Physics Documents

John Denker

The following were written mainly to answer questions that came up on PHYS-L, the Forum for Physics Educators.

Spreadsheets for solving Laplace's equation. Suitable for students. Demonstrating gauge invariance. Demonstrating conservation of charge. Calculating capacitance of oddly-shaped multi-electrode capacitors.
The definition of capacitance, including multi-terminal capacitors.
An explanation of why there is fundamentally only one kind of charge, not two kinds of charge.
Tides. Why are the typical tides twice a day? Why are some tides once a day? Making hands-on models and/or mathematical models of the tide-producing potential.
A discussion of Galileo's celebrated interrupted pendulum (also known as the stopped pendulum) and the related loop-de-loop maneuver.
The real laws of thermodynamics. First law defined as conservation of energy. Second law defined as paraconservation of entropy. Entropy defined in terms of statistics.
A discussion of whether a reaction will proceed spontaneously or not. This is related to the question of whether a reaction is reversible or irreversible. The fundamental criterion involves the total entropy, which is sometimes related to the system's free energy or free enthalpy.
Reality versus Reductionism. Are waves "real"? Is energy "real"?
Conservative flow in spacetime. Continuity of world-lines for energy and other conserved quantities.
A non-sneaky derivation of Euler's equation -- force and momentum-flow in fluid dynamics.
A discussion of How to teach -- and how to learn -- general thinking skills. The point is that thinking is important, portable, and learnable.
Cause and Effect. Why it is important to think carefully about causation, and how to go about it.
A discussion of hard versus soft evidence, why argument from authority is unscientific, and why it is necessary to challenge seemingly-well-established facts.
On a more positive note, a discussion of scientific methods. Notice that I didn't say ``the'' scientific method.
The definition of hypothesis .
An essay on Truth in Contrast to Knowledge and Belief.
A discussion of the notorious fallacy called argument from no evidence.
A discussion of the so-called theory of intelligent design.
A discussion of breadth, depth, and interdisciplinary connections.
A rant about story problems including ill-posed problems, and the importance of not always following instructions.
A discussion of how to report measurement uncertainties -- which is related to the heavily flawed notion of significant digits or significant figures.
A discussion of Velocity, Speed, Acceleration, and Deceleration , et cetera.
A careful definition of weight, definition of gravitational force, definition of gravity, definition of g, et cetera.
A discussion of how to define mass.
A careful definition of vapor, gas, and fluid.
A discussion and definition of motion in a rotating reference frame, including ideas such as centrifugal force, plus better ideas such as centrifugal field and centrifugal acceleration.
Can You Feel Gravity? What you feel is not explainable just by the gravity at your own location; what you feel is due to the difference between gravity at your location and gravity in distant parts of the world.
A Simple Home-Made Accelerometer that can be made in about 20 minutes with ordinary materials: a lead weight, two rubber bands, a dowel rod, and some bailing wire.
A discussion of inertial reference frames, Newtonian reference frames, freely-falling reference frames, unaccelerated reference frames et cetera.
The definition of anode and cathode, and a discussion of why these terms are usually not worth memorizing.
A discussion of the definition of electrical resistance and its relationship to Ohm's law.
Spectral Data for FD&C Food Coloring Dyes.
Jodi Smith's book on Medieval Dyes -- plants, materials, dyeing procedures et cetera.
My book on how to fly an airplane, including a chapter on how a wing works.
A pattern for making a paper airplane that flies well.
A detailed discussion of the question, What makes the car go? -- i.e. how to balance the energy budget and momentum budget.
A discussion of why we need more than one definition of kinetic energy and more than one work / kinetic energy theorem. This is related to our notions of Momentum, Force times Time, and Force dot Distance.
A discussion of Why the Sky is Blue.
A brief discussion of localization, which explains Why White Things Are White and How Electrical Insulators Really Work.
Physics Books. Recommended as a "starter kit" for a college library.
A discussion of how to evaluate research projects or other creative, risky-but-worthwhile endeavors.
