Chapter 1 Principle of Relativity
*What two quantities can change when an object accelerates?
speed = total distance traveled / total time required Write down some examples of speed. Give the number and the units for the speed.
e.g. 60 miles/hour
uniform motion = constant speed in a straight line
*What is the value of acceleration of an object that is moving with uniform motion?
page 1-3 Exercise 1 Use your imagination. The author thought his bus was
moving. What direction was the other bus traveling?
Thought Experiment (Gedanken Experiment)
The person on the plane might claim that the ground was moving under the
plane. A person on the ground would claim that the plane was moving over
the ground. In physics it is important that you know where the observer who
reports the data is located.
Principle of Relativity
There is no experiment you can perform that will allow you to tell whether
or not you are moving with uniform motion.
*Exercise 2 Write down something you might try to test the Principle of
Relativity if you were flying in a plane at night.
Basic Law of Physics
What convenience is possible due to the Principle of Relativity?
*What role did the "ether" play regarding light in the thinking of
physicists shortly after 1860?
Has the "ether" been detected?
Wave Motion
We will not use the equation for the speed of a pulse in this chapter. You
should note that the speed depends on the characteristics of the medium.
Remind me to stretch out a slinky in class and observe the speed of a pulse
while we vary the characteristics of the medium.
We will discuss the speed of sound in a later chapter.
Measurement of the Speed of Waves
Does anyone have any questions on the slinky example with one student moving
away from the instructor and one student moving towards the instructor?
Why is the instructor special?
Continue reading on page 1-9a (a = left column of the page)
The constants in equation 5 are related to electrical effects and magnetic
effects. Find the values of the constants and calculate the speed of light,
c, using equation 5. Are you surprised by your result?
Why is the speed of light approximately 1 foot per nanosecond?
page 1-11a Why would have Bill and Joan violated the principle of
relativity?
Michaelson-Morley Experiment
This experiment was done for several years around 1880. The data from the
experiment suggested that light travels at the same speed regardless of
motion of the observer. As a consequence they could not demonstrate whether
or not the earth is moving in the "ether." Does this agree or disagree with
the result of the slinky thought experiment?
Einstein's Principle of Relativity
Most historians of science believe that Einstein was not aware of the
results of the Michaelson-Morley experiment when Einstein developed his
ideas on Special Relativity. Michaelson and Morley performed their
experiment near Cleveland, Ohio. Einstein was a patent clerk in
Switzerland.
Physicists prefer simple formulas. The equations of Maxwell have a simpler
form for the case of an observer at rest. These equations predict that the
speed of light is c. Einstein claimed that every observer (in uniform
motion) should be able to use the simpler form of the equations. Einstein
believed that the Principle of Relativity was correct. In order for it to
be correct all observers (in uniform motion) must measure the speed of light
to be c.
Does anyone have questions on the illustration of freeway traffic on page
1-12b? (b = right column on the page)
*In what two ways does light differ from traffic on a freeway?
Special Theory of Relativity
"Special" = this theory only applies to uniform motion, no acceleration is
allowed
Einstein came to conclusions about the nature of time and space (and other
quantities) as a result of accepting two postulates:
1. The Prinicple of Relativity (i.e. you cannot perform an experiment that
indicates whether or not you are at rest or you are in uniform motion.)
2. All observers can use the simpler form of Maxwell's Equations ( i.e. the
speed of light is the same (c) for all observers)
Moving Clocks
List two types of clocks.
If your clocks are sitting next to each other and are not moving with
respect to each other, will they indicate the same "time" day after day
(assume they don't run down)?
Does movement affect time on any of your clocks? (i.e. If you drive or fly
do you have to reset your clock?)
If one clock is put into uniform motion with respect the other clock will
they indicate the same "time?"
*page 1-14 Describe the clock proposed by Einstein.
*Suppose two mirrors face each other and are at rest with respect to each
other and an observer. This constitutes a "light clock." If light takes
one nanosecond to move from the bottom mirror to the top mirror, how far
apart are the mirrors? Why?
page 1-14b One "g" of acceleration represents a situation in which the
speed of an object changes by 9.8 meters/second every second. Five "g's"
is a situation in which the speed changes by 5 times 9.8 meters/second every
second (49.0 meters/second every second).
*Define "coasting."
Why couldn't the astronaut tell that she was moving?
Figure 16 Imagine the astronaut moves by you (not directly away or towards
you) and you can see the light clock at all times. The astronaut will later
report that the beam of light hit the top and bottom mirrors while it was in
the "moving" (from your point of view) spacecraft. Why does the light
travel on a slanted path from your point of view?
Which is the longer interval of time?
A) the time required for the light beam to travel from the bottom mirror to
the top mirror in the light clock that is at rest beside you,
B) the time required for the light beam to travel from the bottom mirror to
the top mirror in the light clock that is at rest with respect to the
astronaut?
*What conclusion about the length of time intervals (the time between "tick"
and "tock" in the two clocks) do you come to as a result of your choice
between A) and B)?
*Why does the book state that the astronaut's clock must be running slower?
Isn't it true that the time required for the light to travel to the upper
mirror in the astronaut's clock is larger!?
Exercise 4 What questions do you have about this exercise?
