Matter and Energy
Unit 4: Matter and Energy
Chapter 11: Relativity
 11.1
Relationship between Matter and Energy
 11.2
Special Relativity
 11.3
General Relativity
11.1 Investigation: Frames of Reference
Key Question:
How does your frame of reference
affect what you observe?
Objectives:

Explain how physicists define a frame of reference.

Set up an experiment to analyze frames of reference from
the perspective of different observers.
The Relationship between Matter and
Energy
 According
to Einstein’s formula, in a nuclear reaction,
some mass is converted to energy.

The c2 factor means that even a tiny amount of
mass is equivalent to a huge amount of energy.
Matter and energy
 The
speed of light (c) is 3 ×
108 m/s, so the speed of light
squared (c2) is 9 × 1016 m2/s2.
 During
the radioactive decay
of carbon-14, a tiny amount
of mass is converted to a
relatively large amount of
energy.
Einstein's formula
 This
equation tells us that matter and energy are
really two forms of the same thing.
Energy (J)
E = mc2
Speed of light
3.0 x108 m/sec
Mass (kg)
The speed of light
 The
speed of light is so important in physics that it
is given its own symbol, a lowercase “c”.
 When
you see this symbol, remember that “c” is 300
million m/s, or 3 × 108 m/s.
The speed of light
 Einstein’s
theory of
relativity says that nothing
in the universe can travel
faster than the speed of
light.
 If
the Sun was to vanish,
we would still see it in the
sky for 8 minutes and 19
seconds.
Antimatter

Up until the 1930s, scientists were confident that they could
explain all the elements with three subatomic particles, then
they discovered antimatter.

Antimatter is the same as regular matter, except properties
like electric charge are reversed.
Antimatter

When antimatter meets an
equal amount of normal
matter, both the matter and
antimatter are converted to
pure energy.

A bit of antimatter the size of a
grain of sand would release
enough energy to power a city
for a week if it combined with
an equal amount of normal
matter.
Strange particles: neutrinos
 Huge
numbers of neutrinos are created by nuclear
reactions in the Sun.
 Neutrinos
are lighter than electrons and are very
difficult to detect.
 Neutrinos
are affected only by the weak force, so
most neutrinos pass right through Earth without
interacting with a single atom.
Particle accelerators
 Other
particles even
heavier than the proton
and neutron have also
been found.
 Physicists
use highenergy accelerators to
produce the heavy
particles so we can study
them.
Strange particles: quarks

Today, we know that protons and neutrons are made of even
smaller particles called quarks.

Quarks come in different
types and the lightest two are
named the up quark and the
down quark.

The six kinds of quarks are
named: up, down, strange,
charm, top, and bottom.
Unit 4: Matter and Energy
Chapter 11: Relativity
 11.1
Relationship between Matter and Energy
 11.2
Special Relativity
 11.3
General Relativity
11.2 Investigation: Special Relativity
Key Question:
What are some of the implications
of special relativity?
Objectives:

Explore consequences of time dilation.

Calculate the equivalence of mass and energy using
Einstein’s formula, E = mc2.
Special Relativity
 The
theory of special
relativity describes what
happens to matter,
energy, time, and space
at speeds close to the
speed of light.
Simultaneity
 When
we say that two events are simultaneous,
we mean they happen at the same time.
 Since
time is not
constant for all
observers, whether two
events are simultaneous
depends on the relative
motion of the observers.
Simultaneity
 Two
lightning strikes are
simultaneous to the
observer at rest, but the
observer moving with the
train sees the lightning
strike the front of the train
first.
Special Relativity
These effects are observed in physics labs:
1.
Time moves more slowly for an object in motion than it
does for objects that are not in motion. This is called time
dilation.
2.
As objects move faster, their mass increases.
3.
The definition of the word “simultaneous” changes.
4.
Space itself gets smaller for an observer moving near the
speed of light.
Special Relativity
1.
2.
3.
Clocks run slower on moving
vehicles compared with clocks on
the ground. By moving very fast, it
is possible for one year to pass
on a spaceship while 100 years
have passed on the ground.
The closer the speed of an object
gets to the speed of light, the
more of its kinetic energy
becomes mass instead of motion.
The length of an object measured
by one person at rest will not be
the same as the length measured
by another person who is moving
close to the speed of light.
Speed of light paradox
A paradox is a situation that does not seem to make sense.

A ball thrown from a moving train
approaches you at the speed of
the ball relative to the train plus
the speed of the train relative to
you.

The speed of light appears the
same to all observers independent
of their relative motion.
Speed of light paradox


If the person on the train were
to shine a flashlight toward you,
you would expect the light to
approach you faster.

