Transcript Lecture 8 - Twin Cities - University of Minnesota

Lecture 8
6/15/07
Astro 1001
Relativity
• Two kinds: one with gravity (general
relativity) and one without (special
relativity)
• Thought experiments play a critical role in
understanding SR
Some Results
• No information can travel faster than the
speed of light
• You would conclude that time runs more
slowly for any person that is moving
• Simultaneity doesn’t strictly exist
• Something’s size changes as its speed
changes
• Mass changes as the speed changes also
What is Relative?
• Motion is only relative
– Moon vs Earth viewpoints
• Only two facts (axioms)
– The laws of nature are the same for everybody
– The speed of light is the same for everybody
• We have no common sense in the situations
in which relativity is important
Some Basics
• SR makes heavy use of
reference frames
– Two people share a
reference frame if they are
not moving with respect to
one another
• Speed of light axiom is
somewhat surprising
– Experimentally true
Thought Experiment 1 (page
415)
• Jackie is moving away from you at 90
km/hr
• Jackie has no reason to believe that she is
moving
– Jackie sees you moving away at 90 km/hr
Thought Experiment 2 (page
415)
• Same as TE1, but now you throw a baseball
at Jackie at 100 km/hr
• Jackie sees the ball coming at 10 km/hr
towards her
• Ball is moving at 100 km/hr according to
one person, at 10 km/hr according to
another
Thought Experiment 5 (page
416)
• You are moving at .9c and shine a flashlight
at Jackie
– Would naively think that it approaches Jackie at
.1c
• Beam approaches Jackie at c
Thought Experiment 6 (page
418)
• Image you are on a rocket traveling faster
and faster: do you ever exceed the speed of
light
– In what reference frame?
• Turn on headlights: lights are traveling
away from you at c
• Everybody else sees them moving away
from you at c
Reference Frames and Distance
(page 418)
• Imagine you are throwing a ball up and
down in a moving train
– You see the ball go straight up and then come
straight down
• An observer by the side of the track sees the
ball go up and down, but also sideways
– Ball travels a greater distance in the same
amount of time, so it appears to be moving
faster
Thought Experiment 7 (page
419)
• Jackie flashes a laser off of a mirror on the
ceiling of her moving spaceship
– The light appears to travel a longer distance to
you
– Light must be traveling at the same speed in
both cases
– Thus, time must be traveling slower in Jackie’s
moving spaceship
Group Work
• Jackie is now in a very long spaceship with
a red light at one end and a green light at the
other. She is traveling past you at .9c. The
lights both flash at the moment the middle
of the spaceship passes you. What do you
see, and what does Jackie see? What does
this say about simultaneity?
Experiments
• In 1887 Michelson and
Morley showed that the
speed of light is not affected
by the Earth’s motion
around the Sun.
• Particle accelerators can
demonstrate time dilation
– Particles have known halflives, but those are modified
by time dilation
Thought Experiment 12
• Jackie moves away from you at nearly the
speed of light and both record each others
movements
– Jackie will say that you are moving in slow
motion, you will say that Jackie is moving in
slow motion
• The book compares this to the Moon being
up or down
On To General Relativity
• If you send two people in exactly opposite
directions, they will eventually meet since
the Earth is round
• If you send two people in space in opposite
directions, they might meat because of
gravity, or because space is curved
Major Ideas
• The three spatial
dimensions and the time
dimension form a four
dimensional spacetime
• We can envision changes
in the shape of spacetime
by thinking of a rubber
sheet
Ideas from GR
• Gravity arises from
distortions of spacetime
• Time runs more slowly in
gravitational fields
• The universe has no
boundaries or center, but it
might have a finite volume
• Large masses that undergo
changes in structure or
motion emit gravitational
waves
Acceleration is Different
• Acceleration causes forces,
so you can tell who is
accelerating and who is not
• The effects of gravity are
exactly equivalent to the
effects of acceleration
– Called the Equivalence
Principle
Geometry
• Consider the Earth’s
surface: there is no such
thing as a straight line on
Earth
• Great circles are the
straightest possible path
between two points on the
Earth’s surface
– Philadelphia to Beijing
great circle does NOT just
follow a line of latitude
Different Geometries
• Flat geometry (Euclidean
geometry) is what you learn
about in high school
• Spherical geometry is
similar to that of the Earth’s
surface
• Hyperbolic geometry goes
the opposite way and is
shaped like a saddle
The Universe
• The four dimensional
universe has to have one
of these geometries
• The straightest possible
path feels no force, but
curved paths represent
forces
• Gravity curves
spacetime, creating a
force
Testing General Relativity
• Mercury
– Newton’s Laws incorrectly
predicted the orbit of
Mercury, while GR did it
correctly
• Gravitational Lensing
– Uniquely predicted by GR
– Observed in 1919
• Gravity Probe B
Weird Stuff
• Gravitational Waves
– Ripples in spacetime
• Wormholes
– Create lots of paradoxes
The Quantum Revolution
• Protons, neutron, and electrons are not the
most basic particles
– Quarks and leptons
• Antimatter is real
• Four fundamental forces
– Gravity, weak and strong nuclear,
electromagnetic
• All particles exhibit wave particle duality
Basic Properties of Particles
• Most important properties are mass, charge, and
spin
• Spin is analogous to spin angular momentum
– Used to describe angular momentum that belongs to
particles inherently
– Divides all particles into two groups: fermions and
bosons
– Spin can be orientated in different directions
Quarks
• Six “flavors” of quarks: up,
down, top, bottom, strange,
and charmed
• Different combinations of 2
or 3 quarks produce all of the
fermions except for the
leptons
• Leptons are very small
particles that appear to be
fundamental
– Electrons, neutrinos are the
best examples
The Four Forces
• Gravity
– Weakest force by far
– Works at very large distances
• Electromagnetism
– Important in biology and chemistry
– Stays constant in strength
• Weak Nuclear
– Weak pretty much everywhere
– Important in radioactive decays
• Strong Nuclear
– Exceptionally strong in atomic nucleus, weak everywhere
else
The Uncertainty Principle
• The more we know about where a particle is
located, the less we can know about its
momentum and vice versa
• Example with electrons
– If we use visible light, we can only pin its
location to within 500 nm (5000x the size of an
atom)
– If we use high energy light, we kick the
electron too hard when we observe it
Wave Particle Duality
• Particles don’t even
really follow a specific
path, their paths are
smeared out
• We can tell exactly
(within the limits of the
HUP) where a particle
is when we measure it,
but no idea what its
doing when we aren’t
observing it
Exclusion Principle
• Simply stated: two particles can’t be in the
same place at the same time
– We use the phrase “quantum state” to describe
the current conditions of an object
– More precisely: two particles can’t occupy the
same quantum state at the same time
– Example: energy levels of an atom
Group Work
• Determinism is the thinking that the
universe can be predicted from its initial
state. In what ways is quantum physics
deterministic and in what ways is it not
deterministic?
Quantum Tunneling
• HUP means you can’t know exactly where a
particle is
– Maybe the particle will appear on the other side
of a barrier
• Seems silly, but its of critical importance
– Many electronics rely on it
– Many stars wouldn’t exist without it