Bending Time

Physics 201 Lecture 11

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

LightPath

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

Time warp: Redshift, GPS Space warp: PrecessionSpace warp: Precession

Gravity gone wild: black holes

• The apparent speed of light drops tozero 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”

• 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 havenegative total energy

• “Penrose process” is possible to pull energy from the black hole’s spin

• Source of quasars, gamma ray bursts?

Supplies a kind of “negative pressure”

a.k.a.Dark energy

Einstein’s biggest blunder

Space-time curvature

Density of mass-energy

Cosmological constant

Creates curvature,

also collapse

• 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

• 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

• Mathematically speaking, the term on the right doesn’t need to be there

• 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

• Mathematically speaking, the term on the right doesn’t need to be there

• 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