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About the Resource
Welcome to Perimeter Institute’s Revolutions in Science, 
a classroom resource based on three serious-but-fun 
Alice & Bob in Wonderland animations.
Challenge and inspire your students with the wonder and 
mystery of our universe—we really do live in an “Alice in 
Wonderland” world where things are not always what they 
seem to be:
• Gravity is not a force pulling down; it is the ground 
accelerating up in “curved spacetime.”
• Atoms cannot exist in a commonsense universe; they 
require a strange “quantum” reality. 
• Energy has inertia; our energy to be alive comes from 
literally eating the mass of the Sun!
Engage your students in the powerful, but surprisingly 
accessible, creative and critical thinking processes that led 
to three of the most profound revolutions in science. 
The resource focuses not only on basic scientific literacy—
what these enduring understanding are—but more importantly
how they were discovered. Using these discoveries as
exemplars of the power of inquiry, students can experience 
for themselves how new scientific knowledge is created.
About the ANimatioNs
The three 60-second animations serve to hook your 
students’ interest—to show them that the everyday world is 
far more fascinating than they may have realized. 
Along with the two characters, Alice & Bob, students will 
discover that the simplest questions can lead to the most 
profound shifts in our understanding of reality.
Alice is a delightfully precocious little girl, brimming with 
curiosity. Each episode opens with Alice wondering about 
something that seems so obvious it sounds silly, such as, 
“What keeps us stuck to the Earth?”
Bob is Alice’s older brother who feels it is his duty to 
‘educate’ his sister. Without thinking, he blurts out the 
commonsense answer to her ‘foolish’ questions.
Alice gives us reason to question the commonsense answer. 
Together, our characters use their imaginations and simple 
reasoning to arrive at amazing insights into the universe. 
Your students are sure to enjoy their mind-warping 
adventures with Alice & Bob in Wonderland!
About the DVD: The accompanying menu-driven DVD contains the plug-and-play Alice & Bob in Wonderland 
animations, as well as the following files, which can be accessed by closing the menu software and using your computer’s 
file browser: this Teachers’ Guide in PDF format and the animations in various file formats. View the animations now! 
The Student Worksheets and Assessments in editable DOC format can be found at www.perimeterinstitute.ca
Curriculum CoNNectioNs 2
What KeepS Us Stuck to the Earth? 3
 Introduction 4
 Teacher Demonstrations 5-6
 Student Worksheets: SW1: Scientific Models: Gravity 7- 8
 SW2: Scientific Revolution: General Relativity 9-11
 Student Assessments: SA1: Scientific Models: Gravity 12
 SA2: Scientific Revolution: General Relativity 13
 Answers 14-16 
How CaN Atoms Exist? 17
 Introduction 18-19
 Student Worksheets: SW1: Scientific Models: The Atom 20-21
 SW2: Scientific Revolution: Quantum Mechanics 22-23
 Student Assessments: SA1: Scientific Models: The Atom 24
 SA2: Scientific Revolution: Quantum Mechanics 25
 SA3: Applications of Quantum Mechanics 26
 Answers 27-28
Where Does ENergy Come From? 29
 Introduction 30-31
 Student Worksheets: SW1: Scientific Models: Time 32- 34
 SW2: Scientific Revolution: Special Relativity 35-36
 Student Assessment: SA: Scientific Revolution: Special Relativity 37
 Answers 38- 40
CredIts 41 
 
