Transcript 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.

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. McCulloch, 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 keV Li+ beam (v=4.4 mm/ns) incident on a thin (3 g/cm2) carbon foil.
The blue light is H-like 4f-5g in Li2+ (4500Å, =3 ns, x=1.3 cm).
The green light is He-like 2s 3S-2p 3P 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#: 1st quant. (inter. Part.) / Even#: 2nd 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 (x1,y1,t1) and (x2,y2,t2) ?
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 (1st 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
2dt
P(r )dr 
T
2 dx

T v
Non-relativistic conservative potential
E
1
2
mv2  V ( x)
Periodic motion with turning points
V ( xm )  E
Distribution (xm x  xm)
Box:
SHO:
dx
P ( x ) dx 
xm
P( x)dx 
dx
 xm  x 2
2
So in general
2
P( x)dx 
T
dx
E  V ( x)
Where V(x) can be any algebraic or numerical function.
Solve Numerically :
First normalize
P(r )dr 
dr / pr (r )

A
A
dr' / pr (r ' )
Then evaluate
r
k
A
  dr r P(r )
A
k
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:
(ni 
where
i
) 
4
i = 0
= 1
=2
=4
1
2

dqi pi (qi )
(rotations)
(tunnelling)
(librations)
(square well)
Topological
Maslov Index
It yields astonishingly accurate results !!!
Average Values of Powers of the Coordinate