Topics
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Assignment
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Review
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Welcome Back!
Review
Ch 15 Special Relativity - Space and Time - 1
- Ch 15 & 16 Pretest
- Ch 15 & 16 Core Ideas, Terms, and Objectives
- Background - 19th century physics in 15 minutes
- General state of physics in 1900
- A few nagging little problems
- If light is a wave, what does it wave?
- Why can't we detect the "a luminiferous ether?"
- Maxwell's "silly" idea
- Lorentz's "downright crazy" idea
- Postulates of Special Relativity
- Laws of physics have the same form in all inertial reference frames
- Speed of light in a vacuum is constant for all observers (all speeds are not relative)
- What's so "special" about special relativity?
- Accelerated versus non-accelerated motion
- Inertial & Non-inertial reference frames
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- Video:
- "Einstein to the Rescue" (30 min.)
- "Uncommon Sense - Stretching Time
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Ch 15 Special Relativity - Space and TIme - 2
- Postulates (review)
- Laws of physics have the same form in all inertial reference frames
- Speed of light in a vacuum is constant for all observers (all speeds are not relative)
- Consequences
of Special Relativity
- Simultaneity
- The "train thought experiment"
- Two observers moving at different velocities will not agree on whether 2 events separated in space occur simultaneously, or which one occurs first.
- Time dilation
- The "light clock"
- (Lorentz transformation)
- Why don't we notice time slowing down?
- At rest, time moves "normally"
- At "c," time is "frozen"
- The effect is reciprocal - you see my time running slower
- Space-time
- The "Twin Paradox"
- Relative Velocity
- Does this really work?
- Ives & Stillwell (1941) - Doppler shift in beams of positive ions
- Rossi & Hall (1941) - studied the lifetimes of muons produced by cosmic rays in the upper atmosphere
- Haefle & Keating (1971, 2005) - cesium clock flown around the world compared to stationary clock
- Confirmed daily in particle accelerator experiments
- Confirmed by accuracy of the GPS system
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Answer:
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Ch 15 Special Relativity - Space and TIme - 3
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- Finish yesterday's assignment
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Ch 16 Special Relativity - Length, Momentum, & Energy - 1
- Further consequences of Special Relativity
- Length contraction
- The Barn Problem
- Momentum, Inertia, and Mass
- Energy
- Eo = mc2
- Mass is a (very concentrated) form of energy
- Correspondence Principle
- Two theories must agree in situations where they overlap.
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Ch 16 Special Relativity - Length, Momentum, & Energy - 2
- Go over the Ch 16 assignment
- General Theory of Relativity (NOT in the text)
- Albert Einstein - 1915
- deals with motion in general (with acceleration)
- but known as a theory (explanation/model) of gravity
- Correspondence Principle revisited in a new context
- equivalence of acceleration and gravitational field
- the elevator problem (once again!)
- Some consequences
- forces are replaced by bending/warping of space time
- gravity pulls light
- time slows down where gravity is intense (black holes)
- Experimental confirmation
- the eclipse experiment - 1919
- Haefle & Keating (1971, 2005) - cesium clock flown around the world compared to stationary clock
- Confirmed by accuracy of the GPS system
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- Finish the assignment from yesterday
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Properties of Matter
- Ch 17 - The Atomic Nature of Matter
- Matter is made of atoms
- "Atoms are eternal"
- Atoms are too small to be seen (approx. 10-10m)
- Molecules are made of atoms
- Atoms are made of protons, electrons & neutrons
- Protons & neutrons reside in the nucleus
- Nucleus is extremely small compared to atom
- Almost all of the mass of the atom is in the nucleus
- Element determined by the number of protons
- Number of neutrons determine the isotope
- Electrons "orbit" the nucleus
- Electron mass is about 1/2000 proton or neutron mass
- Generally, number of electrons = number of protons
- Fewer or greater number of electrons determine positive/negative ion.
- Phases of Matter - solid, liquid, gas, plasma
- Ch 18 Solids
- Atoms are more-or-less locked in position
- Density
- Ch 19 Liquids
- Atoms/molecules are free to slide past one another
- Ch 20 Gasses
- Atoms/molecules are free to expand to any volume
- Plasma
- "Soup" of free electrons (negative ions) and nuclei (plus inner electrons - positive ions) - outer electrons have too much energy to be held in the atom
- Excellent conductor of electricity
- Most matter is in the plasma state
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Unit IV Atomic & Nuclear Physics
Ch 38 The Atom and the Quantum
- Background
- Wave terms review
- Frequency
- Wavelength
- Amplitude
- How do we know that light is a wave (and not made of particles)
- Standing waves on a spring
- Constructive interference
- Destructive interference
- Interference in 2 dimensions
- Interference in light means light is a wave
- Further evidence: the speed of light in water
Review for the quiz
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Small Test/Big Quiz on Ch. 15 & 16 - Relativity
Ch 38 The Atom and the Quantum
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Ch 38 The Atom and the Quantum
- The Ultraviolet Catastrophe
- Theory predicts that hot objects should emit an infinite amount of energy at ultraviolet wavelengths - clearly silly
- Solution:
- Max Planck discovered a "fudge factor" in the equations implying that hot objects emit/absorb light in discrete packets called quanta
- Energy of a quantum depends on frequency: E = hf
- h is a VERY small constant (6.63 x 1034 J.s)
- The Photoelectric Effect
- When light shines on certain metals, electrons are ejected from the metal.
- Brighter light generally ejects more electrons that dimmer light.