2
Curriculum coNNectioNs 
Topic Connection to Resource Module
Nature of Science Science involves both creative and critical thinking, leading to new and sometimes 
revolutionary ways of understanding nature. Educated guesswork and intuitive leaps 
can lead the scientific imagination to very strange ideas, but as long as these ideas fit 
the experimental evidence they must be taken seriously. The ultimate judge of a theory 
is how well it matches the observations, not how well it matches our commonsense. 
Process of Scientific 
Modeling
We build scientific models to explain complex phenomena. Good models must be 
logically self-consistent, explain the observations accurately, make testable predictions 
of new observations, and give new insights into the phenomena.
1, 2, 3
1, 2, 3
Force and 
Acceleration
Newton s second law of motion dictates that acceleration is the result of a net force. In 
Newton s model, gravity is a force causing acceleration; in Einstein s model, gravity is 
not a force so objects in freefall are not accelerating.
1
Weight For Newton, weight is the force of gravity pulling down on you. For Einstein, there is no 
force of gravity; weight is the magnitude of the force needed to accelerate you up along 
with the accelerating ground. 
1
Gravity Students challenge the underlying assumption of Newton s mysterious “force of 
gravity,” which has no known cause, and replace it with an alternative explanation for 
gravity using Einstein s curved spacetime.
1
Frames of Reference All observations and measurements are made relative to a frame of reference. If that 
frame is moving with constant velocity, there is no experiment that can be done to show 
that it is moving. If the frame is accelerating, the law of inertia seems to be violated so 
we invent forces to reconcile our experiences.
1, 3
Bohr-Rutherford 
Model of the Atom
The Bohr-Rutherford model of the atom is an obsolete scientific model. The idea of 
electrons orbiting around the nucleus is examined and shown to fail due to simple, 
classical concepts that are within the students grasp.
2
Quantum Mechanical 
Model of the Atom
The quantum mechanical model of the atom uses waves to describe the behaviour of 
particles. Electrons can behave as if they are in many places at the same time, solving 
the problems encountered by the classical (and Bohr-Rutherford) models. 
2
Wave-Particle Duality The electron is a point-like particle that behaves like a wave. This allows the electron to 
act as if it is in many places, or traveling in many directions, at the same time.
2
Electromagnetic 
Fields
The electron is charged so it is surrounded by an electric field. Accelerating electrons 
have changing electric fields so they emit electromagnetic waves.
2
Relative Motion Two observers watching the same event might have very different descriptions of the 
event if they are moving relative to each other. There is no preferred frame of reference 
in the universe so all motion is relative.
3
Time Dilation The Newtonian concept of absolute time is wrong. Two observers moving relative to 
each other will measure the other s time passing at a different rate—moving clocks 
run slow..
3
Length Contraction Two observers moving relative to each other will measure the other s space to be 
contracted in the direction of motion—moving objects occupy less space.
3
Energy Energy is not just “the ability to do work.” Closer inspection of energy leads to the 
surprising result that all forms of energy have inertia—heating a cup of coffee increases 
its resistance to acceleration.
3
Inertia Inertia is not just “the ability to resist acceleration.” The inertia of even an object at rest 
represents the presence of energy, as described by E=mc2.
3
3
This module contains two single-period lessons based on the Alice & Bob in Wonderland animation: What Keeps Us Stuck to 
the Earth? In this episode Alice and Bob ask questions about the nature of gravity and realize that there is a deep connection 
between gravity and acceleration. Lesson 1 is an introductory level lesson (no prior knowledge of physics is required) that 
guides students through a criticalthinking activity to connect acceleration and gravity. Lesson 2 is a more advanced lesson 
(prior knowledge of dynamics is an asset) that builds on concepts developed in Lesson 1 to show that the effects of gravity are 
actually caused by curved spacetime.
LessoN 1: 
SCIENTIFIC MODELS: GRAVITY
Use D1: Black Box to engage the students in the 
creative process of building and evaluating models.
Follow with D2: Sagging Rod to explore the force model
of gravity and introduce the acceleration model.
Distribute SW1: Scientific Models: Gravity after D2.
This worksheet walks the students through 
an exercise in critical thinking about gravity 
and acceleration.
>> Show the Alice & Bob in Wonderland animation: 
What Keeps Us Stuck to the Earth?
SA1: Scientific Models: Gravity. This worksheet 
includes additional questions to be done in class 
or for homework.
LessoN 2: 
SCIENTIFIC REVOLUTION: GENERAL RELATIVITY 
Use D3: Toy and Bungee Cord to highlight the 
differences between the two models.
>> Show the Alice & Bob in Wonderland animation: 
What Keeps Us Stuck to the Earth?
Distribute SW2: Scientific Revolution: General 
Relativity. This worksheet guides the students into 
a discovery of curved spacetime. In Part B, they 
will use masking tape and beach balls to model 
curved spacetime. 
 SA2: Scientific Revolution: General Relativity. This 
worksheet includes additional questions to be done 
in class or for homework.
Introduction 4
Teacher Demonstrations 5-6
Student Worksheets:
 SW1: Scientific Models: 7-8 
 Gravity
 SW2: Scientific Revolution: 9-11 
 General Relativity
Student Assessments:
 SA1: Scientific Models: 12 
 Gravity
 SA2: Scientific Revolution: 13 
 General Relativity
Answers 14-16
4
WHAT KEEPS US STUCK TO THE EARTH?
“It doesn’t matter ho
w beautiful your theo
ry is, 
it doesn’t matter how
 smart you are. If it d
oesn’t 
agree with experime
nt, it’s wrong.” 
– RICHARD FEYNM
AN 
“…that one body ma
y act upon another, a
t a 
distance through vac
uum, without the me
diation 
of anything else, by 
and through their ac
tion and 
force may be convey
ed from one to anoth
er, is to 
me so great an absu
rdity, that I believe no
 man 
who has in philosoph
ical matters a compe
tent 
faculty of thinking, ca
n ever fall into it.” 
– ISAAC NEWTON 
“I was sitting in a cha
ir at the patent office
 in Bern, 
when all of a sudden
 a thought occurred 
to me: 
If a person falls freel
y, he will not feel his 
own 
weight. I was startled
. This simple though
t made 
a deep impression o
n me. It impelled me
 toward a 
theory of gravitation.
” 
– ALBERT EINSTEIN
 (Happiest Thought)
Science is a process of building models to explain 
observations and then refining those models through 
careful thought and experimentation. Good models explain 
existing observations and make testable predictions. This 
Perimeter Institute classroom resource engages students 
in this process by exploring models of a common real world 
phenomenon—gravity. Students will exercise their critical 
and creative thinking skills to demonstrate why Einstein’s 
model of gravity is better than Newton’s. 
Our everyday experiences of gravity suggest that the 
Earth exerts an attractive force on nearby objects. Newton 
successfully extended this force model of gravity to the Moon, 
Sun and planets. Nevertheless, the force model of gravity 
deeply troubled Newton because it did not explain the cause 
of the force. Moreover, in the 1850’s, a more careful look at 
existing observations suggested that something might be 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
wrong with Newton’s model—Mercury did not orbit the Sun 
quite as predicted. Scientists tried various ways to explain 
this discrepancy within the context of Newton’s model, but 
all attempts failed. Newton’s model of gravity had reached 
its limit.
Newton’s force model of gravity also troubled Albert Einstein. 
In his “happiest thought,” Einstein realized that when you are 
in freefall you do not feel your own weight, like an astronaut 
floating weightlessly in deep space. However, when an 
astronaut’s rocket accelerates, she feels as if there is a 
force pulling her down toward the floor, like weight. In reality, 
what the astronaut feels is the floor pushing up on her, 
accelerating her up. Could gravity be like this? Could it be 
that there is no force pulling us down, but instead the ground 
is accelerating up? Yes! Einstein showed how curving 
spacetime can make it possible for the ground to be forever 
accelerating up without the Earth expanding faster and 
faster! Students explore this idea through a simple, concrete 
activity involving just tape and a ball. 
Einstein’s curved spacetime model of gravity makes several 
testable predictions that distinguish it from Newton’s force 
model. Einstein’s model predicts that time passes more 
slowly at the surface of a planet compared to farther away. 
This effect has been precisely measured and is evident daily 
in the Global Positioning System (GPS). Einstein’s model 
also correctly predicts the bending of light as it passes by a 
massive object, such as a star. Such gravitational lensing 
has become a powerful tool in astronomy. Einstein’s model 
also provides a very accurate description of the orbits of all 
the planets, including Mercury.
Einstein’s model of gravity has passed every experimental 
test to date. These same tests have conclusively ruled out 
Newton’s model. The old idea of gravity as a force may feel 
right but it is wrong. The “force of gravity” is an inference, not 
an observation. We observe the ground compressing under 
our feet. We infer that gravity is a force pulling us down. In 
reality, the ground is accelerating up in curved spacetime, 
pushing up on us, forcing us to accelerate along with it. 
Dropped objects don’t accelerate down: it is the ground that 
accelerates up in curved spacetime. These statements may 
strike us as odd, but they agree with experimental data. 
Gravity is not a force. Our everyday experiences of gravity 
are actually the effects of the ground accelerating up through 
curved spacetime. Gravity is curved spacetime.
5
Teacher DemoNstratioNs
D1 - BLACK BOX: (see building instructions below)
1. Pull the top cords back and forth. Invite students to guess 
how they are connected inside. Now pull one of the 
bottom cords. Continue pulling different combinations 
of cords while drawing students into the mystery. 
2. Ask students to draw a picture of what they imagine is 
inside the box. Encourage creative thinking!
3. Have students share their ideas on the board. Engage 
the class in a discussion about the various models that 
are on the board. Verify that the models correctly explain 
the observations. Highlight the following points:
• The same set of observations can generate 
different models.
• All models that explain the observations are 
equally valid.
• Models that fail to explain one or more observations 
are wrong, or need revision.
4. Ask the students if the models on the board predict any 
new observations that may help distinguish between 
them. For example, shake the black box to see if it rattles. 
Return to the models on the board and re-evaluate them, 
emphasizing the role of testable predictions in 
the process of developing robust scientific models.
Note: Never divulge what is inside the Black Box. 
In science, we only ever have access to indirect 
observations—we never “see reality” directly!
BUILDING YOUR BLACK BOX
Materials: (all dimensions are approximate)
•2 pieces of 8 mm nylon rope, each 70 cm long
• 1 harness ring with a 4 cm diameter
• 35 cm long piece of drainage pipe (7.5 cm diameter)
• 2 drainage pipe end caps (7.5 cm diameter)
Tools:
• power drill with 3/8” drill bit
Procedure:
1. Drill the top holes directly across from one another, each 5 cm from the top. Repeat for 
the bottom holes, each 5 cm from the bottom (see top Figure).
2. Thread one rope through the top holes and the harness ring (see middle Figure).
3. Tie a knot 15 cm from each end of the rope.
4. Thread the other rope through the bottom holes. Again, ensure that the rope passes 
through the harness ring as indicated (see bottom Figure). Tie a knot 15 cm from each 
end of the rope.
5. Secure the end caps. 
Note: Variations on the design (without a ring for example) will enrich the discussion and 
work equally well. You may also wish to encourage students to build their own versions of 
the device with bathroom tissue tubes and string.
6
D2 - Sagging Rod: (a very flexible 2 m long rod with two 
small masses on each end) 
1. Hold the rod horizontally with your hand in the middle so 
the rod sags. Ask students to explain why the rod is 
sagging–typically students will say “force of gravity!”
2. Place the rod on a table. Have two students apply 
horizontal forces on the ends while you hold the middle 
in place by applying an opposing horizontal force. The 
class observes the same shape as in step #1. Reinforce 
the concept that when opposing forces are applied to 
the rod it will bend. 
3. Emphasize the distinction between Observation (when 
opposing forces are applied to the rod it bends) and 
Inference (the sagging rod is bent so there must be 
opposing forces; a “force of gravity” opposes your hand).
4. Have students suggest ways to make the rod bend 
without using opposing forces. Hold the rod vertically 
and accelerate it to the side. The ends of the rod will lag 
behind the middle because of inertia. Emphasize that 
your hand is applying a force but there is no opposing 
“force of gravity.” 
5. Distribute SW1: Scientific Models. Show the animation: 
What Keeps Us Stuck to the Earth? after students 
have worked in small groups to complete the table and 
discussion sections of the worksheet.
D3 - Toy, Bungee Cord and Board: 
1. Show the animation: What Keeps Us Stuck to 
the Earth?
2. Demonstrate Newton’s model of gravity by stretching 
the bungee cord over the toy (see Figure). “According to 
Newton gravity is a force, like an invisible bungee cord, 
that pulls objects to the ground.” Pull the toy away from 
the board and let it ‘snap’ back down. The bungee cord 
exerts a force on the toy making it accelerate.
3. Demonstrate Einstein’s model of gravity by removing 
the bungee cord, holding the toy in the air and 
accelerating the board up to hit it. “According to Einstein, 
gravity is not a force. The toy does not accelerate down; 
rather, the ground accelerates up!” Place the toy on the 
board and accelerate it up. Ask students to imagine that 
they are in deep space (no gravity); what would it feel 
like to stand on an accelerating board?
4. Distribute SW2: Scientific Revolution. Students work in 
small groups to complete the worksheet.
D4 - Curved Spacetime Exemplar: 
1. In SW2, the students will use masking tape and a beach 
ball to model curved spacetime. Read through the 
activity and make an exemplar on a large exercise ball, 
if possible (see Figure). 
2. The tape describing Alice’s path through spacetime 
must lie flat. She is experiencing no “force of gravity” 
and no acceleration so she must follow a straight path. 
3. The tape describing Bob’s path must be crinkled. He is 
experiencing the ground pushing up on him, accelerating 
him up, and so he must follow a curved path.
4. Time dilation is demonstrated by comparing a length of 
tape connecting the tops of the ladders with the length 
of tape connecting the bottoms (Bob’s path). 
Note: The time dilation demonstrated by this beach ball 
analogy is actually reversed to the real time dilation– 
analogies have limits.
7
SW1: Scientific Models: Gravity
 
Scientists use models to try to explain the observations they make. In this activity you are going to use two different models to 
explain the same observations of an everyday phenomenon—gravity.
Force Model: You are standing in a room that is on the Earth; the Earth exerts a downward force on objects inside the room. 
Explain the following phenomena using this downward force. Follow the sagging rod example.
Explain the 
Sagging Rod
- the Earth pulls 
down on the rod and 
your hand pushes up
- the rod bends because your hand is 
only in the middle
- the rod does not accelerate because 
the two opposing forces are balanced
Explain Weight 
(use words and arrows)
Explain Freefall 
(use words and arrows)
Acceleration Model: You are standing in a room that is inside a rocket; the rocket is accelerating “upwards” in deep space. 
Explain the following phenomena using this upward acceleration. Follow the sagging rod example. 
Explain the 
Sagging Rod
- the room is accel-
erating up; so are 
you and the rod
- the rod accelerates up because there is 
now only one force—your hand pushing up
- the rod bends because the ends 
have mass, which resist acceleration 
(inertia)
Explain Weight 
(use words and arrows)
Explain Freefall 
(use words and arrows)
SUMMARIZE: 
Force Model Acceleration Model
What is the “big idea” behind each 
model? How does each explain 
effects we call “gravity”?
8
Discussion:
1. Examine both of your explanations for freefall. 
(a) What do you actually observe about an object in freefall? 
 
 
 
 
 
 
(b) What can you infer about the nature of gravity from your observations of freefall? 
 
 
 
 
 
2. A flexible rod bends when opposing forces act on it. The same rod bends when suspended horizontally from the middle. 
Does this prove that gravity is a force? Explain.
 
 
 
 
 
 
3. A friend shows you a video on the Internet of a guy who can make objects “float” in the air. You know this is impossible—
how might you explain the video? 
 
 
 
 
 
 
4. You wake up in a closed room with no windows, with no idea how you got there. Describe an experiment you could do to 
determine if the room is on the Earth or inside a rocket accelerating in deep space. 
 
