Download The story of Relativity

The story of Relativity
WHS Honors Physics
Spring, 2011
Before we begin
• Most of what we will discuss goes against “common
sense”. If you accept Einstein’s ideas, it will
dramatically change the way you view reality
• That said, Einstein’s predictions have been
validated and tested to unimaginable precision.
Without his theories, we wouldn’t have GPS, along
with many other recent technological luxuries.
• Claiming you don’t “believe” Einstein’s relativity places
the burden of proof on you. Whether or not it defies
your intuition is irrelevant when compared to the
immense body of scientific study that’s validated its
merit.
Two Great Revolutions for the New
Physics
• Quantum Mechanics
and Relativity
– The latter, exclusively
due to the work of
Einstein, deals with
space, time, and
motion. Its
consequences are
just as baffling and
profound as the
quantum theory, and
challenge many of our
old notions about the
nature of the
universe.
Two Theorys
• Special Relativity
• Time is NOT absolute. Your watch ticks at a
different rate than mine
• Spacetime is a “fabric”, and time and space can be
thought of as “intertwined”
• Everything moves at light speed.
• General Relativity
• Einstein’s famous equation
• Spacetime curves and warps in response to
gravitational fields
Space, time, and the eye of the
beholder
• 1905
– A 26-year old patent clerk sends a paper he
has written in his free time to the German
“Annals of Physics”, a publication ran by Max
Planck, one of the most famous scientists in
the world
– Upon finishing the paper, Max Planck realized
that classical physics had been overthrown
Physics at the time of Einstein
• NEWTON
– Still professed as the “king of physics”
– Laws of motion and gravity were accepted as
absolute
• JAMES MAXWELL
– Discovered electromagnetism
– Discovered that EM waves never slow down,
never speed up, and always travel “light
speed”
Albert Einstein
• In his teens,
Einstein began
pondering a
simple question:
– What happens if
you chased after a
beam of light at
light speed?
Intuition and It’s Flaws
• Example: You are driving
– From your perspective, the trees and houses
outside your car are moving. However, a
hitchhiker on the side of the road sees them
as standing still
– From your perspective, your hood and
dashboard are motionless, but from the
hitchhikers perspective they are moving.
So what?
• Observers in “relative motion” will have
different perceptions of space and time
– As we will see, your stereo clock ticks more
slowly than this wristwatch, and your car looks
compacted (or, more specifically, shorter) to
him as you drive by.
• This fact is not a flaw in measurements or
your watches. This is a fact of the
universe!
• See illustration on page 845 of your book
Why don’t we “see” and “feel”
relativity?
• Relativity depends on how fast an object
(or person) moves
– For the speeds of cars, planes, or even
spaceships, these effects are miniscule and
hardly even detectable.
– Clever experiments have proven relativity to
be one of the most monumental properties of
our universe
– Let’s read sample story ONE…Ty and
Garrett go super-charge a camaro
The Principle of Relativity
• Two simple structures form the foundation
of special relativity
– The properties of light
• Light ALWAYS travels at 299792458 m/s,
regardless of reference frame!
– Who or what is doing the measuring?
• We call this the “Principle of Relativity”
• All laws of physics are the same for all observers,
regardless of reference frame.
• Read sample story TWO
The Speed of light
• Contrary to our claim that there is no
meaning to the statement “Cheryl is
traveling 10 miles per hour”, light always
travels 670 miles per hour, regardless of
benchmarks for comparison!
• Read sample story THREE
Truth and consequences
• Speed is a measure of how far an object
can travel in a given duration of time
– If a car goes 65 mph, it would travel 65 miles
in one hour. Similarly, it would travel 130
miles in two hours.
• Distance is a notion about space, or how
much space there is between two objects
• Duration is a notion of time, or how much
time passes between two events
The effect on time (Part I)
• The speed of light can easily show us that
our everyday conception of time is wrong.
• TIME IS NOT UNIVERSAL!
• Simultaneity depends on the motion of the
observer, and is NOT absolute
• Read sample story FOUR
The effect on time (part II)
• It’s hard to define time
– Attempts in dong so usually invoke the word
time itself
– Some might try to define time as being
measured by clocks…but this shifts the
burden to defining a clock.
– We shall define a clock as an object that
displays perfectly regular cycles
TIME
• “Regular cycles of motion” require equal
time durations.
– Our goal is to understand how motion affects
the passage of “time”.
– Under constant motion, we will consider
simple “ticking light clocks”. These clocks are
highly accurate and easily explainable, being
as they involve just two mirrors and a photon.
