Transcript Beyond Astronomy

Beyond Astronomy
The Theory of Relativity
Albert Einstein surprised the world in 1905 when…
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he theorized that time and distance can not be measured absolutely
they only have meaning when they are measured relative to something
Einstein published his theory in two steps:
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special theory of relativity (1905)…how space & time are interwoven
general theory of relativity (1915)…effects of gravity on space & time
What is “relative” in relativity?
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motion…all motion is relative
measurements of motion (and space & time) make no sense unless we are told
what they are being measured relative to
What is absolute in relativity?
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the laws of nature are the same for everyone
the speed of light (in a vacuum), c, is the same for everyone
What is Relative?
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A plane flies from Nairobi to Quito at 1,650 km/hr.
The Earth rotates at the equator at 1,650 km/hr.
An observer…
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on the Earth’s surface sees the plane fly westward overhead
at a far distance sees the plane stand still and the Earth rotate
underneath it
A Good Paradox
Paradox…is a situation that seems to violate common sense
or contradict itself.
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the paradox is resolved when the rules of nature are better
understood
Ideas & consequences of relativity are not evident in
everyday life.
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we do not experience the extreme speeds & gravity required
so we have no common sense about relativity
The “Up” Paradox
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In childhood, we regard “up” as a single direction above our head.
When we realize that people in Australia do not stand upside-down…
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we revise our common sense
“up” is defined relative to the center of the Earth
Reference Frames
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Two or more objects which do not move relative to each other share the same
reference frame.
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Objects moving relative to the other are in different reference frames.
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they experience time and measure distance & mass in the same way
like the plane and ground below
they experience time and measure distance & mass in different ways
Since ground observers see light move at c, the plane passenger is always slower.
Time Dilation
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To an observer outside the train, the ball
appears to move faster.
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makes common sense
Now lets consider Jackie moving by at
close to the speed of light .
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she bounces light instead of a ball
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The outside observer can not see the light
moving faster than c.
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yet the light does travel a longer distance as
seen by the observer
so time must run more slowly for Jackie!
Ticket to the Stars
Although we can not travel faster than the speed of light…
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special relativity will make the journey seem shorter if we can travel close to the speed of
light
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Time moves more slowly for
the space traveler.
The distance to be covered is
contracted.
Space travelers can reach
distant stars in their lifetimes.
Their friends and family will
not be there to greet them
when they return home to
Earth.
Order or Simultaneity of Events
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The red & green flashes occur simultaneously for you.
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Jackie’s fast motion causes the green light to reach her first
you both agree on that
But Jackie considers herself stationary in her reference frame.
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she sees both lights travel the same distance at velocity c
yet she sees the green light first
so the green flash occurs before the red flash in her reference frame
Length Contraction
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As Jackie moves past you at high velocity…
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she tries to measure the diameter of your ship
but time moves more slowly for her
so she measures a shorter length than you do (distance = velocity x time)
Objects appear shorter to you in the direction which they are moving.
Mass Increase
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As Jackie moves by at high speed, you give both her & her identical sister a push.
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time runs more slowly for Jackie, so she feels the push for a shorter time
Jackie accelerates less than her sister does
Newton’s 2nd Law (F = ma) says if F is same, Jackie’s mass must be greater
Objects moving by you have a greater mass than when at rest.
The Topic is Gravity
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Albert Einstein stunned the scientific world again in 1915…
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Isaac Newton saw gravity as a mysterious “force.”
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with publication of his general theory of relativity
it is primarily a theory of gravity
he could explain its actions, but not how it was transmitted through space
Einstein theorized that the “force” of gravity arises from distortions of space (or
spacetime) itself!
spacetime…the 4-dimensional combination of space & time that forms the very
fabric of the Universe
matter shapes and distorts spacetime
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space(time) itself can be curved
you may think you are traveling a straight line
but your motion is actually curved
Matter Distorts Spacetime
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Matter distorts spacetime like weights on a taut rubber sheet.
The greater the mass, the greater the distortion of spacetime.
Accelerated Motion
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The special theory of relativity states that all motion is relative…
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for objects moving at a constant velocity with respect to each other
everyone (every reference frame) can claim to be stationary
What if you fire your rockets and move away from Jackie?
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your velocity increases 9.8 m/s every second…you are accelerating
you feel a force (1 g) which pushes you to the “floor” of your ship
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Jackie sees you moving away from her
stationary position.
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you claim that Jackie is moving away
but she sees you pinned to the floor while
she is still floating
this proves you must be accelerating
you are feeling a force; she is not
Apparently we can distinguish between
motion & non-motion.
The Equivalence Principle
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This scenario bothered Einstein.
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his intuition told him that all motion should be relative
until he had a revelation…the idea for the equivalence principle
The effects of gravity are exactly equivalent to the effects
of acceleration.
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Suppose you were in a closed room.
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whether on Earth or accelerating through space at 9.8 m/s2
you would never know the difference
your weight would be the same
Accelerated Motion or Standing Still?
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Now…back to Jackie!