 
 
 
 
 
>> Watch the animation: What Keeps Us Stuck to the Earth?
Thinking Deeper:
1. Both the force model and the acceleration model make claims that are hard to accept. What are they?
2. Both models of gravity explain everyday observations equally well. However, Newton’s force model fails to correctly 
describe the orbit of Mercury, so it ultimately fails the test for a valid scientific model. Inspired by the acceleration model, 
Einstein developed an alternative model of gravity. His curved spacetime model made several successful predictions that 
have conclusively ruled out Newton’s model. Does this mean we should throw out Newton’s model? Does a model have 
to be correct in order to be useful?
9
SW2: Scientific Revolution: General Relativity
 
Scientific models must make predictions that match our observations, or they must be revised or replaced. New scientific 
models can be revolutionary. In this activity you are going to examine two models of gravity: Newton’s classical force model, 
and Einstein’s revolutionary curved spacetime model.
Part A: Modeling Gravity
Complete this table after watching >>Alice & Bob in Wonderland: What Keeps Us Stuck to the Earth?
Force Model Acceleration Model
Gravity: How 
does it work?
What’s hard 
to accept?
Alice steps off 
the top of a 
tall ladder
Bob stands at 
the bottom of 
the ladder
In the boxes,sketch snapshots of Alice as she falls to the ground and Bob as he stands at the bottom of 
the ladder, showing their progression in time. [Hint: Alice moves faster and faster as she falls.]
Connect-the-dots of Alice’s position in SPACE
(height above the ground) as TIME goes on. 
Is her path through spacetime straight or curved?
Connect-the-dots of Bob’s position in SPACE
(height above the ground) as TIME goes on. 
Is Bob’s path through spacetime straight or curved?
According to 
Newton...
Alice’s path through spacetime is ______________ because she is accelerating. She is accelerating 
because gravity is a force pulling on her. Bob’s path through spacetime is ______________ because he is 
not accelerating —the force of gravity is balanced by the ground pushing up.
There is no “force of gravity” pulling down on Alice so she _________ accelerating. Her path through 
spacetime should be ______________ . The ground pushes up on Bob and since there is no opposing 
“force of gravity” to balance this force, he should accelerate up and follow a _______________ path 
through spacetime.
Discussion:
1. Alice has a video camera in her hands as she falls. If she takes a video of herself as she falls, could she tell that she was 
accelerating by viewing the video? (Ignore the background.)
2. Alice takes a video of Bob as she falls. Could she tell who was accelerating by viewing the video? (Ignore the background.)
3. Alice closes her eyes as she falls. What does she feel? Can she tell that she is accelerating?
4. Bob closes his eyes. What does he feel? Can he interpret this feeling as accelerating up?
(straight/curved) 
(straight/curved) 
(straight/curved) 
(straight/curved) 
According to 
Einstein... (is/is not) 
10
Einstein knew that Newton’s model of gravity is wrong. For one thing, it fails to correctly predict the orbit of Mercury; for 
another, it fails to obey the speed limit of the universe—the speed of light. In his search for a better model, the simple fact that 
acceleration up mimics force down was too strong of a coincidence to ignore. Einstein needed to find a way to make sense of 
the ground accelerating up without moving up. How can the ground be accelerating up when the Earth is not expanding? He 
found the answer in the geometry of spacetime.
Part B: Bending Spacetime
In Part A, we used the fact that accelerating objects trace out curved paths in spacetime and non-accelerating objects trace 
out straight paths. We also saw that Newton and Einstein would disagree on who is accelerating and who is not. In this part 
of the activity you will use tape to transfer the spacetime diagram from Part A onto the surface of a large ball to reveal how 
curving spacetime resolves the problem of who is accelerating.
1. Use a strip of tape to connect two points on your desk with a straight line. Use another strip of 
tape to make a curved line. Compare the two pieces of tape. Which strip of tape lies flat on the 
desk and which is crinkled?
2. Build your spacetime diagram on the surface of a large ball. Start with the space and time axes.
 • The space axis is a strip of tape that runs vertically along a line of longitude. 
 • The time axis runs horizontally along a circle of latitude (about 15˚ above the equator).
3. Add three identical strips of tape to represent the ladder in three consecutive snapshots. The 
ladders must follow lines of longitude on the surface, starting about 2 cm above the time axis and 
ending about 10 cm from the top.
4. Alice’s path is a strip of tape that connects the top of the first ladder with the bottom of the last 
ladder. Can you make it a straight line? Why would you want to?
5. Bob’s path runs parallel to the time axis along a circle of latitude. It will connect the bottoms of the 
three ladders. Does the tape lie flat or is it crinkled? What does this indicate?
6. The time elapsed for Bob at the bottom of the ladder is the length of his path (i.e. distance in the time direction). If Alice 
stayed at the top of the ladder, would her elapsed time be the same? Einstein’s model predicts time dilation: time passes 
at different rates depending on height about the ground, which has been verified by atomic clocks. Newton’s model makes 
no such claim. Models cannot be proven right—but they can be proven wrong and time dilation proves that Newton’s 
model of gravity is wrong!
Curved 
Spacetime:
When we transfer the spacetime diagram to the ball we find that the tape for Alice’s path can be
______________ , which means the line is ________________ so Alice is _____________________
through curved spacetime. The tape describing Bob’s path is ______________________, which
means the line is _________________ so Bob is ____________________ through curved spacetime.
Drawing the spacetime diagram on a curved surface reverses who is accelerating and who is not—
just what Einstein needed to make the acceleration model make sense. The ground can be forever 
accelerating up without moving up! Gravity is not a force—it is curved spacetime.
(flat/crinkled) 
(flat/crinkled) 
(straight/curved) 
(straight/curved) 
(accelerating/not accelerating)
(accelerating/not accelerating)
Evaluating 
Models:
Newton’s model fails to predict the orbit of Mercury accurately. Einstein’s model does and it also 
accurately predicts time dilation and the bending of light. We must conclude that the best model of 
gravity is __________________ ______________________ model.
(Newton’s/Einstein’s) (force/curved spacetime) 
11
By curving spacetime, Alice’s path changes from curved to straight—she experiences no “force of gravity” and no acceleration. 
By curving spacetime, Bob’s path changes from straight to curved—he experiences the ground pushing up on him, continually 
accelerating him up, but without him moving up. Einstein was able to show that gravity is not a mysterious, invisible force—it 
is the curvature of spacetime. This curved spacetime model asserts that you feel heavy because the surface of the Earth is 
forever accelerating up without actually moving up.
Part C: Accelerating Up without Moving Up
Consider the type of motion (accelerating or not) in each of the following scenarios:
In Deep Space Near the Ground
Rocket 1: Floating in deep 
space, engines off
Rocket 2: Accelerating “up” in 
deep space, engines on
Rocket 3: In freefall near the 
ground, engines off
Rocket 4: Hovering near the 
ground, engines on
1. In Rocket 1, the astronaut knows she is not accelerating; the rod is straight and she is floating. In which other rocket does 
she make these observations? 
 
2. In Rocket 2, the astronaut knows he is accelerating; the rod is bent and he feels the force of the floor pushing up on him. 
In which other rocket does he make these observations? 
 
3. The astronaut in Rocket 3 uncovers the window and looks out. She can see the ground and Rocket 4. 
(a) What was her type of motion before looking out the window? (Accelerating or not accelerating) 
(b) How would she describe her motion when she looks out the window? 
(c) Combine your answers from (a) and (b) into a statement. 
 
4. The astronaut in Rocket 4 uncovers the window and looks out. He can see the ground and Rocket 3. 
(a) What was his type of motion before looking out the window? (Accelerating or not accelerating) 
(b) How would he describe his motion when he looks out the window? 
(c) Combine your answers from (a) and (b) into a statement. 
 
We have discovered that astronauts in very different scenarios can experience the same type of motion. This insight is called 
Einstein’s Equivalence Principle: Freefalling in a uniform gravitational field (Rocket 3) is physically identical to floating in deep 
space (Rocket 1). Hovering in a uniform gravitationalfield (Rocket 4) is physically identical to constant acceleration in deep 
space (Rocket 2). The mass of the Earth curves spacetime so that objects in freefall appear to accelerate down, but there is no 
force causing this “acceleration”. It is the same kind of “acceleration” you feel when a car accelerates towards you. You are not 
accelerating—the car is!
12
SA1: Scientific Models: Gravity
1. Observation: using your senses to gather information from your environment. 
Inference: using logic to interpret the information gathered from your environment. 
 
Identify the observations and inferences in the following narrative. 
 
Bob wakes up and looks out the window. There are drops of water on the window. “It must have rained last night,” he 
thinks. He goes downstairs and notices that the ladder is leaning against the house, so he goes outside to help his dad 
with the roof repair work. “Hey Alice, what are you doing up there?” shouts Bob. Alice is so startled that she loses her 
grip on the ladder. As she falls to the ground, she sees Bob getting closer and closer. “The force of gravity is making me 
accelerate down at 9.8 m/s2,” yells Alice. Bob reaches out and catches her just before she hits the ground. “Good thing I 
was accelerating up at 9.8 m/s2 so I could rescue you,” says Bob. Alice gives Bob a quizzical look and then she tells him 
about how she was washing the windows when he made her fall. 
 
 OBSERVATIONS INFERENCES 
 
 
 
 
 
 
 
 
 
 
 
2. True or False? Rewrite any false statements to make them true. 
 
(a) There can only be one model that explains a set of observations. 
 
 
(b) We prove a model is right when we observe the predictions it makes. 
 
 
(c) Models that do not make new predictions are wrong. 
 
 
(d) A model is valid if it can explain the observations. 
 
 
(e) Any model that cannot explain the observations is useless and should be discarded. 
 
 
(f) We design experiments to prove that a given model is correct.
13
SA2: Scientific Revolution: General Relativity
1. Alice and Bob are arguing over whether gravity is a force or curved spacetime. Bob says, “You honestly believe the 
ground is accelerating up? That’s weird!” Alice replies, “Mysterious invisible force? Who’s weird now, Bob?” Which side of 
the argument do you hold? How would you convince someone to agree with you? 
 
