Heisenberg Time-Energy Uncertainty

• The Heisenberg energy-time uncertainty principle is

• 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.

hE t

4pD D ³

Section 28.5

Heisenberg Time-Energy Uncertainty

• Heisenberg energy-time uncertainty

• 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.

hE t

4pD D ³

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 wall Section 28.6

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

Section 28.6

Electric fields

from the tip can

also manipulate

individual atoms!

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 wave-

like properties was first proposed by Louis de Broglie

• De Broglie suggested that if a particle has a

momentum p, its wavelength is

• His doctoral thesis is said to have been only two

pages long!! Probably an apocryphal story.

h

pl =

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 arrivedSection 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

• 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

Ditto for

the other

two

colors

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.”