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But the equivalence principle of general
relativity tells us that…
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because you are feeling a force, she
claims that you are accelerating
she is the stationary one
you can legitimately consider this force
to be the weight of gravity
you are firing your rockets in order to
remain stationary (to hover)
the weightless Jackie is in free-fall
General relativity makes all motion
relative again!
Dimensions
dimension… an independent direction of possible motion
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A point (0D) moved in one direction creates a line (1D).
A line moved in a direction 90º to itself creates a plane (2D).
A plane moved in a direction 90º to itself creates a space (3D).
A space moved in a direction 90º to itself creates a 4D space.
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we can not perceive this hyperspace…any space > 3D
Spacetime for All
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The reality of spacetime is the same in all reference frames.
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we can not visualize the 4D spacetime since we can’t see through time
we perceive a 3D projection (view) of spacetime
while spacetime is the same for all observers, their 3D perceptions of it (e.g. space &
time) can be very different
By analogy…
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we can all agree on the shape & size of
this book in 3 dimensions
But…
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(views) of the same book all
look very different
The Rules of Geometry
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The geometry you know is valid when drawn on a flat surface.
The rules change if the surface is not flat.
spherical (curved-in) geometry
flat (Euclidean) geometry
saddle-shaped (curved-out) geometry
Mass and Spacetime
According to Newton, all bodies with mass exert a gravitational force on each other.
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even Newton had problems accepting this concept of “action at a distance”
General relativity removes this concept.
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mass causes spacetime to curve
the greater the mass, the greater the distortion of spacetime
curvature of spacetime determines the paths of freely moving objects
Orbits can now be explained in a
new way.
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an object will travel on as
straight a path as possible
through spacetime
The Strength of Gravity
The more that spacetime curves, the stronger gravity becomes.
Two basic ways to increase gravity/curvature of spacetime:
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increased mass results in greater curvature at distances away from it
curvature is greater near the object’s surface for denser objects
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for objects of a given mass, this implies smaller objects
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All three objects impose the
same curvature at a distance.
White dwarf imposes steeper
curvature at Sun’s former
position.
Black hole punches a hole in
the fabric of spacetime.
Nothing can escape from
within the event horizon.
Gravitational Time Dilation
We use the equivalence principle to
study the effect of gravity on
time.
You & Jackie in the ship have
synchronized watches
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the ship accelerates
the watches flash
Moving away from Jackie, you see larger time intervals between her flashes.
• time appears to be moving slower for her
Moving towards you, Jackie sees shorter time intervals between your flashes.
• time appears to be moving faster for you
• you both agree
So, in the equivalent gravitational field…
• time moves more slowly where the gravity is stronger
Gravitational Lensing
Light will always travel at a constant velocity.
therefore, it will follow the straightest possible path through spacetime
if spacetime is curved near a massive object, so will the trajectory of light
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During a Solar eclipse in 1919, two stars near the Sun…
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were observed to have a smaller angular separation than…
is usually measured for them at night at other times of the year
This observation verified Einstein’s theory…
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making him a celebrity
Gravitational Lensing
Since that time, more examples of
gravitational lensing have been seen.
They usually involve light paths from quasars &
galaxies being bent by intervening galaxies
& clusters.
Einstein’s Cross
an Einstein ring
galaxy directly behind a galaxy
Gravitational Redshift
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If time runs more slowly on the surface of stars than on Earth…
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spectral lines emitted or absorbed on the surfaces of stars
will appear at a lower frequency (cycles/s) than measured on Earth
the length of 1 second is longer on the star’s surface than on Earth
This gravitational redshift has been observed.
Gravitational Waves
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General relativity also predicts that…
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rapidly accelerating masses should send ripples of
curvature through spacetime
Einstein called these ripples gravitational waves
similar to light waves, but far weaker
they have no mass and travel at the speed of light
They have not yet been directly observed.
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but the loss of energy from binary neutron stars
the “Hulse-Taylor” binary
is consistent with the energy being emitted
as gravitational waves
Science Fact or Fiction?
Do the theories of relativity prohibit interstellar travel?
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we can not travel faster than the speed of light
but what if we made the distance to our destination shorter?
We might tunnel through hyperspace
in a wormhole.
A wormhole connects two distant
points in the Universe.
Or perhaps we could warp spacetime
so that two locations of our
choosing could touch
momentarily.
None of these ideas is prohibited by our current understanding of physics.
Most scientists are pessimistic about the possibilities.
• wormholes would also make time travel possible, with its severe paradoxes
For the moment, the Universe is safe for science fiction writers!
Quantum Mechanics
At the same time Einstein was developing the principles of relativity, our
theory of the very large…
Physicists were developing new theories of the very small.
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1905: Einstein shows light can behave like a particle
1911: Rutherford discovers atoms consist mostly of empty space
1913: Bohr suggests that electrons in atoms have quantized energies
They called this new discipline quantum mechanics.
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it has revolutionized our understanding of particles & forces
it has made possible our modern electronic devices
Fundamental Particles
The most basic units of matter, impossible to divide, are called fundamental
particles.
