Download Special Relativity: Slides 1 to 16

Special Relativity
Physics 12
Key Terms - Copy
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Postulate:
a thing suggested or assumed to be true as
the basis for reasoning, discussion, or belief
Inertial Frame of Reference:
When your frame of reference (ie, how you
see the world) where Newton’s First Law of
Inertia is correct. This occurs when you are
moving (or not moving) at a constant velocity.
Key Terms
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Light year (ly): A measure of distance: the
distance that light can travel in one year (in a
vacuum). It is roughly 9,461,000,000,000
km. (add to formula sheet)
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Space-Time: Comprised of 3 dimensions of
space (length, width, height) and 1 dimension
of time. It is a continuum of space and time.
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Equation (please add to sheet): d = ct
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https://www.youtube.com/watch?v=M9sbdrP
VfOQ
https://www.youtube.com/watch?v=ScdLqAA
_64E
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Key Terms- from Grade 11
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Copy if you don’t remember
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Electromagnetic Waves: Type of waves
that do not require a medium for the energy
to travel through. Example: Light waves.
However, originally it was believed that all
waves needed a medium. (Mechanical
waves like sound waves do need medium).
Light
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One theory of light is that it acts as a wave.
At one point in time, it was thought that
waves needed a medium for the energy
carried to travel.
However, we now know that light waves
(electromagnetic) do not need a medium
(only mechanical waves do).
Michelson-Morley Experiment
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Prior to experiments by Michelson and
Morley, it was assumed that light needed a
medium to propagate (travel) through
This medium was called the “luminiferous
ether” and Michelson and Morley set out to
test for the presence of this substance
around Earth
They used an interferometer, which is a
device designed to measure wavelengths of
light
Michelson-Morley Experiment
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Michelson performed an experiment in 1881
that was “unsuccessful” in detecting ether
Michelson and Morley performed a refined
experiment in 1887 where they tried to find
that light moving back and forth parallel to
the motion of the Earth took longer to
complete the same trip as light moving
perpendicular to the motion of Earth
Michelson-Morley Results
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Michelson and Morley set the apparatus so
that one beam was travelling parallel to the
ether and the other was travelling
perpendicular to the ether
They then rotated the apparatus and
attempted to measure changes in the
interference patterns
Unfortunately, they were unable to observe a
change in interference patterns
Confused Yet???
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Think about relative velocity from grade 11.
Remember how confusing it was to think
about? Remember how the actual speed
was not what the observer witnessed? This
is similar!
Let’s watch some videos to help!
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https://www.youtube.com/watch?v=uMaFB3j
M2qs (10 min)
https://www.youtube.com/watch?v=7qJoRNs
eyLQ (5 min)
http://www.upscale.utoronto.ca/PVB/Harrison/
SpecRel/Flash/MichelsonMorley/MichelsonM
orley.html
Speed of Light
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Michelson and Morley’s results remained a
mystery for about 20 years until Einstein
published his special theory of relativity
Einstein was attempting to address an
inconsistency in Maxwell’s equation for the
speed of light:
c
1
 0 0
Einstein’s Theory Of Special
Relativity (summary)
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Einstein came up with his Special Theory of
Relativity in 1905 which helped explain this:
He postulated the following:
1) The laws of physics are the same in all
inertial frames of reference
2) The speed of light in a vacuum (3.00 x 108
m/s) is the same in all inertial frames of
reference, regardless of the motion of the source
or the observer.
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Question: This theory was not well received
at the time. If you were alive at the time,
would you accept these as truths? Why do
you think it was not well received?
Special Relativity Implications
Summary
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Because special relativity deals with inertial frames
of reference, it restricts its application to systems
with no acceleration.
It also means that, regardless of your speed relative
the source, you will always observe light as moving
at 3.00 x 108 m/s.
This implies that your speed, relative to the speed of
light, will determine your speed of passage through
time: all things pass through time at the speed of
light.
Questions to Ponder…
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What happens as you approach the speed
of light then?
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Time physically slows down.
Why doesn’t time slow down or speed up
if we are traveling in a car then?
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The amount that we speed up in a car is not
significant enough to effect time. It is so much
slower than the speed of light.
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https://www.youtube.com/watch?v=ttZCKAMpcAo (7
min)
Why doesn’t time travel work?
http://www.perimeterinstitute.ca/videos/alice-andbob-wonderland-can-we-travel-through-time (1 min)
Extras:
https://www.youtube.com/watch?v=30KfPtHec4s (8
min)
Time Dilation
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Time itself is measured differently for the
moving object than the unmoving object.
Moving at high, relativistic speeds causes
time to slow down. It is not just the
measurement of time that is affected, but
time itself.
Chemical and biological processes slow
down (and stop if moving at light speed).
Derivation of Time Dilation
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*** See pdf files online for derivation (Physics
12 advanced)
Time Dilation
Units
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The units for t and t0 can be any form of time
as they will cancel each other out (but must
be the same).
The units for c and v must be the same so
they cancel. If the units are in m/s then they
can be used easily. If v is measured relative
to the speed of light, they will cancel as well.
If v is measured in km/h it must be changed.
Remember: d = ct
How do I know if I am correct?
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To see if you are roughly on the right track
(and make sure you are using t and t0
appropriately), make sure that length gets
longer for the observer of the non-relativistic
speed!
IE: The spaceship has been orbiting Earth
for 10 years so the people in the spaceship
should be YOUNGER than expected! The
people on Earth think they have been
travelling than they have!
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Example: A spaceship carrying a light clock
moves with a speed of 0.500c relative to an
observer on Earth. According to the
observer, how long does it take for the
spaceship’s clock to advance 1.00s?
