Its Time to Reinvent Introductory Physics It is

It’s Time to Reinvent Introductory Physics It is first about Nature, and only later about History, Mathematics and Philosophy Larry Curtis Distinguished University Professor of Physics and Astronomy University of Toledo

What we are doing now? Prof. Robert Holcomb, Cornell University “The current standard model syllabus reflects a 1950 world view. New topics are simply draped across the existing skeleton. Left untouched are evolutional ways of thinking about physics developed over the past 60 or 70 years. Physics Education Research accepts the current model & focuses on ways to teach within the confines of the status quo. ”

John Rigden … the only way departments of physics touch future national leaders is through introductory physics courses. Those equation-driven courses do not, in my judgment, qualify as a science education. …the value of an introductory physics course, 6 months after the final exam, is negligible. …I wager that adults who once took an algebra- or calculusbased introductory physics course are unable to discuss common physics phenomena and cannot demonstrate a better understanding of basic physical concepts than can those who never saw the inside of a physics classroom.

HOW PHYSICS LOOKS TO A BEGINNING STUDENT

What should be the public awareness of Physics? Is Physics a coherent body of useful contemporary knowledge? Or… only a Method of Inquiry unchanged since the Age of Enlightenment? Intro. Phys. I – to American Revolution Intro. Phys. II – to American Civil War Modern Phys. – to the Great Depression

Relearning the ignorance of the “Enlightenment” Planetary motion (Copernicus, Galileo, Brahe, Kepler 1500 -1600) Newton’s laws (Newton 1687) Electricity (Coulomb 1777) Magnetism (Gilbert 1600, Oersted 1819) Line spectra (Kirchhoff 1859) Kinetic theory (Maxwell 1860) Relativity E&M (Voigt 1887) Atomic confirmation (Einstein 1905)

‘The only justification for a historical treatment is when you must explain how things got to be so messed up. ’ Many textbooks introduce the topic through history. Why? Because there is a compelling need to explain how things came to be so muddled and confused, and you won't understand the situation unless you appreciate the history. - Gary Bradshaw Until you know it yourself, it doesn’t matter who discovered it! ‘First things first, but not necessarily in that order. ’ - Dr. Who (J. Flanagan & A. Mc. Culloch, Meglos)

Stephen Jay Gould: ‘We have to extract meaning out of the confusion of the world around us. We do it by telling stories, and by looking for patterns. And whenever we see a pattern, we have to tell a story about it. ’ David Layzer: ‘There is a peculiar synergy between mathematics and ordinary language. Without adequate verbal support, formulas and diagrams tend to lose their meaning; without formulas and diagrams, words and phrases refuse to take on new meanings. ’ Richard Dawkins: ‘if solid things are mostly empty space, why don't we see them as empty space? " The answer lies in our own evolution. You might think that our sense organs would be shaped to give us a ‘true’ picture of the world as it ‘really’ is. Instead they have been shaped to give us a useful picture, designed to understand the mundane details of how to survive in the stone-age African savannah’

Discover Magazine - October 2005 Issue

The Force Concept Inventory

‘the concept of force has reached the end of its life cycle … (suggesting) its disbarment from the inventory of fundamental concepts in physics. ’ Max Jammer, Concepts of Force, 1957 ‘In all methods and systems which involve the idea of force there is a leaven of artificiality… there is no necessity for the introduction of the word “force” nor the sense-suggested ideas on which it was originally based. ” Peter G. Tait, Dynamics, 1895 ‘If people were to learn to conceive the world in a new way, without the old notion of “force, ” it would alter not only their physical imagination, but probably also their morals and politics. ’ Bertrand Russell, The ABC of Relativity, 1925

Quotes from Force-Trained students: ‘How can a rocket work in outer space where there is nothing for the force to push on? ’ ‘The moon doesn’t fall to earth because the centrifugal force holds it out. ’ ‘If weight is gravitational force, and orbiting astronauts are weightless, then they must be outside the range of gravity. ’ ‘We know that nuclei are small because -projectiles miss them and go mainly forward. If nuclei were large, -particles would hit them, feel a force, and bounce backward. ’

(Ohio State Board of Education – 12/10/02)

Are the problems we assign even realistic? __________________ Am. J. Phys. 71, 1152 (2003); dispute / R. K. Adair 73, 184 (2005). 1. Viscous drag nonlinearly couples horizontal & vertical – solve numerically. 2. Aerodynamics of backspin dominates the range achieved.

A lousy approximation!

THE NATURE OF MATTER _____________________________ All matter consists of little bits of positive and negative electricity: in perpetual motion; attract each other at short distances; repel each other when pressed too close together. ____________________________ The most important discovery ever made. If all other scientific information we know were lost in some cataclysmic event, and only this information survived, all could be rediscovered in a very short time. //// - Richard P. Feynman `

Iron atoms positioned on a carbon surface

Second Quantization - The Discrete Photon

700 ke. V Li+ beam (v=4. 4 mm/ns) incident on a thin (3 g/cm 2) carbon foil. The blue light is H-like 4 f-5 g in Li 2+ ( 4500Å, =3 ns, x=1. 3 cm). The green light is He-like 2 s 3 S-2 p 3 P in Li+ ( 5485Å, =44 ns, x=19 cm).