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Democritus of ancient Greece thought they were atoms
physicists of the 1930s thought they were protons, neutrons, & electrons
the advent of particle accelerators has given us a zoo of new particles
Murray Gell-Mann in the 1960s proposed a standard model where all these particles
could be built from a few fundamental components
Fermilab particle accelerator in
Illinois
Basic Properties of Particles
Important basic properties of a subatomic particle:
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mass
charge
spin angular momentum…or spin
All particles of the same type have the same spin.
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but they can have two possible orientations… up & down
Particles do not really spin like a top.
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the term describes angular momentum
which is measured in units of ħ
Particles having half integer spin are called fermions.
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particles of which matter is composed
Particles having integer spin are called bosons.
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such photons, gluons, & other exchange particles
The Building Blocks of Matter
Protons & neutrons, which are more massive than electrons…
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are themselves made up of less massive particles
we call these particles quarks
quarks come in six flavors
protons & neutrons consist of different combinations of two of these flavors
the up quark (+2/3)
the down quark (1/3)
Particles made from quarks
(hadrons)…
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can contain 2 or 3 quarks
a quark never exists alone
The Building Blocks of Matter
The electron is not made up of lighter particles.
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it is fundamental
it is one of six particles called leptons
leptons do exist by themselves
Here are the six flavors of quarks & six leptons:
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Quarks & leptons are the
fundamental particles of
which all matter is made.
Quarks & leptons are all
fermions.
All of these particles have
been experimentally verified.
Antimatter
Every quark & lepton has its own antiparticle.
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when two identical particles of matter & antimatter meet…
they annihilate each other into pure energy (E = mc2)
When conditions are right (like immediately after the Big Bang)
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collision of two photons can create a particle & its antiparticle
we call this pair production
Forces of Nature
Natural forces allow particles to interact and exchange momentum.
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mass is always positive, allowing gravity to dominate on large scales
each force is transmitted by exchange particles
exchange particles are all bosons
the graviton has not yet been detected
The EM & Strong forces are aspects of the same electroweak force.
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physicists are trying to unify all of the natural forces (GUT)
Heisenberg Uncertainty Principle
The more we know about where a particle is located…
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the less we can know about its momentum
The more we know about a particle’s momentum…
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the less we can know about its position
We can not know the precise value of an object's position &
momentum (or energy & time at which it has that energy)
simultaneously.
x  p  h
x = location; p = momentum; h = 6.626 x 10
–34
joule x sec
Electron Clouds
As a consequence of the uncertainty principle…
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if we locate the precise position of an electron
we have no idea of where it will go next
it appears in different locations over time, it is thus “smeared out”
we can calculate the probabilities of where it could be located
electron probability patterns for several energy levels of Hydrogen
Wave-Particle Duality of Matter
If we think of the electron as a wave, it has a well-defined momentum.
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but a wave has no single, precise location
it is spread out over a volume, like an electron cloud
electrons bound in atoms can be described as standing waves
Just like light, all matter has a wave-particle duality.
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in different situations, it is more convenient to describe it as one or the other
Pauli Exclusion Principle
Two fermions of the same type cannot occupy the same quantum
state at the same time.
Quantum state… specifies the location, momentum, orbital angular
momentum, & spin of a subatomic particle
…to the extent allowed by the uncertainty principle
Each of these properties is quantized.
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they can take on only particular values
Consequences of the Exclusion Principle
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In an atom…
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electron in lowest energy level
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has a certain orbital angular
momentum
a restricted range of locations
quantum state is determined,
except for spin
two electrons can fit in this level
a third must go to a higher level
This creation of higher energy levels makes chemistry possible.
Although atoms are mostly empty space, the solidity of matter is explained.
 uncertainty principle ensures electrons are not packed into very tiny spaces
 exclusion principle ensures that each electron gets to have its own “space”
These principles govern the sizes of nuclei.
Quantum Tunneling
Uncertainty principle also states
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product of uncertainties in time & energy are
constant
the shorter the time, the greater the range of
probable energies
a particle could briefly have enough energy to
overcome a barrier (like escaping from a cell)
this will not violate conservation of energy if
stolen energy is returned before it is noticed
Quantum tunneling can explain how two
protons can fuse.
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protons can instantly overcome EM
repulsion
Virtual Particles
Matter-antimatter pairs of particle can pop into existence.
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if they annihilate before the uncertainty time, they go unnoticed
If one particle is lost to the event horizon of a black hole…
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the other stays in existence
it will eventually annihilate with another “stranded” particle
we would observe Hawking radiation emitted just outside the event horizon
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Ultimate source of this
radiation is the gravitational
potential energy of back hole
The black hold would
eventually evaporate.
This effect has not yet been
observed.
Summary
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The view we have of the Universe is very limited. It
skews our perspective and common sense.
When dealing with objects that are very small, very fast
or very massive – the results are non-intuitive.
In order to understand the extremes in space and time,
astronomers turn to advanced physics, chemistry and
mathematics.
Our advanced theories explain the Universe we
observe, but interpreting the results can often border
on philosophy.
We will continue to learn more about the nature of the
Universe as we continue to explore and probe its’
mysteries.