Example 2: Biological Aging
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Astronaut Benny travels to Vega, the 5th brightest
star in the night sky, leaving his 35.0 year old twin
sister behind on Earth. Benny travels with a speed
of 0.990c, and Vega is 25.3 light years from Earth.
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How long does the trip take from the point of view of
Jenny? (Hint: remember back to grade 11… there
is no “relative” velocity in this part)
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How much has Benny aged when he arrives at
Vega?
Example 3
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Example: An astronaut travelling with a
speed, v, relative to Earth takes her pulse
and finds that her heart beats once every
0.850s. Mission Control on Earth, which also
monitors her heart activity, observes one
heart beat every 1.40s. What is the
astronaut’s speed relative to Earth?
Try this!
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A rocket speeds past an asteroid at 0.800c.
If an observer in the rocket sees 10.0s pass
on her watch, how long would that time
interval be as seen by an observer on the
asteroid?
(16.7s)
Page 819, Questions 1 to 3
Muons…
The Special Theory of
Relativity
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Based on his consideration of Maxwell’s
lack of a frame of reference, Einstein
proposed his special theory of relativity
based on two postulates:
1.
2.
All physical laws must be equally valid in all
inertial (non-accelerated) frames of reference
The speed of light through a vacuum will be
measured to be the same in all inertial frames
of reference
Length Contraction
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If observers are moving relative to each
other, than time dilation from one observer’s
point of view will be balanced by a
corresponding length contraction from the
other’s point of view.
Something to think about…
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A metre stick moving with a speed of 0.5c
would appear noticeably shorter than a metre
stick at rest.
As the speed of an object approaches c
(speed of light), its length diminishes to 0.
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WOW!
Jenny and Benny again…
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From Jenny’s point of view on Earth, Benny’s trip
took 25.6 years and covered a distance of 25.3 light
years (d = 0.990c x 25.6 years)
From Benny’s point of view in the spaceship, the trip
took 3.61 years. As far as Benny is concerned, he
traveled 3.57 light years (d = 0.990c x 3.61 years)
So how did Benny travel so much less distance than
what Jenny thinks? How can Earth and Vega be
separated by such a small distance (3.57 light
years)?
Length Contraction!!!
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A moving object has two measurable lengths:
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Lo = Its proper length (the length on the
moving object).
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L = its contracted length (seen by outside
observer)
Length Contraction Formula
So what is Benny’s contracted
distance traveled?
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How can both be correct???
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Everything is RELATIVE! Both are correct
depending on who is the observer.
Two more things…
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Length contraction applies ONLY to lengths
measured PARALLEL to the direction of the
velocity.
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Remember that the objects travelling at
relativistic speeds will be SHORTER
according to the observer not at those
speeds!
Example:
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A spaceship passes Earth at a speed of
2.00x108 m/s. If observers on Earth measure
the length of the spaceship to be 554m, how
long would it be according to its passengers?
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743 m
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Length should be SHORTER (contracted).
Questions for You
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A rocket 75.0m long moves at 0.50c. What
would its length be according to an observer
at rest?
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65.0m
Question
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A spaceship is 98m long. How fast would it
have to be going to appear only 49m long?
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0.87c
Questions page 824
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4-6
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Page 825
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1, 2, 4, 5
Questions on Time Dilation
and Length Contraction
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1) A clock ticks once each second and is 10cm long
when at rest. If the clock is moving at 0.80c parallel
to its length with respect to an observer, the
observer measures the time between ticks to be
______ and the length of the clock to be ______.
A) More than 1s, more than 10cm
B) Less than 1s, more than 10cm
C) More than 1s, less than 10cm
D) Less than 1s, less than 10cm
E) Equal to 1s, equal to 10cm
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2. Before takeoff, an astronaut measures the
length of the space shuttle to be 37.24m long.
Once aboard the shuttle, while traveling
0.10c, he measures the length again and
finds a value of:
A) 37.05 m
B) 37.24m
C) 37.43 m
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3. As a spacecraft heads directly to Earth at
a velocity of 0.8c, it sends a light signal to
Earth. When those light waves arrive on
Earth, their velocity relative to Earth is:
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A) 0.8c
B) c
C) 1.8c
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4. A 30 year old woman takes a trip on a rocket
leaving her 20 year old brother behind. She travels
at a speed of 0.8c and is gone 20 years, according
to the younger brother. When she returns how
many years older/younger is she than her brother?
A) 2 years younger
B) 2 years older
C) 3 years older
D) 10 years older
E) 8 years older
So How Fast Can We Go???
The Universal Speed Limit
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When we consider the formulae for time
dilation and length contraction, we know that
we must be dealing with real numbers so the
value under the root must be positive
Therefore speed (v) cannot be greater than
or equal to the speed of light (c) or the
denominator becomes imaginary or zero
This speed limit only applies to objects with
mass (therefore light and the massless
photon can travel at the speed of light)
The Universal Speed Limit Summary
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Nothing with mass can travel faster than or at
the same speed as light.
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Why can’t we travel at the speed of light?
The mass increases and therefore
prevents enough acceleration to get to the
speed of light (or beyond)
Mass and Energy
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Mass increases as you increase your speed
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Equation:
m
m0
2
v
1 2
c
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As the speed of the object increases, the value of the
denominator decreases so that m gets larger and
larger.
If v approaches c, the mass approaches m0/0, or
infinite.
Special Theory of Relativity
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As you travel at speeds closer and closer to
the speed of light…
1) Time dilates
2) Length contracts
3) Mass increases
So what about E = mc2?
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This famous formula surrounds the theory
that the total energy of a particle is equal to
its mass times the speed of light squared.
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http://www.universetoday.com/114617/a-funway-of-understanding-emc2/
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Want more info? Read page 830 in text.