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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”