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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 !
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