- Higher frequency light generally ejects faster (more energetic) electrons than lower frequency light.
- There is a "threshold frequency," which depends on the type of metal, so that light of a lower frequency will not eject any electrons, no matter how bright the light.
- Einstein's explanation (1905):
- Light is made of particles, called photons.
- A photon is a quantum of light, so the energy of a photon depends on its frequency (E = hf).
- An electron is ejected from the metal when a single photon transfers its energy to a single electron.
- Brighter light means more photons, so more electrons are ejected by brighter light.
- Higher frequency light means more energetic photons, so more energetic electrons are ejected by higher frequency light.
- For light below the threshold frequency, photons do not have enough energy to eject an electron.
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- None (you've suffered enough - for now)
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Ch 38 The Atom and the Quantum
- Particles as waves
- Louis De Broglie proposed that all particles have wave properties.
- The wavelength of a particle is inversely proportional to its momentum.
- The wavelengths of people-sized particles is much too small to be noticed or detected.
- The wave nature of electrons can be demonstrated
- Electrons can produce interference patterns.
- Technology: the electron microscope.
- Waves as particles
- Compton Effect (1923) - When an x-ray strikes an electron, the electron recoils as if it had been struck by a particle.
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Ch 38 The Atom and the Quantum
- Video:
- Lecture 18 - Wave or Particle?
- Lecture 19 - Quantum Uncertainty - Farewell to Determinism
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- Work on the Ch 38 assignment.
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Ch 38 The Atom and the Quantum
- Models of the Atom
- Lab Activity - observing line spectra
- Plum Pudding Model
- positive charge is spread out with electrons embedded in it
- Planetary Model
- a "miniature solar system" with the electric force replacing the gravitational force
- can't be true, since Maxwell showed that accelerating electric charges emit waves (and therefore lose energy)
- The Bohr Model
- electrons don't radiate energy in certain allowed orbits
- can predict the emission/absorption of specific wavelengths of light by atoms
- When an electron "jumps" between orbits, the energy difference is emitted/absorbed as a photon of the corresponding frequency (E = hf).
- Problems:
- Why don't electrons emit electromagnetic waves in certain orbits?
- Why these particular orbits (aside from the fact that they can be made to fit the data)?
- Electrons can't really "jump", since they cannot exist between the allowed orbits - so how do they get there?
- Electrons disappear from one orbit and immediately appear in another (with the emission/absorption of a photon) without ever being between the two orbits.
- The De Broglie Model
- The wave properties of electrons determine the possible orbits of electrons in the atom.
- An orbit is allowed where the electron wave interferes (with itself) constructively to produce a standing wave.
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- Work on the Ch 38 assignment.
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Ch 38 The Atom and the Quantum
- Quantum mechanics
- Heisenberg (German)
- Uncertainty Principle
- Position/momentum and Energy/time cannot be measured to arbitrary precision
- The end of the "Clockwork Universe"
- "Empty" space - The Law of Conservation of Energy/Mass can be violated for a (very) short time.
- Developed a quantum mechanics based on matrices
- Schroedinger (Austrian)
- Developed a quantum mechanics based on waves
- Equivalent to Heisenberg's matrices, but waves are more familiar to physicists
- Schroedinger's wave equation (state vector)
- There is a wave equation that describes the evolution of each property of an object.
- Square of the amplitude of the wave function is the probability that a measurement will give that value.
- Bohr and the Copenhagen (Standard) Interpretation of Quantum Mechanics
- The wave function is a complete description of reality.
- Collapse of the wave function occurs when a measurement is made.
- Probability of measured value becomes one, probability of every other possible value becomes zero.
- Before the measurement, the quantity was in a "superposition of states".
- Before a property is measured, its value does not exist. (What you can't measure doesn't exist.) The value is created by the measurement.
- Many people say that quantum mechanics says that "measurement affects the value being measured" but this is a classical - not quantum - idea!
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- Finish the Ch 38 assignment.
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Ch 38 The Atom and the Quantum
- Quantum mechanics (continued)
- The Schroedinger's Cat Thought Experiment
- Einstein's objections to quantum mechanics
- "God does not play dice..."
- It is silly to say that an object has no definite momentum (for instance) before a measurement is made. It has a value, we just don't know what it is.
- Einstein vs. Bohr (continued)
- Einstein raises objections to quantum mechanics - twice - Bohr responds - twice - Einstein is embarrassed - twice
- The Einstein-Podolsky-Rosen Experiment (EPR) - 1935
- Principle of Locality - One object can't influence what happens to another object unless a signal (traveling at the speed of light) can be sent from one to the other.
- Principle of Reality - If you can predict the value of a measurement of some quantity before the actual measurement is made, then that quantity must actually exist.
- Entangled/twin particles
- The EPR thought experiment
- Einstein - The universe must be real and local, therefore quantum mechanics cannot be a complete description of it.
- Bohr - one particle must "influence" the other - what Einstein called (sarcastically) "spooky action at a distance."
- Bell's Theorem - suggests an actual experiment to decide who's right (1965)
- The experiment was performed and ______ (its a surprise).
- Consequences of EPR
- Alternate interpretations of quantum mechanics
- The Many-Worlds Interpretation
- When a measurement is made, the universe "splits" so that every possible value occurs in some universe.
- popular among string theorists
- Hidden-Variable Interpretations
- Bohm and others - very restricted due to the results of EPR
- Quantum Theory vs. Special Relativity - black holes
- The theories violate the Correspondence Principle - at least one of them needs some serious work!
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- Finish the Ch 38 assignment.
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