Does this exercise agree with the Principle of Relativity?
page 1-16 You should make your own drawing of the path of the light in the
two clocks. Label the lines as shown in Figure 18. What does T represent?
What does v represent?
What does T' represent?
You should write down the Pythagorean theorem yourself and do the algebra
steps yourself. Follow the steps in the book but be sure that you
understand every step. Come to my office and ask questions if you don't
understand each step in the book up to equation 11.
The quantity 1/sqrt( 1-v2/c2 ) is often called gamma.
Calculate the value of gamma for the case of v = 30,000,000 meters/second.
Before you do the calculation let's simplify the representation of v.
Divide V by the speed of light, 300,000,000 meters/second. What is your
result?
In Special Relativity problems it is common to express v in terms of the
speed of light.
Calculate gamma here for the v given above.
Calculate gamma for v = .8c.
Calculate gamma for v = .99c.
Try to calculate gamma for v = 50 miles/hour (about 25 meters/second).
page 1-18 Memorize the principle "Moving clocks run slower than a clock at
rest with respect to me."
Suppose a clock moves by you at .99c. 40 minutes elapse on your clock. How
much time would you observe to elapse on the moving clock? (You can
conveniently ignore the difficulties of keeping a telescope focused on the
moving clock!)
Other Clocks
page1-19 Why does the above discussion on time apply to all clocks?
Real Clocks
page 1-20
What evidence do muons provide in support of the Special Theory of Relativity?
When was this support provided?
Get some popcorn and your favorite soft drink( if you are in your room, not the computer lab). Play the "MuonLife" movie on the CDROM that came with the book. The movie is in the Movies folder! The movie was made in 1962. It is a "talkie" so the computer should have speakers installed or you should use headphones in the computer lab. The movie runs for about 35 minutes.
*Why do more muons than predicted by Classical Physics reach sea level?
(There are two acceptable answers.)
What clocks show the "Time Dilation" effect?
page 1-22b Space Travel
If it takes light 200 years to travel from a certain star to the earth, is it possible that a human could make the journey from the earth to that same star?
page 1-23b In the last paragraph I would like you to do the calculation in a little more detail. Calculate gamma for the speed of v = 0.994c.
Calculate the time required for a spacecraft traveling at a speed of 0.994c
to cover a distance of 200 light years, as observed by a person who stays on
the earth.
Calculate the time elapsed on a clock on the moving spacecraft, as observed
by a person who stays on the earth.
Lorentz Contraction
page1-24b Your calculations above should produce values close to some of
the numbers in this column.
Why does the author not apply the calculations to the time period when the
spacecraft is accelerating?
page 1-26b Do you have a question on how the astronauts calculated a
distance from the earth to the star of about 22 light years?
page 1-27 The astronauts come to the conclusion that the distance from
earth to the star has gotten shorter by a factor equal to gamma.
page 1-28a The conclusion at the bottom of the column is correct. Lengths
in the direction of motion change by a factor of gamma but distances
perpendicular to the direction of motion are constant.
Lorentz was Hendrik Lorentz, a famous scientist who was about 26 years
older than Einstein. George Fitzgerald was 28 years older than Einstein.
Even though Lorentz and Fitzgerald came up with an empirical formula for
length contraction, the greater recognition goes to Einstein because his
development of the same formula has a theoretical foundation.
Relativistic Calculations
I prefer to use gamma for relativistic calculations. but there is nothing wrong with using the sqrt(1 – v2/c2) method. I will try to use both methods in examples that are worked out in class. It is IMPORTANT that you memorize that less time elapses on moving clocks and moving lengths are shorter than when the object is at rest.
page 1-29a Muons and Mt. Washington
Reminder: At the end of one half life only one-half of the original muons remain. The other half have changed into particles we are not concerned with at this point in the course. If you are interested view the Google web site and search for muon decay .
Which observer would measure 19.8 microseconds for the half life of the moving muons: A) an observer who is standing on a muon as it moves through the earth’s atmosphere, or
B) an observer at rest on the surface of the earth who is watching the moving muons.
From the point of view of the observer at rest on the earth, why do most of the muons survive the trip from the elevation of the top of Mt. Washington to sea level?
From the point of view of the observer standing on a muon that moves down through the earth’s atmosphere, why do most of the muons survive the trip from the elevation of the top of Mt. Washington to sea level?
page 1-29b Slow Speeds
Why are ordinary calculators unable to do relativity calculations when the speed is small (i.e. v < .00001c)?
In class we will convert 0.00001c into miles/hour.
More examples will be worked in class.
PHY151 students can skip pages 1:30-39
PHY161 students will cover the key points of these pages in our Tuesday class.
PHY161
page 1-30
You do not have to memorize the approximation formulas. We will use equation 25 in examples on Tuesday.
page 1-32 A Consistent Theory
Both the observer on the muon and the observer at rest on the earth reach the same conclusion. Special Relativity is a consistent theory.
Lack of Simultaneity
Events that are simultaneous from the point of view of one observer may not be simultaneous to an observer in uniform motion with respect to the first observer.
page 1-33a What questions do you have regarding the phrase "simultaneous events?"
What questions do you have about the views of the situation from the Martian and Venusian?
page 1-36 to 1-39 Causality etc.
We will skip this material
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