Can we picture attractive and repulsive interactions without the force concept? Quantum Field Theory is conceptually easy!

ACTION-AT-A-DISTANCE Exchange of a ‘gauge boson’ Particle exchange can produce both attraction and repulsion. It is intermittent, like rain on the roof. The Force concept requires an average over a time interval.

Interactions between any two particles involves all the particles in the universe.

Strike a billiard ball so it rolls w/o slipping? If we use the line of action of the impulse as the fulcrum, there are NO torques ! The angular momentum is the same before and after the impulse.

Speed at which a sliding ball rolls w/o slipping ? at release alley exerts friction rolls w/o slipping Use conservation of angular momentum about the point-of contact with the floor, so there are no torques.

Intrinsic Action Quantized: ħ/2 = building blocks Odd#: 1 st quant. (inter. Part. ) / Even#: 2 nd quant. (gauge bosons) Odd #: FD stat. / Even #: BE stat. / Together: MB stat. Least Action – gives conservation laws, dynamics Energy = Action/Time; Momentum = Action/Length Least Action + Quantization = Uncertainty Principle A Lorentz Invariant Mechanical action parity

LEAST ACTION – What is the path between (x 1, y 1, t 1) and (x 2, y 2, t 2) ? Total Energy = Kinetic Energy + Potential Energy “Action” = [Kinetic Energy – Potential Energy] t The particle does whatever it wants, but we see the path where the Total “Action” summed over all points adds up to the smallest value. On this path the Total Energy is the SAME for each point

Principle of Least Action Interactive

Nature chooses the space-time path of minimum action and that path must contain an integer number action “quanta” Action canonically welds: Momentum-to-Length Energy-to-Time This leads to an “Uncertainty Principle” between them

Nature has revealed a beautiful secret! The behavior of the Universe becomes very simple if it is described in a way in which space and time are symmetric. What makes it seem hard, is the fact the we must live our lives by standing at a point in space and watching time pass, but not the reverse. It’s like our perspective in riding the Earth around the Sun, which seems as if the Sun were going around us. However, the heliocentric equations are much simpler.

Model for a current in a wire Woldemar Voigt 1887 Variously delayed photon arrivals make lengths appear shorter and charge appear denser. If q moves with the electron drift, the positive charge appears denser, giving a repulsion. If q moves opposite to the electron drift, the negative charge appears denser, giving an attraction. This is magnetism, and results from relativity at speed ~ 0. 1 mm/sec !

TIME “Time is what keeps everything from happening at once. ” - Attributed to John Archibald Wheeler Quoted by Woody Allen “Time flies like an arrow; fruit flies like a banana. ” - Groucho Marx ‘Backward turn, turn backward, O time in your flight. Make me a child again, just for tonight. ’ - Elizabeth Akers Allen

Electron-Positron Pair Creation and Annihilation Once created, e+ and e- are stable until annihilated

Are they all really the same electron? time Future Here-Now space Past

Laplacian Determinacy – A Costly Mistake Pierre Simon Laplace - 1776: “An intelligence that knows all of the relations of the entities of the universe at one instant could state their positions, motions, and general effects any instant in the past of future. Henri Poincare – 1903: “Small differences in the initial conditions can produce very great ones in the final phenomena – prediction Then becomes impossible (1 st recognition of chaos). Werner Heisenberg – 1924: There is a fundamental limit on the accuracy to which position and velocity can be co-determined. Stephen Hawking – 1988: In the cosmology of the Big Bang and Black Holes, space and time themselves break down.

Position Probability Density Dwell Time

Why didn’t Isaac Newton think about the possibility of getting hit on the head when he sat under the apple tree? x

Where does the pendulum spend the most time? The least time?

Time exposure Dwell time: High: many / slow Low: Few / fast

Equal time inside No time outside Most time at end points Least time at center Most time at aphelion and perihelion

The secret of life, computers, & transitors

1 -D Periodic Motion Non-relativistic conservative potential Periodic motion with turning points Distribution (xm x xm) Box: SHO:

So in general Where V(x) can be any algebraic or numerical function.

Solve Numerically : First normalize Then evaluate

Einstein-Brillouin-Keller Action Quantization (1917) (1926) (1958) Bohr-Sommerfeld-Wilson quantization used fuzzy math, neglecting caustics at turning points in librations. The correct semiclassical action quantization condition is: where i = 0 (rotations) = 1 (tunnelling) = 2 (librations) = 4 (square well) Topological Maslov Index It yields astonishingly accurate results !!!

Average Values of Powers of the Coordinate