The Light Clock
• If a photon bounces back and forth one
billion times in a second, we can time
events based on how many times the light
bounces back and forth.
– If a horse starts and finishes a race in 55
billion cycles, it took 55 seconds to cross the
finish line.
– If Leo fell asleep during notes today in 120
billion cycles, he fell asleep in 2 minutes
But what if the light clock is in
motion?
• Notice that if our light clock moves
eastwest, the photon moves too.
Because it is moving NorthSouth as well
as EW, it must travel further to complete
one cycle. This slows the clock.
• Suppose our "light clock"
were traveling sideways at a
very high (but constant)
speed. Now the photons
would follow the "saw tooth"
path shown on the right side
of the drawing. The light must
travel a greater distance now
to make a round trip. Since its
speed is the same as before
(remember, the speed of light
is not changed by the speed
of its source), it will take
longer to make a round trip.
Life on the run?
• So, if moving fast makes time tick slowly,
can I live longer going faster?
– Well, yes AND no
– You will live longer, but you will also be living
in slow motion relative to others. Let’s say a
stationary person can read 100 books in a
lifetime. You would also read 100 books in
your lifetime because everything you do in
your reference frame will be at a slower rate
according to a stationary observer, including
your rate of reading.
So, who’s moving, anyway?
• You may have noticed that reversing the
roll of who is watching reverses the image
of who’s clock is ticking slower…
• With all the seeming paradoxes in
relativity, we gain a great deal of insight
into the workings of the universe.
• Read Sample Story FIVE
Motion’s effect on space
• As you saw in Ashley and Cheryl’s
example, time is affected by motion. We
will now see the effect that motion has on
time.
• Read Sample Story SIX
The sharing of motion through
dimensions
• Let’s consider three dimensions
– The corner of Wentworth and Halsted, 8th floor…three
dimensions in real-life.
• Everything around us is aging, moving from one
moment in time to the next (Einstein and many
other physicists think of time as the 4th
dimension)
– Remember, time doesn’t “move”, just like spatial
dimensions don’t move.
– We move through THEM, but they don’t move!
Einstein’s bold claim
• Every object travels through space-time at
the speed of light
– It’s combined speed through all four
dimensions will equal exactly that of light
– This one fixed speed can be shared between
dimensions
How Space-time works
• As you sit motionless in your chair, all of your
movement through space-time is in the TIME
dimension (your time ticks away as fast as it can
here on Earth)
• As you run about half the speed of light, half of
your speed is taking place in 3-D space, while
half is in time (your clock ticks twice as slow as
someone not moving)
• Light, which clearly moves light speed, has ALL
of it’s speed through space-time locked up in
motion, and because of this light does not
experience time!
About light…
• Light never “ages”
– A photon that emerged at the big bang is the
same age today as it was when it was
created.
– There is no passage of time at light speed.
Time can be thought of as forever frozen at
that rate.
– The age of light is a universal minimum (0)
while something not moving at all ages at a
maximum rate.
What E = mc2 says about motion
• The higher the mass of a particle, the
more energy it has, and vice versa.
• The faster something moves, the greater
its energy (Think of the KE equation)
• Objects moving extremely fast become
more massive, and hence harder to get
going faster
It’s fun to think about traveling
light speed, but…
• It’s easy to accelerate a shopping
cart, but harder to accelerate a
truck.
• According to Einstein’s famous
equation, the faster something
gets, the more it weighs, and the
harder it becomes to make it go
faster.
• In fact, you can never pass the
speed of light because the weight
of the object moving will
approach infinity!! Nothing can
travel faster than the speed of
light.
Part II
General Relativity
…if you thought Special Relativity
was stupid…this will be REALLY
exciting!
• Through special relativity, Einstein realized
that Newton’s idea that you could “catch
up” to a ray of light was wrong.
– Newton’s law of universal gravitation seemed
to have been violated.
• For the next years, Einstein nearly drove
himself mad through his constant work
and study. Finally, Einstein’s “GENERAL
THEORY of Relativity” was born, and this
theory revolutionized our understand of
space and time by showing how they warp
and distort to communicate the force of
gravity.
Newton’s Perspective on Gravity
• Everything exerts gravitational force on
everything else. Regardless of physical
composition, every object in our universe
exerts an attractive gravitational force on
everything else.
• Every object exerts AND feels the force of
gravity.
– The gravitational force is communicated
instantaneously, according to Newton.
