Transcript Teaching Modern Physics - IMSA Digital Commons

Dr. Peter Dong
Illinois Mathematics and Science Academy
Friday, March 2, 2011
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“Modern” really means “post-1905” – it’s more
than a hundred years old now
Major parts are Einstein’s theory of relativity
and the theory of quantum mechanics
After initial controversy, these have been
accepted by practicing physicists for well over
50 years
To a professional physicist, modern physics is
real physics – almost no one does Newtonian
physics anymore
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High school physics classes ought to:
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Teach fundamentals to future physicists and
engineers to build on in college
Teach those who will not be physicists and engineers
to understand the basics of how physics works
Get students interested in studying physics who
otherwise would not
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Modern (post-Maxwell) physics,
particularly quantum mechanics, is
essential to all fields of physics and
many engineering fields (e.g.,
semiconductors and
nanotechnology)
The twentieth-century view of
physics necessitated by relativity and
quantum mechanics is something
non-physicists should know as well.
People are fascinated by modern
physics concepts (e.g. A Brief History
of Time or The Elegant Universe)
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No one sells books about torque
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Illinois state science standards mention only
small parts of modern physics, such as
supernovae and cosmology
AP Physics B contains 10% atomic and nuclear
structure – which means it has less modern
physics than AP Chemistry (20%)
Serway’s book spends about a sixth of the book
on modern physics (often skipped, since it is at
the end)
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Modern Physics offered as a one-semester class
When the difficulty increased, enrollment also
increased
Students responded strongly:
“I had my mind blown every class”
“This is the most interesting class I’ve ever taken”
“ModPhys was the highlight of my day”
“Before this semester, I hated physics, but now, that hate
has subsided and I actually find myself interested enough
to pay attention, take notes, do my homework, and look
up other resources in my free time.”
 Two students said they decided to become physics majors
because of this class
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Increase the modern physics
component of physics survey
courses
Emphasize the weirdness of
modern physics: time and
length are not absolute,
geometry changes with
different observers, particles
do not have a position,
particles can go through
walls…
Problem-solving is good, but
conceptual understanding is
more interesting (and harder)
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Quantized energy levels of atoms in the Bohr
model are the most applicable part of quantum
mechanics, but:
They aren’t that exciting
 AP Chemistry already does that part
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Many students love the weirdness of quantum
mechanics
The most interesting part of quantum mechanics is
not uncertainty
People are used to being unsure
 We are not used to our observations changing the
behavior of the universe
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(From Serway/Faughn, 7th edition)
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Blackbody radiation
Requires advanced thermodynamics
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The photoelectric effect
Requires circuits
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X-rays
Nothing to do with quantum mechanics
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X-ray diffraction
Hard to explain
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The Compton effect
Not useful for deeper understanding
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Wave-particle duality
The important part!
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The wavefunction
The important part!
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Heisenberg’s uncertainty principle
Poorly explained
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Scanning-tunneling electron microscopes
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The Bohr model
Covered by AP Chemistry
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The hydrogen atom
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Spin
The important part!
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Semiconductors
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Why go in chronological order? We don’t teach
any other physics that way
Skip the boring stuff – kids don’t get it anyway
Jump right into the interesting stuff:
The wavefunction and measurement
 Compatible and incompatible observables
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Focus on the easiest QM systems:
The double-slit
 Spin
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For students who like to talk about such things,
spend some time on the philosophy
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This example best explains the
mechanism of quantum mechanics
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Show that light is a wave with an
interference pattern (lab)
Mention (or show, if you want) that
Einstein found light is a particle
Ask: what happens if you shoot only
one particle at a time at slits?
Show YouTube video of actual
experiment
Discuss why this is weird
Add sensors to see which slit the
particle passed through – show how
interference disappears
See attached talk at the end of this
presentation
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The fundamental difference of quantum mechanics is that you
cannot write any expression such as x = 3 m
You can only give probabilities of being at a particular place
The probabilities are represented by an (unobservable)
wavefunction
The strangest part – when we make a measurement, the
wavefunction collapses to the value we measured, thus changing
its behavior
Our observation affects the behavior of the universe!