Instructions for how to tell time by the stars.
An introduction to rapidities and boosts, and some insights on the structure of spacetime.
A introduction to vectors, including the two meanings of the word "vector": either (1) a purely numerical object, i.e. just a list of numerical elements; or (2) a physical object, with geometric properties unto itself, independent of the choice of reference frame, and therefore not having -- nor needing -- any unique decomposition into elements. (This is related to the matrix elements of tensors, but if that doesn't mean anything to you, don't worry about it.)
A discussion of odometers and clocks in introductory special relativity. In particular, we use rulers that are not Lorentz-contracted and clocks that are not time-dilated. This does not require much beyond high-school notions of geometry, trigonometry, and vectors.
A discussion of the geometry and trigonometry of spacetime ... in particular an inquiry into how literally we can take the idea that time is the fourth dimension.
A discussion of velocity and acceleration in spacetime, including the important dissimilarity between 3-velocity and 4-velocity
Some fine points of Fourier Transforms and Spectrum Analyzers, including techiques for normalizing the abscissas and ordinates of Fourier transforms. Also a discussion of why you might want to increase the resolution of discrete Fourier transforms.
An Introduction to Clifford Algebra.
If you know about complex numbers, and a little bit about vectors, you can use that to jump-start your understanding of Clifford Algebra. So here is a side-by-side comparison of complex numbers and Clifford Algebra.
A discussion of N-Dimensional Rotations, Including Boosts. Includes a review of various ways to represent rotations, including Clifford algebra, matrices, Rodrigues vectors, and/or Euler angles.
An exercise using vectors to calculate direction (or heading) along a great circle from point a to point b. Mentions Clifford Algebra in passing.
How to calculate the area of parallelograms and the volume of parallelepipeds using wedge products (Clifford Algebra).
An exercise checking the correspondence between the Clifford Algebra formulation of electromagnetism and the old-fashioned vector formulation of Maxwell's equations.
Another exercise, calculating the magnetic field of a long straight wire from scratch, using the Clifford Algebra formulation.
The force and work associated with a current in a wire in a magnetic field.
The microscopic origins of the magnetic field of a current-carrying wire, in terms of bivectors and a space-time diagram, explaining magnetism in terms of electrostatics plus relativity.
How to Make Antimatter -- An Exercise using Four-Vectors.
A discussion of pressure, degeneracy, exchange energy (exchange force), neutron stars, etc.
A discussion of the ideal gas law and adiabatic gas law, plus osmosis, osmotic pressure, and osmotic flow
A fluid has pressure everywhere, not just at tangible boundaries.
A puzzle about the inertia of a cube, illustrating qualitative reasoning, and illustrating the geometrical and physical significance of a tensor, with applications to the Wigner-Eckart theorem.
The famous Twelve Coins Puzzle with a discussion involving Design-of-Experiment, Information Theory, and Communication Theory.
An analysis of the famous Twenty Questions game, including a method for winning 100% of the time. The analysis is a good illustration of information theory.
Pierre's Puzzle -- which asks about the symmetry of electromagnets and permanent magnets (such as compass needles) -- solved using bivectors.
A riddle about how a jet engine works.
An analysis of clocks that use pulses of light to keep time.
A special relativity puzzle, involving the infamous twins, one of whom goes on a trip.
A puzzle illustrating some points about general relativity, namely how various forms of energy contribute as sources of the gravitational field.
Setting the Alarm Clock -- A Story about Symmetry and Information.
An illustration of Liouville's phase-space theorem as applied to the light passing through a thin lens.
How to build a table-top model of Straight Lines in a Curved Space -- Geodesics, General Relativity, and Embedding Diagrams.
A discussion of the expansion of the universe, which addresses some fundamental questions about what we mean by distance.
Here are some diagrams that may help you visualize a non-conservative field, i.e. one that is not derived from any potential. More precisely, this shows how to visualize an inexact one-form.