 
 
 
 
 
2. According to Newton, gravity is an invisible, attractive force that acts between massive objects. If his model of gravity is 
wrong does that mean his equation for universal gravitation is also wrong? 
 
 
 
 
 
 
3. According to Einstein, gravity is the curvature of spacetime. If Einstein’s model of gravity is better, why do we still use 
Newton’s model? When do we have to use Einstein’s model? 
 
 
 
 
 
 
4. How is the “force of gravity” similar to centrifugal force? Explain. 
 
 
 
 
 
 
5. Newton and Einstein are looking at a book sitting on a table. How would each of them describe the forces acting on that 
book and how would they justify their description?
14
D
is
cu
ss
io
n:
1.
 (a
) Y
ou
 o
bs
er
ve
 th
at
 th
e 
di
st
an
ce
 b
et
w
ee
n 
th
e 
gr
ou
nd
 a
nd
 th
e 
ob
je
ct
 
de
cr
ea
se
s 
at
 a
n 
ac
ce
le
ra
tin
g 
ra
te
, r
eg
ar
dl
es
s 
of
 th
e 
ob
je
ct
’s
 m
as
s.
 
(b
) Y
ou
 c
an
 in
fe
r e
ith
er
 th
at
 g
ra
vi
ty
 is
 a
 fo
rc
e 
th
at
 c
au
se
s 
th
e 
ob
je
ct
 to
 
ac
ce
le
ra
te
 o
r t
ha
t g
ra
vi
ty
 is
 o
ur
 fr
am
e 
of
 re
fe
re
nc
e 
ac
ce
le
ra
tin
g.
2.
 T
he
 fa
ct
 th
at
 a
 s
us
pe
nd
ed
 ro
d 
w
ill
 b
en
d 
ex
ac
tly
 li
ke
 a
 ro
d 
th
at
 h
as
 o
pp
os
in
g 
fo
rc
es
 a
ct
in
g 
on
 it
 d
oe
s 
N
O
T 
pr
ov
e 
th
at
 g
ra
vi
ty
 is
 a
 fo
rc
e.
 W
e 
ca
n 
al
so
 
m
ak
e 
th
e 
ro
d 
be
nd
 th
is
 w
ay
 w
ith
ou
t a
n 
op
po
si
ng
 fo
rc
e 
by
 a
cc
el
er
at
in
g 
it.
 
Th
e 
“fo
rc
e 
of
 g
ra
vi
ty
” c
ou
ld
 b
e 
a 
fic
tit
io
us
 fo
rc
e 
w
e 
in
ve
nt
 to
 e
xp
la
in
 th
e 
ob
se
rv
at
io
ns
 m
ad
e 
in
 a
n 
ac
ce
le
ra
tin
g 
fra
m
e 
of
 re
fe
re
nc
e.
3.
 T
he
re
 a
re
 s
ev
er
al
 w
ay
s 
to
 d
o 
th
is
: e
ith
er
 a
 fo
rc
e 
is
 a
pp
lie
d 
th
at
 y
ou
 a
re
 
no
t a
bl
e 
to
 s
ee
 (m
ag
ne
ts
 o
r w
ire
s)
, o
r t
he
 ro
om
 is
 in
 fr
ee
fa
ll 
w
ith
 a
ll 
ob
je
ct
s 
fa
lli
ng
 a
t t
he
 s
am
e 
ra
te
 a
s 
th
e 
ro
om
. A
st
ro
na
ut
s 
tra
in
 fo
r w
ei
gh
tle
ss
ne
ss
 b
y 
fa
lli
ng
 in
si
de
 a
 p
la
ne
 th
at
 is
 d
iv
in
g.
4.
 T
he
re
 is
 n
o 
si
m
pl
e 
ex
pe
rim
en
t t
ha
t y
ou
 c
ou
ld
 d
o 
to
 d
is
tin
gu
is
h 
be
tw
ee
n 
th
e 
tw
o 
sc
en
ar
io
s.
Th
in
ki
ng
 D
ee
pe
r:
1.
 T
he
 fo
rc
e 
m
od
el
 c
la
im
s 
th
at
 th
er
e 
is
 a
 m
ys
te
rio
us
, i
nv
is
ib
le
 fo
rc
e 
th
at
 
re
ac
he
s 
ou
t t
hr
ou
gh
 s
pa
ce
 to
 in
flu
en
ce
 m
as
s 
bu
t c
an
no
t e
xp
la
in
 th
e 
ph
ys
ic
al
 n
at
ur
e 
or
 c
au
se
 o
f t
hi
s 
fo
rc
e.
 T
he
 a
cc
el
er
at
io
n 
m
od
el
 c
la
im
s 
th
at
 
th
e 
gr
ou
nd
 is
 fo
re
ve
r a
cc
el
er
at
in
g 
up
 w
ith
ou
t m
ov
in
g 
up
.
2.
 N
ew
to
n’
s 
m
od
el
 is
 s
til
l v
er
y 
us
ef
ul
. I
t g
iv
es
 a
 s
im
pl
e 
in
tu
iti
ve
 p
ic
tu
re
 o
f 
gr
av
ity
 th
at
 w
or
ks
 fo
r a
lm
os
t a
ll 
si
tu
at
io
ns
. A
 m
od
el
 d
oe
s 
no
t h
av
e 
to
 
be
 c
or
re
ct
 in
 o
rd
er
 to
 b
e 
us
ef
ul
—
th
er
e 
ar
e 
m
an
y 
m
od
el
s 
th
at
 a
re
 u
se
fu
l 
in
 li
m
ite
d 
co
nt
ex
ts
 th
at
 u
lti
m
at
el
y 
fa
il.
 W
e 
do
n’
t n
ee
d 
to
 u
se
 E
in
st
ei
n’
s 
cu
rv
ed
 s
pa
ce
tim
e 
m
od
el
 to
 c
al
cu
la
te
 th
e 
tra
je
ct
or
y 
of
 a
 b
as
eb
al
l; 
N
ew
to
n’
s 
m
od
el
 is
 a
de
qu
at
e 
fo
r t
hi
s 
ta
sk
. E
in
st
ei
n’
s 
m
od
el
 is
 n
ec
es
sa
ry
 o
nl
y 
to
 
un
de
rs
ta
nd
 w
ha
t i
s 
re
al
ly
 h
ap
pe
ni
ng
 to
 th
e 
ba
se
ba
ll.
 U
si
ng
 N
ew
to
n’
s 
m
od
el
 
is
 a
na
lo
go
us
 to
 s
ay
in
g 
th
at
 th
e 
S
un
 re
vo
lv
es
 a
ro
un
d 
th
e 
E
ar
th
—
it 
is
 s
til
l a
 
co
nv
en
ie
nt
 w
ay
 o
f t
hi
nk
in
g,
 e
ve
n 
if 
it 
is
 g
ro
ss
ly
 in
co
rr
ec
t.
E
xp
la
in
 W
ei
gh
t (
us
e 
wor
ds
 a
nd
 a
rr
ow
s)
- t
he
 E
ar
th
 p
ul
ls
 d
ow
n 
on
 th
e 
ob
je
ct
 
an
d 
yo
ur
 h
an
d 
pu
sh
es
 u
p
- t
he
 o
bj
ec
t d
oe
s 
no
t a
cc
el
er
at
e 
be
ca
us
e 
th
e 
tw
o 
op
po
si
ng
 fo
rc
es
 a
re
 
ba
la
nc
ed
E
xp
la
in
 F
re
ef
al
l (
us
e 
w
or
ds
 a
nd
 a
rr
ow
s)
- t
he
 E
ar
th
 p
ul
ls
 d
ow
n 
on
 th
e 
ob
je
ct
- t
he
 o
bj
ec
t a
cc
el
er
at
es
 b
ec
au
se
 
th
er
e 
is
 n
o 
op
po
si
ng
 fo
rc
e
A
cc
el
er
at
io
n 
M
od
el
E
xp
la
in
 W
ei
gh
t (
us
e 
w
or
ds
 a
nd
 a
rr
ow
s)
- t
he
 ro
om
 is
 a
cc
el
er
at
in
g 
up
; s
o 
ar
e 
yo
u 
an
d 
th
e 
ob
je
ct
- t
he
 o
bj
ec
t a
cc
el
er
at
es
 u
p 
be
ca
us
e 
th
er
e 
is
 n
ow
 o
nl
y 
on
e 
fo
rc
e—
yo
ur
 
ha
nd
 p
us
hi
ng
 u
p
- w
ei
gh
t i
s 
th
e 
se
ns
at
io
n 
of
 
pu
sh
in
g 
up
 o
n 
an
 o
bj
ec
t t
o 
fo
rc
e 
 
it 
to
 a
cc
el
er
at
e 
up
, a
lo
ng
 w
ith
 th
e 
 
ac
ce
le
ra
tin
g 
ro
om
E
xp
la
in
 F
re
ef
al
l (
us
e 
w
or
ds
 a
nd
 a
rr
ow
s)
- t
he
 ro
om
 is
 a
cc
el
er
at
in
g 
up
- a
n 
ob
je
ct
 in
 fr
ee
fa
ll 
ha
s 
no
 fo
rc
es
 
ac
tin
g 
on
 it
 s
o 
it 
do
es
 n
ot
 a
cc
el
er
at
e
- t
he
 fl
oo
r c
on
tin
ue
s 
to
 a
cc
el
er
at
e 
up
 
an
d 
m
ee
ts
 th
e 
ob
je
ct
- t
he
 o
bj
ec
t a
pp
ea
rs
 to
 a
cc
el
er
at
e 
do
w
n 
bu
t i
t i
s 
ac
tu
al
ly
 th
e 
ro
om
 (a
nd
 
yo
u)
 a
cc
el
er
at
in
g 
up
SW
1: 
A
ns
w
er
s
 F
or
ce
 M
od
el
S
um
m
ar
iz
e:
A
cc
el
er
at
io
n 
M
od
el
O
ur
 fr
am
e 
of
 re
fe
re
nc
e 
is
 s
om
eh
ow
 
