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Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
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Inelastic Collision Conversion to Internal Energy Brownian Motion Animation 2D Using Hard Sphere Scattering Large Disc Kinetics 2D Condensation of a Gas on a 2D Solid Maxwell's Demon Energy Seperator 2D Minimize Final Energy 2D and 3D Gas Diffusion 2D Gas Expansion 2D Linear Gas Expansion 2D Constant Pressure Gas Expansion 2D Circular Gas Explosion 2D Circular MagnetoCaloric Effect 2D Convection Loops in a Numerical Gas Chapter 3: Gas Energy Equipartition Energy Equipartition of a Two Dimensional Gas with Two Different Masses Energy Equipartition of a Three Dimensional Gas with Two Different Masses Gas Energy Equipartition 3D
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Photoelectric Effect Alpha Particle Emission from a Large Nucleus 2D Black Body Emission from Charged Harmonic Oscillators Quantum Animation of Energy Band Gap 1D Animation of Quantum Wave Packets in a pn Junction 1D Quantum Mirror Focusing by Iterating the Schrodinger Equation Quantum Lens Focusing by Iterating the Schrodinger Equation Quantum Two Mirror Resonator by Iterating the Schrodinger Equation Entangled Quantum Object Propagation in a Parabolic Potential Classic and Quantum Object Propagation in a Parabolic Potential Accurate Wave Packet Propagation in a Parabolic Potential Comparison of Quantum to Classical Physics 1D-Time Dependent Accurate Wave Packet Propagation in a Swaged Potential Series Solution of Wave Packet Propagation in a Infinite Square Potential Propagation of a Wave Packet in a Parabolic Potential Propagation of a 2D Wave Packet in a 2D Parabolic Potential Propagation of an Asymmetric Shaped Wave Packet in a 2D Parabolic Potential Two Slit Diffraction by Iterating the Schrodinger Equation Two Potential Slit Diffraction by Iterating the Schrodinger Equation Propagation of an Electron Wave Packet in an Infinite Square Well (Series Solution) Propagation of a Free Wave Packet (Series Solution) Series and Algebraic Solutions for Propagation of a Wave Packet in a Parabolic Potential Comparison of Quantum to Classical Physics 1D-Time Independent Mexican Hat Stationary Quantum States of a Finite Square Potential Well Various Wave Packet Motion in a Finite Square Potential Well Various Wave Packet Motion in a Swaged Potential Well Comparison of Quantum to Classical Physics 1D-Time Independent Cosine/Parabola Electromagnetic Modes of a 2D Cavity Black Body Radiation Experiment and Theory Emission of the Inner Walls of a Black Body Cavity Multiple Slit Diffraction Statistics of Indistinguishable Dice or Particles Quantum Field Collapse Visualization Matrix Operations and Eigenmodes
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Tumbling Block on Inclined Plane New Roller on Inclined Plane Sliding Block on Inclined Plane Classic Objects Motion 1D Generation of Curve for Fastest Time between Two Points Curve for Fastest Time between Two Points Bead Sliding On a Stiff Wire Sound Wave in Two Solid Media Mechanical Properties of a 2D Numerically Modeled Lattice Vibrating Reed Numerical Model 2D Laminar Flow of a Fluid in a 2D Bearing Animation of a Fountain 2D Gravity Leveling of a 2D Liquid Longitudinal and Shear Wave Sound Speed in a 2D Lattice Mechanical Properties of a 2D Numerically Modeled Lattice Vibration Frequencies of a 2D Numerically Modeled Lattice Damped Harmonic Oscillator Motion and Modes of a Particle in a Mexican Hat Potential Forced Oscillator Roller Bearing Cam and Roller Follower Simple Hybrid Gear Train Ratchet Animation Child's Swing Height Increase Mechanics Roller Chain Animation Elasticity of 3D Gas Driving a Piston Free to Forced Harmonic Oscillator Transition Physics of Mounting a Tire on a Rim Physics of a Pendulum Clock Escapement Physics of a Gas Pressure Gauge
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Physics of a Gas Pressure Gauge Ion Drift in Neutral Particle Sea Diffusion Equation Solved by Finite Difference Method Linear Particle Diffusion Heat Flow 1D with Time Dependent Boundary Solid Cube in Liquid Column Drag on a Large Sphere Due to a Digital Gas Animation of a Gas Centrifuge Laminar Flow of a Gas in an Annular Space Laminar Flow of a Fluid in a 2D Bearing Incompressible Fluid Flow through a Constriction Fluid Flow Due To Pressure Gradients
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E=mc^2 and Mexican Jumping Bean Radar Pulse Return Time Interval Experiment to Determine Gamma Current Loop with a Rotating Test Particle Moving Fabry-Perot Interferometer Space Time Invariant Intervals of a Moving Clock Relativity Transformations by Requiring Simulataneity Accelerated Space Trip Clock Times and Rates Minguzzi Invariant Inertial Frame Time Accelerated Space Trip with Light Pulse Signaling
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Semiconductor Electron Energies and Band Gap 1D Semiconductor Electron Energies and Band Gap 2D Simple Fermi Surface p-nJunctionDiode Depletion Width Temperature Dependence of 2D Fermi-Dirac Particles
Chapter 4
Chapter 5
Chapter 6
Chapter 7
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Assembly of 3D Parts Using Javascript Web Graphics Library 3D Compared to Javascript 3D Graphics 3D Graphics Tutorial Beginnings Proof of Pythagoras a^2+b^2=c^2
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Multiple Slider Animation Template for Plotting with HTML Enhanced Sliders or Ranges Collapsible Dropdown Menu Example Arrow Functions Fast Fourier Transform (FFT) Demonstration
Animation of a Progress Bar
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Time Dependent Wave Equation 1D One Dimensional Optical Resonator Modes
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Probability of Birthday Match Random Creation of Probability Function Profiles Two Dies Probability Distribution Three Dies Probability Distribution
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Light Rays in a Transparent Isosceles Prism Light Ray in a Series of Wedges of Various Index of Refraction Snells Law of Refraction Refraction Due to Dipoles in Two Media Refraction and Reflection Two Media Animation of Concave Mirror Reflection Animation of Convex Lens Refraction Prism Refraction-Wave Picture Thick Lens Ray Trace Monochromator (Czerny-Turner Type) Wavelets from Concave Mirror> Thick Lens Focusing
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Sagnac Effect Fiber Optical Gyro (FOG) Ring Laser Gyro (RLG)
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Paticle Motion in a Venturi: Wall Reflections Paticle Motion in a Venturi Potential Elliptical Ion Trap Using Boundary Potential Distribution Prediction of Hard Disc Collision Time and Position Rigid Rotor Collisions
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Acoustic Wave with Built-in Pressure Acoustic Waves in 2D Numerically Modeled Solid Wave 1D on a Linear Array Waves on Discrete Model of Vibrating String Linear Acoustic Wave in a 3D Gas Spherical Acoustic Wave in a 3D Gas Laterally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces Longitudinally Perturbed Two Dimensional Gas with Lennard Jones Repelling Forces
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Bicep and Forearm Animation Blood Pressure Measurement Multiple Dose Residual Medicine Vs Time The Eye and its Resolution Breathing Animation Scoliosis Animation Muscle Animation
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Scattering from a Crystalline Target 2D Scattering from a Crystalline Target 3D
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
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Chapter 12
Energy Conduction in a 2D Numerically Modeled Solid Lattice Unbalanced Gas Dynamics:Energy Flow in a Gas
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
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Finding Gamma by Experiment

