests.

Bending of Starlight Light travels on the shortest path through spacetime. Prediction: Gravity bends light passing a massive object Confirmed: 1919 Solar Eclipse Gravitational Lenses (1980s)

Bending of Starlight (side view) True Position Sun Apparent Position Scale is exaggerated Earth

00.51 Deflection (arcsec) 1o1o 2o2o 1o1o 2o2o View from Earth Data from 1922 Eclipse

Gravitational Lenses

Gravitational Waves Newton thought the force of gravity was instantaneously transported through space But, remember, in special relativity, information travels at the speed of light Gravity waves Travel at the speed of light Carry energy away Have not been directly detected (yet!)

Binary Pulsar 2 pulsars orbiting each other Can use the arrival of the pulses to map the orbits and periods very accurately Strong gravitational field – test of theory See system losing energy Pulsars are getting closer together 75 millionths sec/year different in period Nobel Prize for Hulse & Taylor

Binary Pulsar

Direct Detection of Gravity Waves Gravity waves distort spacetime Detected by laser beams moving along 2 different arms One length squeezed, one length stretched No detections yet Many things can cause the path length to change Tested by using duplicate facility

Clocks in Accelerating Spaceship Clock B emits one photon pulse every 1 second according to Person B Acceleration in this direction Clock A emits one photon pulse every 1 second according to Person A

Clocks in Accelerating Spaceship Person B will see Clock A’s photons arrive closer together than 1 second, as the photons have to travel less far as spacecraft catches up to them Clock A is running fast to Person B Person A will see Clock B’s photons arrive farther apart than 1 second, as they have to travel farther to catch up Clock B is running slow to Person A

Gravitational Redshift Gravitational field affects time Clocks in stronger gravitational fields run slow Predicts a gravitational redshift Smaller number of waves/second for observer in weaker gravity (=faster clocks) Gravitational redshift observed: Pound & Rebka (1960 ) -- Harvard Tower Hafele & Keating (1971) – jetlagged clocks Scout D rocket (1976) – clocks on rockets

Practical Relativity Global Positioning System (GPS) 24 satellites in high Earth orbit 20,000km altitude, 12 h period (14,000 km/h) Carry on-board atomic clocks Relativistic effects on these clocks: Special Relativity: 7  sec/day slower General Relativity: 45  sec/day faster Combined correction: 45–7 = 38  sec/day

Whither Newton? Newton’s laws are approximations of GR. Conditions: weak gravitational fields speeds much slower than the speed of light. Newton’s Laws: Work accurately in the “everyday” world. Are mathematically much simpler.

Status of General Relativity Passed every test – will continue to be tested Its effects must be included in binary pulsar calculations, in collapses of stars to black holes, and in cosmology, among other applications Not the last word in gravity – we need a theory of quantum gravity.

Applying GR to the Universe Einstein applied his original GR equations to the whole Universe and found it should be expanding or contracting Added this term to keep the Universe in a delicate balance

Cosmological Constant We refer to  as the cosmological constant – constant amount of energy for each chunk of space Turns out that Doesn’t make the Universe safely static Universe is actually expanding Einstein’s greatest mistake? Not the end of the story Accelerating Universe indicates a new source of energy – cosmological constant?