Download Chapter 28 - Purdue Physics

Heisenberg Time-Energy Uncertainty
• The Heisenberg energy-time uncertainty principle is
h
DE Dt ³
4p
• The strong nuclear force has a very short range, around
10-15 m, which is about the distance light travels in
3.3x10-24 s. This force dies exponentially with distance.
• Massive force carrying particles, pions, have masses
around 140 MeV/c2, which is a mass energy = 140 MeV
• The pions can wink into and out of existence for about
3.3x10-24 seconds by uncertainty, “embezzling 140 MeV
at the energy bank”, so long as the debt is paid back
quickly enough. Energy is conserved over longer times.
Section 28.5
Heisenberg Time-Energy Uncertainty
• Heisenberg energy-time uncertainty
h
DE Dt ³
4p
• The EM force has an “infinite” range (meaning 1/r2 form,
this force is never quite “dead”.) This dependence is
NOT exponential in r.
• That’s because photons have zero rest mass, so it’s easy
to create “soft” photons (low energy) by “embezzling” ,
which can last for longer times, therefore allowing longer
range for these photons to reach out and carry the EM
force to arbitrarily large distances.
Section 28.5
Third Law of Thermodynamics
• According to the Third Law of Thermodynamics, it is
not possible to reach the absolute zero of temperature
• In a classical kinetic theory picture, the speed of all
particles would be zero at absolute zero
• There is nothing in classical physics to prevent that
• In quantum theory, the Heisenberg uncertainty
principle indicates that the uncertainty in the speed of
a particle cannot be zero
• Quantum “zero point energy” -- can’t be tapped, used
• The uncertainty principle provides a justification of the
third law of thermodynamics
Section 28.5
Quantum Tunneling
• According to classical physics, an electron
trapped in a box cannot escape
• A quantum effect called tunneling allows an
electron to escape under certain circumstances
• Quantum theory allows the electron’s wave
function to penetrate a short distance into the
Section 28.6
wall
Tunneling, cont.
• The wave function extends a short distance into the
classically forbidden region
• According to Newton’s mechanics, the electron must stay
completely inside the box and cannot go into the wall
• If two boxes are very close together so that the walls
between them are very thin, the wave function can
extend from one box into the next box
• The electron has some probability for passing through
the wall
• This probability dies exponentially fast with increase of
the wall thickness
Section 28.6
Scanning Tunneling Microscope
• A scanning tunneling
microscope (STM)
operates by using
tunneling
• A very sharp tip is
positioned near a
conducting surface
• If the separation is
large, the space
between the tip and the
surface acts as a barrier
for electron flow
Scanning Tunneling Microscope, cont.
• The barrier is similar to a wall since it prevents
electrons from leaving the metal
• If the tip is brought very close to the surface, an
electron may tunnel between them
• This produces a tunneling current
• By measuring this current as the tip is scanned over
the surface, it is possible to construct an image of
how atoms are arranged on the surface
• The tunneling current is highest when the tip is
closest to an atom
Section 28.6
STM Image
Electric fields
from the tip can
also manipulate
individual atoms!
Section 28.6
STM, final
• Tunneling plays a dual role in the operation of the
STM
• The detector current is produced by tunneling
•
Without tunneling there would be no image
• Tunneling is needed to obtain high resolution
•
•
•
•
The tip is very sharp, but still has some rounding
The electrons can tunnel across many different paths
• See fig. 28.17 C
The majority of electrons that tunnel follow the shortest path
– more distant paths are exponentially suppressed
The STM can form images of individual atoms even though
the tip is larger than the atoms
Section 28.6
Wave-like Properties of Particles
• The notion that the properties of both classical
waves and classical particles are present at the
same time is also called wave-particle duality
• The possibility that all particles are capable of wavelike properties was first proposed by Louis de Broglie
• De Broglie suggested that if a particle has a
momentum p, its wavelength is
h
l=
p
• His doctoral thesis is said to have been only two
pages long!! Probably an apocryphal story.
Section 28.3
QUIZ
• An electron with a KE of 100,000 eV has
momentum p with pc = 0.33 MeV. What is its
DeBroglie wavelength, λ = h/p, in meters?
• helpful: hc = 2 x 10-25 J m = 1.25 x 10-12 MeV m
• A) 9.0 nm
• B) 5.5 μm
• C) 3.3x10-24 m
• D) 7.5x10-15 m
• E) 3.8x10-12 m
Color Vision
• A complete understanding of human vision depends
on the wave theory and the particle theory of light
• Light is detected in the retina at the back of the eye
• The retina contains rods and cones
• Both are light-sensitive cells
• When the cells absorb light, they generate an
electrical signal that travels to the brain
• Rods are more sensitive to low light intensities and
are used predominately at night
• Cones are responsible for color vision
Section 28.7
Rods
• About 10% of the light that enters your eye reaches
the retina
• The other 90% is reflected or absorbed by the cornea and
other parts of the eye
• The absorption of even a single photon by a rod cell
causes the cell to generate a small electrical signal
• The signal from an individual cell is not sent directly
to the brain
• The eye combines the signals from many rod cells
before passing the combination signal along the
optic nerve
• About 50 photons within about 0.1 s must be received for
the brain to know light as actually arrived
Section 28.7
Cones
• The retina contains three
types of cone cells
• They respond to light of
different colors
• The brain deduces the
color of light by combining
the signals from all three
types of cones
• Each type of cone cell is
most sensitive to a
particular frequency.