ac
ce
le
ra
tin
g.
 W
ei
gh
t a
nd
 fr
ee
fa
ll 
ar
e 
ef
fe
ct
s 
of
 th
is
 a
cc
el
er
at
io
n.
Fo
rc
e 
M
od
el
Th
e 
E
ar
th
 s
om
eh
ow
 e
xe
rts
 a
n 
 
at
tra
ct
iv
e 
fo
rc
e 
on
 n
ea
rb
y 
ob
je
ct
s,
 
lik
e 
a 
m
ys
te
rio
us
 in
vi
si
bl
e 
ha
nd
.
15
SW
2:
 A
ns
w
er
s
P
ar
t A
: M
od
el
in
g 
G
ra
vi
ty
Fo
rc
e 
M
od
el
A
cc
el
er
at
io
n 
M
od
el
G
ra
vi
ty
: H
ow
 d
oe
s 
it 
w
or
k?
G
ra
vi
ty
 is
 a
 m
ys
te
rio
us
 
in
vi
si
bl
e 
fo
rc
e 
th
at
 
em
an
at
es
 fr
om
 o
bj
ec
ts
 
th
at
 h
av
e 
m
as
s.
O
ur
 fr
am
e 
of
 re
fe
re
nc
e 
is
 
ac
ce
le
ra
tin
g.
 W
ei
gh
t a
nd
 
fre
ef
al
l a
re
 e
ffe
ct
s 
of
 th
is
 
ac
ce
le
ra
tio
n.
W
ha
t’s
 h
ar
d 
to
 
ac
ce
pt
?
G
ra
vi
ty
 is
 a
 m
ys
te
rio
us
 
in
vi
si
bl
e 
fo
rc
e
Th
e 
gr
ou
nd
 is
 a
cc
el
er
at
in
g 
up
 w
ith
ou
t m
ov
in
g 
up
A
lic
e 
st
ep
s 
of
f t
he
 
to
p 
of
 a
 ta
ll 
la
dd
er
B
ob
 s
ta
nd
s 
at
 
th
e 
bo
tto
m
 o
f t
he
 
la
dd
er
A
cc
or
di
ng
 to
 
N
ew
to
n.
..
A
lic
e’
s 
pa
th
 th
ro
ug
h 
sp
ac
et
im
e 
is
 C
U
R
V
E
D
 b
ec
au
se
 s
he
 is
 
ac
ce
le
ra
tin
g.
 S
he
 is
 a
cc
el
er
at
in
g 
be
ca
us
e 
gr
av
ity
 is
 a
 fo
rc
e 
pu
lli
ng
 o
n 
he
r. 
B
ob
’s
 p
at
h 
th
ro
ug
h 
sp
ac
et
im
e 
is
 S
TR
A
IG
H
T 
be
ca
us
e 
he
 is
 n
ot
 a
cc
el
er
at
in
g—
th
e 
fo
rc
e 
of
 g
ra
vi
ty
 is
 
ba
la
nc
ed
 b
y 
th
e 
gr
ou
nd
 p
us
hi
ng
 u
p.
Th
er
e 
is
 n
o 
“fo
rc
e 
of
 g
ra
vi
ty
” p
ul
lin
g 
do
w
n 
on
 A
lic
e 
so
 s
he
 
IS
 N
O
T 
ac
ce
le
ra
tin
g.
 H
er
 p
at
h 
th
ro
ug
h 
sp
ac
et
im
e 
sh
ou
ld
 b
e 
S
TR
A
IG
H
T.
 T
he
 g
ro
un
d 
pu
sh
es
 u
p 
on
 B
ob
 a
nd
 s
in
ce
 th
er
e 
is
 n
o 
op
po
si
ng
 “f
or
ce
 o
f g
ra
vi
ty
” t
o 
ba
la
nc
e 
th
is
 fo
rc
e,
 h
e 
sh
ou
ld
 a
cc
el
er
at
e 
up
 a
nd
 fo
llo
w
 a
 C
U
R
V
E
D
 p
at
h 
th
ro
ug
h 
sp
ac
et
im
e.
D
is
cu
ss
io
n:
1.
 If
 A
lic
e 
ig
no
re
s 
th
e 
ba
ck
gr
ou
nd
 s
he
 c
an
no
t t
el
l t
ha
t s
he
 w
as
 a
cc
el
er
at
in
g.
2.
 A
lic
e 
w
ill
 b
e 
ab
le
 to
 te
ll 
th
at
 o
ne
 o
f t
he
m
 is
 a
cc
el
er
at
in
g 
bu
t s
he
 c
an
’t 
te
ll 
w
hi
ch
 o
ne
.
3.
 A
lic
e 
w
ill
 n
ot
 fe
el
 a
cc
el
er
at
io
n.
 S
he
 c
ou
ld
 ju
st
 a
s 
w
el
l b
e 
flo
at
in
g 
w
ei
gh
tle
ss
ly
 in
 s
pa
ce
, w
ith
 a
 b
re
ez
e 
bl
ow
in
g 
ov
er
 h
er
 fa
ce
. S
he
 c
an
no
t t
el
l 
th
at
 s
he
 is
 a
cc
el
er
at
in
g 
un
til
 s
he
 re
fe
rs
 to
 s
om
et
hi
ng
 in
 a
 d
iff
er
en
t f
ra
m
e 
of
 
re
fe
re
nc
e 
(e
.g
. t
he
 g
ro
un
d)
 a
nd
 e
ve
n 
th
en
 s
he
 c
an
 o
nl
y 
te
ll 
th
at
 s
om
et
hi
ng
 
is
 a
cc
el
er
at
in
g—
no
t n
ec
es
sa
ril
y 
he
r.
4.
 B
ob
 w
ill
 fe
el
 a
cc
el
er
at
io
n.
 H
e 
co
ul
d 
ju
st
 a
s 
w
el
l b
e 
in
si
de
 a
 ro
ck
et
 
ac
ce
le
ra
tin
g 
“u
p”
 in
 d
ee
p 
sp
ac
e.
 
P
ar
t B
: B
en
di
ng
 S
pa
ce
tim
e
1.
 T
he
 S
TR
A
IG
H
T 
TA
P
E
 is
 F
LA
T 
an
d 
th
e 
C
U
R
V
E
D
 T
A
P
E
 is
 C
R
IN
K
LE
D
.
C
ur
ve
d 
S
pa
ce
tim
e:
W
he
n 
w
e 
tra
ns
fe
r t
he
 s
pa
ce
tim
e 
di
ag
ra
m
 to
 th
e 
ba
ll 
w
e 
fin
d 
th
at
 th
e 
ta
pe
 fo
r A
lic
e’
s 
pa
th
 c
an
 b
e 
FL
AT
, 
w
hi
ch
 m
ea
ns
 th
e 
lin
e 
is
 S
TR
A
IG
H
T 
so
 A
lic
e 
is
 
N
O
T 
A
C
C
E
LE
R
AT
IN
G
 th
ro
ug
h 
cu
rv
ed
 s
pa
ce
tim
e.
 
Th
e 
ta
pe
 d
es
cr
ib
in
g 
B
ob
’s
 p
at
h 
is
 C
R
IN
K
LE
D
, 
w
hi
ch
 m
ea
ns
 th
e 
lin
e 
is
 C
U
R
V
E
D
 s
o 
B
ob
 is
 
A
C
C
E
LE
R
AT
IN
G
 th
ro
ug
hcu
rv
ed
 s
pa
ce
tim
e.
E
va
lu
at
in
g 
M
od
el
s:
W
e 
m
us
t c
on
cl
ud
e 
th
at
 th
e 
be
st
 m
od
el
 o
f g
ra
vi
ty
 is
 
E
IN
S
TE
IN
’S
 C
U
R
V
E
D
 S
PA
C
E
TI
M
E
 m
od
el
.
P
ar
t C
: A
cc
el
er
at
in
g 
U
p 
w
ith
ou
t M
ov
in
g 
U
p
1.
 T
he
 a
st
ro
na
ut
 is
 a
ls
o 
flo
at
in
g 
an
d 
th
e 
ro
d 
is
 s
tra
ig
ht
 in
 R
oc
ke
t 3
.
2.
 T
he
 a
st
ro
na
ut
 a
ls
o 
fe
el
s 
a 
fo
rc
e 
an
d 
th
e 
ro
d 
is
 b
en
t i
n 
R
oc
ke
t 4
.
3.
 (a
) T
he
 a
st
ro
na
ut
 in
 R
oc
ke
t 3
 is
 N
O
T 
ac
ce
le
ra
tin
g.
 
(b
) S
he
 s
ee
s 
th
at
 s
he
 is
 in
 F
R
E
E
FA
LL
. 
(c
) O
bj
ec
ts
 in
 F
R
E
E
FA
LL
 a
re
 N
O
T 
ac
ce
le
ra
tin
g.
4.
 (a
) T
he
 a
st
ro
na
ut
 in
 R
oc
ke
t 4
 is
 a
cc
el
er
at
in
g.
 
(b
) H
e 
se
es
 th
at
 h
e 
is
 n
ot
 m
ov
in
g 
re
la
tiv
e 
to
 th
e 
gr
ou
nd
. 
(c
) O
bj
ec
ts
 N
O
T 
M
O
V
IN
G
 re
la
tiv
e 
to
 th
e 
gr
ou
nd
 a
re
 A
C
C
E
LE
R
AT
IN
G
.
A
cc
or
di
ng
 to
 
E
in
st
ei
n.
..
16
SA
1: 
A
ns
w
er
s
1.
 
