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Waves and Particles
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Topics
Light as a wave;
Light as a particle;
Particle-wave duality;
The wave-like nature of matter;
Motivation
Learn about the particle-wave duality of
matter and energy.
Learn how physics can blow your brain.
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Light as a Wave
Characteristics of typical waves
• Waves transmit energy;
• Waves move;
• Waves are diffuse, without well defined edges;
• Waves travel through a medium;
• Waves may be longitudinal or transverse;
• Objects can move slower, faster, or the same speed as
waves.
Examples of light being wavelike
• Interference;
• Antireflective coatings.
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Maxwell’s Equations
Gauss’s Law
Gauss’s Law of Magnetism
Faraday’s Law of Induction
Ampère’s Law
Maxwell’s correction
Maxwell added the final term in Ampere’s Law, showing that
electrical fields and magnetic fields are related. A consequence
of that term is that pulses in these fields travel at a speed “s”:
Electricity and magnetism are united, and to optics as well!!!!
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The Aether
Wave Speed
Different types of waves travel at different speeds,
-- Seismic waves: P (5000 m/s), S (3000 m/s)
-- Light and sound waves (hence thunder delays)
The medium affects the wave speed:
-- vsound = 343 m/s (air), 1484 m/s(water),
5120 m/s (steel)
The nature of the luminiferous aether
A medium for light (aether) was proposed in 1678.
Aether must be very stiff to account for light’s high speed.
Michelson interferometer could not detect it in 1887.
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We will wait for Einstein (1905) to understand why.
Light as a Particle
Photoelectric effect
In 1887, Hertz noted that high energy light
(ultraviolet) on polished metal can knock off
electrons.
In 1905, Einstein explained this “photoelectric effect” as discrete light particles
(photons) knocking the electrons out of the
metal surface.
This earned Einstein the Nobel Prize in
1921.
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Particle-Wave Duality
Wave or Particle?
Low energy light (radio waves, microwaves) act very wave-like.
High-energy light (X-ray, gamma rays) act very particle-like.
In general, photons can act either like waves OR particles. Light is
BOTH wave-like and particle-like.
This is called particle-wave duality.
Example: Double-slit diffraction patterns.
Weirder still, we will see that even matter is both wave-like and
particle-like—electron diffraction patterns can be generated. 6
Optics and Matter: Quantum physics
The three postulates of the Bohr atom
1. Electrons occur in stable orbits around a nucleus;
each orbit has an energy.
2. An electron can move from one energy level to
another; the change in energy is associated with a
photon of equivalent energy being emitted or
absorbed.
3. The orbits can have only certain specific energies
(these energy levels are said to be quantized).
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Electrons as Waves?
Electrons are wave-like! The de Broglie wavelength;
λ=h/p
(~ 0.4 nm, the size of atoms.)
Bohr’s electron orbits are set by the sizes needed to
have perfectly arranged de Broglie wavelengths.
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Everything as Waves!
Schrödinger found that any particle could be described as a wave.
And since any material object consists of particles, the object in
turn is really just a wave.
Furthermore, any physical object does not really exist in a single
state; it exists as a “wave function,” with characteristics of many
states at the same time.
Unlike the idea that particles that sharp, clearly defined edges, we
see that particles—close up—are better thought of as just
probability distributions. Their edges are fuzzy.
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A New Way to Think of Matter
Old perspective
You can say where a particle in a box is. This perspective of
physics is called “deterministic.”
New perspective
A particle in a box is potentially anywhere in the box. It exists
as a “wave function.” Its location is not determined until you
measure it.
The wave function exists throughout the entire Universe, and it
is possible that the particle is anywhere in the Universe.
It is the observing of the particle that determines reality, by
“collapsing the wave function” into a value.
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Duality, Multiplicity, Infinitisity
At any moment, you could move to another point in the Universe,
even if you couldn’t normally get there! (Ex. Quantum tunneling)
Consider the double electron gun. Which hole does the electron
travel through? Top or bottom?
Why choose? Schrödinger says the electron exists in TWO states, one state passes
through the top gap, the second passes through the bottom gap.
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This works, even if you fire just one electron at a time!
A Famous Oddity of Reality
An unmeasured system exists, simultaneously, as a combination of many (even
contradictory) states. Hence, Schrödinger’s cat.
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What Does it Mean to be a Wave?
Just as photons reflect and transmit at a glass wall, matter reflects and transmits at
potential energy boundaries!
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Quantum Mechanics
Bohr, Heisenberg, and others formulated the “Copenhagen interpretation of quantum
mechanics” as, essentially, particles do not have inherent attributes like position or
energy, until the moment of measurement collapses the wave function.
Einstein, who believed in determinism in physics, despised this notion, saying instead
that Quantum was simply incomplete, and missed “hidden variables.”
Ex: Temperature and pressure are useful, but hidden variables are energy and density.
Einstein, Podolsky, and Rosen noted that systems experiencing quantum entanglement
seemed to have counter-intuitive properties. They argued that if you believed in the
nondeterminism of quantum physics, entangled systems produced paradoxical results,
as if you could affect things at a distance, hence:
“spooky action at a distance”
People love to talk about quantum entanglement—hardly any of them understand14what
they’re talking about.
Particle-Wave Duality Summary
• Particle-wave duality applies to light;
• Particle-wave duality applies to
matter;
• Particle-wave duality applies to you.
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