Section 28.7
Cones, cont.
• The explanation of color vision depends on two
aspects of quantum theory
• Light arrives at the eye as photons whose energy
depends on the frequency of the light
•
When an individual photon is absorbed by a cone, the
energy of the photon is taken up by a pigment molecule
within the cell
• The energy of the pigment molecule is quantized
•
Photon absorption is possible because the difference in
energy levels in the various pigments match the energy of
the photon
Cones, final
Ditto for
the other
two
colors
• In the simplified energy level diagram (A), a pigment
molecule can absorb a photon only if the photon energy
precisely matches the pigment energy level
• More realistically (C), a range of energies is absorbed
• Quantum mechanics and the existence of quantized
energies for both photons and pigment molecules are
necessary for color vision
Section 28.7
The Nature of Quanta
• The principles of conservation of energy, momentum,
and charge are believed to hold true under all
circumstances, including in the quantum regime.
• Forces are carried by particles (photons (EM force),
weak force bosons W and Z, and strong force
bosons (gluons) or, at a composite level, by “pions”
• The uncertainty theory of force carrying particles
requires very brief, temporary, fluctuations in Energy
that appear to violate energy conservation -- but
rather quickly the fluctuations return to a state of
conserved energy.
Section 28.8
Puzzles About Quanta
• The relation between gravity and quantum theory is
a major unsolved problem
• No one knows how Planck’s constant enters the
theory of gravitation or what a quantum theory of
gravity looks like
• If there were very heavy particles, weighing 1016
times as much as protons and with one unit of
electric charge, the EM and Gravity forces would be
equal. That would be a kind of unification, but still
not a quantum theory of gravity.
Section 28.8
Puzzles About Quanta
• String Theory in 10 dimensions (six extra spatial
dimensions, each curled up in tiny tiny loops) does
deal with gravity as well as the other forces of nature.
String theory even “unifies” the four forces of nature,
in a certain sense.[Grav., E&M, Strong and Weak
Nuclear Forces]
• But the gravity of String Theory is still not quantized
like the other three forces.
Section 28.8
Puzzles About Quanta
• Why are there two kinds of charge?
• Why do the positive and negative charges come in the
exact same-size quantized units?
• Qe=-Qp is measured to be the same to closer than
one part in 1020  H2 molecules are exactly
neutral, to better than 1.6x10-39 Coulombs.
• Experiment: flow of H2 gas from large insulated bottle.
Bottle does not charge up, no electric current has
flowed (within errors of measurement; there always is
measurement error, at some level)
Puzzles About Quanta
• Also, a net charge on the H atom would cause matter
in the universe to repel itself, to expand even faster
than observed. Given that the EM force is 1038 times
bigger than the Gravity force, in H atoms, this again
implies a charge imbalance < 10-20
Puzzles About Quantum Mechanics (QM)
• What new things happen in the regime where the
micro- and macroworlds meet?
• Actually, small silicon “beams” vibrating, with the
position of the beam sensed in silicon, in the right
experimental setup are observed to be in “quantum
states”
• Also, quantum computing research is beginning to
observe quantum coherence in small but
“macroscopic” systems of many kinds
• Puzzle: How do QM and the Uncertainty Principle
apply to living things?
Puzzles About Quantum Mechanics (QM)
• Schrodinger’s cat (from the early days of quantum
theory): a cat, a flask of poison, and a radioactive
source are placed in a sealed box. If an internal
monitor detects radioactivity (i.e. a single atom
decaying), the flask is shattered, releasing the
poison that kills the cat. The Copenhagen
interpretation of quantum mechanics implies that
after a while, the cat is simultaneously alive and
dead. Yet, when one looks in the box, one sees the
cat either alive or dead, not both alive and dead.
This poses the question of when exactly quantum
superposition ends and reality collapses into one
possibility or the other.
Puzzles About Quantum Mechanics (QM)
• More on QM, the Uncertainty Principle, and living
things?
• Does the Uncertainty Principle have anything to do
with “free will” in humans? (Is free will just an illusion?)
• The probabilistic nature of quantum mechanics makes
the future essentially unpredictable, which would seem
to be a necessary condition for free will
• But is it a sufficient condition for free will?
• Yogi Berra: “Making predictions is difficult, especially
about the future.”