In this animation, I show two views of of light propagating along the +x direction from a source for a nominal time t. One view is seen by a viewer, A, where he/she is moving at +v in the +x direction and the other view of the same propagation is seen by a viewer, B, that is moving at -v with respect to the source. Since light travels at speed c in any frame, the equations for the two viewers are similar but the times in the two viewers' frames may be different, we have the following transformation equations for viewers A and B:

`ct_A=cgamma(t_B-vt_B/c)` (A)
`ct_B=cgamma(t_A+vt_A/c)` (B)

where the expansion factor gamma, which is the only difference between the Galilean and Lorentz transformations, must be computed. Multiplying equation A by equation B we easily find that

`gamma=1/sqrt(1-v^2/c^2)`

so that equations A and B become

`ct_A=ct_B(1-v/c)/sqrt(1-v^2/c^2) (A1)`
`ct_B=ct_A(1+v/c)/sqrt(1+v^2/c^2) (B1)`

Note that when we substitute the result for `t_A` from equation A1 into equation B1, we obtain `ct_B=ct_B` as we should expect. Also note that `gamma=1` will not work unless v=0. What is the difference `t_B-t_A`?

`t_B-t_A=gamma(t_A-t_B)+gamma(t_A+t_B)v/c`
`(1+gamma)(t_B-t_A)=gamma(t_A+t_B)v/c`
`deltat=t_B-t_A=v/cgamma/(1+gamma)(t_A+t_B)`

For symmetry let

`t_A+t_B=2t_0`

where `t_0` is a measure of time in the frame of the light source. Since we can choose any increasing value for `t_B`, we choose

`t_B=t_0+deltat/2=t_0+gamma/(1+gamma)t_0v/c=t_0[1+(v/c)gamma/(1+gamma)]`

Then using equation A1 we obtain:

`t_A=t_B(1-v/c)gamma`

or equivalently

`t_A=2t_0-t_B`

This results in a certain symmetry with respect to `t_0` beween `t_A` and `t_B`.

So how will this experiment be carried out?. We will need a pulsed light source that is stationary as well as two space ships to observe the pulse from the source. The space ships must fly along routes parallel to the x axis and displaced from it by a small distance so as not to block the light. The space along the x axis must contain some very fine space dust that will scatter a small fraction of the light from the light pulse so that it can be seen by the space ships. You might comment that this would be an expensive experiment but you must realize that it is just a way to visualize the effect of `gamma` on the light pulses. After pulse B has gone 800 units, the results of gamma for both pulse B and pulse A are stated and they agree with the definition of gamma.

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