Title: Einsteins Theories of Relativity
1Einsteins Theories of Relativity
- inertial reference frame an arena for doing
physics, built out of meter sticks and clocks, in
which Newtons first law is obeyed - Newtons first law ? law of inertia if no force
is acting, an object at rest stays at rest an
object in motion continues in that state of motion
- this excludes accelerating frames speeding up,
or rotating, in which an object at rest would
appear to magically start moving without a force! - Special relativity laws for space and time in
inertial frames - General relativity laws for space and time in
non-inertial frames, and in the presence of
gravitational force - E mc2 equivalence of mass and energy is common
theme
2The special theory of relativity velocity
- basic laws of physics are the same in all
inertial frames - speed of light is c 3.0 x 108 m/s in all
inertial frames - space and time get intermingled in this theory
- consider superposition of velocity weird!!
- Arthur sits in the bleachers, Esther is running
- if Esther throws a ball at 5 m/s, and is running
at 3 m/s, Arthur will say the ball is moving at 8
m/s, right??? - just about but if Esther shines a light while
running at .67 c 2.0 x 108 m/s, shell claim
light travels at c. So does Arthur say the light
travels at 1.67 c 5 x 108 m/s? NO!!
Galileo u v w (velocities merely add
obvious!!)
3The special theory of relativity space and time
- an event is an occurrence something happens at
a point in space x at a moment in time t - A E in frames A (no primes) and E (use primes)
measure the spacetime coordinate of two events I
II. - event I occur at both origins, and event II
occurs at (x,t) (x,t) - a CLOCK is a pair of events that occurs at the
same place, at different times - a LENGTH is a pair of events that occurs at the
same time, at different places - time dilation moving clocks run slow
- A says that Es clock is moving, and her ticks
occur too slowly - length contraction moving rulers are
shortened - A says that Es ruler is moving, and her ruler
is too short - OF COURSE Esther says exactly the same things
about Arthur ...
4Fig.20.22
Spacetime diagrams plot ct against x
- units of ct are meters, just like units of x
- if something moves at c, x ct 45º line
5Fig.20.22
How does length contraction work?
- event I occurs at origins for A and E
- events I II are length measurement of As
ruler - events I III are length measurements of Es
ruler
ct
ct
Green are worldlines of As ruler. E sees it
shortened!!
III
x
Blue are worldlines of Es ruler. A sees it
shortened!!
I
x
II
6The Redshift Parameter z and the Radial Velocity v
- the redshift number z gives the relation between
z and the observed and actual wavelengths lobs
and lrest
- Einsteins relativistic doppler shift for
frequency shift is (converted to wavelength
language)
- combining and rearranging gives
- a formula for v in terms of z, at least
indirectly... let
- note that v is radial velocity (perpendicular to
proper motion)
7Fig.20.23
One cannot exceed c (we think)
8The General Theory of Relativity
- basic laws of physics are the same in all frames
- acceleration is indistinguishable from gravity
effects gut feeling! - matter curves spacetime, so even light falls
toward a mass - so gravity is not really a force it is an
explanation for the way things move through
curved spacetime, as in Newtons first law!! - principle of equivalence inertial m is same as
gravitational m
9Fig.20.27
Fun with non-Euclidean geometry
- on a flat space, angles in a triangle add to
180º - on positive curvature (a lump), angles add to
more than 180º - on a negative curvature (a saddle), angles add
to less than 180º
10What is a black hole?
- so much mass accumulates that neutron degeneracy
pressure cant hold off gravity mass collapses
to a point singularity - the Schwarzschild radius RSchwarschild 3 km
(M/MS) - at this radius there is an event horizon there
is no returning - A would say that for E to fall through event
horizon takes an infinite amount of time to reach
black hole - E would disagree it only took a finite amount
of time - black holes evaporate because quantum theory
allows particle-antiparticle pairs to
spontaneously be created if one falls in, its
counterpart can be emitted, so they radiate
energy - smaller evaporate more quickly!!
- we dont know ANYTHING about the singularity.
- black holes exert gravity on their surroundings,
so we can observe their effects just like
ordinary masses
11A black hole sucks matter from a star
12A wormhole can connect separated regions of
spacetime
13Approaching the black hole
http//antwrp.gsfc.nasa.gov/htmltest/gifcity/rsgro
w.mpg
14Circling a Black Hole at some distance see the
two Orions?
http//antwrp.gsfc.nasa.gov/htmltest/gifcity/cirbh
.mpg
15Approaching the photon sphere
http//antwrp.gsfc.nasa.gov/htmltest/gifcity/gotop
s.mpg
16Circling the black hole at the photon sphere
http//antwrp.gsfc.nasa.gov/htmltest/gifcity/pscir
c.mpg