James A Miller jamesamiller

## keybase.md

      
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                jamesamiller
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              Created
              May 14, 2017 18:34
            
          
    Keybase proof

I hereby claim:

I am jamesamiller on github.
I am millerja (https://keybase.io/millerja) on keybase.
I have a public key whose fingerprint is 06B1 8D7A FB64 382E 292B  858D EC72 8F76 E67A 0E67

To claim this, I am signing this object:

  
## AreaPreservation.tex
\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title:       Area preservation in the Lorentz Transformations
:Author: 	    J A Miller, UAH Physics & Astronomy, millerja@uah.edu
              2020/02/04

Plot to demonstrate how the Lorentz Transformation preserves area. Suppose the primed frame is moving in the $+x$ direction with speed $v$ relative to the unprimed frame.

Consider a unit square in the primed frame, with corners at $A^\prime =(x,t) =(0,0)$, $B^\prime =(0,1)$, $C^\prime =(1,1)$, and $D^\prime =(1,0)$. In the unprimed system, these points are transformed into $A = (0,0)$, $B = (\gamma v,\gamma)$, $C = (\gamma (1+v),\gamma (1+v))$, and $D = (\gamma,\gamma v)$, which outlines a parallelogram (in the unprimed coordinate system).

## TwoSpaceships.tex
\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title:          Two passing spaceships
:Author: 	    J A Miller, UAH Physics & Astronomy, millerja@uah.edu
                   2020/02/14

Two spaceships passing each other

The distance between neighboring grid lines is one.

## AcceleratedCoordinates.tex
\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title: Accelerated coordinate system
:Slug: Accelerated coordinates
:Tags:  special relativity
:Author: J A Miller, UAH Physics & Astronomy, millerja@uah.edu, 2020/05/12

Plot of accelerated coordinates $\xi$ and $\eta$ on an $x$-$t$ inertial spacetime.

## StarWorldlinesInInertialFrame.tex
\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title: Motion of stars in the accelerated rocket frame
:Slug: Rocket frame
:Tags:  special relativity
:Author: J A Miller, UAH Physics & Astronomy, millerja@uah.edu, 2020/05/12

Worldlines of stars and a rocket in the inertial $x$-$t$ frame, with light rays from one of
the stars to the rocket worldline.

## StarWorldlinesInAccelFrame.tex
\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title: Motion of stars in the accelerated rocket frame
:Slug: Accelerated frame
:Tags:  special relativity
:Author: J A Miller, UAH Physics & Astronomy, millerja@uah.edu, 2020/05/12

Worldlines of stars in the accelerated rocket coordinates $\xi$ and $\eta$.

## RocketConstantAcceleration.tex
\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title: Motion of a rocket with constant acceleration along its length
:Slug: Rocket motion
:Tags:  special relativity
:Author: J A Miller, UAH Physics & Astronomy, millerja@uah.edu, 2020/05/21

Worldlines for parts of a rocket (or three separate rockets), each with the same proper acceleration.
We see that the middle and left parts of the rocket partially lie in the event horizon of the right

## RocketWorldlinesInAccelFrame.tex
\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title: Motion of another rocket in an accelerated rocket frame
:Slug: Accelerated frame
:Tags:  special relativity
:Author: J A Miller, UAH Physics & Astronomy, millerja@uah.edu, 2020/05/18

Worldlines of a test rocket in the accelerated coordinates $\xi$ and $\eta$ of an observer rocket. This illustrates that a constant proper distance requires different accelerations.

## LorentzContractionOfAccelRocket.tex
\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title: Lorentz contraction of an accelerated rocket
:Slug: Lorentz contraction
:Tags:  special relativity
:Author: J A Miller, UAH Physics & Astronomy, millerja@uah.edu, 2020/05/28

Illustration of length contraction during acceleration.

## RindlerAccelFrame.tex
\documentclass[crop=true, border=10pt]{standalone}
\usepackage{comment}
\begin{comment}
:Title: Rindler observers in a reference accelerated frame
:Slug: Rindler observers
:Tags:  special relativity
:Author: J A Miller, UAH Physics & Astronomy, millerja@uah.edu, 2020/06/10

Worldlines of 9 accelerated observers in the accelerated coordinates $\xi$ and $\eta$ of a reference observer with proper acceleration of unity (in some inverse time units). These observers are called Rindler observers.
	\documentclass[crop=true, border=10pt]{standalone}
	\usepackage{comment}
	\begin{comment}
	:Title: Area preservation in the Lorentz Transformations
	:Author: J A Miller, UAH Physics & Astronomy, millerja@uah.edu
	2020/02/04

	Plot to demonstrate how the Lorentz Transformation preserves area. Suppose the primed frame is moving in the $+x$ direction with speed $v$ relative to the unprimed frame.

	Consider a unit square in the primed frame, with corners at $A^\prime =(x,t) =(0,0)$, $B^\prime =(0,1)$, $C^\prime =(1,1)$, and $D^\prime =(1,0)$. In the unprimed system, these points are transformed into $A = (0,0)$, $B = (\gamma v,\gamma)$, $C = (\gamma (1+v),\gamma (1+v))$, and $D = (\gamma,\gamma v)$, which outlines a parallelogram (in the unprimed coordinate system).