 
 
O
B
S
E
R
VA
TI
O
N
S
 
 
 
 I
N
FE
R
E
N
C
E
S
 
2.
 T
ru
e 
or
 F
al
se
? 
R
ew
rit
e 
an
y 
fa
ls
e 
st
at
em
en
ts
 to
 m
ak
e 
th
em
 tr
ue
.
(a
) T
he
re
 c
an
 o
nl
y 
be
 o
ne
 m
od
el
 th
at
 e
xp
la
in
s 
a 
se
t o
f o
bs
er
va
tio
ns
. 
FA
LS
E
: T
he
re
 c
an
 b
e 
se
ve
ra
l m
od
el
s 
th
at
 e
xp
la
in
 a
 s
et
 o
f o
bs
er
va
tio
ns
.
(b
) W
e 
pr
ov
e 
a 
m
od
el
 is
 ri
gh
t w
he
n 
w
e 
ob
se
rv
e 
th
e 
pr
ed
ic
tio
ns
 it
 m
ak
es
. 
FA
LS
E
: W
e 
pr
ov
e 
a 
m
od
el
 is
 w
ro
ng
 w
he
n 
w
e 
do
n’
t o
bs
er
ve
 th
e 
pr
ed
ic
tio
ns
 it
 m
ak
es
.
(c
) M
od
el
s 
th
at
 d
o 
no
t m
ak
e 
ne
w
 p
re
di
ct
io
ns
 a
re
 w
ro
ng
. 
FA
LS
E
: G
oo
d 
m
od
el
s 
m
ak
e 
ne
w
 p
re
di
ct
io
ns
, b
ut
 a
 m
od
el
 o
nl
y 
ne
ed
s 
to
 
ex
pl
ai
n 
th
e 
ex
is
tin
g 
da
ta
 to
 b
e 
va
lid
.
(d
) A
 m
od
el
 is
 v
al
id
 if
 it
 c
an
 e
xp
la
in
 th
e 
ob
se
rv
at
io
ns
. T
R
U
E
(e
) A
ny
 m
od
el
 th
at
 c
an
no
t e
xp
la
in
 th
e 
ob
se
rv
at
io
ns
 is
 u
se
le
ss
 a
nd
 s
ho
ul
d 
be
 
di
sc
ar
de
d.
 F
A
LS
E
: M
od
el
s 
th
at
 d
o 
no
t e
xp
la
in
 a
ll 
th
e 
ob
se
rv
at
io
ns
 c
an
 
st
ill
 b
e 
us
ef
ul
 in
 a
 li
m
ite
d 
co
nt
ex
t.
(f)
 W
e 
de
si
gn
 e
xp
er
im
en
ts
 to
 p
ro
ve
 th
at
 a
 g
iv
en
 m
od
el
 is
 c
or
re
ct
. 
FA
LS
E
: W
e 
de
si
gn
 e
xp
er
im
en
ts
 to
 p
ro
ve
 th
at
 a
 g
iv
en
 m
od
el
 is
 w
ro
ng
.
SA
2:
 A
ns
w
er
s
1.
 F
or
ce
 is
 in
tu
iti
ve
ly
 o
bv
io
us
. A
 fa
lli
ng
 o
bj
ec
t a
cc
el
er
at
es
 d
ow
n,
 s
o 
th
er
e 
m
us
t b
e 
a 
fo
rc
e 
pu
lli
ng
 it
 d
ow
n.
 T
he
 id
ea
 th
at
 th
e 
gr
ou
nd
 is
 a
cc
el
er
at
in
g 
up
 w
he
n 
th
e 
E
ar
th
 is
 n
ot
 e
xp
an
di
ng
 ju
st
 s
ou
nd
s 
ab
su
rd
! 
A
cc
el
er
at
io
n 
is
 s
im
pl
er
. O
bj
ec
ts
 “f
al
l” 
be
ca
us
e 
th
ey
 h
av
e 
in
er
tia
. T
he
 fr
am
e 
of
 
re
fe
re
nc
e 
is
 a
cc
el
er
at
in
g 
so
 it
 lo
ok
s 
lik
e 
ob
je
ct
s 
fa
ll 
bu
t t
he
y 
do
n’
t. 
Th
ey
 lo
ok
 
lik
e 
th
ey
 a
re
 a
cc
el
er
at
in
g 
in
 o
ur
 fr
am
e 
bu
t i
n 
sp
ac
et
im
e 
th
ey
 a
re
 a
ct
ua
lly
 n
ot
 
ac
ce
le
ra
tin
g.
 E
xp
er
im
en
ts
 h
av
e 
co
nfi
rm
ed
 th
e 
pr
ed
ic
te
d 
cu
rv
at
ur
e 
of
 s
pa
ce
tim
e,
 
w
hi
ch
 c
on
cl
us
iv
el
y 
ru
le
s 
ou
t t
he
 fo
rc
e 
m
od
el
.
2.
 N
ew
to
n’
s 
eq
ua
tio
n 
fo
r u
ni
ve
rs
al
 g
ra
vi
ta
tio
n 
m
ak
es
 re
as
on
ab
ly
 a
cc
ur
at
e 
pr
ed
ic
tio
ns
 fo
r t
he
 e
ffe
ct
s 
of
 w
ea
k 
gr
av
ity
 (e
.g
. t
he
 e
ffe
ct
s 
of
 th
e 
S
un
 o
n 
th
e 
or
bi
ts
 o
f t
he
 p
la
ne
ts
), 
bu
t g
iv
es
 g
ro
ss
ly
 w
ro
ng
 p
re
di
ct
io
ns
 fo
r t
he
 e
ffe
ct
s 
of
 v
er
y 
st
ro
ng
 g
ra
vi
ty
 (e
.g
. n
ea
r a
 b
la
ck
 h
ol
e)
. T
he
 e
qu
at
io
n 
is
 a
ls
o 
w
ro
ng
 in
 th
e 
se
ns
e 
th
at
 it
 re
fe
rs
 to
 a
 fo
rc
e,
 a
nd
 g
ra
vi
ty
 is
 n
ot
 a
 fo
rc
e.
3.
 W
e 
st
ill
 u
se
 N
ew
to
n’
s 
m
od
el
 b
ec
au
se
 it
 is
 in
tu
iti
ve
ly
 s
im
pl
e 
an
d 
th
e 
m
at
h 
is
 
st
ra
ig
ht
fo
rw
ar
d.
 W
e 
m
us
t u
se
 E
in
st
ei
n’
s 
m
od
el
 w
he
n 
ac
cu
ra
cy
 is
 v
er
y 
im
po
rta
nt
 
(e
.g
. s
pa
ce
 p
ro
be
s 
an
d 
G
P
S
), 
w
he
re
 N
ew
to
n’
s 
m
od
el
 b
re
ak
s 
do
w
n 
co
m
pl
et
el
y 
(e
.g
. b
la
ck
 h
ol
es
 a
nd
 n
eu
tro
n 
st
ar
s)
, o
r w
he
n 
w
e 
ar
e 
try
in
g 
to
 g
et
 a
 c
le
ar
er
 
pi
ct
ur
e 
fo
r h
ow
 th
e 
un
iv
er
se
 w
or
ks
.
4.
 C
en
tri
fu
ga
l f
or
ce
 is
 a
 fi
ct
iti
ou
s 
fo
rc
e 
in
vo
ke
d 
w
he
n 
ob
je
ct
s 
in
 a
 n
on
-in
er
tia
l 
fra
m
e 
of
 re
fe
re
nc
e 
ex
pe
rie
nc
e 
in
er
tia
. F
or
 e
xa
m
pl
e,
 w
he
n 
a 
ca
r t
ur
ns
 a
 c
or
ne
r i
t 
ac
ce
le
ra
te
s 
bu
t t
he
 o
bj
ec
ts
 in
 th
e 
ca
r w
an
t t
o 
ke
ep
 g
oi
ng
 s
tra
ig
ht
 a
he
ad
 s
o 
th
ey
 
fe
el
 a
 “f
or
ce
” p
us
hi
ng
 th
em
 a
ga
in
st
 th
e 
m
ot
io
n 
of
 th
e 
ca
r. 
S
im
ila
rly
, t
he
 “f
or
ce
 o
f 
gr
av
ity
” i
s 
a 
fic
tit
io
us
 fo
rc
e 
cr
ea
te
d 
to
 e
xp
la
in
 in
er
tia
l b
ehav
io
ur
 in
 a
 n
on
-in
er
tia
l 
fra
m
e 
of
 re
fe
re
nc
e.
 T
he
 E
ar
th
 c
ur
ve
s 
sp
ac
et
im
e 
in
 s
uc
h 
a 
w
ay
 th
at
 th
e 
gr
ou
nd
 
is
 a
 n
on
-in
er
tia
l f
ra
m
e 
of
 re
fe
re
nc
e.
 F
al
lin
g 
ob
je
ct
s 
se
em
 to
 a
cc
el
er
at
e 
to
w
ar
ds
 
th
e 
gr
ou
nd
, b
ut
 th
er
e 
is
 n
o 
fo
rc
e 
ca
us
in
g 
th
is
 “a
cc
el
er
at
io
n”
; s
o 
w
e 
in
ve
nt
 o
ne
—
th
e 
“fo
rc
e 
of
 g
ra
vi
ty
.” 
B
ot
h 
fo
rc
es
 d
es
cr
ib
e 
re
al
 e
ffe
ct
s 
ca
us
ed
 b
y 
ac
ce
le
ra
tio
n;
 
ne
ith
er
 o
ne
 d
es
cr
ib
es
 a
n 
ac
tu
al
 fo
rc
e.
5.
 N
ew
to
n 
w
ou
ld
 s
ay
 th
at
 th
e 
bo
ok
 is
 “a
t r
es
t” 
an
d 
th
er
ef
or
e 
no
t a
cc
el
er
at
in
g 
so
 
th
e 
fo
rc
es
 a
ct
in
g 
on
 it
 a
re
 b
al
an
ce
d.
 T
he
 c
om
pr
es
si
on
 o
f t
he
 ta
bl
e 
gi
ve
s 
cl
ea
r 
ev
id
en
ce
 th
at
 th
e 
ta
bl
e 
is
 p
us
hi
ng
 u
p 
on
 th
e 
bo
ok
 s
o 
a 
do
w
nw
ar
d 
fo
rc
e 
of
 
gr
av
ity
 is
 n
ee
de
d 
to
 b
al
an
ce
 th
e 
fo
rc
es
. 
E
in
st
ei
n 
w
ou
ld
 a
gr
ee
 th
at
 th
e 
bo
ok
 is
 “a
t r
es
t”,
 b
ut
 “a
t r
es
t” 
re
la
tiv
e 
to
 w
ha
t?
 
