Gravity as Geometry. Forces in Nature Gravitational Force Electromagnetic Force Strong Force Weak Force.

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Presentation transcript:

Gravity as Geometry

Forces in Nature Gravitational Force Electromagnetic Force Strong Force Weak Force

Electrostatics vs Gravity Coulomb’s Law : F e = k( q 1 q 2 )/r 2 Newton’s Law : F G = G (m g1 m g2 )/r 2 Mass = m g = `` Gravitational Charge “ !

Newton’s Second Law F = m i a Acceleration in a uniform electric field E a = (q/m i )E Acceleration in a uniform gravitational field g a = (m g /m i )g

Equivalence Principle It is observed in nature that m i = m g a = g All bodies move with the SAME acceleration in a uniform gravitational field !

A bowling ball and a feather dropped from the same 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 = mc 2 : Mass and energy are equivalent. Gravitation should also affect light, which carries energy ! Yet, almost no conflict with experiment for 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 turn spacetime 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 sync within an hour, if gravitational time dilation corrections are not taken into account !