TEACHING MODERN PHYSICS Dr Peter Dong Illinois Mathematics

TEACHING MODERN PHYSICS Dr. Peter Dong Illinois Mathematics and Science Academy Friday, March 2, 2011

What is modern physics? “Modern” really means “post-1905” – it’s more than a hundred years old now Major parts are Einstein’s theory of relativity and 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

Why modern physics? High school physics classes ought to: 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

Why modern physics? � � � 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) � No one sells books about torque

Current events 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)

Lessons from IMSA � � � 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” � “Mod. Phys 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

A proposal 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)

Quantum Mechanics � 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 � � 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 �

The standard curriculum (From Serway/Faughn, 7 th edition) Blackbody radiation Requires advanced thermodynamics The photoelectric effect Requires circuits X-rays Nothing to do with quantum mechanics X-ray diffraction Hard to explain The Compton effect Not useful for deeper understanding Wave-particle duality The important part! The wavefunction The important part! Heisenberg’s uncertainty principle Poorly explained Scanning-tunneling electron microscopes The Bohr model Covered by AP Chemistry The hydrogen atom Spin The important part! Semiconductors

Proposal 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 Focus on the easiest QM systems: The double-slit Spin For students who like to talk about such things, spend some time on the philosophy

The double slit This example best explains the mechanism of quantum mechanics 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 You. Tube video of actual experiment Discuss why this is weird Add sensors to see which slit the particle passed through – show interference disappears See attached talk at the end of this presentation

Wavefunctions and measurement 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!

The fun part Classes who enjoy discussions can spend a long time on big questions: 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?

Incompatible observables 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

The Heisenberg uncertainty principle 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

Spin A good illustration of incompatible observables A fundamental, quantized amount of angular momentum intrinsic to all particles Simplest example: spin-½ 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 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

Stern-Gerlach devices 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.

Stern-Gerlach devices 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.

Stern-Gerlach fun Many students enjoy working out larger, more complex Stern-Gerlach networks These be fun aren’t too applicable to physics, but they can

Projects A great way to engage students and test their understanding can be through projects. Some ideas include: 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

The final project � � � 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

RELATIVITY Slides from last year’s talk

A relativity example 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

The bomb paradox 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

The bomb paradox 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

The bomb paradox 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

The bomb paradox Clearly, the observers must agree on whether the bomb goes off or not So what actually happens? ?

Solution 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

Simultaneity This helps drive home points about simultaneity – the order of events changes in different reference frames! In the tunnel’s reference frame: Sensor is triggered Bomb blows up Signal from sensor reaches bomb In the train’s reference frame: Bomb blows up Sensor is triggered Signal from sensor reaches bomb

The punch line

The pole vaulter 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?

QUANTUM MECHANICS AND UNCERTAINTY Peter Dong Sophomore seminar Wednesday, February 25, 2009

What is quantum mechanics? 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. 33

The double-slit experiment 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

The double-slit experiment 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

Light � � � 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

The weird part 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

Huh? 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

Trying to understand 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

The even weirder part 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

WTF? This means that our measurement changes the result of our experiment! Wednesday, February 25, 2009 Peter Dong, Ph. D. 41

The Copenhagen interpretation 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

What this means A measurement is a fundamentally different physical process No mathematical representation The only truly random process The only truly irreversible process What is a measurement, anyway? 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

Measuring a measurement � � � 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

The end of science? 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