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Classes who enjoy discussions can spend a long
time on big questions:
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How can our observation affect reality?
What is a measurement?
Is the universe fundamentally probabilistic?
Is consciousness necessary to induce a measurement?
And, if you dare:
What implications does a probabilistic universe have for
free will?
 Is consciousness just a series of random quantum
measurements that give the semblance of purpose?
 Is it easier or harder to reconcile quantum mechanics with
an intervening God?
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The center of the weirdness of quantum mechanics
Measurements of two incompatible observables
are mutually inconsistent – knowledge of one
invalidates knowledge of the other.
For example, if you measure the x spin of a
particle, then measure the y spin, then measure the
x spin again, you may get a different answer
Position and momentum are incompatible
observables – hence, the Heisenberg uncertainty
principle
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A fundamental result of quantum
mechanics – nothing to do with
experimental error
There is a limit to how sure we can be of
position and momentum simultaneously
You can measure position as well as you
want, and then measure momentum as
well as you want
However, if you then measure position
again, it will likely be different from what
you measured before
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A good illustration of incompatible
observables
A fundamental, quantized amount of angular
momentum intrinsic to all particles
Simplest example: spin-½
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When you measure spin along a certain axis, it can
only be up or down – nothing else
Spin along one axis cannot be known at the
same time as spin along any other axis
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Suppose you measure z spin to be spin up
Then you measure y spin to be spin up
If you measure z spin again, you might get spin
down instead of spin up (50% chance)
Measuring a spin “resets” the spins in the other
directions
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One way (from Feynman) to discuss quantum
mechanical principles is through Stern-Gerlach
devices – devices which measure spin
Thus, SG-z means that you measure the spin in
the z direction
As you can see, in this case you would have no
particles coming out.
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However, a measurement of x spin, which does
not commute with z spin, makes the previous
measurement no longer valid
Thus, our measurement changes the outcome.
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Many students enjoy working out larger, more
complex Stern-Gerlach networks
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These aren’t too applicable to physics, but they can
be fun
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A great way to engage students and test their
understanding can be through projects. Some
ideas include:
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Describe the world if the speed of light were 100
mi/h
Design a game that works on the principles of
quantum mechanics
Write a murder mystery that relies on relativity to
solve it
Write a lesson to teach a simple principle of
quantum mechanics to sixth graders
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A useful way to cover a topic can be by
research projects
As a final project, I choose a major physics
experiment such as CDMS and split into many
pieces
Each student researches one piece in depth
Advantages: students report enjoying the
process, appreciating the individuality of it and
the challenge
Disadvantages: requires lots of time and
expertise on the teacher’s part
Slides from last year’s talk
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Time dilation and length contraction are taught
in most textbooks, and they’re certainly weird
enough, but…
Suppose a train and a tunnel have the same
proper length
Train
Tunnel
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When the front of the train hits the front of the
tunnel, the bomb goes off
When the back of the train hits the back of the
tunnel, the sensor deactivates the bomb
Sensor
Train
Tunnel
Bomb
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In the Earth’s reference frame, the train is
shorter than the tunnel, so the back of the train
hits the back of the tunnel, and the bomb does
not go off
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In the train’s reference frame, the tunnel is
shorter than the train, so the front of the train
hits the front of the tunnel, and the bomb goes
off
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Clearly, the observers must agree on whether
the bomb goes off or not
So what actually happens?
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The quiet assumption is that the sensor can
instantly deactivate the bomb
In reality, it sends some kind of signal to it, which
can go no faster than light
The signal can be shown to never reach the bomb
in time – the bomb will always blow up in both
reference frames
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This helps drive home points about
simultaneity – the order of events changes in
different reference frames!
