Gravity as Geometry

Forces in Nature

• Gravitational Force• Electromagnetic Force• Strong Force• Weak Force

Electrostatics vs Gravity

Coulomb’s Law : Fe = k( q1q2 )/r2

Newton’s Law : FG = G (mg1 mg2 )/r2

Mass = mg = `` Gravitational Charge “ !

Newton’s Second Law

F = mi a

Acceleration in a uniform electric field E a = (q/mi )E

Acceleration in a uniform gravitational field g

a = (mg/mi )g

Equivalence Principle

It is observed in nature that

mi = mg

a = g

All bodies move with the SAME acceleration in a uniform gravitational field !

A bowling ball and a feather dropped from thesame height will hit the ground together!

Spacetime path of an object projected from the origin with a given velocity. Could be a ping pong ball, watermelon or elephant!

Einstein’s Hunch:

If trajectories under the influence of gravity do not depend on the properties of the object, perhaps gravitation is related to the properties of spacetime itself !

What is wrong with Newton’s Theory ?

• Instantaneous action at a distance ! According to Einstein’s special theory of relativity, nothing can travel faster than light!

• E = mc2 : Mass and energy are equivalent. Gravitation should also affect light, which carries energy !

• Yet, almost no conflict with experiment for 200 + years!!!

Particles A and B move in straight lines on the plane because there is no force acting on them

Particles A and B deviate from their straight trajectories because a force is acting on them. Could be due to the attraction of a massive body

Alternative Scenario

Particles A and B move in ``straight lines”, no force acts, but they end up meeting !

Properties of curved spacetime differ from flat Sum of three angles of a triangle > or < 180 deg in non-Euclidean geometry !

Gauss Lobachevsky

Riemann

Einstein’s New Theory of Gravity(1915)

•Gravitation ≡ Geometry of curved spacetime

• Particles follow ``geodesics” of curved spacetime

• Mass /Energy = source of gravity/curvature

Gravitation not really a ``force” in the usual sense !

Einstein’s Equation

LHS : Geometry RHS : Matter/Energy

Matter tells spacetime how to curve, in turnspacetime tells matter how to move !

Spacetime as a rubber sheet

So what ? Is it just a pretty and elegant description of Newtonian gravity ?

• Explained the centuries old puzzle of the precession of perihelion of mercury

• Predicted and confirmed the bending of starlight around the sun.

• Predicted and confirmed gravitational time dilation.

Confirmed by eclipse expedition in 1919

Does curvature of spacetime affect your daily life ?

It turns out that the GPS system on your mobile phone will fail and go out of syncwithin an hour, if gravitational time dilationcorrections are not taken into account !