Th
e 
gr
ou
nd
, w
hi
ch
 is
 a
cc
el
er
at
in
g 
up
 in
 c
ur
ve
d 
sp
ac
et
im
e.
 T
he
 o
nl
y 
fo
rc
e 
ac
tin
g 
on
 th
e 
bo
ok
 is
 th
e 
ta
bl
e 
pu
sh
in
g 
up
 a
nd
 s
in
ce
 th
er
e 
is
 n
o 
“fo
rc
e 
of
 g
ra
vi
ty
” 
op
po
si
ng
 th
e 
fo
rc
e 
of
 th
e 
ta
bl
e,
 th
e 
bo
ok
 m
us
t a
cc
el
er
at
e 
up
, 
al
on
g 
w
ith
 th
e 
ac
ce
le
ra
tin
g 
gr
ou
nd
. U
lti
m
at
el
y,
 E
in
st
ei
n 
w
ou
ld
 ju
st
ify
 h
is
 
de
sc
rip
tio
n 
by
 a
pp
ea
l t
o 
ex
pe
rim
en
ts
—
tim
e 
di
la
tio
n 
ha
s 
be
en
 o
bs
er
ve
d 
 
us
in
g 
at
om
ic
 c
lo
ck
s.
- d
ro
ps
 o
f w
at
er
 o
n 
w
in
do
w
 
- n
ot
ic
es
 th
e 
la
dd
er
 
- d
is
ta
nc
e 
be
tw
ee
n 
A
lic
e 
an
d 
 
 B
ob
 d
ec
re
as
es
 a
t 9
.8
 m
/s
2 
- “
It 
m
us
t h
av
e 
ra
in
ed
”
- d
ad
 is
 fi
xi
ng
 th
e 
ro
of
- t
he
 fo
rc
e 
of
 g
ra
vi
ty
 p
ul
ls
 h
er
 d
ow
n
- B
ob
 is
 a
cc
el
er
at
in
g 
up
17
This module contains two single-period lessons based on the Alice & Bob in Wonderland animation: How Can Atoms Exist? In 
this episode Alice and Bob ask questions about the structure of the atom and discover that the commonly accepted planetary 
model of the atom (including the Bohr-Rutherford model) cannot possibly exist. Lesson 1 is an introductory level lesson (no 
prior knowledge of physics is required) that explores why the planetary model fails. Lesson 2 is a more advanced lesson (prior 
knowledge of waves is an asset) that extends the concepts developed in Lesson 1 to build the quantum mechanical model 
of the atom—a model that explains how atoms can exist. An additional student activity sheet (SA3) is included that could be 
combined with either lesson to address applications and implications of scientific discoveries.
LessoN 1: 
SCIENTIFIC MODELS: THE ATOM 
>> Show the Alice & Bob animation: 
How Can Atoms Exist?
Distribute SW1: Scientific Models: The Atom. 
This worksheet walks students through a critical 
examination of atomic models using existing 
knowledge and a computer simulation to reveal 
the problems with classical models of the atom.
SA1: Scientific Models: The Atom. This worksheet 
includes additional questions to be done in class or 
for homework.
 
 
LessoN 2: 
SCIENTIFIC REVOLUTION: QUANTUM MECHANICS
>> Show the Alice & Bob animation: 
How Can Atoms Exist?
Distribute SW2: Scientific Revolution: Quantum 
Mechanics. This worksheet engages the students in 
the creative process of building a quantum model of 
the atom. Students will use a computer simulation to 
assist in visualizing the atom.
SA2: Scientific Revolution: Quantum Mechanics. This 
worksheet includes additional questions to be done 
in class or for homework.
Introduction 18-19
Student Worksheets: 
 SW1: Scientific Models: 20-21 
 The Atom 
 SW2: Scientific Revolution: 22-23 
 Quantum Mechanics 
Student Assessments: 
 SA1: Scientific Models: 24 
 The Atom
 SA2: Scientific Revolution: 25 
 Quantum Mechanics 
 SA3: Applications of 26 
 Quantum Mechanics 
Answers 27-28
18
How CaN Atoms Exist?
Science is a process of building models to explain 
observations and then refining those models through careful 
thought and experimentation. This Perimeter Institute 
classroom resource engages students in this process as 
they explore models of the atom. Atoms are the building 
blocks of matter. They are central to our existence; and yet, 
there is no “commonsense” way to understand how they can 
exist. The best commonsense atom we can imagine—the 
one with electrons orbiting the nucleus, like planets orbiting 
the Sun—would almost instantly self-destruct. Students 
will exercise their critical and creative thinking skills as they 
examine how various commonsense models fail and how the 
very non-commonsensical quantum nature of our universe 
makes atoms possible.
By the early 1900s, experiments had revealed that atoms 
consist of particles much smaller than the atom itself: one 
tiny, positively charged nucleus comprising almost all of 
the atom’s mass, plus a number of even tinier, negatively 
charged electrons. The challenge was to construct a working 
model of the atom based on these particles and the forces 
between them.
Electrons are attracted to the nucleus (since opposite 
charges attract) and repelled from each other (since like 
charges repel). Any configuration of the atom in which the 
electrons don’t move is not stable; the attractive force always 
wins and the electrons collapse into the nucleus. One way 
to prevent this collapse would be to add “struts” that hold the 
electrons in place, but we have never seen evidence of any 
kind of support structure when we strip electrons off an atom. 
And besides, what type of matter would the struts be made 
from? Another possibility would be to invent a new force 
that acts inside the atom, but such a force has never been 
observed. In science, we exhaust all existing possibilities 
before introducing a new type of matter or force.
If the atom cannot exist with static electrons, then the only 
remaining possibility is a dynamic model where the electrons 
are moving. In order for a moving electron to stay near the 
nucleus, its trajectory must bend. The net attractive force 
towards the nucleus—which defeated the static model—is 
exactly the sort of force needed to bend an electron’s 
trajectory into an orbit around the nucleus. But even in the 
simplest case of a circular orbit,where the electron’s speed 
is not changing, only its direction is continually changing—
the electron is accelerating. This is a problem. When a 
charged object accelerates (changing its speed or direction), 
it emits energy in the form of electromagnetic waves. For 
instance, this is exactly how a cell phone works: electrons 
in the antenna are accelerated, emitting radio waves. In the 
atom, the accelerating electrons would emit electromagnetic 
waves in the form of light. This light would carry energy away 
from the atom, causing the electron to drop to lower energy 
orbits, quickly spiraling into the nucleus.
So electrons can’t stand still (the static model fails); nor can 
they move (the dynamic model fails). Both models would 
result in all the atoms in your body collapsing in a blast of 
light energy on par with an atomic bomb. There is no way 
to escape the catastrophic collapse of any commonsense 
atom. This raises the question: if the electrons in an atom 
can’t stand still, and can’t move, what could they possibly 
be doing?
As a first step towards a working model, imagine spreading 
an orbiting electron into a rotating ring. A perfectly smooth 
rotating ring is moving but you cannot see any motion—it 
appears to be static; this is what physicists call a stationary 
state. A charged rotating ring is stationary so it does not emit 
electromagnetic waves and would be a simple solution to 
the energy loss problem. However, such a spreading out of 
a particle is fraught with severe problems of its own. Each 
part of the ring would be repelled from all the other parts 
(since like charges repel), and there would be very strong 
electrostatic forces tending to make the ring fly apart. We 
would have to invent a new kind of matter or force to hold it 
together. Also, whenever we “look” at an electron we always 
“If, in some cataclysm
, all scientific knowle
dge 
were to be destroyed
, and only one sente
nce 
passed on to the nex
t generation of creat
ures, 
what statement wou
ld contain the most 
information in the few
est words?
I believe it is the atom
ic hypothesis... that a
ll things 
are made of atoms..
.”
– RICHARD FEYNM
AN
19
“see” a point-like particle, with the full mass 
and full charge of one electron. We never see evidence 
of a spread out electron in the shape of a ring, or any 
other shape.
Nature’s solution to the unstable atom problem is very 
strange. An atomic electron does something very much in 
the spirit of spreading itself out into a rotating ring (avoiding 
the energy loss problem), without literally spreading 
out its matter (avoiding the other severe problems 
mentioned above).
How can an electron spread out, and not spread out? In an 
atom, an orbiting electron can be thought of as a particle, like 
a very tiny baseball, but unlike a baseball, one that doesn’t 
move along a definite trajectory. It exists in a profoundly 
weird state in which, at any instant of time, it is not definitely 
at any location in its orbit. Instead, it is only potentially at 
each location in its orbit (all at the same time), with an equal 
potential of being found at any particular location if we were 
to “look” at the atom (e.g. shine light on it). The very act 
of light hitting an electron somehow forces the electron to 
“take a stand”—to assume a definite location. (How this 
happens is still a mystery today.) This potential, or indefinite, 
location is described by a fuzzy donut-shaped wave that 
circulates around the nucleus. It’s not a physical wave, like 
a sound wave or a water wave; nor is it the electron’s matter 
physically spread out; instead, it’s a mathematical wave that 
describes the probability of finding the electron (as a whole 
point-particle) here or there if we were to “look.”
In short, the electron is a particle that behaves like a wave. 
This weird blending of “particle” and “wave” properties into a 
single entity is called quantum mechanics. At the foundations 
of everything we currently know about matter and forces 
is the discovery of the quantum nature of our universe. 
This breakthrough was a 20th century equivalent to the 
Copernican revolution, with equally vast and far-reaching 
consequences that go well beyond the atom. Quantum ideas 
have allowed us to not only understand how atoms can 
exist, and how they work; they also underlie a huge array 
of technologies from cell phones and computers, to laser 
surgery and the Internet, representing millions of jobs and 
trillions of dollars of the world’s economy.
 