In the tunnel’s reference frame:
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Sensor is triggered
Bomb blows up
Signal from sensor reaches bomb
In the train’s reference frame:
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Bomb blows up
Sensor is triggered
Signal from sensor reaches bomb
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The hidden assumption is that only one of these two
events can happen, because one happening stops the
other one
However, the finite speed of light shows that both
events happen, but happen in different orders in
different reference frames
The events can happen in different orders because it is
impossible for one of them to affect the other one
Events that can change orders are called spacelike
separated; events that can cannot change orders are
timelike separated
Mathematically, events are spacelike if 𝑐 2 𝑡 2 < 𝑑2 ,
where t is the time separating the events and d is the
distance between them
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Many problems on the same principle are
possible
Example: A pole vaulter holds a 4-meter pole at
one end. He runs very fast, so that its length in
the Earth’s frame is 1 meter. He runs into a
barn that has proper length 2 meters, closes the
door, and stops. How is this possible? What
happens?
Peter Dong
Sophomore seminar
Wednesday, February 25, 2009
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The good news:
Quantum mechanics
is the only theory we
have that explains
our experiments.
The bad news:
Quantum mechanics
makes no sense.
Wednesday, February 25,
2009
Peter Dong, Ph.D.
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Suppose we shoot
particles through two
slits at a screen on the
other side.
The particles will collect
in two rows on the
screen.
So far, so good.
Wednesday, February 25,
2009
Peter Dong, Ph.D.
34
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Suppose we do the same
thing with waves (e.g.
water waves).
Now waves from the two
slits interfere with each
other.
Get a series of light and
dark rows on the screen.
Wednesday, February 25,
2009
Peter Dong, Ph.D.
35
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Is light a particle or a
wave?
Thomas Young
showed in 1801 that
light has a double-slit
interference pattern
like a wave.
Albert Einstein
showed in 1905 that
light had to be
composed of
particles (photons).
Wednesday, February 25,
2009
Peter Dong, Ph.D.
36
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What if we shot only one photon at a time
through the slits?
Should be impossible to interfere – should get
two rows on the screen.
Here is a video of a real experiment.
Wednesday, February 25,
2009
Peter Dong, Ph.D.
37
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Even though only one particle goes through the
slits at one time, we still see interference!
A photon interferes with itself?
Each photon goes through both slits?
Wednesday, February 25,
2009
Peter Dong, Ph.D.
38
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Okay, a photon can only
go through one slit or the
other.
Put sensors in to figure
out which slit it went
through.
sensors
Wednesday, February 25,
2009
Peter Dong, Ph.D.
39
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The sensors do their job:
the photon shows up in
only one slit or the
other…
But the interference
pattern disappears!
Wednesday, February 25,
2009
Peter Dong, Ph.D.
40
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This means that our
measurement changes the
result of our experiment!
Wednesday, February 25,
2009
Peter Dong, Ph.D.
41
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A particle is actually not at a particular
position; it has a wavefunction that gives a
probability of being at a position.
When we make a measurement, we measure
only one position, chosen at random.
Wednesday, February 25,
2009
Peter Dong, Ph.D.
42
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A measurement is a fundamentally different
physical process
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No mathematical representation
The only truly random process
The only truly irreversible process
What is a measurement, anyway?
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The interaction of a microscopic system with a
macroscopic one?
The transfer of information?
The intrusion of human consciousness?
Wednesday, February 25,
2009
Peter Dong, Ph.D.
43
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Can’t we do an
experiment to find out
more about what a
measurement is?
Not easily – an
experiment needs a
measurement, and we
can’t take a measurement
of a measurement.
We are asking about what
happens before we
measure it – can we ever
know that? Does it even
make sense to ask?
Wednesday, February 25,
2009
Peter Dong, Ph.D.
44
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Measurement is fundamental to the scientific
method.
Thus, it’s not clear if science can tell us
anything about measurement itself.
Quantum mechanics has at its heart the old
question: if a tree falls in a forest…
But who knows? We may figure something
out.
Wednesday, February 25,
2009
Peter Dong, Ph.D.
45