Newton’s Law of Gravity
• Gravitational force between two bodies is
directly proportional to the product of their
masses and inversely proportional to the square
of the distance between them.
• Newton’s law successfully predicted orbits,
baseball flights, cliff divers, and apples falling.
– It’s important to know that Newton wasn’t technically
“wrong”. His laws were just an incomplete description
of nature!
• Einstein’s new discoveries proved to be more
accurate representations of the universe.
Relativity vs.
Newtonian Gravity
• Special relativity is built on
the fact that light sets the
absolute speed barrier.
– This also applies to signals
(cell phones and radio
waves) just as much as
particles
– Nothing truly occurs
“instantaneously”, and
signaling always requires a
time lag
• Things can go slower than
light, but nothing goes
faster.
The flaw of Newtonian Gravity
• According to his equation, if the separation between
two objects changed, they would instantaneously
feel a change in their mutual gravitation.
– For instance, if our sun exploded…
• Earth, which is 93 million miles away, would instantly be thrown
out of orbit. Although light and signals would take nearly nine
minutes to reach us, Newton claimed we would instantly lose
orbit.
• Einstein knew that information cannot travel faster
than the speed of light. A tree cannot be heard
hitting the ground before it actually hits it!
Newton’s Embarrassing Secret
• Newton developed
equations that predicted
gravitational attraction, but
he never actually offered
insight to HOW it works or
WHAT it is.
• His equation was like the
“Owners Manuel”, but he
left the inner workings
locked up in the “black
box”.
Einstein’s Happiest Thought
• In 1907, while sitting at his
patent clerk desk, Einstein had
an idea. He fully explained
“constant-velocity” motion, as
we talked about during our
special relativity examples 1-6.
But what about
ACCELERATED motion?
Perhaps this troubled
you…once again, we shall turn
to an example!
• Read Sample Story SEVEN!
Acceleration
• The force of gravity is
indistinguishable from the
force of acceleration.
• When adjusted properly,
you could not tell the
difference between a
rocket accelerating at 9.8
m/s/s and the Earth
pulling down on you at 9.8
m/s/s, assuming you did
not know the direction you
were facing.
DISCUSSION:
Consider a universe in which the speed of light is just 4.0 mph (typical walking
speeds). How would the laws of physics change?
When Done:
Quietly read sample story 7
Today:
1) Finish Notes 2) consider the justification of invariance 3) math WS
The essence of Relativity
• Special:
– The laws of physics appear identical to all observers
undergoing constant-velocity motion
– When in motion relative to another, your experiences in
spacetime are NOT on equal grounds!!!
• General:
– There is no difference between an accelerated vantage
point WITHOUT a gravitational field and a nonaccelerated vantage point WITH a gravitational field
• Gravity and acceleration are the same thing!
• All observers, regardless of their state of motion, may claim that
they are at rest while the rest of the world moves by them, so
long as they include a suitable gravitational field in the
description of their surroundings.
• The stronger the gravity, the more timewarping that occurs. The more timewarping, the more slowly time progresses.
• What happens to time near a black hole?
Acceleration and the warping of
space-time
• Recall that an object is
“accelerating” if its speed or
direction is changing.
– We will consider
DIRECTIONAL change, as in
circular motion
– Think of the “Gravitron Ride”
at the amusement park.
– A circle drawn on a sphere (3D) will have a shorter
circumference than a 2-D
“Greek circle”.
The Moral to Acceleration and
space…
• The familiar geometric
relationships established by the
Greeks hold true on paper, but in
our universe, accelerated motion
curves space-time 3-D
• Einstein now had a description of
gravity (something Newton could
not achieve), and it was visual as
well as theoretical
The inaccuracy of “bowling ball”
visualization
• When the sun causes the fabric of space
to be warped, it really does not pull
downward, as the image shows. There is
no Earth-like gravity working on the sun.
Experimental Verification of G.R.
• During an eclipse, Einstein predicted that
we could see light being bent around the
sun’s gravitational field from a distant star.
Our stunning conclusions
• The theory of GR has brought about one
of the most dramatic upheavals ever to
occur in our understanding of the universe.
• Space and time, long considered to be a
simple fixed background for all events, are
now seen as dynamic, curving and
changing in response to the matter and
energy within them.
The “Cone of Causality”
• Think of the future as
being the top cone and
the past as the bottom
cone
• Only so many past
events could “cause”
what we see now
• What we do this moment
can only affect so much
of the spatial expanse
• Imagine light speed as
the “edge” of the cones
Quantum Theory and Relativity
• Taken together, these two theories—GR and quantum
mechanics—form our best current understanding of the
physical laws of the universe.
