PHYS 182 Lecture Notes - Lecture 9: Binary Black Hole, Geodesic, Inertial Frame Of Reference
PHYS182: Our Evolving Universe
2017-10-03 LEC 9
4. Space, Time & Gravity
4.1 Curved Space-Time
Einstein’s Revolution in 1916:
• This is actually his 2nd revolution
• Newtonian view of space & time: in his view, space and time
were separate
o Space: absolute, immovable (i.e. you cannot affect
it), R3 (3-D Euclidian space), flat (i.e. not curved)
o Time: absolute, eternal
§ time has always existed – no beginning and
no end
§ -∞ < t < ∞
o Matter: moves in space
§ You get a world line for a particle (see notes)
• Problem’s with Newton’s view
o Why is there a preferred observer
§ I.e. in the example with the world line, the point at rest is preferred
• Mach’s Question: what determines inertial frame (i.e. immovable space)?
o There is a contradiction with Newton’s 3rd law of forces
§ I.e. Every action has an equal and opposite reaction
o But particles don’t affect space
o This lead to Einstein developing a new theory of gravity
Einstein’s Theory of General Relativity
à This theory replaces Newtonian gravity and encompasses all of the rest of physics
1. First principle: Equivalence principle
o F = ma is Newton’s second law
o Fg = mg is Universal gravity
§ Einstein wanted to know why gravity was universal
o Principle: the effects of gravity are equivalent to the effects of acceleration
o In free fall, the effects of gravity disappear
§ E.g. Tube with spring and ball: If you drop the stick into free-fall, the only force
left acting on the ball is the spring and the ball goes into the cup
Side Note: the speed of light in a vacuum is universal, light travels in a straight line
Paradox 1: Pound-Rebka experiment
Paradox 2: Falling box experiment
• Have to abandon either light moving in in straight
lines or you have to abandon space being flat
Curved Space
• The surface of a sphere looks non flat to us
because we are looking at it in 3-D
• Imagine you are an ant confined to the surface of
a sphere, saddle, or a table
o How can the ant tell the difference?
Document Summary
2017-10-03 lec 9: space, time & gravity. < t < : matter: moves in space. You get a world line for a particle (see notes: problem"s with newton"s view, why is there a preferred observer. I. e. in the example with the world line, the point at rest is preferred: mach"s question: what determines inertial frame (i. e. immovable space), there is a contradiction with newton"s 3rd law of forces. Every action has an equal and opposite reaction: but particles don"t affect space, this lead to einstein developing a new theory of gravity. This theory replaces newtonian gravity and encompasses all of the rest of physics: first principle: equivalence principle, f = ma is newton"s second law, fg = mg is universal gravity. Einstein wanted to know why gravity was universal: principle: the effects of gravity are equivalent to the effects of acceleration, in free fall, the effects of gravity disappear.
