Einstein’s Happiest Thought Micro-world Macro-World Lecture 7

Equivalence between gravity & acceleration a Man in a closed box on Earth Man in a closed box on an accelerating rocket in deep outer space. Since m G =m I, if a=-g, the conditions are equivalent g mGgmGg mIamIa

The happiest thought I cannot tell the difference between being on earth or in a deep-space rocket accelerating with a=-g

Imagination This cannot be due to coincidence. There must be some basic truth involved.

Einstein didn’t accept m G =m I as a coincidence These two environments must be exactly equivalent.

Einstein Equivalence Principle in his words we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration o the reference system [Einstein, 1907]

So what? What would happen if I were to shine a light beam through a window on the rocket? sraight line

If the rocket is accelerating, the light beam bends ½at 2

Since the accelerating rocket and gravity are equivalent, gravity must cause light to bend ½gt 2 for our room L≈6m: very, very tiny effect L on Earth’s surface

Does gravity cause light to bend? Very tiny effect: need very strong gravity and a long lever arm. Look at the bending of light from a star by the Sun. (Only possible at an eclipse.) Sir Arthur Eddington g sun ≈ 27xg earth

Eddington’s 1919 Expeditions

Africa 1919 eclipse Measurement:  = ± in agreement with Einstein’s prediction 1919 Eclipse

New York Times:

Gravitational lensing

“Dark Matter” astronomy

Mass induces curvature in space-time

The curvature is what we feel as gravity

Seoul  Rio 12 0

17 0 Seoul  Rio Cartesian vs non-Cartesian coords

The Earth is round 17 0 ?? This is how KAL goes

Geodesics The shortest distance between 2 points is Along a “geodesic.” It is a straight line In Cartesian systems

Great Circles spherical geometry The shortest distance between two points on the Earth’s surface correspond to “Great Circles”: the intersections of planes passing through the center of the Earth with the Earth’s surface.

In this figure, the shortest distances are indicated by the blue lines.