General Relativity (1915)

A theory of gravity, much more general than Newton’s theory.

Newtonian gravity is a “special case”; applies when gravity is very weak.

ground

g = 9.8 m/s2

Describe the motion of the fruit RELATIVE TO the ground…

ground

a = 9.8 m/s2

Suppose gravity didn’t exist, and you accelerate the GROUND up to the fruit. Would the motion of the fruit RELATIVE TO THE GROUND look any different than before?

Einstein says you’ve got two possibilities…

If all objects are observed to accelerate similarly relative to a particular frame of reference then either:

1. Reference frame is inertial and gravity is present

**OR**

2. Gravity is not present but the reference frame is non-inertial (i.e., it is accelerating)

Above is the “Weak” Equivalence Principle: gravitation and (generic) acceleration are equivalent

The Strong Equivalence Principle says that “inertial” mass and “gravitational” mass are identical.

Gravity: Newton vs. Einstein

“Spooky” Action at Distance (Newton):

Sun “tugs” on the planets and pulls them around in their orbits, like a string tied to a whirling kitty toy. But how?? Where’s the string??

If the sun disappears, the planets should instantly “fly off” into space on straight line trajectories. But information can’t travel faster than c, so how can they know “instantly” that the sun is gone?

General Relativity (Einstein):

Matter/mass tells space how to CURVE

Curvature of space tells things how to MOVE

Information about changes comes from gravity waves (ripples of curvature in spacetime) that travel at the speed of light

2-dimensional, rubber sheet analogy to General Relativity(Note, in reality this is 4-dimensional in the universe.)

If you start a marble rolling across the rubber sheet in a straight line, what happens?

Einstein’s view of orbits

Planets move along their natural curves in space, caused by the mass of the sun “warping” space. Now what happens if you pluck the sun out of the center of the solar system?

Who’s right? Einstein or Newton?

Classic tests of General Relativity:

1. Precession of the perihelion of Mercury

2. Gravitational lensing

Einstein’s theory of gravity gives the same answers as Newton’s theory in the limit of extremely weak gravity. They only differ where gravity is particularly strong (e.g., nearby very massive objects such as stars, centers of galaxies, galaxy clusters)

Precession of the Perihelion of Mercury

This effect is noticeable for the innermost planets.

Every century the total change in the location of “periheilon” for Mercury is 43 arcseconds (= 0.012 degrees). For Venus the change is 8.6 arcseconds (= 0.002 degrees), and for Earth the change is 3.8 arcseconds (= 0.001 degrees)

Gravitational Lensing

Light has to follow the curved path of space around a massive object (like the sun).

The closer the light passes to the sun, the more it is “deflected” by the curved path.

Gravitational lensing by the sun first detected in 1919, validating General Relativity over Netwonian gravity.

Gravitation lensing can create multiple images of the same object

“QUASAR” named QSO 0957+561

Two images of the same object, discovered in 1979

Einstein “Cross”; 4 images of the same object

Gravitational lenses make REALLY bad eyeglasses

The images are highly DISTORTED!

Generic Geometries

“Plane”/Euclidean geometry (flat surfaces, like table)

Spherical geometry (“positive” curvature)“Hyperbolic” geometry (“negative” curvature; saddle or Pringle’s chip)

“Co-moving” Coordinates

Co-moving vs. Proper Distance