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Quantum Theory
Black Body Radiation
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Temperature determines the wavelength of
emitted light.
“Red hot”: mostly red light - 3,000 oC.
“White hot”: all colors – 6,000 oC.
It was assumed light could have any energy.
The math of the theory did not match the
distribution of wavelengths observed:
http://www.egglescliffe.org.uk/physics/as
tronomy/blackbody/bbody.html
Max Planck solved the black
body radiation dilemma
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He created an equation that fit the
observed distribution of radiation.
To do so, he had to assume that energy
came in packets, called quanta.
Planck’s Constant
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Frequency/energy = Planck’s constant
Planck’s constant (h) is one of the most
important constants in nature.
(h) = 6.626 x 10-34 joule seconds
Photoelectric Effect
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Certain light beams can knock electrons off of
some metals.
This was independent of the total energy in
the light beam.
It WAS dependent on the wavelength of the
light.
Short wavelengths have larger quanta
(packets of energy) to knock off electrons.
http://hyperphysics.phyastr.gsu.edu/hbase/mod1.html
Light – particle or wave?
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Light followed the wave equation
defined by James Clark Maxwell.
Light also seemed to exist as packets,
like particles.
The particle/wave designation seems
invalid for the subatomic world.
Particles are also Waves
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1923: Louise de Broglie found that matter
had both particle and wavelike properties.
If E = hc/wavelength (from Planck) and E =
mc2 (from Einstein), than wavelength =
h/(mass x velocity).
Very small particles exhibit the same wave
addition and cancellation characteristics as
waves do.
Niels Bohr Planetary Atom
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Electrons orbit the nucleus in specific
circular orbits.
Problem: a charged particle in
acceleration emits light.
Changing direction is a type of
acceleration, yet orbiting electrons
emitted no light.
Schrodinger’s Solution
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The orbit of an electron can only be a whole
number multiple of the electron’s wavelength.
The orbital is a standing wave of an electron.
There is no “changing direction” of the
electron.
The electron simply exists in these locations,
without actually moving from one point to
another.
Schrodinger wave equations
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Any system can be treated as a wave
equation in quantum mechanics.
The orbitals of chemistry are solutions
to Schrodinger wave equations.
Electrons materialize from one location
to another without passing a plane of
zero probability existence.
This is just quantum weirdness.
Paul Dirac’s improvements of
Schrodinger’s wave equations
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He generalized the equations to
relativistic theory.
He mathematically explained electron
spin with angular momentum.
He postulated the existence of
antimatter based on the negative
square root of E=mc2.
Quantum Mechanics gives
probabilities
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1926, Max Born: the square of the wave
equation gave the probability of finding
the particle in a given location.
Many felt that probability was not good
enough.
If we really understood something, we
should know what will happen and what
is really going on “behind the scenes”.
Heisenberg Uncertainty
Principle
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We cannot know both the velocity and
location of an electron. The more we know
about one, the less we know about the other.
High energy light gives a better location, but
disrupts the velocity.
Low energy light disturbs the velocity less,
but gives high uncertainty of location. Lower
energy light gives worse resolution.
The uncertainty of position times the
uncertainty of momentum is greater or equal
to Planck’s constant divided by 4p.
Uncertainty vs. Determinism
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Uncertainty was not just a result of the
crudeness of the instruments, it was a
fundamental law of nature.
Determinism – the idea that you can
state the future if you know everything
about the present.
Einstein favored determinism, but
uncertainty was found to rule.
Double slit experiment
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The same results are obtained with light,
electrons, or any other type of “wave”.
http://www.upscale.utoronto.ca/GeneralInter
est/Harrison/DoubleSlit/DoubleSlit.html
How does the particle going through the slit
“know” that the other slit exists?
Since the electron, like all matter, has
wave characteristics, its final location is
defined by the probability given by the
square of the wave equation for the
given system it is in.
Bell’s Therom
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John Bell used a thought experiment and
logic to prove that reality is non-local.
Non-local means objects are affected by
distant objects and events that cannot reach
them with a force, because they are outside
of the light cone.
Outside the light cone, signals or forces from
one object must travel faster than the speed
of light to create the observed behavior.
Quantum Entanglement
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When two particles or events affect
each other without any signal or force.
Determinism, and our common sense,
says that this is totally impossible.
Quantum mechanics predicts when it
will or will not happen, and what the
probability of the outcome will be.
Collapsing Probability Waves
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Quantum mechanics says that the
measurement of a particle, such as an
electron, collapses the probability wave to a
single event.
With entangled particles, the measurement of
one collapses both of their probability waves
simultaneously.
Any interaction, human or not, collapses
probability waves.
Quantum Theory and the
Universe
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Cause and effect gives way to probability.
The things you do can instantaneously affect
things far away (non-local).
Events can happen without a force or signal
to cause it to happen - the fabric of space
allows, or even causes it to happen.
Objects do not always have specific
properties until they are interacted with; the
properties hang in some sort of limbo.
The Standard Model
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This is the current quantum theory.
Many new subatomic particles have been
discovered.
There are three families of particles.
Each family contains two of the quarks, an
electron (or one of its cousins), and one of
the neutrinos.
These are the building blocks of all matter.
Four Force Particles
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Strong force – The gluon holds the nucleus
together.
Weak force – The W and Z bosons cause
radioactivity.
Electromagnetism – The photon causes light.
Gravity – The graviton is the cause.
Experiments have established all force
particles except the graviton.
Gravitons are expected to be discovered
soon.
Standard Model Equation
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It uses an input of 19 pieces of information,
which are properties of the force and mass
particles.
It has been flawless at predicting
experimental outcomes as probabilities.
Everything that happens in the universe,
besides gravity, can be predicted by the
Standard Model.
Newton’s equations fall out of Standard Model
for normal conditions.
Particle Behavior
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The uncertainty principle allows for extreme
particle behavior on the subatomic level.
There is a trade off between the energy a
particle has and the time it takes to measure
this energy, which allows the energy of a
particle to fluctuate wildly over a very short
duration of time, called the quantum jitters.
“Tunneling” is allowed.
More Unification
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Steven Weinberg and his colleagues
unified the weak and the
electromagnetic forces.
They won a Nobel Prize for this work.
Weaknesses of Standard
Model
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It explains how nature behaves, but not
why it behaves in the way it does.
It does not include gravity; therefore, it
cannot be a complete theory of the
universe.
Its use is primarily for the subatomic
level.