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Lecture 3:Lecture 3:General Relativity IGeneral Relativity I

Background and PrinciplesBackground and Principles

General RelativityGeneral RelativityNewtons Law + Weak Equivalence:

Law of Motion F=maLaw of Gravity F=GMm’/r2

Experiment: acceleration is independent of materialm proportional to m’take m=m’

Experiment Galileo Leaning tower of PisaEtvos 1905 wood/platinum 1in 108

Dicke Aluminium/gold 1in 1011

Idea is old! 517AD John Philoponus of Alexandria

When 2 bodies “differing greatly inweight” are dropped simultaneously “thedifference in their time of fall is a verysmall one”

General RelativityGeneral RelativityThe Role of Equivalence:

Newtonian Gravity and Weak Equivalence

Not logically essential to one-another

Equivalence bolted on at the end

Einstein: Equivalence Central

Need stronger version of Equivalence

General RelativityGeneral RelativityInertial Forces:

Idea is familiarExamples: car going round corner

ascending/descending lift

Particle at rest in inertial frameNon-inertial frame with acceleration –aIn non-inertial frame, particle has acceleration a

In order to extend validity of N2Must say there is a fictitious force

Pseudo-force - Inertial force

General RelativityGeneral RelativityInertial Forces:

Accelerating rocket

General RelativityGeneral RelativityInertial Forces:

Centrifugal Acceleration/Centripetal Force

Tm

v

Stationary FrameN2 in radial directionF=maT=mv2/r

Rotating FrameN2 in radial directionF=maT-mv2/r=0

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General RelativityGeneral RelativityInertial Forces:

Corriolis Force (non-examinable)

Tm

v

Forces all radial fidon’t change angular momentumfi mrv=constant

Change r: r-> r-drv->v+dv

In rotating frame, looks like force

m(r-dr)(v+dv)=const=mrvv ∂tr=r∂tvfia=v ∂tr/r=Ωx∂trfiLooks like Lorentz force F=eBxv, eB=Ω/mfiMore of this later

General RelativityGeneral RelativityStrong Equivalence:

“Gravity is an inertial force”

“Can’t tell the difference between gravityand acceleration by measurement”

“A frame of reference which is free fallingis locally inertial”

General RelativityGeneral RelativityStrong Equivalence:

“Gravity is an inertial force”

Baffling: gravity is an everyday experience

Is the surface of the earth accelerating out?Tied to Netwonian picture:

space is a universal given upon which the business of physics takes place

Relativity forces us to abandon this notion

Our grid of clocks and rulers not universal=> just a map that allows us to navigate locally=> used to maps with only local validity=> spacetime curvature – more late

Spacetime is part of physics – Geometry is physics

General RelativityGeneral RelativityPrinciples of General Relativity:

“Special Relativity+

Strong Equivalence”