Transcript Introduction and Kinematics

Physics 201 Lecture 11
Bending Time
In relativity, perception is not reality
• Gravity affects the way we perceive distant events
• For example, although the speed of light is constant, light
will appear to slow down near a massive object
• Not only is the speed of light slower, but its (apparent)
speed depends on its direction of motion:
Shapiro bounces microwaves off Venus to
observe slower light
Light
Path
Time
Delay
Earth-Sun
53 µs
Around Sun
15 µs
Sun-Venus
27 µs
Total (2x)
190 µs
Slow light creates deflection and explains
acceleration due to gravity
• When a car turns a corner,
its wheels must rotate at
different rates
• The reverse is true: an
object will turn into its
slower speed
• Nothing moves faster than
light, so all objects are
deflected also = gravity
• This deflection can also
create lens-like effects
Why is light slow?
Gravity warps the space-time continuum
Time warp: Redshift, GPS
Space warp: Precession
Gravity gone wild: black holes
• The apparent speed of light drops to
zero at the “Schwarzschild radius”
• As an object falls in it appears to slow as it approaches
this limit and time stands still
• This is the effective radius of a black hole – which was
also called a “frozen star” for this very reason
• If an object is compressed within this radius, nothing can
prevent its collapse to singularity
Black holes are surrounded by an “event
horizon”
• Does time really stop at
the Schwarzschild radius?
• No. Nothing dramatic
happens: one continues to
fall – but once you are in,
you can’t get out
• So events inside the black
hole cannot be seen by
outsiders (they are “over
the horizon”)
• Centrifugal force keeps orbits away from the
center in Newton’s law of gravity
• But Einstein’s law is slightly stronger – which
creates this “pit in the potential”
The event horizon on a spinning black hole
is surrounded by negative energy
• Reference frames around any spinning mass are “pulled”
in the direction of the rotation
– The Earth’s “frame drag” has been verified by Gravity Probe B
• For a black hole, certain frames are dragged faster than
the speed of light = forced rotation
• Inside this “ergosphere” objects have
negative total energy
• “Penrose process” is possible to pull
energy from the black hole’s spin
• Source of quasars, gamma ray bursts?
Einstein’s biggest blunder
• Mathematically speaking, the
term on the right doesn’t need to
be there
Creates curvature,
also collapse
• Einstein included this to allow a
“static” cosmological solution to
his equation
• Hubble’s law in 1929 provided
evidence that the universe is
expanding (not static)
• Einstein immediately removed
it and called this the “greatest
blunder” of his life
• Recent observations of distant
supernovas indicate the expansion
of the universe is accelerating
• This implies that the cosmological
constant Einstein rejected is
actually slightly positive
Space-time
curvature
Supplies a kind of
“negative pressure”
a.k.a.
Dark energy
Density of
mass-energy
Cosmological
constant