XI. Relativity

1. Special Relativity

i) "the laws of physics the same to all non-accelerating observers"

no matter how fast they are moving w.r.t. each other

ii) Speed of light = c
the same for everyone

To get velocity:we need to measure distance and time

b) Einstein's resolution of the dilemma

• Time not absolute (passing slower at high speed)

1. Traveling twin paradox (traveler stays younger)
2. Simultaneity not absolute

• Lengths get contracted at high speed
• Spacetime: observers can agree on combinations of space & time

c) E = Mc2 or why moving things gain mass

• Mass can be transformed into energy --> energy source of the stars
• Then:
  • Energy can also be mass --> M = E/^c2

• Mass into motion --> Kinetic Energy "Kinetic Mass"
• m --> ¥ as velocity --> c
• Can't ever get to c!!!!
• Energy goes into increasing mass rather than increasing speed

2. General Relativity:

A) Basic principles

• Response to gravity is independent of object... or in other words
• acceleration is equivalent to gravity

• based on "Inertial Mass = Gravity Mass" mi = mg

B) Effects of Gravity on Time

a) Gravitational redshift

• in accelerated spaceship: detector faster while light is on the way
• Doppler red shift of light
• in gravity:light looses energy
• Gravity red shift(tests: white dwarfs, precise experiment in lab)

b) Gravitational twin paradox

• time runs slow near huge mass

(test: atomic clocks flown at different elevations)

C) Curvature of space

• Light is bent in gravity fields:
  • Know: light is taking a straight path?
  • Better:light is taking shortest path!!This can be curved!
  • Analogy: on Earth we always take the great circle route as the shortest
  • (transatlantic routes of jet liners)
  • Mass (and energy) produce a curved space-time

D) Tests of general relativity

a) Gravitational deflection of light

• 1919: First test of Einstein's prediction of gravitational deflection of light

During total solar eclipse

b) Spacetime curvature produces non-Keplerian motion

• Analogy: ball rolling on a dented tabletop
• The orientation of the orbit of Mercury turns around (like a rosetta)
  • not a perfect ellipse ("perihelion shift")

c) Gravitational waves:propagating ripples in spacetime

• Observation: Pulsar (a very precise clock!) orbiting neutron star slowing down due to gravity wave emission (energy loss)
• When will they be directly observed?

E). Black Holes

• A hole in spacetime everything falls "out of our spacetime"
• Analogy: A hole in a tabletop everything falls through

a) Principles

• if M > 3(?) Msun, collapse continues
• Gravity increases and even light can't escape

b) Possible example:

• Cygnus X-1: A special binary X-ray source
• 30 Msun normal star moves
• Compact X-ray companion must have > 6 Msun
• evidence that the compact object is a black hole

c) Features of a Black Hole

• Concentrates mass inside the "Schwarzschild radius" = "event horizon"
• (Not difficult for supermassive black holes > 108 solar masses)
• Sun would have to be squeezed to a radius of 3 km!!
• Can only grow: Black Holes dig their own holes in spacetime
• Nothing will ever come back!
• Can only have mass, angular momentum, electric charge
• No structures"Black holes have no hair"

Chapter 12