1. Bending Time Physics 201 Lecture 11

2. 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:

3. Shapiro bounces microwaves off Venus to observe slower light Light Path Time Delay Earth-Sun53 µs Around Sun15 µs Sun-Venus27 µs Total (2x)190 µs

4. 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

5. Why is light slow? Gravity warps the space-time continuum Time warp: Redshift, GPS Space warp: Precession

6. 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

7. 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”

8. 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?

9. 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