The light should come toward
you at 3 × 108 m/sec plus the
speed of the train.
Michelson and Morley found experimentally that the light
comes toward you at a speed of 3 × 108 m/sec no matter how
fast the train approaches you!
Speed, time, and clocks

Einstein thought about a
clock that measures time
by counting the trips made
by a beam of light going
back and forth between
two mirrors.

A person standing next to
the clock sees the light go
back and forth straight up
and down.

The time it takes to make one
trip is the distance between
the mirrors divided by the
speed of light.
Speed, time, and clocks

To the observer in the space
ship, the path of light is
straight up and down.

To someone observing the
spaceship, the light appears
to make a zigzag because the
mirrors move with the
spaceship.

The speed of light must be the
same for both observers, yet
the person on the ground
sees the light move a longer
distance!
Speed, Time and Clocks
Atomic clocks

In the early 1970s an experiment was performed by
synchronizing two precise atomic clocks.

One was put on a plane and flown around the world, the
other was left on the ground.

When the flying clock returned home, the clocks were
compared.

The clock on the plane measured less time than the
clock on the ground. The difference agreed precisely
with special relativity.
The twin paradox

A well-known thought experiment
in relativity is known as the twin
paradox.

Two twins are born on Earth.

They grow up, and one of the twins
goes on a mission into space and
travels at the speed of light.

Upon returning from a 2-year (ship
time) trip, the astronaut is 2 years
older than when she left.

However, her twin brother is 20
years older now!
Unit 4: Matter and Energy
Chapter 11: Relativity
 11.1
Relationship between Matter and Energy
 11.2
Special Relativity
 11.3
General Relativity
11.3 Investigation: General Relativity
Key Question:
What is Einstein’s theory of
general relativity?
Objectives:
Describe how the theory of general relativity builds upon
Einstein’s earlier explanation of special relativity.
 Compare and contrast Newton’s ideas to Einstein’s
explanations about the effects of gravity.
 Research applications of general relativity

General relativity

Einstein’s theory of general
relativity describes gravity in a
very different way than does
Newton’s law of universal
gravitation.

Imagine a boy and girl who jump
into a bottomless canyon, where
there is no air friction.

On the way down, they throw a
ball back and forth.
Reference frame
 In
physics, the box containing the boy and girl is
called a reference frame.
 No
experiment the boy or girl do inside the box can
tell whether they are feeling the force of gravity or
they are in a reference frame that is accelerating.
Curved space-time
 This
equivalence of acceleration and gravity must
also be true for experiments that measure the speed
of light.
 In
order to meet both these conditions, Einstein
deduced two strange things which must also be true.
— 1. Space itself must be curved.
— 2. The path of light must be deflected by gravity,
even though light has no mass.
Curved space-time
 Consider
rolling a ball
across a sheet of graph
paper.
 If
the graph paper is flat
the ball rolls along a
straight line.
 A flat
sheet of graph
paper is like “flat space.”
Curved space-time
 A large
mass, like a star,
curves space nearby.
 If
you roll a ball along
this graph, its path
bends as it rolls near this
place where the graph is
stretched by the mass.
Curved space-time

If you look straight down on the
graph, the path of the ball
appears to be deflected by a
force pulling it toward the large
mass.

You might say the ball “felt” a
force of gravity which deflected
its motion.

This effect of curved space is
identical to the force of gravity.
Black holes
 To
understand a black hole, consider a rocket trying
to leave Earth.
 If
the rocket does not go fast enough, Earth’s gravity
pulls it back.
 If
gravity becomes strong enough, the escape
velocity can reach the speed of light.
 A black
hole is an object with such strong gravity that
its escape velocity equals or exceeds the speed of
light.
Black holes
 The
name black hole
comes from the fact that
no light can get out, so the
object appears “black”.
Because
 Earth’s
escape velocity is
much less than the speed
of light, light easily
escapes its gravity.
Black holes and light
Black holes
 You
might think it would be
impossible to see a black
hole but you can see what
happens around a black
hole.
 Any
matter that falls into a
black hole gives off so much
energy it creates incredibly
“bright” (intense) radiation
as it falls in.
Astronomers believe our
own Milky Way Galaxy
has a huge black hole at
its center.
The Big Bang

The best evidence indicates that
the age of the universe is about 13
billion years, plus or minus a few
billion years.

If the universe is expanding, then it
must have been smaller in the past.

Sixteen billion years ago, scientists
estimate that cataclysmic explosion
occurred and the universe started
growing from a tiny point into the
incredible vastness we now see.
Traveling Faster than Light

Some physicists are looking for
loopholes in the laws of physics in
the hope that one day, science
fiction will become reality.

One idea being explored to bypass
the light-speed barrier involves
Einstein’s concept that space can be
distorted into structures called
wormholes.