 
The quantum nature of the atom is non-commonsensical. 
An orbiting electron behaves like a wave, effectively allowing 
it to be in many places and moving in different directions 
at the same time! If you wiggle both ends of a Slinky 
simultaneously, you will create two waves moving along 
the Slinky in both directions at the same time, resulting in 
a standing wave. In exactly the same way, we can have 
two quantum waves circulating in opposite directions 
around the nucleus. The resulting quantum standing wave 
describes a single electron behaving as if it is orbiting both 
clockwise and counter-clockwise at the same time! The 
mathematics of these waves is well understood. What is not 
well understood, and still the subject of much debate, is what 
this mathematics implies about the ultimate nature of reality. 
The quantum model results in a stable atom and has been 
experimentally verified to unprecedented precision—it’s 
decidedly strange, but it works.
“I think I can safely s
ay that nobody unde
rstands 
quantum mechanics
.” 
– RICHARD FEYNM
AN
20
SW1: Scientific Models: The Atom
 
By the early 1900s, experiments had revealed that atoms consist of 
particles much smaller than the atom itself: one tiny, positively charged 
nucleus comprising almost all of the atom’s mass, plus a number of even 
tinier, negatively charged electrons, such that the total electric charge is 
zero. In this activity you will build and evaluate possible configurations of 
these particles to try to produce a stable model of the atom.
Part A: Static Model
The Law of Static Electricity states that OPPOSITE charges ATTRACT and LIKE charges REPEL.
1. Hydrogen is the simplest atom. It has one negatively charged electron and a positively charged nucleus. What would 
happen if you put the electron near the nucleus and “let go”? 
 
 
 
2. How can Hydrogen exist as a stable atom if its electron and nucleus are attracted to each other? Can you think of a fix for 
this problem? 
 
 
 
 
 
Part B: The Planetary Model
If electrons in the atom cannot be standing still, then they must be 
moving. Maybe the atom looks like a tiny solar system, with electrons 
orbiting around the nucleus, like planets around the Sun. As you 
consider this model, recall that objects that are moving will continue 
moving on a straight path unless pushed or pulled to the side.
1. What has to happen to a moving electron to change its direction 
of motion? 
 
 
 
2. How might the positively charged nucleus of an atom bend the path of a moving electron? 
 
 
 
3. A circular path, or orbit, is the simplest trajectory that an electron could follow. What would happen to the electron’s orbit if 
we gradually removed energy from the atom?
21
Part C: The Failure of the Planetary Model
Any charged object is surrounded by an electric field. It is this field of the nucleus that exerts an attractive force on an electron 
inside the atom. The electron, too, is surrounded by an electric field. Let’s use the PhET simulation (http://phet.colorado.edu/
en/simulation/radio-waves) to investigatewhat happens to that field when the electron accelerates (wiggles around).
1. Begin with the following settings: Manual, Full Field, Electric Field, Static Field. What happens to the electric field when 
you wiggle the electron in the transmitting antenna? 
 
 
 
2. Change the settings to: Manual, Full Field, Electric Field, Radiated Field. What happens when you wiggle the electron in 
the transmitting antenna? 
 
 
 
3. Change the settings to: Oscillate, Full Field, Electric Field, Radiated Field. Watch the electron in the receiving antenna. 
Where does it get the energy to move? 
 
 
 
4. An electron orbiting around the nucleus is accelerating just like the electron you wiggled in the antenna. (Imagine looking 
at the atom from the side. As the electron orbits, it will appear to move up and down.) What would be emitted by the 
electron as it orbits around the nucleus? 
 
 
 
5. Whenever a charged object accelerates (changes its speed or direction of motion), it emits electromagnetic (EM) waves. 
It takes energy to create these waves, and the waves carry this energy away. Why would this be a problem for the 
Planetary Model of the atom? 
 
 
 
 
Summary:
1. Electrons can’t stand still because: 
 
 
2. Electrons can’t move because: 
 
 
There is no way to escape the catastrophic failure of any commonsense atom. This raises the question: if the electrons in 
an atom can’t stand still, and can’t move, what could they possibly be doing? The answer lies in Quantum Mechanics—a 
completely new set of laws that describe how nature behaves at a deeper level.
“How wonderful that we have met a paradox. 
Now we have some hope of making progress.”
– NIELS BOHR
22
SW2: Scientific Revolution: Quantum Mechanics
 
Any commonsense model of the atom is destined to fail. In static 
models, the atom collapses due to the electrostatic force of 
attraction the nucleus exerts on the electrons. Dynamic models, 
like the planetary model, also fail because the atom loses energy 
as the accelerating electrons emit EM waves, again collapsing 
the atom. We need a model in which the electron is somehow 
dynamic (orbiting) but at the same time static (not emitting EM 
waves)—something physicists call a stationary model. For example, 
a perfectly smooth spinning top is dynamic (rotating), but appears 
to be static—you can’t tell that it’s spinning because nothing is 
changing; it always looks the same.
Part A: The Rotating Ring
The electron cannot orbit around the nucleus as a point-like particle. What if we spread the mass and charge of the electron 
out into a rotating ring?
1. A rotating ring of charge behaves like a current-carrying wire. Would the rotating ring emit EM waves? Why or why not? 
 
 
2. Consider the electrostatic forces acting inside the ring. Would such a structure be stable? Why or why not? Would we be 
able to observe it? 
 
 
Part B: Standing Waves
The rotating ring idea is on the right track, but we have never 
observed such rings. We always “see” electrons as point-like 
particles. In preparation for Part C we will need to review some 
facts about waves: (1) A wave can be in many places at the same 
time, and (2) Two waves can exist simultaneously in the same 
place.
1. Stretch a coiled spring (e.g. a Slinky) between two people, on 
a smooth, horizontal surface (hard floor or table). Wiggle one 
end of the spring at a constant rate. Where is the wave? What is the direction of the wave? 
 
 
 
2. Wiggle both ends of the spring at the same rate. This creates two waves travelling in opposite directions along the spring, 
existing simultaneously in the same place. Adjust the rate until you get a stable pattern. Notice that the combined wave 
is not travelling in either direction. It is a wave—it oscillates side to side—but it is not travelling. This is called a standing 
wave. What happens to the standing wave as you gradually increase the frequency of vibration? Can you create standing 
waves at higher frequencies of vibration?
23
Part C: The Quantum Model
In the quantum model of the atom, the electron is a point-like particle 
whose behaviour is described by a wave. If the wave is moving, 
the electron is moving. Wherever the wave exists, the electron can 
potentially exist. The weird thing is that the electron does not exist at 
any definite location until its location is measured. Left undisturbed, 
the electron behaves as if it is spread out like a wave, and 
stationary states similar to the rotating ring become possible. Use 
this simulation (http://www.falstad.com/qmatom/) to visualize these 
waves. Note that these waves are mathematical—the electron’s 
mass and charge are not physically spread out.
1. Start the simulation. In the top-right drop down menu select 
“Complex Combos (n=1-4)”. Click on “Clear” then move your 
mouse over the little circles in the bottom-left panel, noting the yellow text that appears just above the panel. Click on 
the “n=2, l=1, m= –1” circle, which is the top circle in the second column. Finally, rotate the view by clicking on the z-axis 
in the top right corner of the main panel and dragging it down until the z disappears at the origin and the y-axis points 
straight up. This is a “top down” view of a single electron “orbiting” the nucleus of a Hydrogen atom. (The nucleus is at the 
centre, but not shown.) What do you see? 
 
 
 
 
2. The colours represent the “phase” of a donut-shaped wave circulating around the nucleus, showing that the wave 
“crests” and “troughs” are moving. Observe that the moving electron is behaving as if it is in two places at once—actually 
everywhere at once, wherever the wave is non-zero! Select the “View” drop down menu from the top menu bar and 
deselect “Phase as Color.” You will now see a probability pattern: the probability, at any instant of time, of finding the 
electron at various locations around the nucleus. In what way is the electron static? In what way is it dynamic? Do you 
think the electron is emitting EM waves? Draw comparisons with the rotating ring in Part A. 
 
 
 
 
3. Reselect “Phase as Color,” click on “Clear,” and then choose the “n=2, l=1, m=+1” circle. Note the direction of rotation of 
this wave. Now click on the “n=2, l=1, m=–1” circle. You have just combined two waves circulating in opposite directions 
around the nucleus to produce a standing wave. This standing wave describes an electron behaving as if it is moving 
both clockwise and counterclockwise at the same time! Is the electron “moving”? Click on the x-y-z coordinate system 
and rotate it to view this standing wave from different angles. Deselect “Phase as Color” to reveal the corresponding 
probability pattern. In what way is the electron static? In what way is it dynamic? Do you think the electron is emitting EM 
waves? Why or why not? 
 
 
 
 
By describing the behaviour of a particle using a wave, anything a wave can do a particle can do. A wave can be in many 
places at once, or be moving in different directions at once—so can a particle! This leads to very non-commonsensical 
behaviour of electrons inside atoms, and yet these are the lengths scientists have gone to in order to construct a working 
model of the atom—one that allows us to understand how atoms can exist in our universe.
24
SA1: Scientific Models: The Atom
1. Why does the Hydrogen atom collapse if the electron isn’t moving? 
 
 
 
 
 
 
2. Lithium has 3 electrons and a nucleus with a +3 charge. Show that there is no way to put electrons near the nucleus in a 
stable, static arrangement. 
 
 
 
 
 
 
3. Explain how having the electrons move improves the model. 
 
 
 
 
 
 
4. The PhET simulation shows a radio station transmitting EM waves. The energy it takes to create these waves is carried 
off