Download REU 21st - Department of Physics and Astronomy

HOW PHYSICS LOOKS TO A BEGINNING STUDENT
st
A 21
Century Approach to
Introductory Physics
Let’s start with a description of our current
paradigm of the nature of the Universe
Larry Curtis
Distinguished University Professor
of Physics and Astronomy
University of Toledo
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.
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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.
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
Conservation of Action
http://www.youtube.com/watch?v=AQLtcEAG9v0
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.
Action & Quantum Statistics
Least Action
Action Quantization
Minimum Uncertainty
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
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
Principle of Least Action Interactive
THE SPACE-TIME CONTINUUM
The Magnetic Field
Zitterbewegung –
Spin & magnetic moment of a point particle
One unique electron
The PET scan as a time traveler
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
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 !
How can a point particle exhibit
angular momentum and magnetic moment?
Zitterbewegung, averaged over time, has a finite
extent commensurate with Compton wavelength.
Virtual photons possess spin, cause Zitterbewegung
region to precess, circulating mass and charge.
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
PET scan:
Ingest sugar with tagged positron-emitting Fluorine-18 (110 min. halflife).
Sugar concentrates at high metabolism. On decay, positrons encounter electrons.
Positron Emission Tomography (PET) Scan
Ragnar Hellborg
Lund University
Laplacian Determinism – 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
mv 2  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 k P(r )
A
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 
i
) 
4
1
2

dqi pi (qi )
where
i = 0
(rotations)
=2
(librations)
Topological
Maslov Index
It yields astonishingly accurate results !!!
Average Values of Powers of the Coordinate