• The problem is that you can't mathematically merge
them together.
– Every attempt that has been made so far to reconcile the
geometric view of space-time in GR with the fuzziness of
quantum mechanics has led to contradictions.
– The search for a single theory that could bring these two pieces
together—a theory of quantum gravity—occupied Einstein for
much of his life and is still one of the greatest outstanding
challenges in science today.
Can we “marry” quantum and
Relativity?
• There is currently one favored candidate called
string theory, which essentially reworks quantum
mechanics by treating particles as small strings
rather than points.
– This simple idea has dramatic consequences for
the theory, and it seems that it may be able to
resolve the contradictions of quantum gravity.
Unfortunately it's very difficult to do calculations
in string theory, so the theory is still untested.
– This is the leading theory, and if the particle
accelerator in Geneva finds a particle called the
“Higgs Boson”, it would verify string theory as the
top candidate for the “Theory of Everything”
Questions That Science Has
Yet To Answer
• Regardless of whether or not string theory is
correct, many questions certainly still remain.
– The hope is that, pending experimental verification,
string theory WILL provide us answers to the
questions that science is still debating.
• The nature of geometry on small scales where quantum
mechanics is important is not fully understood.
• The history of the universe for the past fourteen billion years
or so is pretty well understood, but what happened before
that is not.
• Was there a big bang?
• What, if anything, happened before the big bang?
• What will be the ultimate fate of the universe in the future?
• Are there parallel universes?
Einstein’s Derivation of General
Relativity
Physics and Religion: Do they
Clash?
• The following issue is being discussed
because of its implications on Physics.
– The information being discussed is
scientifically and philosophically based.
• In no way does it prove or falsify any religious
grounds, nor does it encourage or discourage any
theological belief(s).
• Mr. Cunnings, nor WHS, promote or advocate any
religious faith as being superior to any other.
So, what about God?
• Christians believe that God is
eternal.
– The word eternal has two rather
different meanings
• In simpler versions, eternal means
“everlasting”, or existing without a
beginning or end for an infinite duration..the
second definition will be considered shortly
– Other religions (typically Eastern
Religions) debate this type of God.
• They claim that a God acting IN time is
subject to change, just as we are. But what
causes God to change? If an eternal God
is the cause of all change, then does it
make sense to talk about that ultimate
cause itself changing?
Do you believe in “free will” or “determinism”?
Free Will: You can freely make choices that affect
future events.
Determinism: Everything has already been
decided. You are just following the path that’s
been set for you. You have no control over
anything that happens in your life.
About time and “eternity”
• Time is not “there”, but it is PART
OF THE PHYSICAL UNIVERSE
– Time is directly linked to space, and
time is involved in physical
processes just as much as matter is
– Time is not a divine quality because
it can be altered physically. In fact,
we do it all the time by MOVING!
– Will time cease to exist at some
point in the future? Is this what is
meant by the “end of the world”?
The Great Debate:
• Many philosophers claim that God cannot be
omnipotent (supreme and absolute) if he is
subject to the physics of time.
– A God who is “in time” is therefore subject to the
same laws of physics that we are.
• He is affected by the same laws (gravity, electromagnetism,
etc) that all the universe is subjected to…In other words, he’s
“part of the cosmic symphony”
• These philosophers also claim that God cannot
be the creator of the universe if he did not create
space-time.
Eternal’s second meaning
• “Timeless”
– A timeless God exists outside of our universe.
• Idea dates back to St. Augustine and St. Anselm.
Both suggest that God created time.
• A timeless God meshes “better” with
Relativity for religious people
– But, there are problems with this view also
• This God cannot be a personal God that thinks,
converses, feels, plans, and so forth, for all of these
are temporal activities that occur according to our laws
of physics and within our space-time.
So, what kind of God(s) is/are
possible, according to physics?
• A timeless God cannot be an individual in
any sense of the word we know
– Many modern theologians (religious people)
reject the view of an eternal God
• A timeless God cannot think, being as thinking is a
temporal activity. Acquiring knowledge requires time,
but “knowing” does not. So, if a timeless God
determined all events prior (determinism), God could
still be all-knowing and outside of time.
– Modern physics claims that God can either be
omnipotent (all-powerful) or have a personality,
but NOT both, depending on if God is timeless
or operates “in time”. What do you think?