A simulation illustrating some of the factors that increase and decrease the entropy of a system. Entropy is a statistical measure of how much you don't know about the system.
A discussion of negative temperatures in a spin system.
Some rough notes on formulating thermodynamics in terms of differential forms.
A discussion of why we sometimes observe sublimation and sometimes instead observe melting followed by evaporation. This is easily explained in terms of a tradeoff of energy versus entropy. The same ideas provide a nice explanation for the freezing-point depression when an impurity is added to the liquid.
A pictorial representation of partial derivatives, including a discussion of what is a ``direction'' in terms of pointy vectors, differential forms, et cetera. This gives us not just a geometric interpretation of partial derivatives, but actually a topological interpretation.
A nice way to draw the periodic table of the elements, as a cylinder with bulges.
A discussion of how to balance chemical reaction equations, including charge-balance as well as atom-balance.
A discussion of how to balance chemical reaction equations, or solve any other system of N linear equations in N unknowns, using Gaussian elimination.
Some hints on how to do basic math calculations, including long multiplication and long division.
An introduction to atoms. This includes a discussion of the notions of atom, atomic number, nucleus, proton number, molar mass, nuclide, isotope, neutron number, nucleon number, and baryon number . Also a deprecation of outdated and/or confusing terms such as atomic weight, atomic mass, atomic mass number, and mass number .
A discussion of the correct direction of the arrow representing a dipole moment, in molecules and otherwise.
A deprecation of the alleged distinction of "chemical" versus "physical" changes.
How to think about the specific heat capacity and enthalpy, including the latent heat of a first-order phase transition.
A discussion of how to draw molecules ... like Lewis dot diagrams, except not wrong. It turns out that Lewis dot diagrams have no firm theoretical basis, and despite some successes have many failures.
Various ways to make models and pictures of atomic wavefunctions (aka atomic orbitals).
A discussion of why atomic physics says that electrons hate each other and pair up only as a last resort (Hund's rule #1) whereas high-school chemistry deals almost exclusively with molecules that have all their valence electrons paired up. Why pairs -- Or not?
A discussion of why in the first excited level of a dye molecule, the triplet (T1) always has lower energy than the singlet (S1). This turns out to be a thinly-disguised version of Hund's rule #1. We explain why Hund's rule applies to molecules, not just atoms.
A discussion of what happends to the amplitude and power when you add waves. This includes explaining why the proverbial rule 1 & 1 makes 2 is only valid in the classical limit.
Some notes on static electricity aka contact electrification.
How an electrical battery works.
An overview of the chemical reactions in a lead-acid battery and how they reputedly work --- including some unanswered questions.
Some words about how to understand the Boundary between Quantum Mechanics and the Classical Limit.
An introduction to scaling laws.
An discussion of dimensional analysis.
A discussion of dimensionless units.
A discussion of the Secchi disk pattern, which illustrates the fact that boundaries have zero width and therefore exhibits some interesting scaling properties.
A discussion of The Exchange of Identical and Possibly Indistinguishable Particles and how that relates to the Pauli exclusion principle.
A discussion of what happens as we approach exhaustion of fossil resources of energy, including coal, oil, and uranium-235.
A perl program to calculate your local barometric pressure, based on weather reports. This is useful if you don't own a precision barometer, and don't want to buy one. Also a spreadsheet to calculate your local barometric pressure, based on weather reports.
A discussion of pressure altimetry, including aircraft altimeters. This includes a discussion of how the Kollsman window (altimeter setting) works.
Some examples of weird terminology, where the name of the thing does not provide a good description of the thing.
Print your own triangular-ruled graph paper.
Comments on the ``California Standards Test'' in physics, and the process by which the test is constructed, including the underlying ``Science Content Standards for California Public Schools''.
A discussion of electrical power grid physics and engineering including some thoughts about the 15 August 2003 northeast blackout.
Directory listing. Miscellaneous physics-related diagrams, spreadsheets, et cetera.
jsd home page.